113329
BRAIN
\S A
AD1WES INTERNATIONAL SERIES
IN THE ENGINEERING SCIENCES
THE BRAIN
AS A COMPUTER
F. H. GEORGE
Department of Psychology
University of Bristol
PERGAMON PRESS
OXFORD - LONDON PARIS - FRANKFURT
1962
ADDISON-WESLEY PUBLISHING COMPANY INC.
READING, MASSACHUSETTS, U.S.A.
Copyright 1962
PERGAMON PRESS LTD.
U.S.A. Edition distributed by
Addison-Wesley Publishing Company, Inc.
Reading, Massachusetts, U.S.A.
Library of Congress Card Number 6 1 - 1 0008
Set in Imprint 11 on 12 pt. and printed in Great Britain at
THE AL0EN PRESS (OXFORD) LTD., OXFORD
3VX
CONTENTS
I THE ARGUMENT 1
II CYBERNETICS 13
III PHILOSOPHY, METHODOLOGY AND CYBERNETICS 45
IV FINITE AUTOMATA 90
V LOGICAL NETS 119
VI PROGRAMMING COMPUTERS TO LEARN 157
VII PSYCHOLOGICAL THEORY OF LEARNING 179
VIII BEHAVIOUR AND THE NERVOUS SYSTEM 235
IX THEORIES AND MODELS OF THE NERVOUS SYSTEM 288
X PERCEPTION 314
XI PERCEPTION AND THE REST OF THE COGNITIVE FACULTIES 356
XII SUMMARY 372
REFERENCES 387
AUTHOR INDEX 406
SUBJECT INDEX 411
CHAPTER I
THE ARGUMENT
IN this book an attempt will be made to outline the principles of
cybernetics and relate them to what we know of behaviour, both
from the point of view of experimental psychology and also from
the point of view of neurophysiology.
The title of the book, 'The Brain as a Computer', is intended
to convey something of the methodology involved; the idea is to
regard the brain itself as if it were a computer-type control
system, in the belief that by so doing we are making explicit what
for some time has been implicit in the biological sciences.
Neither the chapters on experimental psychology, which are
explicitly concerned with cognition, nor die chapters on neuro-
physiology, which are intended to outline the probable neuro-
logical foundations of cognitive behaviour, are complete in any
sense ; they are intended to be read and understood as illustrative
of a point of view. It is clear, from the speed with which all these
subjects are developing, and from the vast bulk of knowledge that
we now have, that a detailed analysis would make a lifetime's work
for many people: The emphasis is primarily on the cybernetic
viewpoint, by which we shall mean simply an attempt to recon-
sider the biological evidence in terms of mathematical precision,
and with the idea of constructing effective models as a foundation
for biological theory. This implies no radical departure from much
of biological tradition ; it is no panacea, but it is an indication of the
possibility of constructing a somewhat different conceptual frame-
work, especially one allowing the application of relatively precise
methods, not only because of the need for precision in science for
the positive benefits of quantification, but also in order to avoid
the messiness and vagueness implicit in ordinary language when
used for the purposes of scientific description.
Cybernetics, is a new science, at least in name; it is a new
discipline that overlaps traditional sciences, and proposes a new
1
2 THE BRAIN AS A COMPUTER
attitude towards those sciences. Although it has had its own
historical evolution, the views of modern cyberneticians are both
distinctive and novel. The word 'Cybernetics' has been derived
from the Greek word for 'steersman', and points out the essential
properties of control and communication.
In some respects Cybernetics certainly represents a very old
point of view dressed in a new garb, since its philosophical forbears
are the materialists of early Greek thought, such as Democritus,
and the Mechanistic Materialists of the eighteenth century. This
ancestry is, however, no more than the bare evolutionary thread of a
materialistic outlook, and we are not primarily concerned here
with the philosophical aspects of its development. It should,
indeed, be quite possible for those who are radically opposed to the
Mechanistic Materialists and their modern counterparts to accept
some part of cybernetics for its methodology and pragmatic value
a^one,
"We will now outline the main ideas of cybernetics, and say some-
thing of its importance for experimental psychology and biology.
Cybernetics might be briefly described as the science of control
and communication systems, although it must be admitted that
such a general definition, while being correct, is not very helpful.
Cybernetics is concerned primarily with the construction of
theories and models in science, without making a hard and fast
distinction between the physical and the biological sciences. The
theories and models occur both in symbols and in hardware, and by
'hardware* we shall mean a machine or computer built in terms of
physical or chemical, or indeed any handleable parts. Most usually
we shall think of hardware as meaning electronic parts such as
valves and relays. Cybernetics insists, also, on a further and rather
special condition that distinguishes it from ordinary scientific
theorizing: it demands a certain standard of effectiveness. In this
respect it has acquired some of the same motive power that has
driven research on modern logic, and this is especially true in the
construction and application of artificial languages and the use of
operational definitions. Always the search is for precision and
effectiveness, and we must now discuss the question of effectiveness
in some detail. It should be noted that when we talk in these
terms we are giving pride of place to the theory of automata at the
expense, at least to some extent, of feedback and information theory.
THE ARGUMENT 3
The concept of an effective procedure springs primarily from
mathematics, in which it is called an algorithm. It has been an
important mathematical and mathematical-logical question to ask
whether parts, or even the whole, of mathematics is effectively
derivable. Is it possible to derive all theorems of classical mathe-
matics in a purely machine-like manner? The theorems of Godel
(1931) and Church (1936), and the work of Turing (1937) on the
Turing machine, as it is called, gave answers to these questions as
far as mathematics was concerned. It was possible to show that all
of classical mathematics could not be reproduced in this manner,
although most of it could. These results have actually led to mis-
interpretation outside mathematics, in that they were thought to
imply that there were some mathematical operations that could
not be performed by a machine, whereas they could be performed
by a human being. This is a mistake, and certainly does not
follow from any work done on decision procedures. What does
follow is that, in order to deal with certain mathematical operations
(for example, those involving the choice of new branches for
development), a machine would need to be able to compute
probabilities, and to make inductions. It must necessarily be
agreed, however, that the machine may make some mistakes in its
computations, though we must not overlook the fact that these are
exactly the sort of conditions that would apply to a human being
performing the same operations.
Within this framework a decision procedure is to be viewed as a
mechanical method, of a deductive kind, for deciding what follows
from a particular set of axioms or, if you like, a simple routine
procedure that a person can follow even though he does not
understand the purpose of the operation. Let us illustrate the
point.
If the problem to be solved is one of finding two from a finite
set of numbers that have a certain property A y say, then we can
enumerate all the numbers to which the property might apply
until we either find or do not find two numbers with the said
property. This procedure is clearly one that could be carried out by
an unintelligent helpmate who knows, and can follow, no more
than the simplest routine procedures. There are many such
algorithms in mathematics, and very nearly all classical mathe-
matics can be shown to follow a similar routine pattern; but this
4 THE BRAIN AS A COMPUTER
leaves untouched the problem of how mathematical theories were
constructed in the first place.
By 'effective', then, we shall mean the construction of a theory
that can be translated into a particular blueprint form, from which
an actual hardware model could, if necessary, be constructed. It
has some of the same properties that we associate with operational
definitions. To avoid ambiguity over the terms of our scientific
description we insist that they be clear and precise enough for us
to draw up a hardware system from them.
The principal aims of cybernetics may be listed under three
headings :
\/(l) To construct an effective theory, with or without actual
rafrdware models, such that the principal functions of the human
organism can be realized.
(2) To produce the models and theory in a manner that realizes
the functions of human behaviour by the same logical means as in
human beings. This implies the simulation of human operations
by machines, whether in hardware or with pencil and paper.
(3) To produce models which are constructed from the same
colloidal chemical fabrics as are used in human beings.
The methods by which these three aims are collectively realized
are manifold, and can be summarized in the following list:
(1) Information theory, (2) Finite Automata, (3) Infinite Automata,
including, especially, Turing machines, (4) Logical Nets, which
are particular finite automata, (5) The programming of general
purpose digital computers, (6) The construction of all the models,
in any fabric, which might collectively be called 'special purpose
computers', and may be both digital and analogue, and may be
'pre-wired', or involve growth processes, or both. All these
methods will be discussed later in the book, and more especially
those concerned with finite automata.
Probably all these approaches need to be developed together,
and certainly it seems to be the case that we have lots of partial
models that need to be translated into some common form. We
shall try to show how the various stages of out machine can be
built up, using various different descriptive languages; but first we
must consider what is meant by an inductive machine and, by
implication, a deductive one.
THE ARGUMENT 5
There is no point as yet in trying to give a precise definition of
the inductive process but it can be characterized easily in various
special terms. In the business of language translation, the problem
of translating from one language to another is, at least in principle,
strictly deductive, provided that both languages are already
known; all that is needed is a dictionary and a grammar. If, how-
ever, one of the languages is not known, then the problem is
inductive, at least until such time as a dictionary and a grammar
can be constructed. In the same way it looks as if there are two
phases in learning: firstly, the finding of a solution to the problem
presented; secondly, the application of that solution in perform-
ance. The application, after the problem has been solved, is a
deductive process, although the recognition of the appropriate
place to supply a solution is an inductive one.
There are many other examples, such as in games, where in
learning the tactics one is behaving inductively although, having
learned the tactics, their application is a purely deductive pro-
cedure. In other words, the notion of 'induction* is dependent
upon the transfer of information from one point (or person) to
another.
These matters themselves contribute to a new view of what is
involved in the learning process, and we shall attempt to utilize
this knowledge in framing a clearer picture of what we are search-
ing for under the names 'learning', 'perception', and 'cognition*
generally.
Information theory is 'a precise language, and a part of the
theory of probability. It is capable of giving a precise definition of
the flow of information in any sort of system or model whatever.
It has been used already to describe various psychological and
biological models, especially those of the special senses. It can also
be used in the study of learning and problem solving, and it is,
in fact, an alternative description of these processes.
Information theoretic descriptions are, broadly speaking,
interchangeable with descriptions that are couched in logical net
terms. Sometimes one is the more convenient and sometimes the
other, and sometimes both may be used together (Rapoport, 1955).
The concept of a finite automaton requires more careful atten-
tion. This is another effective method of defining any system that
is constructed from a finite number of parts, which we may call
i
6 THE BRAIN AS A COMPUTER
elements, or cells. Each of these elements may be capable of being
in only one of a finite number of different states at any given time.
The system or model (these words are synonymous here), which is
connected according to certain rules, has an input and an output,
for we are concerned with the structure of the automaton which is
defined by a specified set of rules, and has a specified output for a
particular input.
If we allow the number of states or parts to be infinite, then we
should be describing an infinite automaton. A well-known example
of an infinite automaton is a Turing machine, which is made up of
an infinite tape which is ruled off into squares, a reading head, and
a control. The control scans one square at a time in turn according
to the instructions which make up the programme. It can move
either to the left one square on the tape, or to the right one square
on the tape, and it can write a symbol on the square or erase an
existing symbol which is already on the square. It was with such a
theoretical machine that Turing was able to show the effective
computability of a large class of mathematical functions (Turing,
1937), and his machines will be described more fully in Chapter
III.
Logical nets, which arc of special interest in the biological
context, are paper and pencil blueprints, couched in the notation
of mathematical logic. They are effectively reproducible in hard-
ware, and will be used to describe the class, or some sub-class, of
finite automata.
The general purpose digital computer is a hardware machine
made up principally of an .input and an output system, a storage,
and an arithmetical unify* A control system is included in the
storage. It can be described in logical net terms as a finite auto-
maton and is equivalent to a Turing machine in its capacity
provided that it always has access to all the information it has
used in the past.
Finally, by special purpose machines we mean the class of all
machines, whether in hardware or in paper and pencil, that can be
used to exemplify any process whatever. Here we are especially
interested in the class of finite automata which, when synthesized,
might be described as special purpose computers. We are also
particularly interested in systems that are not fully defined, or
have the property of growth, or both. By a combination of all
THE ARGUMENT 7
these techniques we may hope ultimately to simulate human
behaviour in most of its aspects.
In constructing our models of behaviour, we cannot always
meet the exacting criteria demanded by those scientists mostly
those who do not themselves construct theories and models
when they ask that models should be predictive and testable. In
fact, models must usually start from more modest beginnings, but
eventually they meet these criteria.
It would seem appropriate now to say a word about the sort of
analysis this book attempts, especially in so far as it may seem to
differ from other works which, while having similar ends, proceed
differently in keeping to a policy of deriving particular models
from specific sets of experiments. A recent book by Broadbent
(1958) may be said to represent the best sort of example of this
alternative approach.
In general, the aim of the cybernetic type of analysis as repre-
sented here is really an attempt to provide a conceptual framework
for experimental psychology, and even experimental biology
generally. It does so by careful analysis of concepts as provided by
experimental psychologists and other scientists, and tries to bring
them together, seeking by various means to see what is necessary
to our model making, and what is not necessary. This could be
described in part as a meta-theoretical procedure, and as one
aiming to interest the mathematician and the philosopher as well as
the strictly experimental scientist. This is not to be taken, as
meaning in any sense that the vital role of experiment is being
denied, but rather by way of emphasizing that experiment must be
seen as part of a broader undertaking, involving the effective
synthesis of many different lines of thought.
The view expounded differs from that of such works as Broad-
bent's only in emphasis, the emphasis having shifted somewhat
away from the immediate evidence, and the immediate ad hoc
models, to slightly more general forms of model construction.
Both ways of carrying out psychological research seem equally
valid and necessary, and the writer regards them as being essen-
tially complementary.
At the same time as the cybernetician at least this particular
one is searching for an analysis of concepts and principles and
methods, a theory is being provided at varying levels of generality,
8 THE BRAIN AS A COMPUTER
and this seems to be an apposite place to state a , irly basic
assumption that underlies this work. The assumption is that
science does not only proceed by observing and stating results and
observing again, eventually to generalize. Those many writers who
have said that it is necessary to describe behaviour before we can
hope to explain it are surely while in one sense stating the
obvious missing an important point, the point being that in
constructing models and theories, and in analysing theories and
concepts from various points of view, one is liable to be contri-
buting to the science itself. The assumption here is that the
method of presentation of so-called facts is as important as the
facts themselves; or to put it more crudely, languages and the
references of languages are almost inextricably bound together.
A little more discussion in the field of methodology, by way of
added detail, will be found in chapters III and XII, for the bulk of
the book is concerned with the methods of cybernetics and the
modelling of behaviour, human and otherwise.
It is because of the belief that methods and findings are inter-
mingled that much can come from a logical and a philosophic type
of analysis of existing models, based directly on experimental data,
or a scientific analysis based directly on the data themselves. Every-
one knows that it is fairly easy to carry out experiments as such in
psychology, but the problem arises over the interpretation of the
results. This view has sometimes been mistakenly interpreted to
mean that scientific theories can be built without any reference to
empirical fact which is obviously nonsensical or that logic is
being boosted as a source of empirical knowledge in the same way
as immediate observation. The wiser opinion is surely that they
should be undertaken together, as being complementary to each
other.
In saying that one of the next big undertakings of the cyberneti-
cian involves analyses of cognitive operations in terms of views
proposed by philosophers such as Price (1953), Wittgenstein
(1953), K6rner (1959) and Ryle (1949), among others, we may
possibly be furthering the misunderstanding, so let us say at once
that we do not intend to imply that we shall ignore experimental
results; on the contrary, experimental results are still our basic
material, and the other forms of logical analysis are necessary to
increase our understanding of that basic experimental material.
[ndeed, this is precisely a point where cybernetics and experimental
Dsychology have common ground since models, either of a
Daper and pencil or of a hardware kind, are constructable to
nake precise what is being asserted. This is done in such a manner
;hat it is clear both to the psychologist who wishes to use the
esults and to the logician who wishes to analyse the methods and
heir implications.
To avoid confusions of language, and in order to broaden the
outlook of the experimental psychologist, we hope to carry out the
Tiodel making analysis of experimental results. This means that
;ve should pay attention to the forms of linguistic analyses of
ogicians, and bear in mind the efforts towards precise linguistic
instruction by such writers as Woodger (1939, 1952).
Indeed, the development of artificial languages is intimately
Dound up with cybernetics, since they can be regarded as blueprint
anguages from which actual hardware models can be made.
In the same way we shall bear in mind the distinction made by
Braithwaite (1953) between models and theories, and we shall
:hink of them as having a sort of twofold relation to each other,
tfhere the theory is an interpretation of the model, and the model
i formalization of the theory. Anything whatever could be taken
;o be an interpretation of a model (i.e. a theory), and anything
;ould be taken to be a model of a theory ; the important thing is the
elation between the two. At the same time we shall, of course,
sonsider certain well-defined models, always with an eye to the
ntended interpretation.
The intended interpretations remain primarily on the be-
lavioural level, and although it is hoped that models of a neuro-
:>hysiological kind will eventually be constructed indeed, some
lave already been constructed it is at the molar level of be-
lavioural analysis that cybernetics would be most obviously useful at
:he moment.
Generating schemes such as those of Solomonoff (1957), the
heuristics of Minsky (1959), and the various attempts to meet the
criteria of human thought, are to be derived in a series of stages
: rom a set of conceptual models which start from the concepts of
>stensive rules (Korner, 1951). The ideas of classes, relations,
>roperties, order, process, etc., which are fundamental to our ways
)f regarding the empirical world, will be derived similarly; and
B
10 THE BRAIN AS A COMPUTER
this book can be no more than a link in the long and complex
chain. Initially, the main objects will be both methodological and
behavioural; as we progress, the emphasis will change increasingly
from the first to the second.
Naturally we shall draw on ready made techniques, such as
Theory of games, Linear Programming, Dynamic Programming,
Operational Research, and the like, since they all represent pieces
of the framework of the conceptual world from which the empirical
world must be reconstructed.
Neurophysiologically, we continue to wait for predictive models,
and this primary analysis is intended as a basis for model con-
structions of neurophysiological utility; what it does not claim to
do is to supply them, for that is something that lies beyond the
compass of the present analysis.
It is important that it should be clearly understood that this
book is not about cognition as such, nor indeed about neuro-
physiology as such. It is concerned with models of behaviour
which include cognitive and neurological data, and of course some
attention is paid to modelling these foundation subjects. At the
same time it should be said that the main aim is methodological;
we want to show the power and usefulness of formalized methods
of theory construction, and yet we do not wish to pretend that
these supplant experimental data; they are secondary to them. But
it is also thought important that methods of constructing theories
should themselves be the subject of analysis and experiment; it is
by such means that comparisons between theories are facilitated,
and the implications of a model are made more lucid.
Many criticisms have been levelled at the hypothetico-deductive
method, but although it is sometimes unwieldy, and certainly
there are other possible, and quite valid, approaches, it should be
remembered that cybernetic ideas are largely built up around
axiomatic systems. They are easier to check in axiomatic form,
and even models which are apparently useless and unwieldy, like
Hull's hypothetico-deductive model of rote learning (1940), are of
the greatest use because the reader will bear in mind that, in the
age of the computer, it is possible to take a system that looks
completely and hopelessly obscure and complicated, and yet
derive its logical consequences. In fact, the learning programmes
that are discussed in Chapter VI look very complicated in the flow
THE ARGUMENT 11
chart form, but any models that purport to explain behaviour in
any important sense will be far more complicated than even the
Hullian set of postulates. We must not, therefore, set our face
against the hypothetico-deductive method ; rather, we must find a
way of using it, and the digital computer supplies one such way.
Logical nets, of the kind we shall be discussing, supply yet another
way, but it must be admitted that more research has still to be
done on suitable notation as a shorthand if such models are going
to be handleable on a large scale, for otherwise precision degener-
ates quickly into more verbal discussion which, while useful, and
even essential, is thought to be inadequate to the task of setting up
behavioural models at various levels sufficiently rich and precise to
permit the standard of prediction we are seeking.
In outlining the sections of this book, it may be said that the
first section, contained in Chapters I to VI inclusive, is about
cybernetic models. First they are summarized in a general way,
and then we pay special attention to finite automata, and particu-
larly finite automata in logical net form, which seem especially
useful to the modelling of behaviour. Actually there are many
cases in which other forms of model are more suitable for particular
purposes, but we shall talk largely in logical net terms, although it
will be understood that translation into other terms will usually be
possible.
Chapter III is rather a special chapter. It is about logic and
methods of a quasi-philosophical kind. It is almost in the nature of
an appendix, but there are a number of models and theories there
which might be regarded as being of behavioural interest, and they
are a source of many ideas used at other points in the book.
It is not thought that philosophy can contribute greatly to
psychology, and speculative philosophy can contribute perhaps
nothing at all; but a certain sophistication over linguistic matters
seems to be essential. The writer believes that much that phil-
osophers discuss could be decided, or at least clarified, by ex-
perimental methods, and his position is therefore in a sense
anti-philosophical, but this will not be allowed to obscure the fact
that care and thoughtfulness over concepts and language is vital in
any science.
In Chapter IV we have outlined a very general and loosely
constructed model which is to be used for experimental purposes,
12 THE BRAIN AS A COMPUTER
by analysing the existing empirical data from cognition. At the
end of Chapter VI we start to introduce some examples of learning.
Chapter VII summarizes learning theory, and more space is
given to the traditional theories of Hull and Tolman, and less to
the current and more burning issues on methods of reinforcement.
The reason for this is again that the book hopes to find readers who
are not already familiar with cognitive problems, and whose interest
may be partly methodological.
Chapters VIII, IX and X deal with neurological matters, although
Chapter X represents an all-round approach to the perceptual side
of cognition. Chapter VIII is, in particular, an attempt to sum-
marize the main relevant facts of the neurophysiology of nervous
function, and although it tries to make the explanations simple
and certainly it is not addressed to the specialist in neurophysiology
it can be better understood by those who have already carried
out some previous reading in the subject.
Chapter XI pays lips service to thinking, and also says some
more about perception. The writer is very conscious of the
relatively sketchy nature of the treatment he has given to many of
the problems discussed in the book, but his main hope has been to
persuade experimental psychologists that there is much to be said
for a greater concentration on matters of methodology, especially
from the cybernetic point of view, while continuing to develop
experimental psychology, which the writer thoroughly believes
should still be their chief aim.
The last chapter, Chapter XII, is a sort of summary of attitudes
and findings which are of interest primarily to the experimental
psychologist.
Summary
This first chapter is intended to outline the general purpose of
the book, which is both methodological, and a beginning to a
model-theory construction process based on the methods of
cybernetics. It is, in essence an attempt to utilize to the full our
concepts, whether from philosophy, logic or science, and to
construct a conceptual world in terms of machine analogues, from
which we may ultimately derive more precise theories of behaviour,
and theories of the internal organization of the human being,
especially at the level of the nervous system.
CHAPTER II
CYBERNETICS
'CYBERNETICS' is a word that was first used by Norbert Wiener
(1948), and has since become widely accepted. as designating the
scientific study of control and communication, and applying
equally to inanimate and to living systems.
Wiener's basic idea was that humans and other organisms are
not essentially different from any other type of control and com-
munication system. The principle of negative feedback is charac-
teristic of organisms and closed-loop control systems in general,
and this suggests that organisms could be substantially mimicked
by electronic switching devices which are controlled by negative
feedback.
The word 'cybernetics', although a recent addition to our
vocabulary, in fact refers to much that went on for many years
before in various fields such as electrical engineering, mathe-
matics, psychology, physiology and other disciplines. The actual
area covered by cybernetics is perhaps vague, and certainly very
large. It cuts across many of the accepted divisions of science, and
this means that cybernetics has many different aspects that will be
of interest to scientists working in various branches of scientific
endeavour. jThe main emphasis in this book will be focused on the
interests of the experimental psychologist and the biologist,
although it is believed that it should also have an appeal to those
concerned with many different sides of science.
We shall now say a little about the mathematical and historical
background of cybernetics.
Mathematics
The primary interest of mathematics to cybernetics is due not
only to the direct relevance of mathematical logic and questions
involving the foundations of mathematics and axiomatic methods,
but also because of the design of computing machines.
13
14 THE BRAIN AS A COMPUTER
First let us briefly consider the history of mathematical thought
and the problem raised for the foundation of mathematics.
We should begin by reminding ourselves of the important fact
that mathematics is a language or language form. It is, indeed, a
highly precise and abstract language that handles or is capable
of handling any of the structural relations that actually exist, or
are theoretically capable of existing. An example of this can be
drawn from geometry.
The geometry of the world in which we live appears to be four-
dimensional that is, from the relativistic point of view; but from
the purely mathematical point of view we can develop geometry
in any dimensions whatsoever, and the user of the ?z-dimensional
geometry can choose whatever value of n is necessary or relevant
to his particular problem. This is an example of the imposition of
a theory on to a model.
Pure mathematicians develop mathematical systems (models)
that may have no application whatever; it is like the development
of the grammar of a potential language, and the constructions
follow simply from the various possible sets of rules. At the same
time it is a fact that a great deal of the mathematics that has been
developed has quickly been turned to practical account. One of the
reasons for this is of course the fact that mathematicians keep
their eyes on the problems that scientists are dealing with, and a
new line of development with no applications tends to fade out
very quickly.
The power of the mathematical language lies partly in the fact
that its constituents have a well organized structure, and partly in
the fact that the notion of number seems to be basic to our
descriptions of the world. Mathematics, though, is not always
numerical; there are branches of mathematics, such as those
dealing with shapes and relations of a geometrical kind, that go
under the name of topology; there is also mathematical logic,
which deals with properties and propositions which are not
numerical. Indeed, the main feature of mathematics is that it tries
to pick out the most general structural relations in any situation
capable of description. It is thus a very general language, and a
powerful form of model making.
One possible misconception should be mentioned. Much that is
symbolic and put in terms of algebraic symbols where these
CYBERNETICS 15
symbols represent real or complex numbers, is not mathematics,
or certainly may not be mathematics of any importance; whereas
much that is written in longhand is mathematics. Mathematics is a
language that is ideally a shorthand, but also it is a powerful
system for making deductions, and carrying out reasoning pro-
cesses, because of the ease with which it is possible to see the form
of the deductive or inductive argument. In ordinary, everyday
language this is hardly ever the case if the description is compli-
cated.
.Our interest in mathematics is directly associated with cyber-
netics, for mathematics is concerned with the whole development
of precision, which is also the concern of cybernetics. In particular,
it has been in the search for mechanical methods of computation,
and for proof that mathematics has played an important part in the
evolution of 'thinking' machines.
The theories of Godel (1931), Church (1936) and Turing (1937)
are connected with any symbolic or linguistic system whatever,
and with any axiomatic system. These theorems are important
landmarks in the history of mathematical logic and the foundations
of mathematics. They assert that no theory language (i.e. any
language that is used descriptively in science) can show its own
consistency within itself.
The theorems also deal with what are called decision procedures,
or mechanical methods of finding proofs of mathematical state-
ments, and Church was able to show that, for a system rich enough
to include classical mathematics, no mechanical method was
possible for discovering whether every statement in such a calculus
was a theorem of that calculus or not. By calculus, we shall mean a
particular postulational system, such as Euclidean geometry of the
plane, or what we may call a 'model'. It was Turing who gave the
most suitable expression to the point in developing his theoretical
computer, the Turing machine, which we shall describe more
fully in Chapter III. These are, or should be, matters of con-
siderable importance to those experimental psychologists and
biologists who are interested in cybernetics, because it tells them
something of the nature of machinery, as defined in terms of
simple operations, and the power of precise linguistic forms.
These theorems have also been the foundations of some measure of
misunderstanding, because the word 'machinelike', although
16 THE BRAIN AS A COMPUTER
suggesting what is obviously mechanical, does not exhaust all
possible machines.
Mathematically, the above theorems were formulated in pursuit
of the goal suggested by Hilbert (1922), that all mathematics was a
formal system of symbols (abstract marks or sounds) that were
manipulable according to sets of rules, and that there was a sense
in which mathematics should be capable of being shown to be
complete. This is now known to be impossible ; the sense of com-
pleteness involved, although capable of various precise definitions,
is roughly the sense in which we would expect a self-contained
system to fit together coherently. This means that every statement
made within the system should be capable either of being shown
to be a theorem of the system or not, and all the true theorems
being shown to be true, and those only. It is this which is not
possible.
There are in the main three different schools of thought with
regard to the nature and foundations of mathematics. They are :
The Logistic school of Whitehead and Russell (1910, 1912, 1913),
Peano (1894) and Frege (1893, 1903), which argues that mathematics
is a part of logic; the Intuitionistic school of Brouwer (1924) and
Heyting (1934), which argues that mathematics is independent of
logic, and comes from a direct appreciation of numbers ; and the
Formalist school founded by Hilbert, who believe that mathe-
matics is a formal game with symbols. These three schools have
carried on continued arguments regarding the foundations of
mathematics, and it is perhaps fair to say that the bulk of current
opinion favours the first view: that mathematics is founded upon
logic; but the whole question is a very complicated one, and it is
not obvious that the various views expressed are really at variance
with each other. However, this is not a matter of primary interest
to biologists and psychologists, and it will not be pursued here.
Independently, but still within mathematics, there has been the
development of computing machinery, and although the motive
force was quite different, the results had a great deal in common
with the foundation studies. At the same time, what was to be
regarded as an effective procedure or a mechanical procedure,
sometimes called 'decision procedure' or 'decision process* in the
sense of Turing, easily covered what a computer was thought to
be capable of performing, since computers, in their early days at
CYBERNETICS 17
any rate, were thought of merely as adding and subtracting
machines of an automatic kind. It was only later that they were to
be thought of as having far greater generality, and capable of being
driven by electronic rather than by purely mechanical means.
Even now, few people have come to think of a computer as any-
thing but a deductive system, and it is the inductive use of the
computer which is the one that is of primary psychological
interest; this, indeed, is one of the main themes of this book, and
of cybernetics.
To return to the mathematical foundation of computers, we find
that the first calculator that was used for any widespread computa-
tions was one designed by Pascal and used for insurance purposes
in France, and this same computer was improved by extension
from addition and subtraction to multiplication and division by no
less a personage than Leibniz. Also in France, it was Colmar who
has generally been credited with producing the first commercial
computer. But the father of the large-scale automatic computer
in its modern form is most certainly Charles Babbage.
In his work Charles Babbage anticipated virtually all that is
characteristic of the modern computing machine, and during his
lifetime he also used the technique of punched cards as a classifica-
tion system, a method that was rediscovered in America, some
years later, by Hollerith.
We shall be discussing the main points of the general form that
the modern computer has taken in the next section but one of this
chapter; at the moment we should notice simply that the concept
of a computer, although dependent upon the work of engineers of
every kind, was primarily a mathematical project.
Cybernetics also has roots in applied mathematics, in particular
in the statistical mechanics of Willard Gibbs, and the general
development of statistical thermodynamics and the gas laws. The
common ground here lies in the fact that information, in the
technical sense of information theory, and the distribution of gas
particles have a common descriptive law.
In analytical mathematics, a considerable contribution was made
to the theoretical background of cybernetics (though he was quite
unconscious of the connexion) by Albert Lebesgue with his
special form of definition of an integral. The development of
abstract algebra, and in particular the theory of groups, has also
18 THE BRAIN AS A COMPUTER
contributed to the general theory. The purely mathematical back-
ground of cybernetics will not be developed here except in so far
as it is necessary to an understanding of the biological applications.
Historical
The sudden recent rise to prominence of cybernetics was due,
immediately, to World War II. There existed then a series of
problems which had not previously been met. The main one was
that of range-finding for anti-aircraft guns in high-speed aerial
warfare. The older systems involved human computers and these,
with manually controlled locators, were wholly inadequate for the
job in hand. The essence of the process involved was to track and
predict the direction, velocity, and height of enemy aircraft. The
human being's part in the operation was much too slow and
inaccurate, and there were people available with machines already
developed to do the job adequately; these machines were, of
course, computing machines.
These computing machines had already been designed, and
some built, by Vannevar Bush, Norbert Wiener, and others, and
were almost ready-made for the job. These scientists, as well as
others such as von Neumann, Shannon and Bigelow, were in a
position to see that machines of an electronic kind were ideally
suited to carry out the whole of the operations of range-finding
and location without any human intervention whatever.
These electronic computing machines were already developed to
a very high degree of efficiency for the solution of mathematical
equations, and some technical difficulties had led to the suggestion
that a process of scanning, similar to that used in television, might
be incorporated into the computer. Another innovation was the
use of binary notation rather than decimal notation as in the early
Harvard Mark I computer.
The problem of tracking, however, called for the mimicking of
another characteristically human type of activity in the form of
'feedback'.
Feedback is what differentiates the machines that we are
primarily interested in from the popular docile machine such as an
aircraft or a motor car, or even the most obviously docile machines
of all such as spoons, forks and levers.
CYBERNETICS 19
Feedback involves some part of a machine's output being
isolated, to be fed back into the machine as part of its input a
controlling part of the input. Man obviously operates on a gross
feedback system in so far as he must have knowledge of the results
of the actions that he performs in order that he may continue to
act sensibly in his environment. A man playing darts will not
improve unless he can see the results of his actions. More generally,
a man who cannot see his results in a learning task will not improve,
i.e. he will not learn; this fact has been well understood in experi-
mental psychology.
A fairly well-known machine that exhibits feedback is a ther-
mostat for controlling the temperature of domestic water supplies.
A lower and an upper limit of temperature is set, and when the
water which is being heated gets to the upper limit a mechanical
device cuts out the heat source. The water then starts to cool, and
when the temperature reaches the lower limit the device operates
again, but in the opposite way, and the heat goes on. The
temperature of the water oscillates between the two limits, which
may be as high or as low as we please. The important thing is
that it is the temperature that itself controls the change of
temperature. This is precisely what is meant by a self-controlling
machine.
Self-controlled steering mechanisms, such as are used in ships
and aircraft, also operate on a principle of feedback, and most
human muscular systems work on the same principle. A man
cycling, or a driver driving a car, makes small correcting adjust-
ments in his muscular movements so that small errors in directions
or balance are corrected. The process is one of error-correction by
a series of compensations.
All the instances that we have described are examples of what is
called negative feedback, wherein a part of the response to some
stimulus is used to operate against the direction of the original
stimulus. Positive feedback involves the same compensatory or
self-controlling aspects, but in this case the energy side-tracked for
control purposes operates in the same direction as the principle
energy rather than against it, and thus creates unstable, or 'run-
away' conditions. In general, cybernetics has been concerned with
the negative feedback type of arrangement.
Self-controlling machines, or 'artefacts' as they are sometimes
20 THE BRAIN AS A COMPUTER
called, have been classified according to the following general
characteristics, according to Mackay (1951):
(1) The receiving, selecting, storing and sending of information.
(2) Reacting to changes in the universe, including messages
referring to the state of the artefact itself.
(3) Reasoning deductively from sets of assumptions or postu-
lates, and learning. Here, learning includes observing and control-
ling its own purposive or goal-seeking behaviour.
It is these characteristics that include artefacts within the defini-
tion of the organism. Indeed, as we have seen, the basic assump-
tion of cybernetics is that the human organism definitely comes
within the framework of our definition, and it follows that the
human operator is (in an obvious sense) a machine.
Computers
^The computer, particularly that of the digital type, is of the
greatest importance to cybernetics. Such machines are now con-
structed for a variety of different purposes. As well as solving
mathematical equations, which was their original purpose, they
are, of course, capable of adding up numbers, sorting and classify-
ing information, making predictions that are based on forms of
induction, and performing at least all the operations which are
capable of being stated in precise language. The theoretical
possibilities inherent in such systems are almost without limit,
although in practice there may be serious limits of a definite kind.
It is not always easy for the technician to achieve results in
practice which appear to be perfectly possible in principle. This is
one reason why the technique of machine-construction and
organization has developed far faster in blueprint than it has in
hardware. It costs large sums of money to build computing
machines and, after they are built, further large sums to keep them
working; it is well, therefore, for those who are interested especi-
ally in the potentialities of machines, that it is sufficient to develop
an effective technique for discovering the capabilities of a machine
without going to the enormous expense, in terms both of money
and time, of building it. This subject, and the sort of blueprint
techniques practised, with their close relation to mathematics, is
of the first importance to our subject.
CYBERNETICS 21
Computers have advanced mainly with the advances in techno-
logical methods, especially of the electrical and electronic
techniques which are closely bound up with the realization in hard-
ware of machine theories. This process of realization demands a
whole technology involving the design and manufacture of valves,
resistances, relays and the like, that will function with a certain
degree of efficiency under specified conditions.
It is clear that the building-in of a maintenance and repair
system will be quite vital if the computer needs to be permanently
running. It has been suggested by von Neumann (1952) in this
context that we might use a duplicating technique in construction
which von Neumann called 'multiplexing'.
The general form of a digital computer
The digital computer is, to put it quite generally, composed of an
input and an output system, a control, and a storage system. The
storage system usually contains the control, and is divisible into
two parts: the slower, permanent storage, and the faster, tem-
porary storage which includes the control itself.
The process of operation of the computer could be typically
described as that of accepting instructions in the form of coded
'words', which it stores as pulses in mercury delay lines or as
imprintations on the sides of magnetic drums. Those of the words
which represent numbers are then supplied to the input, and the
instructions, which are usually taken in numerical order, operate
on the numbers as they appear. The process could be likened to
that of saying to someone, who is capable of no more than adding
up and storing information, that you want him to add the first
number, which you will tell him later, to the second, and the sum
of these to the third, and so on. These are the instructions which
he stores. You then give him the numbers in the correct order.
The alternative to ordering the numbers would be to designate
each with a name. Of course, their addresses (their storage locali-
ties) must certainly be known.
Obviously the working of a modern digital computer, operating,
as it does, at extremely high speed, will depend upon efficient
parts of an .electronic kind. These parts are largely comprised of
the staticizors and dynamicizors, which may act both as control
and as temporary storage; the cathode-ray oscillograph; and the
22 THE BRAIN AS A COMPUTER
electronic gates that realize simple logical functions, since the
mathematical operations of the computer are essentially dependent
on the simple logical operations of Boolean algebra. Input and
output mechanisms in the form of readers and writers are neces-
sary for coding and decoding instructions, and translating the
information on the punched card, or tape, into electronic pulses,
which is the form in which the computer generally carries its
information.
Since it is not our purpose to discuss in detail existing com-
puters of the well-known digital and analogue varieties, we shall
make no attempt to do more than summarize their general
structure, with the object of giving the untutored reader *a feel for
the subject* in a general way. For a detailed treatment he should
consult one of the many texts available.
We shall now add a few notes on the language of computers,
input and output systems, storage, circuitry, and finally, pro-
gramming. There will also be a word or two on the difference
between digital and analogue systems.
The language of computers
It is not without significance for biologists and experimental
psychologists that the language that computers generally use is
that of a binary form. Computers can be built to handle decimal
mathematical systems but this involves 10-way instead of 2-way
switches, and runs into great technical difficulties. It is another
foundation point of cybernetics that the neuron is (or can be regarded
as) a form of 2-way switch.
A binary system can represent any symbolic system whatsoever,
not only mathematics or arithmetic in the narrow sense, but any
language, so there is no loss of generality in using a binary form of
language. It is true that this has the effect of making words longer,
but this is offset by the great speed at which it can operate as a
complex 2-way switching system. The following table of samples
shows the conversion from decimal to binary code for arithmetic.
The ordinary operations of mathematics can be reproduced in
binary form in the same way as in decimal form. For addition, if
we think of 108 as being a shorthand form of
Ixl0 2 +0x 10+8x10
CYBERNETICS
23
and 56 as being 5 x 10+6 x 10
then the sum of these, 164, is
Ixl0 2 +6x 10+4x10
TABLE 1
Decimal
Binary
1
i
2
10
3
11
4
100
5
101
6
110
7
111
8
1000
9
1001
10
1010
100
1100100
1000
1111101000
16
10000
32
100000
64
1000000
So in binary form a number such as 19 can be thought of as
Ix2*+0x2 3 +0x2 2 +lx2+lx2 (10011)
and 7 can be thought of as
Ix2 2 +lx2+lx2(lll)
and the sum, 26, is 11010.
If we simply add the binary numbers directly, we see that we
get the same result, remembering to carry one whenever we have
two in a column:
10011
00111
11010
Similarly, we can easily subtract in binary code:
10110
01101
01001
24 THE BRAIN AS A COMPUTER
This says that if we subtract 13 from 22 we are left with 9. The
reader can go on from here and construct other examples, e.g.
multiplication, division, and indeed the whole of arithmetic.
Input- and output-systems and circuitry
The input and output systems of digital computers are usually
in the form of punched tape or punched card. Figure 1 shows an
example of a piece of punched tape with the instructions on it for
the computer control of the Ferranti machine tool cutter. STA
stands for the initial signal, NMC gives type of message, DAX
, DAY and DAZ indicate coordinates in which cutting is
to take place for 'change points' (where the curves are all made up
from circles, and therefore there has to be frequent change from
one circle to another). The other coordinates are of the pole of
curves, and RAT is the cutter feed rate. DIA gives diameter
of circle, and TDC compensation sense.
The use of the pole, and the related notion of the polar, are here
used as convenient means of defining the circles that collectively
define the curve to be cut, The^ofe is defined, for a circle, as being
any point outside the circle which is the point of intersection of
tangents drawn to the two points at which any line cuts the
circumference of the circle; and the locus (the set of points for
which this is true and a straight line with respect to a circle in
Cartesian coordinates) of the intersection of the tangents is called
a polar with respect to the pole.
This example is meant only to show an ordinary piece of tape
with punched holes which are represented here by filled-in black
dots and no holes otherwise ; these represent 1 and respectively
and so in turn represent a binary code. The example itself is a
practical form of computer control.
Figures 2 and 3 show Hollerith cards as used by the DEUCE
computer with essentially the same method of representing 1's
and O's. Figure 2 shows an instruction card where NIS is next
instinction, SOURCE applies to address of number to be operated
on, and DEST to its destination after the operation. Most of the
rest of the instructions are concerned with the careful timing
of the operation.
The fact that each storage location can be thought of as a source
and as a destination is a reminder that the characteristic operation
CYBERNETICS
25
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26
THE BRAIN AS A COMPUTER
of the computer involves the removal of a number from one storage
location, usually to perform some mathematical operation on it,
and the subsequent placing of the number, or the derived number,
at a new storage location.
Figure 3 shows the DEUCE Data card which carries the numbers
themselves, which are confined to the 12 rows and 32 columns of
the DEUCE field. The DEUCE uses 32 binary digit numbers.
Alternative forms of input and output exist. Such methods as
morse keys, the human voice, teleprinter with decimal conversion,
flashing lights (neon and otherwise), have all been used at some
Positive voltage
_L
T
Negative voltage
FIG. 4. FLIP-FLOP CIRCUIT. A typical circuit composed of simple
flip-flop switches. These switches simply take up one of two
positions on or off as in an ordinary electric light switch.
time or another. Reference to the appropriate texts is necessary
when detail is needed, but the principles, at least, are simple.
Binary coded messages are fed into a classification system which
has wires which become electrified whenever they come opposite a
punched hole, and this has the effect of placing a pulse into the
circulation of the machine. The similarity to the human nervous
system is already suggestive.
There are many methods of storage, and the best known can be
summarized quickly. They are the simple flip-flop circuits, of
which Fig. 4 shows a typical example. The idea of a flip-flop is
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CYBERNETICS 27
neatly summarized by analogy with the mechanical behaviour of
a length of tube, sealed at each end, with a freely rolling steel ball
inside the tube. If we pivot the tube over a wedge-shaped block,
the ball is at the lower end and holds the tube against one face of
the block in a stable position. To change to the other state, we have
to apply a force to the other end of the tube to overcome the down-
ward force of the ball acting under gravity, until the ball rolls to the
other end, and the tube takes up a stable position on the opposite
face of the wedge. If the initial position is called 0, the other posi-
POINT OF APPLICATION OF
FORCE NEEDED TO CHANGE
STATE OF SWITCH,
TUBE-
FIG. 5. A FLIP-FLOP. The switch is in one of its two possible
states. When the force is applied the tube tips, the ball moves to
the other end, and the switch goes into its alternative stable
position against the other face of the wedge.
tion can be called 1. Figure 5 shows the mechanical analogue in its
initial position.
The staticizor is another way of using an electronic AND-gate,
Fig. 6, for the retention of information as to whether a pulse or no
pulse was present at an input terminal at a particular instant in
the past.
The proper memory store is not usually composed of staticizers
because of the great expense involved in using two valves for each
binary digit stored, which is what is entailed. The most used
28 THE BRAIN AS A COMPUTER
'permanent* memory stores are the delay-line memory, although
these lose their information when the machine is switched off, the
high-speed electrostatic store, the magnetic drum storage, and the
magnetic core type of storage. In principle, their working involves
the storing of 'words' (in binary form) that can be written in and
taken out of store at will We shall not discuss their detailed
working.
The 'word' of a computer, we should add, is usually a 40-binary
digit set (on the average), which represents an instruction or a
number. A collection of words represents the language of the
computer, which is a translation of ordinary language into punched
lo-
Jr-J
> X
NEGATIVE
VOLTAGE
FIG. 6. AND-GATE. The AND-gate has two input terminals, and
one output terminal. The output is fired if and only if both
inputs are fired simultaneously.
tape or card, and subsequently into pulses inside the computer,
and then back to punched card or tape and ordinary language
again.
We have already shown something of the sort of circuitry
involved in the AND-gate of Fig. 6, and we must now add to this
in OR-gate and a NOT-gate, and we shall see that the use of
: and', 'or' and 'not' is more than sufficient, logically, for our
computational purposes.
We should mention that, in practice, modern computers have
arcuitry which is relatively simple in detail, and complex only by
virtue of the large numbers of relays or two-way switches involved.
CYBERNETICS
POSITIVE VOLTAGE
29
-03
FIG. 7. OR-GATE. The OR-gate has two input terminals, and one
output terminal. The output is fired if and only if either one or
both inputs are fired.
POSITIVE VOLTAGE
STANDARD
-02
30 THE BRAIN AS A COMPUTER
Programming
Programming involves suitably instructing the machine. This
:an be illustrated by the example of a man who is told to add
lumbers for us, and we will not say very much on the technique,
which varies in detail from machine to machine. The simplest sort
rf instruction for the DEUCE, for example, takes the form '13-15',
#hich simply means, replace the contents of temporary store 15 by
Jbe contents of temporary store 13, leaving the temporary store 13
jnchanged. It is not difficult to imagine the suitable stringing
:ogether of instructions of this sort, which will also involve the use
}f the automatic adder, multiplier, and so on. Any set of such
nstructions constitutes a programme, which is usually placed in
:he storage system, to be called up subsequently by the control, as
leeded.
Digital and analogue systems
All that has been said here so far has been about digital systems.
There are also analogue systems and analogue computers. The
difference between digital and analogue methods is essentially the
;ame as between discontinuous and continuous functions in
nathematics.
We shall not be much concerned with analogue systems, but we
shall just say a few words about them. They represent numbers
md other physical conditions by physical variables (e.g. voltages
ind currents) rather than by digital numerical means. They are in
widespread use as calculators, and also as simulators of various
physical states. One example is to be found in the various flight
conditions encountered by an aircraft, which can be wholly or
partially simulated in a computing machine. It is clear that
psychologists are, in a sense, seeking to simulate human be-
lavioural conditions in their theories and models.
Neurophysiology and psychology
Following up a discussion of digital and analogue computers,
we must come to consider the more general questions of artefacts,
Dr machines.
If machines can perform mathematical operations with such
CYBERNETICS 31
success, what else can they do like human beings, assuming that
they do perform mathematical operations in a manner which is at
least somewhat similar to humans?
Psychology and physiology in particular, and the biological
sciences in general, have taken notice of the revolution in machine
design in order to investigate human behaviour and general
physiological function from the machine point of view. We have
already suggested that the similarity between machines and
organisms is so great that the specifications for one appear to be
capable of including the specifications for the other, and we should
be able to make use of this fact in our attempts to understand
human behaviour, build simulators for it, and so on.
This has led, in turn, to the construction of various machines
in blueprint form, and special techniques for their design and
construction; indeed, some of them have been constructed. These
can be described, preliminarily, as mimicking some aspects of
human behaviour. They are models, and they generally mirror
some aspects of human behaviour, but not all of it. Not that it will
necessarily always be impossible to build a complete human
machine, but there are various reasons why it will not be useful to
do so. The models will endeavour to mimic some of the aspects of
behaviour rather as a putting green mimics some aspects of golf,
or a wind-tunnel model of an aircraft mirrors the aerodynamical
aspects of aircraft.
It is clear that electronic devices which mirror some sides of
behaviour will not mirror, for example, the biochemical side, since
the biochemical side is peculiar to the use of protoplasmic materials
which are those materials used in the construction of living
organisms, in its usual sense. But the fact of using different
materials is no barrier to the use of machine artefacts for under-
standing behaviour, although the extent to which such considera-
tions do matter must be given some thought.
What is of obvious interest to the psychologist is the fact that
machines are said to think, and this, too, is why logic is brought
into the picture, since it is logic that helps humans to think, in so
far as they do think in correct fashion.
It is believed that the whole development of machines that can
learn and think is a vital product of the general theory of cyber-
netics, and, of course, first cousin to the process of automation.
$2 THE BRAIN AS A COMPUTER
These models, coupled with methods used in modern psychology,
will occupy most of our attention in the later chapters.
'Can we sensibly and seriously say that machines can think?'
Is it true that humans are, in some sense, just machines?' These
ire matters of philosophical as well as psychological interest.
The answer the cybernetician is inclined to give to these
questions takes one of two forms: (1) Machines do think, and
machines could be made to think just as humans think, or (2)
fn so far as we can only deal with the machine side of humans, we
:an behave as if (1) above were true, even if it is not.
We are concerned with a strictly behaviouristic viewpoint, and
whether or not the word 'thinking' is appropriate, and philosophers
will often object to its use here, the processes inside humans and
:hose inside possible machines are capable of being made the same.
It must be emphasized very strongly that cybernetics as a
scientific discipline is essentially consistent with behaviourism, and
.s indeed a direct offshoot from it. Behaviourists, in essence, are
people who have always treated organisms as if they were machines.
Communication theory
We have already seen that the control and the communication of
.nformation are completely bound up with each other in a com-
puter, as indeed they are in a human. These two closely related
subjects are the focal point of all knowledge. They are most
certainly the central theme of cybernetics.
The theory of commxmication, or 'information theory', as it is
sometimes called, is a very general and rigorously derived branch
rf modern mathematics; a branch of probability theory. The
:heory introduces the notion of an information source and a
ncssage which is transmitted, by any of the many possible means,
LO a receiver that picks up the message. There may also be an
interference source that interrupts or otherwise disturbs the
transmission of the message along the communication channel,
and this is called a noise source; this very general situation may be
represented diagrammatically.
The message may be coded, or it may be sent in language that
itself requires to be interpreted with respect to its meaning. Codes
and languages are essentially the same, and ordinary languages are
really codes for our 'ideas' or concepts. The fact of coding or
CYBERNETICS
33
encoding messages naturally implies the process, at the receiving
end, of decoding or interpreting the same message.
The amount of information that passes along some channel can
be measured, as can the capacity of the communication channel;
this leads us into some mathematical technicalities which we will
take up in the next section of this chapter, but in the meantime
there are one or two other points which must now be mentioned.
In the first place, languages have certain properties of a statis-
tical or probability character. In particular, certain letters and
certain words occur more frequently than others, both in English
Source
Channel
Coding
Decoding
FIG. 9. COMMUNICATION. A generalized picture, in block dia-
gram form, of the communication situation on a noisy channel.
The coding and de-coding may be repeated any number of
times and a filter may be utilized in the channel to regain
information lost through noise.
and any other language. There is a definite probability that can be
associated with the occurrence of any particular letter, which
means that the notion of information is closely associated with
probability. Information is measured by the probability of occur-
rence of the particular message passed.
The sequences of symbols that characterize any sort of language,
or any set of events, have certain statistical properties ; indeed, our
ability to decipher languages or language-codes depends upon its
repetitiveness, what statisticians call its statistical homogeneity.
Generally, we say that any sequence of symbols which has a
14 THE BRAIN AS A COMPUTER
>robability associated with each symbol, is a 'stochastic process',
"low a particular class of stochastic processes, called 'Markoff
>rocesses', has the extra condition that the probability of any
;vent is dependent on a finite number of past events ; often this
iame has been restricted to a conditional probability on one past
ivent, but we can think of it as operating over any finite number of
ivents. If the Markoff process also has the property of statistical
tomogeneity, it is called an 'ergodic process'. These names will be
Iready familiar to psychologists, as they represent closely allied
vays of regarding human behaviour (Bush and Hosteller, 1956).
Ve shall return to this side of the subject later.
Let us consider a very simple language, with an alphabet of only
he four letters A, B, C and D. If the occurrence of each of these
stters is equiprobable, we might expect a typical series, or a
tring, of letters in a message such as ABBACDABDDCDABDB
IABDCACC, and so on, where all the letters occur equally often,
f, however, A is three times as likely to occur as B, and B twice as
ikely as either C or D, then we might get AABBAAAAABCAA
)AACDBBABABAACDBBAAAAACDBAAAAAACAD. We can
aake the matter more complicated by saying that if we get A
hen there is twice as much chance of B following it as there is of
>; D is never followed by A, and so on. We can then build up
loser and closer approximations to any ordinary language what-
oever by using words (collections of letters) and by considering
heir frequency of occurrence and their order. Such a rule as:
J always or almost always follows Q, for example, would be true
>f English. These will be probability statements, it must be
emembered, and therefore there may be exceptions to the rule.
Let us following Shannon and Weaver (1949) use the
pords :
0-10 A
0-04 ADEB
0-06 ADEE
0-01 BADD
0-16 BEBE
0-04 BED
0-02 BEED
0-05 CA
0-11 CABED
0-05 CEED
0-08 DAB
0-04 DAD
0-04 DEB
0-15 DEED
0-01 EAB
0-05 EE
nth the associated probabilities of occurrence next to each word.
This stochastic process, composed of the five letters A, B, C, D
nd E with the words listed above, gives a typical message such as :
CYBERNETICS 35
DAB EE A BEBE DEED DEB ABEE ADEE EE DEB BEBE
BEBE ADEE BED DEED DEED CEED ADEE A DEED
and so on.
In the same manner as this we can approximate to any ordinary
language whatsoever. Thus a zero-order approximation is one in
which the symbols are independent and equi-probable. First-
order approximations have independent symbols, but the same
frequency of letters as in the language. The following is an
estimate of the frequency of letters in English per 1000 letters
(Goldman, 1953).
E 131 D 38 W 15
T 105 L 34 B 14
A 86 F 29 V 9-2
80 C 28 K 4-2
N 71 M 25 X 1-7
R 68 U 25 J 1-3
1 63 G 20 Q 1-2
S 61 Y 20 Z 0-77
H 53 P 20
A second-order approximation has a digram frequency; this
connects two successive letters in terms of probabilities, as in our
conditional probability case mentioned above. A probability
influence that spreads over three successive letters is called a
'trigram' frequency, and this, for English, is a third-order approxi-
mation; and so we go on until the second-order word approxima-
tion is obtained.
The bulk of the mathematical aspects of the theory had been
developed quite independently of the theory of communication,
since it is merely a branch of probability theory. The importance
of the direct relation between die information flow and the change
of the state of the particles of the world and their distribution is
still problematic. Entropy, which is the measure of disorganiza-
tion, is said, in statistical thermodynamics, to be increasing, and
has an analogue in the passing of information. It is a strange
picture, but in terms of the world, control systems are seen as little
pockets of negative entropy that are running against the main
flow of the tide of disintegration.
The full significance of the relation between entropy and
36 THE BRAIN AS A COMPUTER
information is by no means wholly clear, but it has the ring of
fundamental importance.
The idea of a statistical distribution of particles can be made
clearer if we consider the distribution of particles of air in the
ordinary room. Unless conditions are unusual such as the
window being open and causing the door to slam with a gust of
wind we may expect the particles to be, roughly speaking,
equally distributed through the room. Gases, like air, are known
to fill their containers completely and arrange their density
according to the space available. The Clerk Maxwell demons,
those fictional twin characters who, had they existed, would
have made perpetual motion possible are to be pictured as
standing at each of two doors which lead away from the room to a
heat engine and back into the room again. The demons open and
close the doors according to the velocity of the particles which
approach them. The first exit is opened only for the high speed
particles, and the second is opened only for low speed particles,
thus creating a temperature gradient which can be made to do
mechanical work and therefore permitting the possibility of
perpetual motion. This keeps the energy in the system constant,
but does not allow for the increase of entropy, against which the
demons would be fighting a losing battle.
The most important feature of communication theory is
perhaps that, considered as feedback control systems, machines
and organisms are essentially the same, and therefore have the
same problems of communication.
The theory of communication can be regarded from at least
three different levels. In the first place, there is the technical
problem of transmitting accurately the symbols used in com-
munication. It is fairly obvious that telecommunications should be
of interest here, and the problem is primarily syntactical. We mean
'syntactical* to suggest the organization of the basic symbols
according to rules, in a sense to be discussed later.
The second level problem can be called the semantic problem,
and deals with the meaning that the symbols are said to carry.
Thirdly, we want to know whether, or to what extent, the meaning-
ful communications affect behaviour. This last might be called the
'pragmatic' problem* Some attempts have been made to develop
the semantic theory of information, but little has been done at
CYBERNETICS 37
the pragmatic level. This is, again, precisely the domain of
cybernetics.
All that has been said so far in this section has been about the
syntactical problem at the technical level, and has been largely
concerned with pointing out that a technical problem of com-
munication exists. The problem is primarily electronic, at least for
those who are concerned with the development of the theory, and
their interest, and indeed the theory generally, has been directed
towards the more technological forms of communication such as
radio-telegraphy, radio-telephony, radio, television, and a wide
variety of methods of signalling. This involved morse code and
teleprinters and, with it, the essentially mathematical process of
making and breaking codes. It is of immediate interest that the
theory in fact covers much more than these technical problems
technical, that is, in a narrow sense for in particular it covers the
ordinary, though vital, problem of communication between
people, both as individuals and groups.
The technical aspect of communication
Communication theory really represents the attempts of the
communication engineer to understand what he himself is doing.
It should be said, in passing, that information as used by the
technologists has a slightly limited usage (which is characteristic of
any term that has been given a precise meaning), and refers to all
the messages that are capable of being sent, rather than to any
sentence that has already conveyed meaning. The actual measure
of information is given by
H = Zpi logzpt
where pi is a Laplacian probability and such that </>*<!.
A simple example will make the position clear. If the well-known
choice in the Merchant of Venice had been extended from 3
caskets, as in the play, to 16 caskets, and a message had been passed
to the suitor telling him which casket contained 'fair Portia's
counterfeit', he would have been given just 4 bits of information.
This can be seen from the general formula, or it can be thought of
as the number of times that we have to divide 2 into the number
of alternatives before we reduce them to 1. If there were 4
caskets, then a message indicating which casket contained the
38 THE BRAIN AS A COMPUTER
portrait would have just 2 bits of information. The word 'bit 5 is a
contraction of 'binary digit', and the significance of this unit is that
a message containing 2 bits of information needs 2 binary
digits to communicate all the possibilities defined by the situation.
The case of the 4 caskets demands the need for 4 messages for
all possible outcomes, hence these can be coded as 00, 01, 10 and
11, thus requiring only 2 binary digits (bits).
Many other technical facts have been discovered, such as the
Hartley Law which relates bandwidth to frequency of information.
This makes it clear that any signal, being ergodic, will be a con-
tinuous periodic function, and thus will be characterized as a
wave function, having frequency, wavelength, bandwidth and so
on. Similarly, there are problems of noise. A practical example is
that of the needle-hiss on a gramophone record. There is a well-
known theory of filtering, due to Wiener (1949), that is intended
to reduce the noise-to-signal ratio to a minimum. The procedure is,
in essence, a statistical one, and can be thought of as picking one's
way through the noise to minimize its effect. A channel with noise
is a function of two stochastic processes, one for the message and
one for the noise. This is closely connected with the familiar
processes of frequency, amplitude, and other forms of modulation.
Hartley himself developed a theory of information similar to the
one now widely accepted, wherein the concept of meaning was
rejected, and the process of selecting from a set of signs organized
as a language, with an alphabet, characterized the central notion
of 'information'. The concept of bandwidth is quite fundamental
to all communication, and Hartley's Law can be broadly interpreted
for all such systems as meaning that the more elements of a
message that we can send simultaneously, the shorter is the time
required for their transmission. Some applications of these ideas to
psychological data will be discussed in later chapters, although our
primary emphasis in this book will not be on the application of
information theory, but on the application of finite automata.
Let us now return to a consideration of some further aspects of
the technical definition of communication. Wo can graph stochastic
processes in a manner that brings out the importance of the
constraints that are enacted on any code that may be used.
The following graph illustrates the states and the transition,
probabilities that will affect the artificial language of our example
CYBERNETICS 39
with, the worcta A A T^TTR A TM7T? *. mi
TrinH A A v 7 e dots re P resei it states of
a kind and the lines represent the transitions from state to state
with the associated probabilities marked against them
replace phone^
dial engaged
phone 'b**^ mm ^
Tone
^i^^^"
FIG. 10. TRANSITIONAL PROBABILITY DIAGRAMS. The diagram
shows the transitional steps from state to state in terms of the
artificial language described in the text. The second diagram
shows the same thing for a simple telephone system.
The constraints on language are illustrated by this graph If we
consider a language like Morse code it is clear that, having just
transmitted a dot or a dash, anything can follow; whereas if there
40 THE BRAIN AS A COMPUTER
has just been a letter space or a word space only a dot or a dash
can follow. If, for example, we did not have a letter space between
morse letters, it would be quite impossible to tell whether four
successive dots was meant to be four successive E's, or H; such
examples abound. In a sense this is part of the syntax of any
language, and directly affects the technical problem of transmis-
sion.
One further example of a technical problem, code capacity,
will be noticed before we leave the technical and syntactical
problems of communication theory.
The code capacity of a channel has to be appropriate to the
passing of a code, and the code capacity in the simple case, where
all the symbols used are of the same length, has a simple form. If
we have an alphabet with 16 symbols, each of the same duration,
and thus each carrying 4 bits of information, the capacity of the
channel is 4n bits per second, where the channel is capable of
transmitting n symbols per second.
The subject of coding and transmission of codes, as well as the
problems of decoding and breaking codes, is an extensive one. We
shall return to it briefly later when we consider problems of
behaviour.
Language, syntax, semantics and pragmatics
The distinction between syntax, semantics and pragmatics is
fundamentally a logical one, and has here been borrowed to apply
to the general theory of communication. It is a distinction due
largely to Carnap. The idea is that syntax is a formal set of signs
that have certain grammatical properties; they follow rules which
allow certain combinations to occur and not others (in theory
construction we shall think of these as being like models). Mathe-
matics is purely syntactical until we say that the signs that
mathematics uses: 0, 1, 2, 3, +> > and so on are; nought, the
positive integral numbers one, two, three, and the operations of
addition and subtraction, and so on. Similarly, the #, y, and z of
elementary algebra can stand for fish, people or anything at all
that follows the same rules; and when the correlation or association
is performed, we have a descriptive language or theory.
As soon as we say that the symbols in our syntactical model
CYBERNETICS 41
refer to or name certain objects or relations, then we have added
rules of meaning, and we are in the province of semantics ; and if we
then add the reactions of the person talking and the person spoken
to, we are in pragmatics which deals with the behavioural effects of
language.
In many ways it is true to say that syntax is mathematical logic,
semantics is philosophy or philosophy of science, and pragmatics is
psychology, but these fields are not really all distinct. The relation
between syntax, semantics and pragmatics, and the desire to extend
their integration at certain levels of description, is a motive power
involved in the present book, and one that is perhaps not logically
necessary to a cybernetic standpoint; nevertheless it is taken as a
justification for the examination, cursory as it is, of logic and
philosophy in the next chapter. We shall, therefore, be talking
in terms of these distinctions in other chapters when we are dealing
with logic, language, mathematics, as well as general problems of
communication. The closeness of all these to communication
theory will be quite apparent.
Servosystems
^Another pillar of cybernetics appears in the development of that
branch of engineering concerned with servosystems. As with
computers, this is a specialized field, and there are many text-
books available for a suitably detailed study should the reader feel
this to be necessary to his purpose. Here, we shall only outline the
general principles of servosystems.
A servosystem is a closed loop control of a source of power, it is
usually an error-actuated control mechanism operating on the
principle of negative feedback. A servomechanism is a servosystem
with a mechanical output such as a displacement or a rotation,
although the closed-loop of control could be used to model a far
broader range of outputs.
Servosystems themselves can be divided into those that are
continuous (these are the most usual), and those that deal with
error, or whatever is the controlling factor in terms of discon-
tinuities, such as step functions, where the variable makes sudden
jumps from one value to another. They can also be divided into
manually and automatically controlled systems, where we think of
42 THE BRAIN AS A COMPUTER
such characteristic activities as temperature regulators, process
controllers, and remote position controllers.
The power source and the amplification and transmission of
signals in servosystems may take many forms, although the
electronic and electrical are by far the most popular. We should,
however, mention hydraulic and pneumatic methods as alternatives
to electrical ones.
Servosystems are self-controlling systems, and of course in this,
again, they bear some resemblance to human beings.
They are capable of being represented by differential equations.
Linear differential equations represent linear servosystems, and
non-linear differential equations represent non-linear servosystems.
Here again, a great deal of mathematics could be generated, but
this would not be of direct interest to the psychologist. The
mathematical development is in the form of differential equations
and functions of a continuous variable, or variables, and there is an
analogue of this in theories of learning (London, 1950, 1951;
Estes, 1950, and many others) where differential equations are used
as defining certain crude molar changes in learning, remembering
and other cognitive acts.
To put it briefly, a servosystem is a standard engineering method
for producing automatic control in actual hardware components; it
is used as part of most automatic control systems. With the Ferranti
computer-controlled machine tool cutter, mentioned earlier, the
actual positioning and moving of the cutter, relative to the piece to
be cut, depended on the transmission of information to the control
by virtue of servomcchanisms. In that case, one servomechanism
was needed for each dimension of movement.
Similarly, in such devices as automatic pilots we have the basic
manipulations of the control surfaces of the aircraft depending on
servomechanisms. Characteristically, we have the input signal
made up of a desired position signal, and the error or departure
from the desired position which derives from the output,
involving a comparison between the actual and the desired state
of affairs, and then, a compensating message being sent by the
control to the item controlled, effecting whatever changes are
necessary.
There are many physiological processes that appear to operate
as closed-loop systems, and this idea is supported by the appear-
CYBERNETICS 43
ance of the general principle of homeostasis that has been closely
associated with behavioural descriptions of organisms.
Finite automata
The last and most important idea of general cybernetics is that
of finite automata and, rather especially, their representation as
logical nets. It is, in fact, so important as to receive explicit
description in Chapters IV and V. Here, as a brief introduction,
we should say that it was an insight of McCulloch and Pitts (1943)
to see that Boolean algebra (discussed more fully in the next
chapter) could be directly applied to the description of something
very much like idealized nervous systems.
The essential link was, of course, the fact that as we have
already mentioned computers could be described in Boolean
terms, on the one hand, and nervous systems seemed like two-way
switching devices, on the other.
This book is going to be concerned primarily with the develop-
ment of the theory of logical nets, or 'Automata theory', as it is
sometimes called. We hope to show how certain finite automata
can be constructed in a manner similar to organisms, and thereby
to offer an alternative approach to psychological problems.
Universal Turing machines (to be discussed in Chapter III)
are infinite automata, and we shall further distinguish between the
theory and the syntheses of finite automata, by which we mean
simply the difference between paper and hardware machines.
Logical nets are themselves dependent on mathematics, com-
puter design and communication theory, and represent the syn-
theses that are most immediately applicable to biological ends.
Cybernetics has, we shall argue, not only helped the telephone
engineer, and those concerned with the technological problem of
communication, by making their problems explicit, but also and
even more obviously helped the biologist and the psychologist.
For example, for many years the neurophysiologist has been guided
by the idea of a reflex arc, like a telephone switchboard system, but
he is now graduating to the idea of controlling systems of a
homeostatic type. This advance not only broadens our understand-
ing of biological function, but it also makes way for the application
of mathematics, and the generally increased precision of prediction.
44 THE BRAIN AS A COMPUTER
Summary
In this chapter we have summarized the principal constituent
parts of cybernetics. These are: (1) Mathematics, (2) Computers,
(3) Communication theory, (4) Servosystems, and (5) Finite
Automata. The last of these is rather more in the nature of a
development than a foundation constituent part.
These subsections of cybernetics are, of course, subjects in their
own rights. Here we are concerned with experimental psychology
and biology, and have only summarized as much of the above as
seems necessary to our proposed development of cybernetics for
those purposes.
Cybernetics in general is defined as the study, in theory and in
practice, of control and communication systems. Its relation to
language, by virtue of its communication interest, ensures a vital
link with logic, and also encourages the study of language which, in
turn, inevitably touches the domain of philosophy.
CHAPTER III
PHILOSOPHY, METHODOLOGY AND
CYBERNETICS
UP to now we have concentrated most of our attention upon
cybernetics and its relation to experimental psychology. Experi-
mental psychology has been thought of in very broad terms, and it
overlaps neurophysiology and some parts of zoology. Indeed,
experimental psychology, although capable of being interpreted in
a purely molar way, is to be thought of as being concerned with
human biology. By 'molar', here we mean simply to distinguish
the relatively gross behavioural characteristics of organisms from
the details of cellular activity which, by contrast, we shall call
'molecular*. Human biology implies a close relation with all of
biology, and of course with sociology, although this book is not
intended to deal with the social side of the subject.
Now it is impossible to carry out a plan which involves the
application of new methods in science without considering the
philosophical or theoretical consequences, and this is especially so
in cybernetics, which is so closely connected to logic, mathematics
and scientific method; such considerations are the reason for the
inclusion of the present chapter.
The great importance of the contribution made by cybernetics
to biology is that, under certain circumstances, it can formalize
theories and make them precise. This same contribution is often
claimed for mathematical logic, and here it is of relevance to quote
Carnap (1958) on this point:
If certain scientific elements concepts, theories, assertions, derivations,
and the like are to be analyzed logically, often the best procedure is to
translate them into the symbolic language. In this language, in contrast to
ordinary word language, we have signs that are unambiguous and formu-
lations that are exact; in this language, therefore, the purity and correct-
ness of a derivation can be tested with greater ease and accuracy ... A
further advantage of using artificial symbols in place of words lies in the
brevity and perspicuity of the symbolic formulas.
45
46 THE BRAIN AS A COMPUTER
Much more could be said about formalization, but at the least
we may claim the above advantages for cybernetics, with the
additional advantage that our logical model is effectively construct-
able, and is therefore operationally effective. Indeed, as we have
seen, actual hardware constructions are often desirable.
Another side to this matter, which seems to be closely related
though not necessarily connected, is the philosophic (almost anti-
philosophic) movement of pragmaticism, and this at least includes
the general belief that science can contribute to the solution of
philosophical problems, and, by dropping the classical search for
universality and certainty, can solve its own theoretical problems
(George, 1956a, 1957b; Crawshay- Williams, 1946, 1957; Pasch,
1958). This whole matter will be discussed to some extent in this
chapter, but it is in fact a subject which calls for far more detailed
treatment, with its specialized philosophical interests, than it can
be given here. However, we hope we have already said enough to
convince the experimental biologist and psychologist of the neces-
sity for a theoretical analysis of his own activities, assuming he was
not already convinced.
Naive Realism is probably a good starting point for scientific
endeavour, but it is difficult not to believe that there are times when
a more critical appraisal of one's starting point becomes necessary.
Not, we would emphasize, that we wish to become involved in
ontological or epistemological disputes indeed they hardly seem
worthwhile to most scientists but we should at least be fully
aware of our own logical and philosophical commitments.
We must be prepared to revise our scientific theories con-
tinuously, and this means that we arc committed to an under-
standing of our methods for constructing theories in the first place.
There is one possible misunderstanding about this sort of work
that should be cleared up right at the start. The kind of thera-
peutic linguistic analysis and criticism that is to be considered in
this chapter is at least as much meta-thcoretical as theoretical.
Let us put it this way: scientists indulge roughly in the following
activities: making ordinary day-to-day observations, carrying out
controlled observations, making observation-statements which
purport to state what is observed and no more, generalizing about
these observation-statements in the form of hypotheses, theories,
etc., and finally, criticizing their findings, both the practical and
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 47
the theoretical. Criticism is what is meant by meta-theory, as
against theory which is inside the science itself, as it were.
It is a commonplace that virtually anything can be a model of
anything else, and that description and explanation depend on this
fact. Similarly, any theory or language can be described in another
theory or language, which we call a meta-theory or meta-language.
In turn, the meta-theory can be the subject of a meta-meta-theory,
and so on.
In psychology certainly, theory and meta-theory are often
:onfused. The tough-minded experimentalist asks how a piece of
inguistic analysis can help him in his work, and looks for theore-
ical help when he is being offered rneta-theoretical help. The idea
}f methodological analysis is to help clarify the viewpoint of the
scientist about his theories, point out his logical and linguistic
confusions whenever possible, and help to orientate him in an
explicit point of view. Science is, more than anything else, an
ittitude, and the object of our methods is to try to inculcate a clear-
leaded attitude. This whole purpose is to be distinguished from
heoretical science which constitutes, broadly speaking, the
jeneralizations within the subject and remains, in the form of
cybernetics, our principal topic.
We should mention that the term 'psychology' will be used
hroughout this chapter in the broadest sense, to cover all and any
Darts of the science of behaviour. Thus, physiology may be sub-
iumed under the same term, as may any other part of biological
icience.
A particular problem that arises is the relation of psychology to
)hilosophy. This is a vexed question in the eyes of philosophers,
ind it is noticeable that there is all too often an attitude of armed
neutrality between the two camps which leads, needless to say, to
he detriment of both. The writer takes the view that the distinc-
ion between science and philosophy is essentially one of degree,
ather than a division marked by a sudden gulf, as is suggested by
he sharp distinction sometimes made between the analytic and the
ynthetic, or between formal and factual sciences (for example
iuine, 1953; George, 1956a).
We are not concerned here with discussing possible distinctions
)etween the pragmatists and the formal semanticists, the logician
ind the experimentalist. A useful distinction certainly can be
48 THE BRAIN AS A COMPUTER
drawn between the logical and the empirical, and at a certain level
it is possible to distinguish formal from factual commitments,
without pressing the matter too far. The reason this is important to
the scientist is because he must decide what end his generalizations
are to serve. In this chapter we shall explicitly state the theory-
construction methods that are to be adopted in the application of
cybernetics to psychology and say something of the relation of
philosophy to cognition. One reason for this is that psychologists
should be familiar with the work of the philosophers, as has been
suggested already, and in this pursuit the whole question of the
relation between the two approaches is brought into relief.
It is not our intention to claim that a methodological analysis of
learning or perception is an alternative to a scientific theory of
learning or perception; indeed, we believe that the scientific theory
is the proper aim of the psychologist, and the methodological
analysis is only a preliminary which helps to clear the way. We
believe that much that has been said by philosophers about per-
ception is either misleading or wrong, and indeed it must be so in
the eyes of scientists when philosophers write in terms of their own
'casual* observations of themselves and others.
An important reason for encouraging the psychologist to read
at least an outline of philosophical problems is to make him more
sophisticated about language and its use, since one distinction that
generally seems to hold is that philosophers are far more percep-
tive of linguistic difficulties than are their psychological counter-
parts, although in fact the psychologist needs this sophistication
just as much. He has recently been blinded in these matters by his
overwhelming faith in experiment, and while experiment is vital to
science, so also is theory, and the need to avoid conceptual con-
fusion. Wittgenstein (1953) has said:
The confusion and barrenness of psychology is not to be explained by
calling it a 'young science' ... for in psychology there are experimental
methods and conceptual confusion ... The existence of experimental
methods makes us think we have the means of solving the problems
which trouble us; though problems and methods pass one another by.
There has been some doubt as to what Wittgenstein meant by
this passage, and it is possible that he meant one or other of at
least two different things. Certainly it is true that psychology has
sometimes foundered on methodological rocks, in that some of the
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 49
workers in the field appear to think that experimental methods of
the 'molar' kind can be used to solve problems of thinking,
imagination, and the like, in a manner in which behaviouristic and
molar techniques could not possibly succeed. Thus it sometimes
appears that the essence of the problem is often missed by a parti-
cular experimental approach. This usually means that the problem
demands methodological rather than experimental techniques, or
waits on the advance of neurophysiology ('Molecular* experi-
mental methods), or both. We shall continue throughout the book
to use the words 'molar' and 'molecular' as relative to each other,
and meaning 'with respect to large scale variables' and 'with respect
to small scale variables', respectively.
In a sense, pragmatics and cybernetics together attempt to give
an answer to Wittgenstein that might have satisfied him. The
choice of the sensory, perceptual and learning fields arises only
because, needing a particular and central problem on which to
exercise the techniques, they appear to be the most central ones for
behavioural studies.
Our approach to cybernetics is through a methodological or
analytic approach to psychological problems. Our interest, then, is
no longer in the problems that can, in any narrow sense, be made
to follow from certain assumptions ; we are now interested in the
development of a scientific theory, the second half of Braithwaite's
'zip-fastener' theory. In other words, we may start by appeal to
marks on paper and give an interpretation to these in developing
descriptive statements, on the one hand. On the other hand we can
turn to what is the more important business for scientists, the
making of inductive generalizations based on a series of observa-
tions. Philosophers are really concerned with what it means to
talk of making observations, and so really only one part of the
formal half of the zip-fastener theory is touched upon in their
domain, the other formal part and the factual half being utilized in
the field of science. Our main interest here is in trying to make a
Braithwaitean type of approach more realistic in meeting scientific
needs.
Implicit in this whole work is the feeling already alluded to, that
the division between philosophical and descriptive sciences is
artificial and, at best, one of degree; thus, when words like
'factual' and 'formal' are used, they are used on the understanding
50 THE BRAIN AS A COMPUTER
that they are rough classifications employed merely for con-
venience, and in no sense fundamental. This approach has an
explicit attitude to the mind-body problem which, from the
scientific point of view, is not a problem at all, and from the
philosophic viewpoint is capable of a new interpretation (Pap,
1949; Sellars, 1947; Quine, 1953; George, 1956a; Morris, 1946).
Descriptive pragmatics, in which the observer and the speaker both
occur (as well as the signs they use), are regarded as wholly con-
tinuous with semantics or pure pragmatics, and no sort of gulf or
sudden discontinuity is thought to arise between them.
Cybernetics and philosophy
Philosophical or linguistic analysis may be regarded, then, as
being preliminary to any sort of scientific process, and we are in
fact limiting our science to cybernetics. In other words, our
explanations are intended to be in the form of blueprints for
machines that will behave in the manner made necessary by the
observable facts.
There is some evidence that all scientific explanations take this
form, or should take this form if they are to be effective. The same
sort of insistence on the empirical reference of scientific theories is
seen in so-called Operational definitions (Bridgman, 1927).
It seems worth repeating that cybernetics, which is only in-
cidentally concerned with the actual construction in hardware of
machine manifestations of its theories, is consistent with behaviour-
ism. It takes behaviourism further along its path in making it
effective, without destroying any of the increasing sophistication
that behaviourism has recently acquired.
Our next task is to outline, for the non-philosopher, the various
philosophic categorizations and classifications. This must neces-
sarily be brief*
Viewpoints in philosophy
In trying to draw up brief and yet coherent classifications of
different philosophical viewpoints, one is confronted with a certain
measure of difficulty and ambiguity. This is, of course, true of
most classifications, and stems from the fact that there arc virtually
as many different philosophical views as there arc philosophers.
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 51
Furthermore, all the different philosophical categories cannot be
placed in a single dimension; indeed, apparent inconsistencies in
terminology would quickly arise if such were attempted.
Bearing in mind these basic difficulties, an attempt will be made
to give a brief account of the principal philosophical views, with the
idea of providing an orientating background to the analysis of cog-
nition from a philosophic and ultimately cyberneticviewpoint. Since
such an analysis must necessarily be brief, it will not serve every
purpose, and it is only intended here to be sufficient for an under-
standing of the various philosophical approaches to knowledge and
perception. It may be thought of as attempts to classify on the
philosophical level what psychologists have called learning and
perception.
Convenient classifications
As a basis for discussion it will be useful to consider the cate-
gories suggested by Feigl (1950) as being roughly appropriate for
the study of methodology and epistemology. Feigl lists the
following nine views:
1. Naive (physical realism).
2. (Fictionalistic agnosticism) fictionalism.
3. Probabilistic realism.
4. Naive (conventionalistic) phenomenalism.
5. Critical phenomenalism (operationism, positivism).
6. Formalistic (syntactic) positivism.
7. Contextual phenomenalism.
8. Explanatory (hypothetico-deductive) realism.
9. Semantic (empirical) realism.
(These views will be referred to hereafter without use of that
part of the title which is placed in brackets.)
We consider these nine possible philosophical viewpoints
sufficient for our initial classifications. The issue could be narrowed
by overlooking even more of the differences between the various
views held, and combining 1, 3, 8 and 9 under the heading of
Realism, and combining 2, 4, 5 and 6 under Phenomenalism, and
leaving 7 as a sort of half-way house between the two. Thus, in one
dimension our main distinction is to be between some form of
Realism and some form of Phenomenalism. Any attempt at a final
52 THE BRAIN AS A COMPUTER
integration, which may leave many particular questions undecided,
would probably say that Critical Realism and Critical Pheno-
menalism (if in each case they are sufficiently critical) would differ
very little, and there would still be internal differences with respect
to questions of cognition.
Language
Cutting across almost all that has been said is the question of
language and its use, and the more general problem of communica-
tion. There are at least two apparently different views about the
nature of the linguistic problem. We may on one hand take up
G. E. Moore's view that natural language is the proper and
sufficient description of a realist world, and that the problem of the
philosopher and of the scientist is to see that he uses natural
language in its correct way. This view of language could be
maintained independently of an epistemological or ontological
commitment. It would hold, roughly speaking, that to say as the
fictionalists do that 'atoms do not really exist* is to misuse the
term 'exist', for whatever one conceives to be the sense of existence,
the fact that atoms exist is certainly true. In a sense the problem
here has been to push language away from the ideas underlying it.
We can interpret what you say according to common usage, but its
underlying sense may not be so obvious.
In fact, we shall not accept this viewpoint, but shall try to be
aware of the ways two at the very least in which realistic
philosophers such as Moore regard language. Realists holding the
second view, while trying to keep as far as possible to natural
language, would feel free to lay down conventions and rules about
language, although these constructed languages would ultimately
be within the structure of a natural language. This docs not
necessarily mean that what the constructed languages say can be
wholly reduced to natural language without the vagueness that
attends the use of simile and metaphor, since the whole point of
such constructed languages is to avoid such vagueness. What, on
the other hand, we cannot do is to explicate 'truth' or 'meaning', or
any other problem term of natural language, within a constructed
language and hope to explicate its natural use, which may of
course be vague. A formalized system lays down rules by which
such vagueness may be ruled out, but it does not by virtue of this
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 53
explain the meanings of the basic terms. This, we personally
conceive, is closely related to the study of signs from a pragmatic
viewpoint.
It is, indeed, along these lines that we believe that science can be
as vital to philosophy as philosophy is to science.
Scientific theory construction
Now we shall turn to the explicit process by which we shall
construct theories of science, and by which we believe they should
normally be constructed. This is the theme of the remaining
section of this chapter. Again, as in the case of philosophical
analysis, we believe and for the same reasons that an explicit
statement of methods is necessary. Psychology has continually
suffered from verbal and methodological muddles, and this at
least might be avoided with a little care.
First of all we shall illustrate our conception of the nature of the
scientific procedure in a simple, anecdotal manner, showing its
close and crucial relationship to the role which cybernetics plays
in the scientific process. This relationship will be clarified at the
end of the present chapter.
The nature of science in general
In order to relate our intuitive ideas of logic to the general
process of communication and to the very basic ideas of science,
let us suppose that an observer has just arrived at a town in
Erewhon, where he is to study the behaviour of shop-keepers.
For the sake of the example we will assume that he does not know
the language of the country, and that in any case he is too shy to
ask questions (physicists cannot ask questions of particles with any
hope of an answer). His mission is to construct a scientific theory
that describes the shopkeeping behaviour of the Erewhonians.
He starts by observing the behaviour of shopkeepers on the first
day, a Monday, and he finds that they work from nine until five.
On Tuesday he finds that the same times are observed, and he is
now in a position to make his first inductive inference, to the effect
that they work every day from nine until five. The next day,
Wednesday, confirms this hypothesis, but his observations on
Thursday show that his first hypothesis is inadequate, since on
this day the shops are closed at one o'clock. Friday brings working
54 THE BRAIN AS A COMPUTER
hours of nine until five again, and Saturday is the same, but on
Sunday the shops do not open at all. This upsets completely any
second hypothesis which he might reasonably have formulated on
the evidence up to that point, and it will be some weeks before our
observer begins to see the repetitive nature of the facts.
After a few months the observer may be reasonably sure that he
now has a hypothesis that adequately covers all the facts, and it will
not be shown to be inadequate until the occurrence of a national
holiday or its equivalent. It is probable that he will never be able to
understand completely the variation of certain national holidays,
such as Easter, and even if he does learn the rule which governs
this particular holiday, it is quite certain that he will never be able
to understand what rule governs the occurrence of certain other
holidays which are given merely to celebrate some unique event,
and never recur.
In the above analogy the rules will never be quite sufficient to
make a completely watertight theory, but the method will be
sufficient for most purposes, and this is all science is ever con-
cerned with : a theory and a model/or some purpose.
For similar reasons we can never have more than probability
laws in science, since we can never be sure that they will not
subsequently be in need of revision.
There are other aspects of the analogy that also hold good. If we
had employed only one observer to discover the shopkceping laws
of Ercwhon, he would have been in the akward position of having
to decide at which particular point he should set up his observation
post. We should be interested to know whether what our observer
saw was typical of the behaviour of all the shopkeepers, or not.
Suppose our town was such that different rules applied to other
shopkeepers that he did not see; how would he know how to
answer such an implied criticism? All he could say would be that
he tried to take a fair sample of the population* The efficiency with
which he carried out his sampling is a measure of the accuracy of
the results. This is really a matter of individual differences, and is
treated in experimental psychology by statistical methods.
This story has represented roughly what scientists are doing,
and we can now discuss the problems of the psychologist in
particular, bearing in mind that our illustration still needs to be
explicitly linked to the cybernetic approach.
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 55
THEORY CONSTRUCTIONAL PRINCIPLES
Psychological theory
The psychologist has to construct theories of behaviour:
learning, perception, etc., that satisfy some logical standards, quite
apart from incorporating our knowledge of behaviour, neuro-
physiology, and what is intuitively accepted in behavioural terms.
Indeed, the process of producing any theory of behaviour requires
the production of effective procedures for determining the applica-
tion of the theory at a variety of different descriptive levels.
This of course is already widely accepted in the physical
sciences.
The essential steps that need to be outlined are: (1) that any
particular scientist must go through the process of making observa-
tions, as already illustrated; (2) he must generalize upon these
observations, and (3) will eventually produce scientific theories
which are initially hypotheses, and become laws' when they are
highly confirmed. Now it is not important whether what is being
described or constructed is mathematics or a science such as
psychology. Whatever it is that is under discussion or investigation
at any particular time is what we will call the object-language, and
we must discuss it in some other language, a metalanguage. This
meta-language may be itself an object-language for some other
investigation, but this is of no importance at the time.
We are also vitally concerned with the construction of object-
languages, and these can be represented as models of whatever the
non -linguistic entities are that need to be modelled.
Scientists are forced to start from assumptions, which represent
their prior agreements with themselves for the sake of a particular
investigation. The assumptions are represented by only partially
analysed statements ; the notion of partly analysed terms is secon-
dary to this, and will represent an internal analysis of sentences
into their parts. Language and that is what a scientific theory is
part of has the sentence as its natural unit. The syntax of the
prepositional calculus or any systematic marks on paper, any
structure such as a lattice, blueprint, or map, is capable of being
used as a model for a scientific theory, and here we accept the
essential distinction, made by Braithwaite (1953), between a model
for a theory and the theory itself. The model will be explained in
56 THE BRAIN AS A COMPUTER
the theory. All this is couched in the natural or symbolic language
that is used for descriptive purposes by particular scientists.
It may be necessary to add certain pragmatic devices to any
scientific explanation, in the form of ostensive rules or definitions,
operational definitions, and the like. These may serve to sharpen
the meaning of the language used for the theory, or the meta-
theory, for even here we soon find that only very few and very
limited investigations can be restricted to one clearcut theory
language. We must therefore be prepared to think in interconnected
chains of such theory languages, which will give repeated descrip-
tions of different facts of nature on different levels and in different
ways. It is, in a sense, the particular investigation that is the
scientist's working unit. The whole of science or any of its
divisions can thus be reconstructed in any number of ways.
For the psychologist, working beyond a narrow behaviourism
and yet determined to avoid that which cannot be treated on a
basis of public observation alone, the problem is to find more and
more models and interpretations, as well as theory languages,
for the coherent description of his vast collection of empirical
facts.
The result of an uncertainty about the correct progress of theory
and explanation in science has sometimes led to models being used
descriptively, whereas in fact what needs to be developed is a
model with a theory that has a controlled vagueness : that of the
surplus meaning of its theoretical terms. This lack of specificity, this
possibility of many interpretations of the same model, rather than
the attempt to construct a model which fits in detail one possibly
non-representative piece of the whole set of observations to be
explained, is necessary to the fruitfulness of science.
The psychologist will be concerned with the following pro-
cedures that may be listed in the order they usually occur:
(1) Learning by description the existing information (George,
19S9a) on a branch of the subject we will call A, Testing this
information for consistency (internally and externally) and finding
it wanting in certain respects either in generality or consistency.
(2) The stating of simple, observational facts collectively with
inductive generalizations originally called A, and now A' (if
different from A). This requires a language the foundations of
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 57
which are to be agreed upon; it will not necessarily be the same as
in (1), but necessarily capable of being interpretable in the same
language, at some level, as (1), or alternatively (1) in (2).
(3) The generalization process, based inductively on a certain
number of instances, and always subject to revision.
(4) A model for A, essentially deductive, which is utilized in
terms of the inductive parts of the theory. It may be pictorial,
symbolic, or anything at all that is capable of interpretation in
terms of the language of either (1) or (2).
(5) If we use a merely descriptive language for the generaliza-
tions, we must be prepared to show the nature of the underlying
structural model, since a description of empirical facts is really a
description of structural relations. This process is called the
formalizing of a theory.
(6) This whole process is sufficient for psychology.
(7) This process may go on without end, with continual check-
ing, criticism and analysis, which may take any part of the whole
(or the whole) of science as the object of its investigation.
So much then for the initial complications, wherein theories are
particular (or particularized) languages, or parts of independently
formulated languages, ultimately capable of interpretation in
natural language (or a slightly more rigorous equivalent). Thus, if
we use the word language* for the interpretation of a system of
marks, we are already committed to a certain theoretical structure.
This is why a scientific theory and a language are interdependent,
and may be one.
Models
We are concerned with cybernetics and therefore with logic
and, what is essentially the same, logical nets as models of be-
haviour (see Chapters IV and V). We do not intend, here, to describe
in any detail the whole of the possible range of models that can be
used in the processes of scientific theory construction. The most
obvious of those that have already been used are the syntax of the
propositional calculus, the functional calculus, and the various
existing calculi that are intended to be given an interpretation as
propositions and functions, and have thus been widely used by
E
58 THE BRAIN AS A COMPUTER
philosophers and mathematicians. These are open to use in science
and will, if the logistic foundation of mathematics can be believed,
lead to the whole of mathematics. Mathematical structures such as
lattices, abstract algebras and other symbolic models or structures
may also serve as such models. From the viewpoint of cybernetics,
these systems may be constructed in hardware; indeed, any
symbolic model can be regarded as a physical system and produced
in hardware.
The model that we have been mainly using one that can be
seen to be closely related to other models and theories that we have
mentioned is that of a finite automaton which, for all practical
purposes, is an idealized organism.
At first our aim here was certainly not strictly neurological, but
rather, while using a model that can also be used for neurology, to
seek to develop a theory that has usefulness, precision, and the
possibility of predictability at every level.
The logical nets which we are to discuss are roughly isomorphic
with a part of logic, that part called the propositional calculus
coupled with a part of the lower functional calculus, all suffixed for
time. The word 'roughly' occurs above because in fact the logic
concerned is actually supplemented by a time-delay operator.
There is a relationship between the nets that can be drawn, and
the formulae that can be written which is closely analogous to the
relationship between geometry and algebra.
Logic and cybernetics
We have already said something about logic and its relation to
logical nets; now, we must try to be more specific, and describe a
least as much of logic as is necessary to an understanding of
cybernetics and of our theory of logical nets.
In the first place, logic arises because logic seems to represent
the process of ideal reasoning, and it is reasoning that the machines
in which we are interested can do. They have to be able to perform
the operations of a deductive and inductive character if they are to
be of cybernetic interest. Such machines have sometimes been
directly described in logical terms; in fact there has been a general
theory of machines, of the control and communication type, that
draws on mathematical logic in its description. We shall now
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 59
describe something of the development of modern logic and deci-
sion processes in paper machines.
Logic in ordinary language
In an historically given or natural language such as English it is
not always possible to draw strict inferences, because of the vague-
ness and ambiguity of some of the words we ordinarily use. We
sometimes mean something special by a word, but there is no
complete and definite set of rules for what words should mean, and
vagueness is therefore inevitable, for inferences depend on mean-
ings, and meanings in natural language are vague. But in spite of
this there are many obvious examples of the use of logic. Thus,
when I say 'Jack is a man', I do not need to know any more facts
about Jack to know that he is also a featherless biped, since all men
are featherless bipeds. This simple inference follows from the
meanings of the words 'man' and 'featherless biped', and I arn
assuming that there is little chance of these words being mis-
understood; but there are very many sentences which refer to
classes, events and relations which are very far from clear.
For a long time philosophers have analysed language with the
object of trying to sort out logical puzzles, but in the meantime
mathematicians have developed a mathematical theory.
Since mathematics has to be definite in a way that ordinary
language does not, we should expect to find, and do find, that
mathematical logic is a perfectly precise arrangement of symbols,
like ordinary algebra wherein instead of saying that x stands for
anything at all, we say that x stands for a class of objects: x is all
featherless bipeds, or all automobiles, or all of anything at all.
Now the most interesting sort of relations are those of class-
inclusion and class-exclusion. All red shoes for example, are
included in the class of all red objects, and excluded from the class
of all green objects. Of course, difficulties can arise, because it can
be argued that red shoes are perhaps not all-red, or that green
shoes may not be all-green, and that both are a mixture of different
colours. The answer to this is that the algebra of classes, or
Boolean Algebra as it is often called, only holds for objects which
are capable of being classified as a member of some class. More
complicated algebras have been developed, and some mention of
these will be made later in this chapter.
60 THE BRAIN AS A COMPUTER
One particular interpretation of the Boolean algebra of classes
is of special interest. This involves the assumption that all the
classes are to be understood as propositions or sentences. Thus, if
we say in the algebra, where the dot V between x and y is taken to
be 'and', that x.y is the class of all objects that are (say) red and
round, then, following the convention of changing x and y to
p and q, we can say that p.q is the conjunction of two statements,
say, 'Jack is a man' and 'All men are featherless bipeds'.
The mathematician, having said that he means his variables
p, q y r, . . . to be understood as sentences, then constructs relations
between his symbols that seem to be in keeping with the way we
use logical inference in ordinary language. In fact he will preserve
the intuitive meanings of 'and' and 'or' (for which he uses V, and
which he means to be an inclusive 'or', meaning^ or q or both);
he will also have a symbol for 'not', i.e. *~', and from these he
builds up a whole system of mathematics.
We shall just repeat here, using the ordinary calculus of classes,
the essential relations from which, by use of careful rules, the
whole system is built up.
X.Y means X and Y
Xv Y means X or Y
~J? means not-X
FIG. 1 A. AND. X. Y is short for X and Y and is represented by the
area of the overlap of X and Y, where X may represent all red
objects say, and Y all round objects, then X and y represent all
red and round objects.
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 61
FIG. IB. OR. Xv Yis short for X or Y in the inclusive sense of or
and is represented by the whole area of X and Y taken together.
FIG. Ic. NOT. Everything not within the circle of X, is not
-X. If X represents all green objects, then all objects of other
colours lie outside the circle because they are not green.
The diagrams show clearly the significance of these
simple relations. Let the square stand for the whole possible
universe under consideration and be symbolized by 1, then the
opposite, or nothing, is symbolized by 0.
It will be easily seen that simple reasoning can be carried out in
this system. Let us use the symbol *C for 'is contained in*
*-V for 'implies', and '=' for an equivalence relation, then,
A.B = A
62 THE BRAIN AS A COMPUTER
The syllogism about Jack and featherless bipeds can now be
written
ACB. BCC^ACC
With these simple examples we shall leave Boolean algebra and
turn to the propositional calculus, which interprets the variables
of Boolean algebra as propositions.
Before stating the formal requirements of the Propositional
Calculus as an axiomatic system we would explain that we are now
explicitly stating, in a meta-language, the symbols to be used in the
object language (here, the propositional calculus), and the way
they can be formed into acceptable units, like words, sentences, or
formulae. In English, for example, the word *word' is well-
formed and the word 'xxyyzz* is not. This reminds us that all
combinations of symbols do not satisfy our formation rules. We
set down, then, certain well-formed formulae called axioms, and
use a rule of inference to generate further well-formed formulae
which have the additional property of being true in the system,
i.e. theorems.
THE PROPOSITIONAL CALCULUS
The propositional calculus is said to formalize the connectives
and, or, not, and if ... then. There are many different systems and
various notations for the propositional calculus. The formulation
(called jP) which we shall give is one of those used by Church
(1944). P is composed of:
(1) Primitive Symbols: [,], D,^ and an infinite list of pro-
positional variables for which the letters p, q, r 9 s, u, v, w (with or
without numerical subscripts) may be used.
(2) Formation Rules:
(A) Any variable alone is well formed (wf).
(B) If A and B are well formed, so are ~A and A DB.
Where A and B are syntactical variables (variables ia the syntax
language) which designate formulae of the calculus (in this case P).
(3) Rules of Inference:
(A) From A and A DB to infer B (modus ponens).
(B) From A to infer S A | where Sj, A \ means the result of
substituting B' for A' in all its occurrences in A.
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 63
(4) Axioms:
(A) pD[qDr]D.pDqD.pDr
(B)
(C)
It should be explained that the dots (.) in these axioms take the
place of brackets, and that the general rule is one of association to
the left. Thus p Dq Dp is ambiguous as it stands, and could mean
either (p Dq) Dp or p D(q Dp) ; if no dot occurred, then it should
be taken to be the former, but the dot in axiom B implies the
latter. Similarly, axiom C with full brackets reads :
~pD~qD(qDp)
As a result of these axioms and the rules of inference we can
define a theorem. A theorem is a well formed formula (wff ) which
is obtainable from the axioms by a finite number of applications of
the rules of inference. We could, it should be noticed, reduce the
list of rules of inference to only one by the omission of substitution
and the use of an infinite list of axioms.
We are not, of course, concerned with what might be called
the technicalities of logic, so we shall not discuss the deduction
theorem, regular formulae, completeness, duality, independence,
etc. However, it is worth mentioning that the decision problem
(the effective procedure for discovering whether any wff is a
theorem) has been solved for the prepositional calculus, and it says
that every tautology is a theorem and every theorem is a tautology.
By a tautology we mean a wff of the prepositional calculus which
has the truth value t (see below) for all possible combinations t and
/ (to be interpreted as 'truth' and 'falsehood') replacing the pro-
positional variables in the wff. The decision problem for the lower
functional calculus, and therefore all higher functional calculi, has
been shown to be unsolvable. In the network models of Chapter V
we shall use '=' rather than ' D', where '=' means 'if and only if
rather than the one-way relation 'if then ... '.
We shall also mention the Sheffer stroke (used by von Neumann
in his logical nets), which is another constant in the prepositional
calculus. It is written --- [ and is defined a \b = df,~av~b,
where 'df.' means 'is defined as'. There is also a conjunction stroke
symbol I which is defined by a \ b = df.< >a*~b. It was of
64 THE BRAIN AS A COMPUTER
interest that the prepositional calculus can be constructed in terms
of the one single primitive constant term, the Sheffer stroke, and
this is the reason for von Neumann's choice of basic logical net
elements.
THE FUNCTIONAL CALCULI
To go from P to F l (the functional calculus of the first order) we
need to add individual variables: x, y, z, x l9 y^ z ... , and
functional variables .P 1 , G 1 , H\ F\, GJ, flj, ... F\ G\ H\ F\, Gf,
H\, ... F n t G 71 , H n , Fl, GJ, #J, ... these being singularly, binary
. . . w-ary functional variables.
The functional calculi permit the analysis of predicates and
functions, and we shall wish to make assertions such as 'for all
x, F l (#)' and 'there exists at least one x, such that F 1 (#)', and
we shall thus need to add the Universal and Existential quanti-
fiers, respectively, to our notation; they are (x) and (Ex) respec-
tively, which makes the above two sentences:
(x)F l (x) and (Ex)F l (x) respectively.
We shall need, also, to construct new formation rules, rules of
inference and axioms to meet the needs of our new primitive
symbols which will include, as part of it, the whole prepositional
calculus.
It is, of course, possible to generalize further to the functional
calculus of order 2, (F 2 ), there are many different kinds of such
functional calculi and so on up to F n .
We shall now add a word on truth-tables. We cannot discuss the
Matrix method, as the tabular method is called, in detail here, but
it is sufficient for a two-valued interpretation where t and / are
used (these may be thought of as 'truth' and 'falsehood', or as
'firing' and 'not firing' in the logical networks) if we ascribe t and/
exhaustively to all the variables in our formulae. Thus, to take a
simple formula of P such as <-^>p, its truth-table is:
t
f
f
PHILOSOPHY, METHODOLOGY AND CYBERNETICS
65
and pvq (where V may be read as 'inclusive or', i.e. porqor both)
has truth-table :
p
?
pvq
t
t
f
f
t
f
t
f
t
t
t
f
then p DJ, which can be translated as r^pvq^ has truth-table arri-
ved at by combining the above two truth-tables; it is as follows:
p
9
P^q
t
t
f
f
t
f
t
f
t
f
t
t
For the functional calculus the truth conditions on the existen-
tial and universal operator demand that one or all values of x
satisfy the respectively given formulae:
(Ex) F 1 (x) and (*) F 1 (x).
It is easy to see how it may be possible to extend the notion of
truth-tables to 1, 2, ..., n truth-values. Thus a truth-table for V
in a three-valued logic could be written:
p
9
pvq
1
1
1
2'
1
1
3
1
1
1
2
1
2
2
2
3
2
2
1
3
1
2
3
2
3
3
3
66 THE BRAIN AS A COMPUTER
Much thought and effort have gone into the construction of
many- valued and modal logics (Rosser and Turquette, 1952), and
we can do no more here than summarize the general scheme of
things, while suggesting a little of their possible value for cyber-
netics.
It is clear that just as we can generalize geometry from the best
known two- and three-dimensional cases to any number of dimen-
sions, so we can for logic. We can simply say that we do not wish to
limit our interpretation to 1 and as 'truth* and 'falsehood* ; we
can have n truth values whether we give the other n-2 values an
interpretation or not. We shall say something later of the signi-
ficance of this matter for switching systems, but straightaway we
can see that the law of the excluded middle, which says that
everything is either a or not-#, may be discarded if this sort of
logic is to be used descriptively. Indeed, intuitionistic logics have
long denied the law (Heyting, 1934). However, we can regard our
many-valued logics as satisfying this law by retaining some
corresponding law of the excluded (n+l)th. Intuitionistic logics
and many-valued logics, it should be noted, are not necessarily
the same.
The modal logics give a specific interpretation to the truth values
beyond true and false. Reichenbach, for example, has attempted to
analyse the foundations of Quantum Mechanics in terms of a
three-valued logic wherein the third truth-value had the interpreta-
tion of 'undecidable*. Other qualifying modalities can be intro-
duced as interpretations, such as Necessarily true, Contingently
true, Possibly true, Impossible, etc., and modal operators such as
Np, Cp, Pp, Ip, etc., have been introduced into the literature.
There has been much discussion as to the possible usefulness of
many-valued logics, and it seems that on most occasions when it
might be useful, the descriptions are usually capable of being
reduced to the usual two-valued terms. Yet again there are many
sorts of situations, both with regard to truth and in ordinary
empirical descriptions, where things are not conveniently regarded
as being either a or not-a. This, of course, involves matters of
probability, and is the reason for our later discussion of what have
been sometimes called empirical logics.
The horseshoe sign D that we have used for material implica-
tion in the prepositional and functional calculi is by no means the
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 67
only sort of implication sign that might have been introduced into
our formal logical scheme of things, and much argument has
surrounded the interpretation of this symbol as 'material implica-
tion'. C. I. Lewis (1932) has developed a logic based on strict
implication which he believes comes nearer to what we normally
mean by 'implication' in ordinary language. He takes 'Op' to
mean 'p is possible', and V as meaning 'is consistent with', and
this leads to the possibility of p being given a definition in terms of
the self-consistency of p:
OP = pop
Similarly for two variables p and q, we have
Opq=p oq
and implication, which is symbolized by ... -S , is defined
which, on application of the above, leads to
P "3 q =
This sort of logic is more important in the analysis of language
than in logical networks, nevertheless in the study of networks the
various possible logics should be borne in mind, and the evident
infinity of possible logical calculi.
To take our artificial languages or calculi one step farther we
should introduce predicates P, Q, R, ... which can be associated
with particular 'argument expressions' a, b, c, . . . so that by P(a),
Q(b) y R(c) is meant 'a has the property P', etc., or to take a parti-
cular example, 'Napoleon was a Corsican'.
It is now possible to construct calculi (and therefore models) of
enormous complexity and richness, many of which are directly
important to cybernetics. In this context special notice should be
taken of the artificial languages of Woodger (1952); unfortunately
we lack the space to illustrate his work here. (See page 86 et seq.)
Generally, we shall remember as much as we can about logic
for three reasons: (1) Logical calculi can. be used as models and be
reproduced in hardware. (2) Logical calculi can be given explicit
interpretations for descriptive purposes in scientific theories.
(3) Logical calculi and their interpretations are, like scientific
theories, examples of some of the most complex and sophisticated
68 THE BRAIN AS A COMPUTER
human behaviour, and are thus of considerable psychological
interest.
Paper and pencil machines
Our next subject for discussion concerns what are sometimes
called Paper Machines (specialized automata). The aspect which
has our particular interest springs directly from the decision
procedure considerations described earlier. The idea is, as has been
said before, that there are some aspects of mathematics that are
machine-like in their characteristics and, once the directions are
laid down, even a stupid person could follow them and eventually
find an answer to whatever problem is posed. What is so important
about this is the fact that we have a ready-made method for laying
down a blueprint, or a theory, that we shall know is effectively
constructible, without the need for actual construction to take
place. It means that we can build paper machines without going to
the expense of finding out in practice whether the blueprint will
work or not.
But before pursuing this notion further, a little more must be
said on that vitally important matter, the postulational or axio-
matic method. This involves making a set of basic statements
usually taken to represent facts or hypotheses that we are going to
assume. The process is then to have some rule of inference, such as
the one used in the last section for the syllogism, whereby we can
deduce theorems from the postulates. It is the complementary
process to that gone through by our Erewhonian observer, and is
dependent upon it.
The most widely known examples of postulate systems are
those of geometry, such as Euclidean geometry in two or three
dimensions, and group theory, which is a part of modern abstract
algebra. There the problem of proving theorems was one of show-
ing that the statement in the theorem was reducible to the state-
ment of the postulates; if this could be shown, then the theorem
was true or, as mathematicians sometimes say, provable.
We should remind ourselves that mathematics, in view of its
incompleteness, is not quite the cut-and-dried system we once
thought it to be, though some of its partial systems, like geometry,
are sufficiently precise and complete. Geometry is a symbolic
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 69
system, like all other constructed languages, that contains general
concepts which are themselves an offshoot of behaviour.
There is one point, before we return to 'paper machines', that
we must make quite clear: we could produce in hardware all the
machines we have in blueprint, given the time and the money, and
provided our blueprint methods have a decision procedure, and
they could also be of immeasurably greater complication than
anything that actually exists. In the meantime we have these
effective theories, and indeed many of our most exciting discoveries
have been theoretical. The problem now arises, in view of a certain
widespread distrust of theory, as to how we can convince the world
at large that the theories work, without actually building the machine
in hardware, and it is here that 'paper machines' become important.
The words 'paper machine' were used, probably for the first
time, by Turing in an unpublished paper on 'Intelligent
Machinery', and we can describe a paper machine as the process of
writing down a set of instructions or rules, and a procedure that
could be carried out by a man who was quite ignorant of the pur-
pose of the rules or the procedure. This has already been discussed,
and now we must explain the position a little further.
Consider, for example, a problem demanding such a machine-
like procedure. One might ask a child to look through all the
integers between one and one thousand to see if any one or two or
more of the numbers have some special property. To take a trivial
example, are there two such integers whose product is 827? And if
so, how many such pairs are there? Granted that the child knows
how to multiply integers together, and has the most ordinary
intelligence, he could give a definite answer to the question. We
have already seen how this works for the propositional calculus in
discovering whether any wff is a theorem or not.
Now this sort of 'blind' procedure of following rules when
given them, and using paper and pencil for the process, is in
effect a computing machine. It is now a reasonable question to ask
what sorts of problems can be solved by such procedures. The use
of a man, a pencil, a piece of paper and a rubber, is what we call
a 'paper machine', and what we now have to face in programming
the man are some of the most important problems in modern science.
It is one obvious approach to the subject of the theory of machines.
Let us look at this matter in a more historical context. The notion
70 THE BRAIN AS A COMPUTER
of an effective procedure, or a decision procedure, has its place in
mathematics and logic, and we will consider some of the simpler
cases.
There are various examples in mathematics of the search for
such decision procedures or methods. For example, there is an
algorithm (synonym for decision procedure) called Euclid's
algorithm which will tell us whether or not, in the elementary
theory of integers, two numbers are relatively prime. If we are
presented with a statement to the effect that any two numbers p
and q are relatively prime two numbers are said to be relatively
prime if they have no factor in common except unity then the
algorithm will tell us whether this is so or not, i.e. whether the
statement for any particular values is true or false. Thus the whole
set of such statements can be divided into two groups, those that
are true and those that are false, and no such statement is un-
decidable. This process has been described as machine-like.
The point that is of special interest is that undecidable formulae
do occur in any system sufficient to generate all we now refer to as
classical mathematics, and although it does not follow on this
account that there is no decision procedure for all of classical
mathematics, this nevertheless is also a fact, a fact that has been
shown to be the case by Church (1936).
Church's theorem, as we have called it, shows that if there are
no undecidable formulae in a formalized system, then it must have
a decision procedure. These are matters of paper machines that are
vital to a consideration of what can and what cannot be built, from
a theoretical point of view. Let us now consider the problems
outlined in this paragraph from another aspect, that developed by
Turing under the title of Turing machines.
Turing machines
A Turing machine consists of a length of tape which may be as
long as we please, and therefore potentially infinite. The tape is
marked out into squares on each of which a symbol can be printed.
The body of the machine is a scanner that scans, one at a time,
squares which each contain one symbol. The machine can alter the
symbol on the scanned square, move to the right one square, move
to the left one square, or stop. The symbol actually scanned, to-
gether with the internal configuration of the machine at the
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 71
moment of scanning, decide which actual operation will next be
performed. The machine indeed is not one that needs to be built; it
is a paper machine, and is mainly of interest to consider precisely
what machines are capable of in principle.
Turing was able to show that there existed a Universal machine
that was capable of doing anything that any other machine what-
soever was capable of doing, provided a description of the other
machine was forthcoming, i.e. if the details of any machine
whatsoever are printed on the tape of a Turing machine, then it
will be able to carry out the operations of the machine so described.
This means, of course, that all machines are, in a sense, reducible
to a Universal Turing machine.
A Turing machine is completely defined by a set of quadruples
(set of four symbols) which act as the orders that determine the
behaviour of the machine and its process of calculation.
We shall now define, by way of illustration, a simple Turing
machine, and show how it operates. (See Fig. 2.)
A simple Turing machine is defined by three types of quad-
ruple, using symbols q l9 q z , ..., q n to indicate the state of the
machine, and *So, 1, ..., 5m to indicate the symbols on the tape.
The three types of quadruple are:
The first two symbols of each quadruple give the present states of
the machine and the symbols scanned, whereas the next two sym-
bols of the quadruple tell us the next act of the machine and its sub-
sequent state. For example, the quadruple
says that the machine, when in the state j x , scanning the symbol 5 2 ,
will move one square to the left and go into state q.
Two particular symbols S and S v written B and 1, have special
significance, in that overprinting with a B amounts to erasure of a
symbol on the tape, and S^ will be used to represent 1's which are
of special importance, since we wish to represent decimal numbers
by collections of Ts.
We will now observe a Turing machine performing a very
72
THE BRAIN AS A COMPUTER
simple operation, that of addition. Our numbers are to be repre-
sented on the tape by one more 1 than actually occurs in the
number, which means that 2 is written 1 1 1, 4 is written 1 1 1 1 1, and
so on. If we wish to add 2 to 4, or indeed any two numbers m l and
m& say, we proceed in the following way.
Let/ be the function /(#, y) == x+y which represents addition;
in our case we are interested initially in m-^+m^ Z is a Turing
SCANNER
B B B
WITH BLANKS (B's)
AND NUMBERS (I's)
TO ERASE SYMBOL
OVERPRINT OR TO MOVE
TAPE TO LEFT OR RIGHT.
(QUADRUPLES FORM
THE INSTRUCTIONS)
FIG. 2. TURING MACHINE. A Turing machine is composed of a
tape ruled into squares, a scanner and a set of instructions that
moves the tape to the left or right one square at a time, or
allows the symbol on the square to be overprinted.
machine which will compute this function. Let Z consist of the
following quadruples:
B a,
1
B
1
B
B
Now if AI is the initial instantaneous description, where by
instantaneous description we mean an expression containing only
one ^-symbol and containing otherwise only S-symbols, without
*- or -*, which means that it is of the form
PqtS,
or
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 73
where P and Q are expressions possibly empty, that is, involving
no symbols whatever, then here
A 1 =q 1 (m l9 m 2 ) = q I m 1 Bm 2
where A^ is simply a way of writing the two numbers to be added
in Ts, remembering that there is one more 1 in this rendering of A I
than in the number itself. We may incidently write m 1's as l m .
The B separating the m, mi and m 2 is effectively a comma. If we
suppose initially that m l 0, then m^ = 1, since it has one more
1 than the number represented, and
Therefore A I ->q 1 B B 1 1 2 -+B q 2 B 1 1 2 -+B B q 2 1 1 2 -+
B B q B B I m 2 > and this last is terminal ( nneans 'yields' here), since
of course there is no quadruple starting q z B, and therefore no
instructions on which to proceed further.
Therefore the computation yields an answer as above in the
terminal instantaneous description, and this expression contains
I m 2 or 77^2 1 >S > an d this means (by convention) that the answer is
7ft 2 , where at the end of the computation the number of 1's in a
number correctly represents that number. The result of our
addition is thus seen to be 0+w 2 , on the assumption of m^ = 0.
If we had supposed m ^ 0, then A I = j x 11 lay 1 Bl'V 1
-*h B 1 li - 1 B 1 V 1 -^ 1 I!' 1 B 1 2 +1 B ft B l^- 1 B l^^ 1
which is terminal.
This gives m^+m^ as answer, and of course if we had made
m =2, and m 2 =4, and written them in as 111 and 11111
respectively, we would have found the tape containing six 1's at
the end of the computation.
This example has been, of course, of a simple Turing machine,
and shows it performing merely a simple operation; more compli-
cated Turing machines can be constructed, using more quadruples
and even more than one tape, and with such machines we would of
course be able to deal with more complicated functions. This
would have led us in time to a consideration of recursive function
theory and its identification with effective computability, but that
is a pathway we shall not tread here, since it is primarily of mathe-
matical interest, and the general results have already been men-
tioned. However, perhaps this much should be said by way of
elucidation : The idea of a recursive function is important because,
74 THE BRAIN AS A COMPUTER
as we shall see in computer programming, it represents a general
method for manifesting the totality of mathematical operations
or virtually so.
One thing that should be made quite clear is that although a
Turing machine can make any machinelike computation whatso-
ever, it will take a long time to do the more complicated operations,
and so will often be extremely wasteful of time. This, of course,
is not a practical difficulty, since we are here only interested in
what a machine is capable of, in principle.
We do not wish to push the matter of mathematics and logic
any further. What seems to be of vital importance for the theory of
machines is this : whatever can be done by humans can be done
by machines. This is, of course, contrary to many opinions which
have resulted mainly from misunderstanding the processes of
these paper machines, but there is in fact no obvious reason to
doubt that a machine could be built to do what a human being
could do in all cases, provided that an adequate description is
available of what the system to be mirrored actually does.
The fact that there exists no decision procedure for mathe-
matics as a whole does not mean that there are parts of mathe-
matics that are not investigatable by machines. It does mean,
however, that the methods to be employed are beyond the reach of
what has been called a decision procedure. Other methods are
needed, of a more random character, such as cannot be put in a
manner that could be followed by an unintelligent helpmate. Let
us try to throw a little more light on this point.
The theorems of Godel, Church and Turing are not a barrier
to what machines can do, any more than they are a barrier to using
an unintelligent helpmate. If we can tolerate an occasional wrong
result such as human computers sometimes produce then
we can use machines that can be constructed to pursue the further
mathematical inquiries just as humans pursue them. This point
can hardly be overemphasized, since it has sometimes been used
as an argument against cybernetic development, which of course it
is not. We can now discuss these same methods of paper machines
from a more positive standpoint.
Machines and biology
Although nearlv all of the discussion in this chapter has been
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 75
concerned with the development of logic, it is not here that our
primary interest lies. Mathematics is a convenient place to try out
such machine theories of logic, and it is an historical fact that it is
mathematicians who have so tried them out, but the machines with
which this book is primarily concerned are of other kinds.
Learning machines of various sorts have been built, and these
are of great psychological and behavioural interest. What are the
problems here? The main point is that it is not possible to build all
the machines we would like. But we can and do build the blue-
prints, and by such decision procedures we can discover what is
and what is not possible.
It is certainly the case and this is exhibited by the develop-
ment of computing machinery that we can construct an analogue
. that could do anything that can be described sufficiently definitely
by biologists. This, perhaps, may not appear helpful, and indeed
it is certainly not the reason for studying 'thinking machines', but
the fact is that such a criterion may be taken in a sense as a measure
of the meaningfulness of a biological statement, 'Is it effectively
constructible or reconstructive?' might be the form of such a test.
If not, then it seems that the mechanism has been insufficiently
described.
There are, of course, technical difficulties. We do not as yet
know sufficient of colloidal chemistry to construct systems of the
same colloidal materials of which humans are built; but though we
cannot at present construct the analogue of human behaviour in
hardware, these purely technical difficulties are irrelevant to
matters in principle.
The general argument about paper machines and their implica-
tions in the general field of biology may seem trivial, but it is being
emphasized for the reason that it is not widely recognized by
biologists and psychologists that there is a field of mathematics and
mathematical logic that has a direct relevance to their own fields of
interest. The fact is that paper machines tell us a great deal about
the nature of machine construction, and which thinking operations
are possible, and about the possible construction of nervous and
other biological systems, and their possibilities. Their main use
and it is indeed a very valuable one for most scientists may be
to suggest experiments, but such investigations have an even
greater value than this in that they suggest theories, not only of
76 THE BRAIN AS A COMPUTER
particular branches of knowledge but also about the nature of
reality.
Now we must return to our discussion of scientific theories and
their evolution.
The evolution of scientific theories
The next stage in our analysis of the theoretical problems for
psychologists is to enlarge on the methods of the earlier sections
of this chapter at the most general level, and consider the possible
modes of development of scientific theories. In particular, we shall
continue to consider, but more explicitly, the case of experimental
psychology.
The existing state of experimental psychology is perhaps at the
transition from the 'taxonomic' stage (collecting data) to the
theoretical stage. The second stage of a theory is marked by the
fact of having a theoretical language that allows the role of the
experiment to become primarily that of a test for theoretical
predictions. This clearly expresses the need for theory, and it also
re-emphasizes the need for carefully considered experiment. So
much of psychological theory is limited in value by the fact that
most writers in the field use imprecise, discursive methods, and so
many of the experiments carried out are ill-conceived. It is surely
obvious that while not all the questions involved in scientific theory
construction are merely linguistic, a great many of them are ; and
even those which are not merely linguistic are coloured by
linguistic considerations. What is needed in psychology, apart
from rare skill in experimental techniques, is some of the linguistic
skill of the methodologist and the logician.
We will now turn to a more explicit consideration of the recent
work of Braithwaite, in which the relation of models to theories
has been analysed.
Braithwaite (1953) has pointed out the relation between models
and scientific theories with great clarity. His view is that there is a
sort of parallel between the development of scientific theories from
observation statements, on one hand, and the reconstruction of
empirical data from a model, on the other. These are two parallel
zip-fasteners, as it were, the theoretical-zip being tied to observa-
tions at the bottom, and the model-zip being tied to observations
at the top. In this chapter we have discussed some of the problems,
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 77
and the structure, of the formal languages and the cybernetic
models, which start from sets of marks on paper and proceed by
rules to generate further sets of marks or strings. These sets of
marks are models, and are then open to interpretation as languages
which may be used for any purpose whatsoever that is consistent
with the interpretation placed on the marks. It is rather as if, to
speak metaphorically, the collection of marks (called calculi) have
certain structural properties like maps of anywhere at all, and the
problem is to select a map that fits the country in which the
scientist is interested at any particular time. Braithwaite's analogy
of a zip-fastener depends on the fact that the model at the lowest
level and the theory-language at the highest level are both attached
to reality, and we can go up and down the levels (meta-levels) in
between, in either direction. We are using hierarchies of languages
as the bases of the themes.
It is generally believed as our earlier anecdote illustrated
that we can proceed from a set of statements of direct observation
to generalizations by inductive inference, and from the generaliza-
tions back to the testable particulars by deduction. This is the
theory; the model is in essence the skeleton logical structure of this
theory, and it is therefore clear that there is the closest relation
between theory and model.
Before proceeding to make any comment on this view of
Braithwaite's, it is important for theoretical psychologists to note
that he has also given considerable support to a view held by F. P.
Ramsey (1951) that the theoretical terms that occur in scientific
theories are not merely logical constructs. This means that the
theoretical terms cannot be defined solely in terms of observed
entities if we wish our theory to be capable of expansion to incor-
porate new information as it arises, and this of course we surely do
ultimately need.
Let us now consider the broader nature of psychological theories.
We shall start with natural language and its use as descriptive of
particular occurrences and generalized hypotheses, and we shall
try to refine its statements by setting up glossary (George, 1953a,
1953b) definitions for our principal logical constructions and
observable variables. This involves the necessity of adding refining
contextual definitions to all except the explicitly primitive terms of
the system. We could, on a more precise level, do the same thing
78 THE BRAIN AS A COMPUTER
by using either reduction-sentences, or by reformulating from
time to time our sets of explicit (eliminable) definitions. Rules of
inference are not usually explicitly formulated at the natural lan-
guage end of our continuum, but are so formulated, of course, as
and when we proceed to the use of formalized languages. Indeed,
we regard the important sense of the word 'formalization' as that of
'making rigorous', and making the rules of use for a set of
symbols explicit. We should proceed from the observables on the
molar levels of observation and, by use of theoretical terms (in-
ferred entities, logical constructs, or intervening variables, are
points on a continuum of the Realist-Nominalist kind by which we
may mean that they stand for actual physical systems in one
extreme or mere functional connexions without any implied
physical existence at the other) to build a psychological qua
psychological theory. From this as our datum, the process of levels
of language allows us to expand the system in many different (as it
were) dimensions. The most obvious extension that seems to be
necessary is to descriptions of a neurophysiological kind. Thus, the
constructions on the 'molar' level should be capable of redefinition
in the language of neurophysiology. There is, however, an
important sense in which this procedure of redefinition on any
level of description has been confused with a different thesis known
as 'reductionism', but what is intended here is only the ability to
translate from the language of one level of description to the
language of another level; indeed such translation should be
possible between different linguistic frameworks on the same level
of description. There is no obvious way, on a purely molar level, of
granting priority to one linguistic system, with a certain choice of
terms and categorizations, rather than to another, except by the
tests of a pragmatic kind that can be carried out at all levels of
description. Actually, any particular molar theory must be tested
by seeing whether it uniquely defines, in certain test cases, such as
under classical or instrumental conditioning, a definite operator
such as those that have been suggested by Estes (1950) or Bush
and Hosteller (19Sla). They may be further tested, of course, by
any logical nets that may be derived from them. Theories that are
so vague that any mathematical operators or logical nets can be
derived from them are insufficiently precise, and can only be tested
on molar-pragmatic grounds as to alternative interpretations of
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 79
the same precise operations. The psychological theorist is there-
fore under obligation to show the breadth of utility of his theory,
and its plasticity in allowing precise rules, etc., to be derived from
it whenever the need arises.
The above statement argues that a theory must at least satisfy
the following conditions : It must have certain molar explanatory
properties that place it in advance of any existing theory; it must
therefore have some, even if crude, explanatory powers in a lan-
guage that has been made sufficiently precise for its use. It will be
realized parenthetically that the precision of the questions to be
answered will decide the precision of the theory to be used. Then
the molar theory must be flexible enough to allow implicit re-
definition of its primitives and theoretical terms at any other level
of description (either more or less molar than the datum-language).
We should then be able to translate it into a molecular language
that permits of being made precise at any moment, and from which
logical nets and mathematical models are capable of being derived.
It is extremely important that a theory be tested in this ramified
way since, at the purely molar level, it appears that we cannot
always adequately distinguish the predictive value of the different
theories offered. It may, of course, turn out that there is an
important sense in which the purely molar theories are little more
than scaffolding for the presentation of the important questions
which are concerned with, say, the relations of logical nets with
each other; or the more general problem of producing a blueprint
for the relation of the internal parts (variables) of the human
machine.
We should notice the difficulty that the work of Braithwaite has
made for the view that logical constructs are definable in terms of
observable entities. This becomes more acute as we approach a
more formalized level of language. However, Braithwaite's own
suggestion that such theoretical terms should be reserved for the
high level statements, and can only be implicitly defined, is
certainly acceptable. The writer has drawn attention to the use of
logical constructs in psychological theory before (George, 1953a),
and has pointed out that it is precisely the vagueness attendant on
the surplus meaning of such logical constructs that gives them
both their power and their vagueness. The difficulties of theoretical
terms in more formal languages still demand some further research ;
30 THE BRAIN AS A COMPUTER
ndeed, this problem appears already to have reared its head in the
ittempts that have been made to apply mathematics to psychology.
There are two further matters that now demand comment, the
irst being a sort of criticism of Braithwaite, in that there is some-
:hing of a gap between the way science actually works and the cut
md dried systems he suggests. It is as if he were giving a prescrip-
:ion for the ideal state of an ideal science, whereas we have tried to
:alk realistically in terms of the actual situation with which the
experimental psychologist is faced. He starts with a great mass of
data, based mostly on observation, upon which generalization is to
DC made ; the nature of the generalization will depend upon intui-
:ive and anecdotal notions. Thus, although one may start in
principle from a model and give interpretations of that model, one
nay also formalize a theory, i.e. one may proceed from a set of
scientific generalizations to the logical core of those generalizations,
[n fact, the original generalizations will be partially confused with
i model as often as not, and the explicit stages of Braithwaite only
arise, if at all, after much work has been done on the confused mass
rf empirical data that represents the normal growth of a science.
The second point takes us outside the theory-construction to
:he directives and foundation principles upon which the theory is
:o be built. Here, the cleavage is along the lines of behaviourism
md introspection, and it is a dispute characterized at some level
by the 'Mind Body problem*. At the working level of the scientist
there are still problems of what behaviourism implies, i.e. how
Droadly or how narrowly the behaviouristic notion is to be
employed, and if taken too narrowly, how much of a science of
psychology is lost, if anything.
The answers to these last questions can be given here only
Driefly. Some form of behaviourism, involving at least the study
}f that which is obviously public, is quite vital. A science of
behaviour so based should include all the data that the intro-
spectionist deals with, but it will not use the same language.
Indeed, self-observation is essentially part of the subject matter of
behaviouristic psychology, but necessarily approached in a public
manner. Self-observation statements are therefore indispensably
involved in a behavioural science, and such statements are
continuous with (ordinary) observation statements. There should
be no confusion here at the level of the absolute behaviouristic
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 81
science, but in fact confusion does sometimes arise, since we do
not always see where the observer enters into the apparently
public scientific system. In the practice of psychology we have to
combine, for many purposes, information from introspective and
behaviouristic sources, and we are forced into a degree of eclecti-
cism. It is to the behaviouristic approach that our processes of
formalization, the applications of logic, and all the matters dis-
cussed in this chapter, are applied. Failure to recognize the nature
of the complicated problems of constructing scientific theories has
vitiated a great deal of the work of psychologists; recognition
should improve his scientific standards.
One last, clarifying word should be said on the matter of
behaviourism. What it is hoped to avoid in modern psychology is
on the one hand, the narrowness of early behaviourism, which
simply ignored problems which did not fit into its over-simplified
notions. On the other hand, it is equally vital not to become
embroiled in a morass of ontological and epistemological disputes.
We are concerned with the systematic construction of scientific
theories, meta-theories, and criticisms of both ; and with the nature
of the actual assumptions, and the interbehavioural interpretation
that is both possible and desirable for psychology, and indeed for
the whole of science.
Explanation
We have seen that explanations may take more than one form.
The reduction-sentence methods of Carnap are made necessary by
the notion of 'dispositional properties'. The notion of causal
consequence certainly presents a difficulty for logic, i.e. in the logical
model, but for science it is not a genuine problem. We simply act
in accordance with what we believe would happen if some action
were performed. This is, in fact, induction at work, and no scientist
is worried by the knowledge that he cannot be certain of what
would have happened if he had done something that he did not
actually do. The general form of the Hempel-Oppenheim (1953)
theory looks something like what is needed as a form of scientific
explanation. The conditions they set down are certainly too strong,
but the general form comes nearer to what scientists actually do.
Let us consider this matter a little further.
82 THE BRAIN AS A COMPUTER
Hempel and Oppenheim's theory can be stated (oversimply) as
that of finding true sentences Ci, Ca, ..., C r which are ante-
cedent conditions, and Z/i, 2, ...,# which are general laws
together forming the explanans for the explicandum (E), which is
made up of statements which are the description of empirical
phenomena: that particular phenomenon (or phenomena) that is
to be 'explained*. Their method deals with what they call causal
(as opposed to statistical) explanations, and demands many special
properties of the explanans. The sentences of the explanans, which
are the general laws, are to be true (they will not accept 'confirmed
to some degree* with respect to certain evidence) ; they must also
be 'familiar' in a certain sense, and testable. The language they
would use to formulate a model theory would be that of the lower
functional calculus without the identity relation. There are many
more complicating conditions which cannot be discussed here,
and with which the writer would generally agree, but the total sum
of their plan while it should be familiar to every psychologist
is in fact too strict to be followed by every scientific theory.
The same criticism of over-strictness is applicable to Carnap's
conditions as laid down in 'Testability and Meaning' (1937),
which expresses the process of reduction (to be distinguished
from definition) of sentences to observation sentences.
Most of the predicates of science being dispositional predicates,
everyone now knows of the non-eliminability of such predicates as
'soluble', the ordinary word used for the property of being capable
of being dissolved in water. This led Carnap to the process of
reduction sentences of the form: If x is immersed in water then, if
and only if x is soluble in water, x will dissolve. This is of the
logical form
The process of reduction of the dispositional predicate by
reduction-pairs may finish in non-dispositional predicates,
referring to a test-operation. A weaker test, involving unilateral
reduction-pairs, is usually used in experimental situations. (A
brief account of this process can be found in Pap (1949, Chapter
XII) and, again, should be familiar to every psychologist.) This
process of 'reductionism' is an alternative to explicit definition,
and has some advantages.
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 83
The psychological theories of Hull use the traditional theory-
construction method of psychology; it is hypothetico-deductive,
a postulational method (with complications) which uses logical
constructs', and derives consequences. Operationism is not
excluded from such a system, and the more nearly operational such
definitions, etc., can be, the better for most purposes. This is not
to be taken as an indication of a final answer to the most suitable
method of constructing even the molar sort of behaviour theory.
Investigation of theory-construction in science is as much a subject
in evolution as science itself.
What is needed by the psychologist is a systematic method for
translating statements of observation into generalized laws or
hypotheses, without hopeless vagueness. This demands that the
meta-language assumed, and the language refined for the actual
statement in the theory, are sufficiently clear. For this, definition is
probably vital; there is certainly no point in introducing false
rigour, but for the more rigorous part of psychology, where
disputes are mostly about terminology, the calculus of empirical
classes and relations is perhaps the ideal form of description. Here,
the terms and their relations are relative to the context of inquiry;
they do not insist on rigid class membership, but permit a degree
of vagueness that heralds the use of probabilities. Here, as in all
formalized systems, the theory and the model are closely and
explicitly related. Such a formal, yet elastic, language also goes a
long way to avoid the hazards of talking of 'things having pro-
perties', etc.
The use of natural language, languages, and scientific theories,
has one further complication. A precise, descriptive language
(including an explicit or implicit model) is a scientific theory. The
marks on paper (or sounds in the air) which have no meaning
(interpretation) are not, of course, a language. The point is that
our precise, descriptive language should be capable of interpreta-
tion in natural language, but that the precise relations themselves
are not necessarily capable of being precisely produced in the
natural language, other than by analogy. To believe that natural
language (a theory of the world on a crude level) is sufficient for
science simply because the final interpretations of precise language
have to be in natural language, is surely a mistake.
What is vital for the psychologist to notice is that logic (all
84 THE BRAIN AS A COMPUTER
systematic languages) has two different roles to perform for him :
(1) in clarifying their existing statements and theories, and (2) as a
precise, descriptive language itself. Both roles are vital, and it is
vital to distinguish them.
We shall now leave philosophy of science and return to the
closely related matters of logic.
Empirical logics
We have referred to empirical logics and their use to behaviour-
istic-cybernetic methodology, and we shall now say something
more about them.
It has generally been thought that the logics of the type of the
propositional and functional calculus are too precise to deal with
the vagueness in most of the ordinary situations that we wish to
describe. This has suggested to many people that more realistic
descriptive languages could be found by using probabilistic logics,
and we shall see later that the use of probabilistic logics has a
direct application to logical networks, which are at the very heart
of cybernetics. However, the main idea is to avoid vagueness in
description and still retain enough rigour to avoid the pitfalls of
ordinary language. These methods may be thought of as analytic
tools, or as descriptive methods for a science (Kaplan and Schott,
1951; Woodger, 1937, 1939, 1952; Korner, 1951). We shall here
merely outline what we believe is likely to prove a very powerful
linguistic tool in both experimental and social psychology. Its
importance lies partly at least in its close link with logical nets,
because these logics can, like the logical nets, be given an interpre-
tation at any level of investigation, making it easy to pass from a
description at one level of generality to another.
To put the matter simply, the idea is to map the calculi of
classes, relations and predicates on to the calculus of probability.
This means that when we talk of class membership, or of relations
between classes, we talk rather of the probabilities that exist
between these items or classes. In other words, instead of saying
'Jack is a man', we shall simply say that ']ack is probably a man',
where we mean, of course, to imply an incomplete description of
Jack which leaves us in doubt and implies that the probability
falls short of 1. This example may at first sound over-simplified,
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 85
but on the basis of a perfunctory description one might be
unsure as to whether the person referred to as 'Jack' was a
human; even if human, 'Jack' could be a woman disguised,
and so on.
If we bear in mind that in logic we are concerned with giving an
interpretation to a system of formal symbols, then we will realize
that an alternative interpretation of such empirical logics would be
to say that 'Jack is a man to some extent'. This may seem a less
plausible interpretation, but it could at least apply to those un-
fortunate cases of endocrine disorders where change of sex is
involved. If we use the example 'Jack is to some extent a neurotic',
we can clearly see the point of substituting a probability in place
of a certainty with respect to class membership.
It is not being suggested that imprecise description is to be
preferred to precise description, but rather that where the facts
described are imprecise (our own knowledge of them is incomplete)
it is better to have a precise description of their imprecision.
Mathematics is a language with which you can actually carry out
the measurements, and there is some point in saying by analogy
with well known methods in statistics that empirical logics are
non-parametric mathematical descriptions.
It is clear that a description of any situation can be couched in
terms of a probabilistic language of this sort, where the interpreta-
tion on the variables may be anything we like. The probabilities
may be computed on the basis either of a priori probabilities or of
empirical probabilities. Let us briefly illustrate the method in one
of its many forms.
Suppose that a set of variables of a physiological kind are asso-
ciated with a certain piece of molar behaviour, then, if we can
obtain a set of measures for a certain range of behaviour, we can
describe the total behaviour pattern as a relation. Let us say Rob
is such a relation, where a and b are two states of the organism and
R is to be interpreted as 'probably follows in time*. A definite
value may be calculated from the cases measured.
R itself is made up of the measurable variables A, B, ..., N.
Then we may measure these variables, and although they may not
constitute a complete basis for describing R, we can discover
which are the best indices for R. Then we might also consider
relations between the variables and so on, so that, given any
86 THE BRAIN AS A COMPUTER
subset of the variables, on some future occasion we can ascribe a
probability to the relation
Rab
Alternatively, we can interpret the logic as we did above with
respect to an utterance such as 'Jack is married to Jill', also of the
form
Rab
If we assume we do not know all the facts but know certain
indices of marriage, such as 'they live in the same house', 'they
appear to be affectionate towards each other', and so on, then we
can ascribe a priori probabilities to these subrelations r, s, ..., t
which are a basis for the relation R. The more we know of the sub-
relations the more completely can we ascribe a probability to R.
Obviously, we may weight the subrelations so that they do not
necessarily contribute equally to the total probability ascribed at
any particular time.
As far as the notation is concerned we need not bother about
that here (see Chapter V), except to notice that we can easily think
of a, b, .,., n as either items or classes, to be distinguished where
necessary, and jR, 5, ..., T as relations which may be monadic,
diadic, etc., having subrelations r, s, ..., t and so on, with sub-
subrelations for as many levels as we want. Then the X. Y 9 Xv Y,
~X of Boolean algebra become two diadic and one monadic
relation:
Rab, Sab, Na
where it will doubtless be wise to retain particular letters for
particular relations, as in the Lukasiewicz type of notation where
the relational operator is written first to save the bother of mani-
pulating brackets. Here, of course, the relational operators conceal
a probability, and to make this explicit we could write
Rab P or Rab(p)
say, to remind the reader that a probability^) will be ascribed to the
relation under description.
It should be added that Woodger, in his biological language
previously mentioned, uses explicit predicates of a biological kind,
over and above the symbols of the prepositional and functional
calculus. He introduces such predicates as
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 87
which is read as '# is before y in time* ; and
Sli (oc, y)
meaning '# is a slice of the thing y 9 ; and then again
Org (*)
meaning 'x is an organic unit', which can be put into an axiomatic
form :
Org (*) DTh (*)
which means to say that 'each organic unit is a thing*.
These simple beginnings are soon made quite complicated, and a
precise biological description is built up and used to describe
processes of genetics and cell division. Although these descriptive
languages may sometimes seem to state the obvious with unneces-
sary precision, it must nevertheless be admitted that this is a
beginning of a somewhat different, yet similar, descriptive lan-
guage which, with the help of the computer, may become of great
importance.
Stochastic processes
In discussing logical net models we have frequently mentioned
the important part played by stochastic processes, and the fact that
they had been used in cybernetics. They have at least been used in
attempts to apply the mathematical descriptions to psychological
phenomena, and this is part of cybernetics.
The work of Bush and Hosteller (1951, 1955) comes to mind in
a consideration of Stochastic Processes. They have tried to apply
the mathematical paraphernalia of certain types of stochastic
process to behavioural problems, and in particular, to the analysis
of particular experiments.
It will be remembered that a stochastic process is a sequence of
symbols that implies a temporal order and yet is itself random. A
particular stochastic process, of importance in behavioural
analysis, was called a Markoff net, in which the steps of the
sequence are related by definite probabilities. Furthermore, if
nature is something like an ergodic source we may expect that the
Markoff processes, with which behavioural descriptions are going
to be concerned, will be of the statistically homogeneous kind.
88 THE BRAIN AS A COMPUTER
For Bush and Mosteller the process starts with a stochastic
model, and proceeds through statistical methods to the mathe-
matical model for some aspect of behaviour. This is all meant to
apply to molar behaviour activities. They are thus concerned with
operators, especially matrix operators, and the statistical descrip-
tion of behaviour in terms of these operators, which represent the
response tendencies implicit in a class of events as described by
probability variables.
We shall later show briefly some of the close connexions that
exist between the work of Bush and Mosteller and the work of
logical nets. We can straight away say that both conceive of molar
behaviour as capable of statistical description and indeed as being
essentially a Markoff process. The methods actually used differ
largely in that logical nets are concerned in deriving a description
of molecular behaviour as well as molar behaviour, and so have
involved themselves more deeply in descriptions of the organisms.
The end of the anecdote
We should now add an epilogue to the anecdote which we related
earlier. The cycle of events involving assumptions, tests and
generalizations is claimed to be typical of science, but what we
should now notice is that it is typical of human behaviour. The
processes of deduction and induction may be irrational and private
in man, but the essentials are identical.
Cybernetics is concerned with showing that the inductive as well
as the deductive part of the Erewhonian observer's behaviour
could be carried out by a machine.
The whole field of methodology in science is vast, and the subject
matter could be extended to many volumes. However, what is
perhaps most obvious is that logic and language can be applied to
all sorts of problems. The method is to construct artificial lan-
guages and then place the appropriate interpretation upon them.
From one point of view, cybernetics can be regarded as being
precisely a branch of this general field of applied logic.
It should be emphasized that linguistic problems will occur in
science, even in the realm of applied logic. As long as this is
remembered, then such matters can usually be cleared up in the
contexts in which they occur.
PHILOSOPHY, METHODOLOGY AND CYBERNETICS 89
Summary
This chapter has outlined a many-levelled method of modelling
human behaviour by the use of empirical descriptive methods and
of theoretical terms that are capable of redefinition on other levels
of description.
A particular view of science is delineated by which the scientific
process is seen as the collecting of data and the making of inductive
generalizations from those data, and then the drawing of deductive
inferences from the generalizations. This, it is claimed by many of
those interested in cybernetics, is a process that can be achieved
by machines as well as organisms.
Logical systems which are to be used as models for our cyber-
netics theories are summarized briefly, and some mention is made
of the more obscure logical calculi.
Effective procedures are seen to be paper computers, and are of
the utmost value in a discussion of what is possible for hardware
construction. This is one of the firmest links between mathe-
matics, computer design and the construction of effective theories
of behaviour.
Some further discussion has also taken place with respect to the
evolution of scientific theories, and some of the difficulties met in
constructing such theories. Finally, a point of view of relevance to
philosophy has been implied, although the programme of prag-
matics suggested has not been carried through. The emphasis is on
methodological rather than philosophical forms of analysis, since
from this aspect classical philosophical analysis seems to have only
a limited contact with the needs of modern science, which is con-
cerned not with absolutes but with limited contexts of meanings.
CHAPTER IV
FINITE AUTOMATA
A FINITE automaton, in the sense of McCulloch and Pitts (1943),
was a stimulusresponse system which could involve representa-
tions of the previous stimulus states of the system. From this
model we must go on to ask, with Kleene (1951), about the general
nature of finite automata, and what kinds of events can be repre-
ssnted by them.
We shall first set out the McCulloch Pitts definition of a finite
automaton, and we shall call our particular automata 'neural nets',
initially, thus preserving the original title of the founders. We shall,
however, change the title to 'logical nets' in the next chapter (and
from then on), when we outline the particular finite automata that
this book will use for its analysis and synthesis of psychological
problems. The reason for this change of name is largely to preserve
the distinction Braithwaite (1953) makes between a model and a
theory, and in this way to make it clear that a finite automaton is
not in any way committed to being a model for a theory of the
central nervous system.
McCulloch-Pitts neural net
A neuron is a cell body whose nerve fibres lead to one or more
endbulbs, where we can think of an endbulb with respect to one
element as being simply the next element in the net. A nerve net is
an arrangement of a finite number of neurons in which each end-
bulb of any one neuron impinges on the cell body of not more than
one other neuron. A special case arises where that cell body is its
own. The separating gap between cells is a synapse, and an end-
bulb may be one of two kinds, excitatory or inhibitory, but not
both. The neurons are called input neurons where no endbulbs
impinge, and otherwise, inner neurons. The conditions on the
firing of input neurons are determined by conditions outside the net,
while for inner neurons a threshold number h must be exceeded, or
90
FINITE AUTOMATA 91
at least equalled, by the balance of excitatory over inhibitory in-
puts, firing the instant before the time t (say) under consideration.
The conventions on which the networks are drawn are as follows :
A circle represents an element (or neuron) which is in one of two
states at any instant t, it is either live or dead. If live, then its output
fibre will be sending out an impulse at the instant it is live. The
output fibre must be in one state at any instant, and an instant is
assumed to be the firing time of all the elements. The output may
bifurcate as often as is needed, but it can only be in one state for all
its bifurcations. There can be as many inputs as we like, and these
inputs can be divisible into two classes, excitatory and inhibitory.
The excitatory ending is represented by a filled-in triangle, and
the inhibitory by an open circle. A heavy dot is used to indicate
that wires crossing over are also having contact, except that when
three wires are involved, since no loose endings will occur apart
from the input and output elements, there will be no ambiguity in
omitting the heavy dot. This replaces the 3- notation sometimes
used in electrical circuits. The number h in the circle is the
threshold number which is such that, if e be the number of
excitatory fibres live at any instant and i the number of inhibitors
live at any instant, then the condition for the element to fire is that
e^i+h. The neural net of Fig. 1 illustrates some of the principles
so far described.
Since in describing finite automata we shall be using matrix
algebra to some small extent, let us give the simplest of the
necessary definitions. A matrix ay
(an ai2
021 #22
ami OmZ
is written with brackets as above or with square brackets [,]. The
use of suffices a*j labels the element of the rth row and jth column.
A matrix can be written A, where A stands for an mm matrix, as
above. Two matrices of the same order (having the same number
of rows and columns) can be added. Thus, if
(#11 #12 #13\
#21 #22 #23 )
#31 #32 #33/
92
and
then
THE BRAIN AS A COMPUTER
(*11 *12 *13\
*21 *22 *23 1
*31 *32 *33/
FIG. 1. A LOGICAL NET FOR SIGNS. The logical net is one that
could be taken to represent a sign. If A and B fire together this
fact is 'remembered* by the loop element B, and if then A fires
alone G fires as if B had fired; A is 'a sign for* B.
Matrices can also be multiplied so that A multiplied by B is
written AB, and this is generally not the same as BA.
32
^31*13+^32*23 + ^33*33
If we substitute numbers for letters and have
/2 3
A- (1 2
\2 3
:)
FINITE AUTOMATA 93
and
B
then
AB
while
BA
/I 2 3\
=(l 2 l)
\1 I/
/9 10 13\
= ( 9 6 11 )
\6 10 10/
(10 16 19\
6 10 171
4 6 5/
We can also multiply a matrix, such as A above, by an ordinary
number (called scalar) such as 2 where we represent it by the
letter k.
/4 6 8\
kA. = ( 2 4 12 )
\4 6 2/
We should notice also two particular matrices, those having only
one row or one column. These are called row and column vectors,
and they may be written (an a2 ... ai n ] and {an 021 ... a m \}*
The braces are used, in the second case, to save having to write the
column vector in column form.
A specialist text should be consulted for a detailed analysis of
matrices and other related algebraic forms; we shall, however,
develop other properties of matrices if and when they are needed.
To return now to finite automata. If we assume that a nerve net
has k input neurons N I9 N& ..., N^ for positive k, then for any
period of instants, reading back from the present^) (say r instants),
we can represent the total activity of the automaton by a k by r
matrix. The matrix will be made up of O's and Ts according to
whether the particular input neuron fired at a particular instant or
not.
A typical matrix for k 2, r 3 is :
R
\o i/
for columns JV X and N 2 and rows p, p 1, p 2.
94 THE BRAIN AS A COMPUTER
Such a matrix represents, or could be taken to represent, the
whole history of the input, and in terms of this we define an event
as a property of the input of an automaton. An event is any sub-
class of the class of all possible matrices describing the inputs over
all the past time right up to the present. Such matrices will be
called input matrices.
An example of an event in terms of the above matrix would be
the firing of N^ zip I and the non-firing of N% at the same time.
This event would be one of the events represented by the above
matrix.
We must now, following Kleene (1951), narrow our definition of
an event. First we shall define a definite event as an event that took
place within a fixed period of the past, and that matrix is said to
cover definite events of duration r.
It will be noticed that there are kr entries in a kr matrix which
covers k neurons over a period of duration r. This means that there
are 2* f possible matrices, since they can be made up of all possible
combinations o'f and 1, and there will be 2 2 r definite events
represented by such a set of matrices. A positive definite event is
one in which at least one input neuron fires during the duration of
the event.
Now we must briefly consider the representation of definite
events, since we must be sure that when we use neural nets for our
behavioural purpose, they are within the safe ground of logical
consistency; they are, in fact, taken to represent regular events,
for which we must seek a definition. In this respect Kleene has
proved many theorems which are primarily of mathematical
interest, and those interested in the mathematical theory of finite
automata should consult his work.
One of the important consequences of Kleene's theorems should
be stated immediately. He has shown that almost any event which
is likely to be of biological or psychological interest can be con-
structed in our neural nets; he has even shown an effective
procedure for the construction of the necessary net.
An indefinite event is one that cannot be described by precise
reference to a past firing of an input element. Figure 2 shows a
simple example of an indefinite event. It uses the notation of the
lower functional calculus as well as that of the prepositional
calculus suffixed for time.
FINITE AUTOMATA 95
Figure 2 can be represented by the logical formula
(Et)t<*N 9 oMki (1)
where (Ei) is the existential operator, and means 'there exists a t
such that'. Here we use the usual symbol for a material implication.
The element of Fig. 2 could, of course, be characterized in
simpler terms. If we label the element M x in terms of its input and
output (say A and B respectively), we could write either
or we could write
Bt = At-i v At-z v . . . v At-n (2)
i.e.
Bt = At-i v Bt-i
which clearly characterizes the behaviour of the element.
FIG. 2. A LOOP ELEMENT, If Ni fires, it fires Mi, and then Mi
continues to fire itself indefinitely. Mi is called a loop or looped
element.
There are many mathematical complications over the 'starting
conditions' of automata, and further complications of detail, but
our main concern is now over that further class of events called
regular events. These will be defined.
A regular event exists if there is a regular set of input matrices
that describe it in the sense that the event either occurs or not
according as the input is described by one of the matrices of the set
of input matrices or none of them.
A regular set of matrices shall be the least class of sets of matrices
(including unit and null sets) which is closed under the operation
of passing from E and F to EvF, to EF and to E*F, where v is
the Boolean disjunction, EF means E.F where . is the Boolean
conjunction and * is defined by EE . . . EF.
96 THE BRAIN AS A COMPUTER
These regular nets (nets that represent regular events) are
primitive recursive (Kleene, 1951) and realizable, and logical
difficulties can be wholly avoided as long as we keep within their
domain. This we shall do, and all the logical nets discussed from
here on are ones that represent regular events and can be described
by a regular set of matrices. This refers to a certain kind of finite
automaton within the compass of which our investigations will
operate.
We cannot explain the full significance of such terms as 'primi-
tive recursive', but we should state that primitive recursive func-
tions are those defined by Godel in search of a function that
encompassed all the familiar mathematical functions. Primitive
recursive can be taken to be identified with 'effectively comput-
able*.
Uneconomical finite automata
Most of our later discussion of finite automata will not be
concerned primarily with economy of elements used. Culbertson
(1950, 1956) has explicitly investigated the properties of un-
economical automata; his work is close to the needs of experi-
mental psychologists who are concerned with the construction of
models for molar use, as well as those which are primarily con-
cerned with being interpreted as a 'conceptual nervous system*.
Culbertson (1948), in his earlier work, developed scanning
mechanisms and models of visual systems in neural network terms,
and these will be discussed later at the appropriate time. The same
is true of memory devices and other mechanisms that might help
towards the construction of robots, where, by 'robot', we mean a
hardware finite automaton.
He also devised the outlines of a theory of consciousness,
designed to elucidate the mind-body problem by exhibiting the
relationship between subjective awareness and the objective
activities of the human organism.
A further interesting discussion of memoryless robots has
shown that they could exhibit behaviour that might be called
intelligent, and this intelligence (or apparent intelligence) can be
increased by making the memoryless robot probabilistic rather
than deterministic. In the same context Culbertson has also
FINITE AUTOMATA 97
investigated the possibility that a robot can be constructed satis-
fying any given probabilistic input-output specifications.
Von Neumann (1952) has investigated the alternative problem
of showing how deterministic robots can be constructed in terms
of unreliable elements.
Von Neumann's work is of great importance and of great
practical value. His paper was significantly entitled Probabilistic
Logics, and it is concerned primarily with the role of error in logic
and, by implication, in finite automata. He constructed his own
notation, built like Kleene's in terms of the logical notation of
McCulloch and Pitts, and he was able to show that typical syn-
theses of logical nets are possible by simple and effective devices.
Some of these findings have been incorporated into the particular
models which we shall be discussing in the next chapter.
The main part of von Neumann's work and although we shall
not be considering this very much further, we must continue to be
aware of it is the manner in which he deals with error. First, to
summarize his findings, we shall look at what he calls the 'majority
organ', the 'Sheffer stroke' element, and then the 'multiple line
trick'.
It is well known that the whole of Boolean algebra can be derived
from the one connective called the Sheffer stroke and symbolized I ;
von Neumann makes this a basic organ of his system. The follow-
ing figures indicate the nature of the Sheffer stroke in logical net
a p . \ o/b
b
FIG. 3. SHEFFER STROKE. The Sheffer stroke element fires unless
both inputs a and b fire together when the ouput is inhibited.
terminology, and also the derivation of the other well known
Boolean connectives from it where 'I'll- ' means permanently stimu-
lated. Figure 4 shows the shorthand symbol for the full Sheffer
stroke organ of Fig. 3.
THE BRAIN AS A COMPUTER
a/b
FIG. 4. SHEFFER STROKE. Von Neumann's symbolic representa-
tion of the Sheffer stroke element of Fig. 3. The two diagrams
are synonymous.
Now we can derive 'or', 'and' and *not* in terms of Sheffer stroke
organs as follows:
A [
FIG. 5. OR. The inclusive or of logic as represented by Sheffer
stroke elements.
FIG. 6. AND. The and of logic as represented by Sheffer stroke
elements.
FIG. 7. NOT. The not of logic as represented by Sheffer stroke
elements.
FINITE AUTOMATA
99
The other basic organ to be considered is the majority organ,
and this can be written
m (a, b, c) = (a v V) . (a v c] . (b v c)
= (a , b) v (a . c) v (b . c)
and this can be drawn as in Fig. 8.
M(A,B)
FIG. 8. THE MAJORITY ORGAN. The output fires if a majority of
the inputs A, B, C fire.
The operations of conjunction and disjunction can be derived
from the majority organ quite easily:
a.b
FIG. 9. AND. Representation of logical and by the majority
organ.
where 'I In-' means never stimulated, and
avb
FIG. 10. OR. Representation of logical or by the majority organ.
100
THE BRAIN AS A COMPUTER
The multiple line trick
The basic problem that von Neumann sets himself to solve can
be stated in the following way. Suppose we construct an auto-
maton, and that we build it in terms of the single organ repre-
sented by the Sheffer stroke, and then we represent the probability
of the malfunctioning of a particular element by *(<-). If we are
given a positive number 5, where 5 represents the final allowable
error in the whole automata, can a corresponding automaton be
constructed from the given organs which will perform the neces-
sary functions while committing an amount of error less than or
equal to S? How small can 8 be? Are there many different methods
of achieving the same end?
FIG. 1 1 . MULTIPLEXED SYSTEM, With inputs a, b, c and outputs
x, y the system is connected by n lines, represented here by ===.
The probability of outputs firing for inputs firing can be cal-
culated at different rates of error of connexion.
We see straight away, of course, that 8 cannot be less than r,
since the reliability of the whole system cannot be greater than
that of the final neuron, which may have error e. This applies to
the first question but not to the second.
Consider Fig. 11. The multiple line trick, as von Neumann
calls it, merely involves carrying messages on multiple lines instead
of on single or even double lines.
We first set a fiduciary level to the number of the lines of the
bundle that is to be stimulated. Let this level be k. Then for
0<A<i, at least (1^) N lines of the bundles being stimulated, the
bundle is said to be in a positive state; and conversely, when no
more than kN are stimulated, it implies a negative state. A system
which works in this manner is called multiplexed.
FINITE AUTOMATA
101
Von Neumann next proceeds to examine the notion of error
further for a multiplexed automaton.
The rest of this section gives a fairly rigorous example of von
Neumann's argument, and this may be omitted by the reader who
is not explicitly interested in the mathematical theory. The
argument is only a part of the general form by which von Neumann
was able to demonstrate the point that reliable automata can be
constructed from unreliable components; or, more simply, that
error in an automaton can, if limited, be controlled.
FIG. 12. THE MULTIPLEXED CONTROL. The replicated inputs to
majority organs increase the probability of successful trans-
mission of information.
Denote by X the given network (assume two outputs in the
specific instance pictured in Fig. 12). Construct X in triplicate,
labelling the copies X 1 , X 2 , X* respectively. Consider the system
shown in Fig. 12.
For each of the final majority organs, the conditions of the
special case considered above obtain. Consequently, if N is an
upper bound for the probability of error at any output of the original
network X, then
AT* = +(l-2) (3JV 2 -2JV*) s/c (N) (3)
is an upper bound for the probability of error at any output of
102 THE BRAIN AS A COMPUTER
the new network Jf*. The graph is the curve N* ==/ (A/), shown
in Fig. 13.
Consider the intersections of the curve with the diagonal N* =
N. First, N = \ is at any rate such an intersection. Dividing
N-f (N) by JV-1 gives 2 ((1 -2e) jV-(l-2e) JV+ ), hence the
other intersections are the roots of (1 2e)N 2 (1 2*) AT+ = 0,
i.e.
i.e. for e> they do not exist (being complex (for
or = | (for e =&)); while for < they are A/" = No, 1 No,
where
For Af = 0; AT* = >N. This, the monotonic nature and the
continuity of AT"* =/< (N) therefore imply:
First case, e>: 0<AT<J implies AT<AT*<|; <AT<1 implies
Second case, e<: Q^N<No implies N<N*<No; No<N
<^ implies No<N*<N; $<N<lNo implies N<N*<lNoi
l-No<N<l implies l-No<N*<N.
Now there are numerous successive occurrences of the situation
under consideration, if it is to be used as a basic procedure, hence
the iterative behaviour of the operation N-+N* =/e (N) is
relevant. Now it is clear from the above that, in the first case, the
successive iterates of the process in question always converge to
, no matter what the original N; while in the second case these
iterates converge to Afa if the original AT<, and to 1 N0 if the
original AT>|.
To put the matter another way, in the first case no error level
other than N^% can maintain itself in the long run, where ~
means 'approximately the same as', or 'the same in the limit', i.e.
the process asymptotically degenerates to total irrelevance. In the
second case the error-levels N^No and JV~1 No will not only
maintain themselves in the long run, but they represent the
asymptotic behaviour for any original AT<| or N> , respectively.
These arguments make it clear that the second case alone can
be used for the desired error-level control, i.e. we must require
FINITE AUTOMATA
103
<, i.e. the error-level for a single basic organ function must be
less than ~16 per cent. The stable, ultimate error-level should
then be No (we postulate that a start be made with an error-level
N< ). No is small if is, hence e must be small, and so
This would therefore imply an ultimate error-level of about
10 per cent (i.e. JV~(M). (For a single basic organ function error-
level of ~8 per cent (i.e. 0*08).)
No
FIG. 13. ERROR CONTROL GRAPH. N is upper bound for the
probability of error at any output of an original network (X in
Fig. 12), and N* for the new network derived by multiplexing
e is the error. N0 is a root of the equation for N* shown in
graph as curved line (see text for explanation).
This argument is taken a great deal further, and made very
much more rigorous, and von Neumann introduces the concept of
a 'restoring organ' which helps to control the error. He hazards the
guess that 'neuron pools' in the human nervous system may work
on such a procedure as he outlines.
It is probable that von Neumann's principal contribution to the
behavioural theory of neural nets lies in his demonstration that
error in the components at least will not be a reason for believing
that very large switching devices would be hopelessly inadequate
104 THE BRAIN AS A COMPUTER
because of the multiplication of error. There are, of course, many
other ideas that spring from his work, and which we should bear in
mind in our search for suitable behavioural models.
Turing machines
We shall say a little more here about work on Turing machines
(see also Chapter III). Their interest lies in the question as to
what is capable of being computed by a machine, and the questions
raised by current research on Turing machines are largely concerned
with that branch of mathematics known as recursive function
theory.
Among the most interesting of recent results on Turing
machines are those obtained by de Leeuw, Moore, Shannon and
Shapiro (1956); they have been able to compare a deterministic
machine with probabilistic machines for a certain set of tasks.
A study of Turing machines has a special interest for the psycho-
logist because of its relation to the nature of paper machines in
general, which are so important for the consideration of effective
theories.
Lastly, it should be mentioned that a Turing machine is equi-
valent to a general purpose digital computer, provided that the
computer is able to have access to all the tape or cards it has used
throughout its operation.
Many discoveries are still being made about the nature of finite
and infinite automata. Rabin and Scott (1959) and Shepherdson
(1959) have shown that two-way automata (those that can move
both ways along their input tape) are effectively equivalent to
one-way automata.
Extensive theorems have been proved about one-tape, two-
tape, three-tape and w-tape automata, and this is of special
behavioural interest since, if the tape is to be regarded as repre-
senting a temporal flow, then it is important in relating Turing
machines and other two-way automata to a one-way automaton,
whether or not the one-way automaton is single or multi-tape.
The syntheses of finite automata
We next turn to the subject of the actual hardware machines
that have been built as syntheses of the general theory of finite
FINITE AUTOMATA 105
automata. We shall exclude some machines from this discussion
and leave them until the end of the next chapter, where they may
be better understood after the discussion of the particular set of
finite automata there described.
There are many difficulties confronting a discussion of the
syntheses of finite automata, and we can but summarize some of
the better known of these models. We shall subsequently make
some generalizations about the nature of syntheses.
We should bear in mind that we have already outlined the
structure of digital computers, and these are the most obvious of
all examples of such syntheses that are of interest to us in the
behavioural sciences. We shall say no more about them at the
moment, although their special use when programmed as learning
machines should be borne in mind.
Grey Walter's models
Grey Walter (1953) has produced two syntheses of finite auto-
mata. The simpler one is called Cora, a conditioned reflex analogue,
and its general structure and function are briefly noted in the
following description.
Cora's response to changed conditions is indicated by a short
discharge in a neon glow tube, seen as a flash of pink light, which
is the response to a particular stimulus. With such a system, a
sound such as a whistle can be made a sign of a forthcoming light
stimulus. In other words, it is a simple association system, and it
will be seen later that this is the basic idea underlying our logical
networks of the next chapter.
Machina Speculatrix (popularly known as 'the tortoise') is some-
what more complicated. It has two sensory elements in the form
of a simple contact receptor and a photoelectric cell. The tortoise is
mobile, being driven by an electric motor, and it carries an accumu-
lator, two valves, registers, condensers, and a pilot light (Appen-
dices B and C, Walter, 1953.)
Technical description of M. Speculatrix
M. Speculatrix is intended as a model of elementary reflex
behaviour, and contains only two functional elements: two
receptors, two nerve cells, two effectors. The first receptor is a
H
106 THE BRAIN AS A COMPUTER
photoelectric cell, mounted on the spindle of the steering column
always facing the same direction as the single front driving wheel,
which is one effector. In the dark the steering is continuously
rotated by the steering motor (the other effector) so that the photo-
cell scans steadily. The scanning rotation is stopped when moderate
light enters the photo-cell, but starts again at half speed when
the light intensity is greater the dazzle state. The driving motor
operates at half speed when scanning in the dark, and at full speed
in moderate or intense light. The other receptor is a ring-and-
stick limit switch attached to the shell, which is rubber-suspended.
When the shell touches something, or when a gradient is en-
countered, its displacement closes the limit switch. This connects
the output of the 'central nervous* amplifier back to its input
through a capacitator so that it is turned into a multivibrator. The
oscillations produced by the multivibrator stop the circuit from
acting as an amplifier, so that simple sensitivity to light is lost;
instead, the connexions alternate between the 'dark' and 'dazzle'
states. The steering-scanning motor is alternately on full- and
half-power, and the driving motor, at the same time, on half- and
full-power, the effect of which is to produce a turn-and-push
manoeuvre. The time-constant of the feedback circuit is selected
to give about one-third of the time on 'steer-hard-push-gently',
and two-thirds on 'push-hard-steer-gently*. This gives a prompt
response to the first contact with an obstacle. Though there is no
direct attraction to light in the obstacle-avoiding state, the feed-
back time-constant is shorter when the photo-cell is illuminated,
so that when an obstacle is met in the dark, the avoidance drill is
done in a leisurely fashion, but when there is an attractive light
nearby, the movements are more hasty.
The electrical circuit is shown in Fig. 14. This is only one of
many possible arrangements, but it is probably the simplest in
components and wiring. The photo-cell is a gas-filled type, and
generally needs no optical system, a single light-louvre giving
sufficient directionality. It is convenient to connect the tube
between the grid of the first amplifier tube and the negative side of
the 6V accumulator needed to run the motors. The grid of the
input tube is connected to the positive side of the 6V battery
through a 10 megohm resistor; illumination of the photo-cell can
therefore only change the bias on the input tube from zero to
FINITE AUTOMATA
107
about 4V negative. In the dark the first tube, having zero bias,
passes its full current, and the relay in its anode is 'on*. This
tube is a triode, or a triode-connected pentode. The relay should
have a resistance of about 10,000 ?, or rather less than the anode
impedance of the tube, and a single pole change-over contact. The
resistance of this relay and the anode impedance of the first tube
form a potentiometer which fixes the screen voltage of the second
tube. The anode of the first tube is thus connected directly to the
screen of the second and also, through a 0*5 mF capacitor, to its
grid. This provides a relatively high gain for changes in illumina-
o+45
+ 6
FIG. 14. CIRCUIT OF M. speculatrix. This figure shows the
circuit of M. speculatrix (after Grey Walter).
tion and steady-state amplification when the input is larger. The
effect of this coupling is to permit transient interruption of the
scanning motion when a faint light enters the photo-cell, thus
gradually bringing the model on to the beam at a distance, then a
steady inhibition of scanning when the light is brighter or nearer.
The relay in the anode of the second tube is of the same type as the
first, but the moving contact goes straight to the positive terminal
of the 6V battery, instead of through the pilot light. The stationary
contacts are connected in the same way, 'on* to the driving motor,
'off' to the scanning motor, in both relays. In faint light, relay 2 is
closed momentarily; in moderate light it is held closed, and in
108 THE BRAIN AS A COMPUTER
bright light it remains closed but relay 1 opens, thus providing for
swerving away from a bright light.
The pilot light, which is in series with the moving contact of
relay 1, is short-circuited when relay 2 closes, and is therefore
extinguished when the driving motor is turned to full power and
the scanning movement is arrested by light. When the light from
the pilot bulb is reflected by a mirror into the photo-cell, it is
extinguished, but the disappearance of this light restores relay 2
to 'off', and the light appears again.
Grey Walter tried the interesting experiment of connecting Cora
to the obstacle-avoiding device in the 'tortoise and, as a result of
associating touch with the onset of trouble, it was found that the
whole model would retreat when touched. The education process
involved, in Grey Walter's own words, 'blowing the whistle and
kicking the shells a few times'. This simple sort of associative learn-
ing is of the greatest interest from the point of view of learning
theory.
One special point of interest arises with the combined model,
and it is one of those which justify the construction of hardware
models. After the defensive backing reflex had been conditioned
the whistle was blown and, without reinforcement by kicking, the
flash of light that indicated the activation of the memory circuit
occurred without an explicit eliciting stimulus. This meant that
every time the dodging operation occurred the pink light flashed,
and although this could have been predicted from the blueprint, the
prediction was not in fact made.
But we must curtail discussion of these machines and carry on
to the next model. As in all these cases, the original references
should be used when the full detail is required.
Ross Ashby's model
Apart from Ashby's lengthy justification of the principle of
ultrastability in the design of human brains (Ashby, 1952), he has
produced the well-known 'Homeostat'. This models the process of
ultrastability, and is of special interest to psychologists.
The Homeostat is an analogue computer, and consists of four
boxes with a magnetic needle pivoted on top of each. The magnets
can be deflected from their neutral positions from which they will
FINITE AUTOMATA
109
return to a position of equilibrium, although the return is not
always by precisely the same method. The magnets are connected
to water potentiometers, and the four boxes are interconnected
with each other.
The Homeostat is thus composed of four main units, and the
angular deviation of each magnet constitutes the variables in the
situation. Each of the four units emits a d.c. output proportional
to the deviation of its magnet from the neutral. In front of each
FIG. 15. THE HOMEOSTAT. Wiring diagram of one unit. ^provides
anode potential at 150V, while H is at 180V, so E carries a
constant current. M is the magnet. A, B and C are coils. X is a
commutator, P a Potentiometer, S a switch, U a uniselector, G
a coil of a uniselector and F is a relay.
magnet is a trough of water, and electrodes there provide a poten-
tial gradient. The magnets carry wires which dip into this water
and pick up a potential difference that depends on the position of
the magnet, sending it to the grid of the triode (see Fig. 15). J
provides the anode potential at 150V, while H is at 180V, so E
carries a constant current. If the grid-potential allows just this
current to pass through the valve, then no current will flow
through the output; whereas if the valve passes more or less than
this amount of current, the output circuit will carry the difference
110 THE BRAIN AS A COMPUTER
in one direction or another. So, having been fixed, the output is
proportional to M 's deviation.
The next stage involves the interconnecting of the units so that
each sends its output to the other three. This leads to the torque
on all of the magnets being proportional to the sum of the currents
in coils A, B and C (see Fig. 15). There is also an effect from D
itself as a self-feedback. Each input passes through a commutator X
and a potentiometer P before it reaches the coil, and these determine
the polarity of entry, and the fraction of input to reach the coil.
This system, so Ashby claims, exhibits the important character-
istic of purposiveness, and he believes that the variations in the
manner of achieving ultrastability are a characteristic not normally
seen in machines, but usually seen in living organisms. The point
is well made that organisms show this purposiveness, and any
machines that purport to be humanlike must exhibit such charac-
teristics. In the logical nets of the next chapter we shall find that a
motivational system will exhibit some of the same characteristics as
Ashby' s Homeostat. One cannot but wonder at the possible out-
come of connecting the Coxa-Speculatrix compound to the
Homeostat; it seems that it might, under appropriate circum-
stances, exhibit even more intelligent behaviour, if such connexions
proved to be a practical possibility.
Ashby (1956a, 1956b) has set out a large-scale design for a brain
in terms of step functions and the characteristic of ultrastability
and, more recently still, has argued on behalf of set theory for the
appropriate description of finite automata. This is, in fact, a form of
description that is implicit in our own logical nets. A more recent
set-theoretic description by Beer (1960) is also of relevance here.
Let us next consider Shannon's maze-running machine.
Shannon's model
Figure 16 shows the Shannon's maze-runner which will be
briefly described (1951).
The top panel of the machine shows a maze derived from a 5 x
5 array of squares. There is a sensing finger which has contact by
touch with the walls of the maze, and the finger is driven by two
motors which orient it in a north-south and an east-west direction.
The finger now has to feel its way to its goal.
The finger searches each square in turn, and if it reaches a
FINITE AUTOMATA
111
Carriage wheels
Carriage
Flexible cable
to carriage
Track
Indicating^ lamps -^^^^
~ oo obooo
O O QO
FIG. 16. MAZE-RUNNER. On the panel there is a 5 x 5 range of
squares, these can be rearranged to any desired pattern thus
changing the maze through which the sensing finger must find
its way.
112 THE BRAIN AS A COMPUTER
partition it goes back to the centre of the square and starts again.
The systematic search depends on previous knowledge and certain
strategies. It can also get into a sort of 'neurotic* cycle when an old
solution becomes a part of another path which leads back into
itself.
The strategy involves the use of two relays for each square of the
maze, and they can remember any of four possible directions such
as north, south, east and west. This means that any square has a
special orientation associated with it. Solutions lead to the locking
in of relays, and there are also ways in which the machine can
forget. If, for example, the goal is not reached in a specific number
of moves, then the previous solution is regarded as no longer
relevant, the assumption being that the maze-runner has got into
a cycle.
Shannon's model shows some of the same characteristics as do
the logical nets we are to consider, and it certainly exhibits many
of the simple characteristics of learning. It has, indeed, all the
essential features of a learning machine in the form of a memory,
a receptor system, an output system and is selective in its operation.
Uttley's models
In many ways Uttley's syntheses of finite automata are the
most interesting of all, from our point of view, since the essential
process of classification and conditional probability are both
accepted as necessary parts of the logical net system that we are to
use to analyse behaviour.
Uttley's original classification system had the following pro-
perties: it was based on the sensory system of an automatic card
filer of the Hollerith type. The idea that the human senses worked
on a classification principle had previously been suggested by
Hayek (1952), and Uttley was able to build a simple classification
system in hardware. Its circuit is given in Fig. 17.
The principle is a very simple one, and merely demands that
any number of elements can be gathered together into any or all
the possible sets of combinations of their elements. We can
extend this in both a temporal and a spatial manner by considering
the same element an instant or two instants later as being effectively
a different element in the sets that one is classifying. Since this is
an essential part of our argument on perception and sensory
FINITE AUTOMATA
113
processes, and is going to play a major part in the rest of the book
we shall not pursue it at the moment.
Uttley's second machine (1955) is a conditional probability
machine. This, again, is a hardware representation of a basic
concept that will be taken over into the logical nets. Its essential
ABCD
ABD
x-W 1>
DBC
FIG. 17. CLASSIFYING SYSTEM. This is a simple example of a
hardware realization of a classifying system, constructed by
Uttley, and classifying the inputs, A, B, C and D into every
possible combination.
characteristics are that it is capable of counting different combina-
tions of occurrence, and computing that, given a particular
stimulus a y then the probability of b following is the number of
occurrences of a in the past when followed by i, divided by the
total number of occurrences of a in the past, regardless of whether
or not they have been followed by b.
114 THE BRAIN AS A COMPUTER
It should be emphasized that in Uttley's system we can regard
what he calls the 'tunes' (patterns of occurrences) as being spread
out either spatially or temporally.
It is also of interest that Uttley's work, unlike that of Shannon,
Walter or Ashby, has been explicitly aimed at the synthesis of the
principles on which organisms behave, and less in terms of
actually presenting miniature organisms.
George (1958) has built models that have the same essential
properties as Uttley's two models, but since these were con-
structed in terms of the theory of nets we shall not discuss them
until a later stage in the present work. A model called Flebus has
been built by Stewart (1959), and a model by Chapman (1959).
Chapman's model will be described now, and Stewart's since it
is closely related to logical nets will be dealt with in the next
chapter.
Chapman's self-organizing classification system
The principle of Chapman's classification system differs from
that of Uttley's in its demand that any number of elements can be
gathered together into several of the possible sets of combinations
of their elements, not exceeding an arbitrary number. There is a
further condition: that the several combinations of elements which
can be gathered together shall be those which occur most frequently
together.
At first sight, the limitation on the number of combinations that
can be classified appears to be a simplification imposing an un-
justifiable constraint on the system. However, if we consider a
situation similar to that of visual perception, where the number of
elements is so large that only a tiny fraction of the possible
number of combinations occurs, the economy of Chapman's
system becomes obvious. The condition of relating priority of
classification to frequency inevitably means that the system does
not classify elements as soon as it is conceived, and at that stage it
is therefore not strictly a classifying system. Its structure is such
that, by operating on it with groups of elements, it 'grows', and
learns to classify them.
The technique by which this is achieved in the hardware model
is one of inhibition. Each of the inputs to the machine representing
an element or primitive stimulus is connected to every one of the
FINITE AUTOMATA 115
outputs, representing events, by a number of barely conducting
paths, consisting of threads of cotton moistened with lime water.
When a group of elements is 'fired' by application of a positive
potential to the ends of the cotton threads, the event is registered
by the lighting of several of the output lamps. For each such
event, all conducting links connecting inputs which were not
active to outputs which were active, are rendered less conducting
by the passage of a large current, and the consequent evaporation
of moisture. In addition, the active links are rendered less con-
ducting, at a different rate, unless or until the output on which
they terminate only just fires (i.e. its threshold is only just exceeded
by a small quantity e). In general, if a number of different events
occur, a tendency is observed for the outputs to distribute them-
selves among the events, and eventually to represent each event
uniquely. However, with suitable adjustment of the rates at which
the two sets of conducting paths for each event are modified, it is
possible for certain outputs to respond, not to separate events, but
to several events all containing a common subset of elements. In a
sense the machine has recognized a general characteristic of its
environment.
By careful control of the vapour pressure surrounding the
cotton threads, the machine can be made to forget events which
have not occurred recently, or whose frequency has diminished,
and so allow more frequent events to overwrite them. Although a
system which allows overwriting would cause confusion if used to
store detailed information, it has a very obvious advantage as an
early warning system in an organism whose environment is
changing, and it seems likely that a system of this type plays an
important part in directing attention.
Chapman's machine is significant in itself as a pointer to the
way in which economy can be achieved in a large classification
system; but what is of more importance is that he, like Pask
(1958, 1959), has demonstrated that a very highly organized specific
system can grow from a non-specific medium with a relatively
simple structure, obeying generalized rules of growth.
An interesting comparison occurs between Chapman's model
and the Mark II Cell Assembly of Milner, which will be discussed
in Chapter X.
Another approach to the 'growth nets' which are implied by
(7 10 5\
6 8 4)
5 4 6/
116 THE BRAIN AS A COMPUTER
Chapman's model is through matrices. An input matrix has rows
which represent input elements, and columns representing the
successive states of the input. The initial structure of the net is
given by a structure matrix, a square matrix whose elements
represent the sensitivity of the various links (cotton threads)
between input and output elements. This structure changes as a
function of the input matrix, and there is a series of structure
matrices with links whose sensitivities are changing. For example,
where the critical threshold is 0*10, the following structure matrix
defines a simple growth net with three inputs and three outputs
(the rows and columns of the structure matrix) :
10 5>
8 4
4 6,
Now for input vector (1, 1,0} the resultant output is { 1, 1, }.
The result is that a new structure matrix is formed, and the
elements of Si are all diminished, the links which are fired being
diminished less than those not fired.
This whole problem of matrix description of growth nets is now
undergoing a careful analysis, and will be discussed no further
here.
General synthesis
Obviously if one asks general questions about syntheses of
theories, one is immediately transported back to those theories
from which the syntheses emanated. We should say, though, that a
very important account of the synthesis of two-terminal switching
circuits has been written by Shannon (1949), and this deals with
questions as to which logical theories can be translated into hard-
ware, and it deals especially with questions about the simplest
form that such syntheses should take. This matter is rather con-
cerned with mathematical and electrical engineering aspects of
switching circuits, and will hold no immediate and direct interest
for the experimental psychologist.
Except to say that there have been many other models built
apart from those here briefly discussed, we shall be content at this
point to leave the question of synthesis of automata, and return to
it much later after we have seen more clearly what sort of systems
FINITE AUTOMATA 117
we might next try to convert into hardware models. It should
perhaps be said, from the psychological point of view, that the sorts
of models that are likely to be most useful are liable to be a very
great deal more complicated than anything that has so far been
built.
An alternative method of approaching the same problem
(George, 1957d) is to consider the possibility of programming a
general purpose digital computer with a full description of the
automaton we are interested in, and then feed the inputs into the
automaton that is now inside the computer. The difficulty here is
the inadequate size of memory stores in any of the existing general
purpose digital computers. However, it might be possible to use
this idea in one of two ways, (1) either by enlarging existing
memory stores, or (2) by giving a most abbreviated description of
the automaton. This last suggestion might reduce to a simple form
of mathematical operator, in the same way as when we approxi-
mate to a description of a molecular model by a molar description,
and in turn to a mere mathematical operator or set of operators.
This again suggests the possible usefulness of the work of Bush
and Mosteller (1955).
By use of the same molar theoretic ideas as mentioned above, we
might hope to be able to reproduce, in the future, many of the
best understood psychological variables in an analogue computer,
and study their relations there under various sets of conditions.
This is something that waits primarily on the search for well-
defined behavioural variables, and well-defined relations between
them.
Summary
This chapter has been concerned with introducing finite auto-
mata. It starts by considering the general properties of finite
automata as defined by McCulloch and Pitts and followed up by
Kleene. The form that these finite automata take is that of logical
or neural nets, although of course they could also be regarded as
tape automata, with input and output tape, a scanner, and a storage
system which is either independent or a part of the input and
output tapes.
The next type of automata considered was the net designed by
von Neumann, and this led to a brief discussion of his treatment of
118 THE BRAIN AS A COMPUTER
error and the control of error in automata. Von Neumann's
automata had the interesting property of being defined in terms of
a single basic element, the Sheffer stroke.
The second half of the chapter deals with the synthesis of
automata, and we considered a few well-known and representative
hardware models built by Grey Walter, Ashby, Uttley, Shannon
and Chapman.
In this chapter the microscope has, as it were, been turned on
to that part of cybernetics that is concerned with constructing, in
paper and pencil and in hardware, models of behaviour systems.
These models are of both conceptual and general methodological
interest, and from among the conceptual models we are interested
in models which predict behaviour accurately. Ultimately, of
course, we are interested in the particular model or set of models
that bear structural as well as behavioural similarity to the human
being.
CHAPTER V
LOGICAL NETS
WE shall now develop a general notation for the use of 'logical
nets', as we shall call them from now on. These are essentially the
same as the neural nets of the early sections of the previous
chapter; they are finite automata, and we are interested in the
pursuit of effective methods for constructing psychological
theories, rather than in developing a mathematical theory for its
own sake, or in the logical or philosophical aspects of the analysis.
Using such means, our interest lies in improving their predictive
value, as well as in their property of allowing easy revision of
existing psychological and biological theories. This can be done by
making clear the assumptions and the process of theory construc-
tion.
After we have outlined the principles on which the nets are to be
constructed, with suitable illustrations, we shall proceed to a
preview of the sort of finite automaton we need to reconstruct
organisms in terms of the known experimental psychological facts.
These are to be thought of, initially, as being broadly descriptive
or molar only, and not until later chapters shall we start to con-
sider possible neurological interpretations of these models.
We shall not only attempt some sort of preliminary reconstruc-
tion, but we shall also consider existing theories of cognition in the
light of the models we are using. Such theories of learning as those
of Guthrie, Hull and Tolman are typical of those we have in mind
(these theories will be discussed on pages 179 to 234) to begin with,
but the later modifications of Hull by Spence, and the more recent
theories of Seward, Deutsch, Broadbent and Uttley must also be
considered.
We wish, then, to outline an automaton that mimics human
behaviour; to build a machine which is capable of learning, not
merely by utilizing what has been built into it, but also by acquiring
information to which the machine is exposed, and using this
120 THE BRAIN AS A COMPUTER
information predictively. We must therefore 'build in' the capacity
to learn, and not the details of the learning itself, as this is essential
to adaptive behaviour. However, we shall not pursue this general
discussion here, but rather we shall consider how the psychologist
may use his information in building up a conceptual nervous
system in the form of logical nets.
We must first assume certain properties of a somewhat simplified
character about the net we are going to construct, in the same way
as did McCulloch and Pitts. We can then develop and test the
suitability of the construction principles as we compare the nets
with what we know of actual behaviour and neurology. The com-
plications of individual differences can then be introduced.
Just as physics started by considering ideal spheres, or ideal
particles, neglecting moments of inertia, and friction, so we must
start with some idealizations, as we have already done with
neural nets.
Our building bricks we shall call 'elements', rather than neurons.
These are intended to be interpreted later as neurons after the
principle of Braithwaite, which makes the elements initially
formal symbols like those used in symbolic logic. These elements
are connected by wires or fibres of two sorts: input fibres and
output fibres. Impulses are assumed to run down these fibres in
one direction to elements which are strung together in the form of
a net.
Briefly, and informally, the principles on which these nets
operate are as follows : Each element is assumed to take the same
time to fire (an instant), and to be refractory for just that instant of
time which is the same for all elements. Each element has a thres-
hold value that has to be overcome before the element will fire.
Furthermore, two sorts of inputs can occur: one that will excite
and help to fire the element, and one that will inhibit and stop the
element firing. These will be called excitatory and inhibitory
fibres respectively (represented by closed-in triangles and open
circles in the diagrams). If the threshold of an element is only 1,
say (see Fig. IA), then it is excited by the firing of the single
excitatory input. If there are more inputs, and the threshold of the
element is still 1 (Fig. IB), then the element will fire if there is
one more excitatory input firing than inhibitory inputs.
If the threshold is more than 1 , say, 2 or 3, then the condition for
LOGICAL NETS
121
FIG. IA
FIG. IB
FIG. Ic
FIG. ID
FIG. IE
FIG. 1. LOGICAL NET ELEMENTS. Figure IA shows the simplest
element which simply delays an impulse for one instant. IB shows
five excitatory inputs, and like IA, has a threshold of 1. Ic has a
threshold of 2 and since it has only one input it can never fire.
ID fires if either input fires and thus if we label the inputs A and
B and the output C, the equation for firing is C t+1 = A t v Bt,
where s means *if and only if' and v is the logical c or'. IE shows
the logical 'and' with formula. C t+1 s= A t . B t .
122 THE BRAIN AS A COMPUTER
the element firing is that the number of excitatory fibres firing at
any instant must exceed the number of inhibitory by the amount
of the threshold. By this token, Fig. lc will clearly never fire
because there is only one input, and it needs at least two to fire
simultaneously to overcome the threshold. Figure ID will fire if
either one of the inputs fires, whereas Fig. IE will fire only if both
the inputs fire together.
What is extremely interesting about these nets is the fact that
they can easily be built by using the ordinary relays, or two-way
switches, so common in electronic engineering; but they can also
be taken to represent the ordinary relations of simple mathematical
logic. For example, Fig. ID fires if either of the inputs (let us call
these A and J5) fires, and this represents the logical connective
'or'. If we call the output fibre C, we can say that C fires if either
A or B fires, and since we mean the 'or' to be 'inclusive', then it
will fire if A and B both fire as well as if either A or B fires alone.
In symbols,
C ss AvB (1)
where ' = ' means 'if and only if, and V means (inclusive) 'or'.
By exactly the same sort of reasoning Fig. IE represents 'and'.
Thus, using the same lettering as for Fig. ID, we can say that C
fires if and only if both A and B fire together. In symbols,
C^A.B (2)
where V means 'and'.
We can write the formulae for any elements whatsoever in the
same logical terms, and could thus replace all our nets by formulae
precisely as in the previous chapter, and rather as geometrical
figures can be replaced by their equations in Cartesian coordinates.
It will be noticed that A and B must fire simultaneously for C to
fire, and this can be brought out by using time-suffices in our
system. Thus, instead of (2) we could write:
Ct = A+-\ . Bt-i (3)
The fact that these nets are correlated with logical notation is, of
course, the reason for calling them logical nets, and later we shall
wish to give them an interpretation as nerve cells, axons, dendrites,
and the like, and we must even now bear in mind that this is our
ultimate aim.
LOGICAL NETS
123
We shall pursue the logical notation to some extent in terms of
those branches of logic already described in Chapter III; it
involves no more than the prepositional and lower functional
calculus. The value of the mathematical logic is that, when the
subject becomes very much more complicated, it can be regarded
more and more as a branch of mathematics, and we can be led on
from mathematical logic to other suitable mathematical techniques.
Our discussion here is entirely for experimental psychologists and
biologists, and it is therefore concerned primarily with the manner
of interpretation of such simple nets, both as molar and molecular
models.
The elements mentioned above, and their type of connexions,
are typical of the elements in all the nets in which we are interested.
FIG. 2. LOOP ELEMENT. A simple loop element which once fired
continues to fire itself indefinitely.
They are all elements which are capable of being in one of two
states, that of excitation or inhibition. They are, as we put it, either
'live' or 'deaf. However, we find it convenient to add to our
number of elements, or rather, to consider one other kind of
connexion; this is illustrated in Fig. 2. These are what McCulloch
and Pitts called 'circles' (the element M^, and were illustrated in
the formulae of Fig. 2 of Chapter IV, in a discussion of indefinite
events.
Here the output fibre is also part of the input of the element.
This is very important in that it could be interpreted as a primitive
form of remembering. The element, when fired, will go on firing
itself until some inhibitory later stops it firing. If one has such a
'looped' element, or loop element as we shall call them, and that
124
THE BRAIN AS A COMPUTER
loop element has no inhibitory fibre as part of its input, or if the
threshold number is always greater than the number of the
inhibitory inputs, then of course the loop, once fired, will never
stop. It will not be possible for the element to erase this particular
'memory'. If, however, we added another input fibre capable of
inhibiting the loop element, then, of course, the loop element's
firing could be stopped. Figure 3 shows this simple element.
Bearing in mind an ultimate neurological purpose, it is natural
that we should think of a whole network of such elements as being
capable of division into input elements, inner elements and output
elements. It should, however, be noted that the input elements have
output fibres and input fibres which are free at the other end;
FIG. 3. LOOP ELEMENT. This is the same as Fig. 2, except that
we have added an inhibitor input that can stop the element
firing if necessary.
output elements have free output fibres ; and of course the inner
elements are free at neither end, for they have both input and
output fibres connected to other elements.
Let us next consider one of the simplest significant networks.
Figure 4 shows such a simple net which has A and B as input
elements, C, D, E as inner elements, and F, G and H as output
elements.
First let us see what happens. If A fires alone it fires F directly,
and also fires D which fires an ineffective inhibitory into E.
If, however, A and B fire together, then C is fired and not D,
and this fires E which then goes on firing until A is fired alone
again, and then the inhibitory fibre from D becomes useful in
LOGICAL NETS
125
stopping the firing of E. This erases the memory, which was that
A and B had fired together. The importance of this is that if A
fires alone after A and B had fired together, then G would have
been fired without the need for B to fire. This process is a simple
analogue, or representation, of a conditioned reflex, and is, of
course, a logical equivalent to Cora (see page 105).
Consider A as the unconditioned stimulus and F as the uncondi-
tioned response to A, and G as the response which can become
conditioned to A. This conditioning will take place when A and B
have fired together, so that, in the future, A firing alone will fire
G y which it would not have done previously.
FIG. 4. LOGICAL NETWORK. This is a slightly modified version of
Fig. 1 (Chapter IV) and is a 'sign* or 'association' net which
associates the firing of A with the firing of J5.
Since conditioning experiments will frequently be mentioned,
let us say straight away that we are thinking of the typical experi-
ment whereby a flash of light, say, which is to be the conditioned
stimulus, is associated with the act of salivating, this itself being
the unconditioned response to the unconditioned stimulus of the
smell of food. Salivating then will become the conditioned
response to the flash of light if light and food occur together for
some number of trials. Extinction of this association will occur
subsequently unless the flash is reinforced from time to time by the
presence of food.
We would emphasize that the above interpretation is for illustra-
126
THE BRAIN AS A COMPUTER
tive purposes. The net of Fig. 4 has, of course, a very short
memory, since it forgets as soon as either A or B fires alone.
Although the next firing of A alone will elicit G, it will do this
once only, which means, of course, that the association is soon
extinguished.
As one would expect, more complex nets can and have been
constructed, nets that will remember for any number of times we
want them to; such, for example, as will remember either A and jB
FIG. 5. BELIEF NETWORK. We have referred to this network
which is an extension of Fig. 4 (showing more loop elements
connected in a particular way) as a Belief-net or jB-net. In
general it associates any number of inputs and counts the
degree of association to any extent.
together or either of them apart. It is possible, also, to construct
nets that associate events like A and B even if they do not happen
together.
So much for the basic informal idea of nets. Not only do they
seem to mirror, or be capable of mirroring, some of the properties
of nervous tissue, but they can now be used as tools for research.
We shall now give a somewhat more rigorous account of the
principles upon which these logical nets are to be constructed.
Figure 5 illustrates a simple association net based on the same
LOGICAL NETS 127
principle as the net of Fig. 4. This is the net we have elsewhere
described as a 5-net (George, 19S6a, 1957a, 1957d), and is to be
thought of as the basis of the C-system. The terms '.B-net' and
'C-system' in the model are to be interpreted respectively as
belief-unit or belief (a theoretical term) and cognitive system in the
theory.
The equations of the J3-net element by element, in terms of
its firing conditions, are as follows :
(4)
(5)
(6)
ft = (M-i - ~#-i) v (ci-i . (Jajci.!
. ~(U-i v l|-i)) (7)
In deriving (7), use is made of the obvious simplifying condition:
*0~(lJ*lf) (8)
Then the generalized equation for any number of ^-counters
(the name we give to sets of ^-elements) is :
5s(*J_i.#tJ.(a)4-i) (9)
(In equations (1) to (6) any delay elements (see Fig. IA) that may
be necessary are ignored.)
The generalized equation here makes use of (8), and of the
obvious condition that results from the fact that if c n+I fires, then
c n must necessarily be firing. Similar equations can be derived
for the {/-counters (as we shall call the sets of J-elements), and a
final condition on the 'key' element, (ab) 1 in Fig. 5. The primed
notation always indicates an output element, and the combined
primed elements are the 'key' elements. These key elements will
be composed of every combination of all the primitive inputs a, b,
...,n that the system contains. The final condition on the key ele-
ment (ab)' is:
(ab)' = (( . bt-i . 4-i)
v (flfr-i . bt-i) v (a t -i . c}_!) (10)
v (bt-i . 4-i) ~^-i)
We will next show that our methods of devising these J5-nets are
perfectly general, and that we can cater for any number of input
fibres, and can count to any number of combinations whatsoever.
128 THE BRAIN AS A COMPUTER
The methods for counting can be extended indefinitely; this
should be self-evident, for the counters are essentially linearly
connected, and any number can be added to either the c- or rf-
chains. By 'chain' we mean simply a linearly connected set of
elements. It is also obvious that we can think of the inputs as any
number of the full set of possible combinations of any finite set of
inputs, a fact which disposes of the only serious question posed by
the need for generalization, that of the counting of any number of
inputs.
In considering the net so far described it should be borne in
mind that events of duration (or length) 1 are the only ones counted
where the distinction is made between a.b and either ~a.b or
a.~b, and there is no counter system for ~a.~b. Elements of
threshold could be easily introduced to allow the counting of the
last sort of event, and a distinction could easily be drawn between
events a.~b and ~a.b if it were necessary; that would simply
involve a separate chain of counter elements. Indeed, as we increase
the number of inputs in the system, so we shall need new chains of
counters. In fact we can radically reduce the number of elements
by indulging in a binary counting system which records directly,
in numerical form, the number of times a particular event has
occurred.
Another distinction we may need later will be that between
classification systems which count all events, and those that count
only 'positive' events. By 'positive event' we mean an event of
which the description does not include any c ~' symbol. Thus we
include events of the kind a.b> but not of the kind ~a.b.c. which
would merely be regarded as b.c. For these positive counters the
problem of generality is easily solved, since we only need as many
fe-elements as there are combinations of events, and they can be
fed straight into the chain of counters. The first case, where
'negative' events occur, calls for a shade more care since we now
have to multiply greatly the number of /-elements. Thus, for
three inputs, where all the combinations of events are to be
counted, we must have an /-element for the events a.b~c,
a.~b.Cy ~a.b*c, etc., and, given these /-elements, they can now
be attached to chains of counters as before.
We might now say a few words about the duration of events.
We are normally interested, in behaviour theory, in the relation
LOGICAL NETS
129
between events that occur close to each other in time, but not
always occurring simultaneously. This suggests that we should be
concerned with events of greater length than 1, and it can easily be
seen that we can arrange to count events of any duration whatever
simply by multiplying the number of inputs for each and every
combination that occurs at as many different instants as is neces-
sary. This, of course, would be grossly uneconomical in practice,
and we shall be generally concerned with events of relatively
short duration and with events occurring at successive intervals
of time.
FIG. 6. AN EXTENDED BELIEF NETWORK. This network is a farther
extension of Fig. 5 and shows the possible temporal relations
between two inputs A and B*
This whole question of temporal order in events becomes
extremely complicated, and it will be referred to in more detail
from time to time throughout the rest of the book. A consideration
of uncompleted tasks and delayed responses, especially in human
behaviour, reminds us of the problem, and this immediately
raises the question of the relation of the memory store to the
classification and control system.
Figure 6 shows the classification of events of length 2, where
each event is composed of all combinations of A and B and their
negations. In the figure, not-^is indicated by A. The boxes
containing the events such as AB/AB represent sets of counters
130 THE BRAIN AS A COMPUTER
arranged as in Fig, 5, or any other of the many possible arrange-
ments.
Classification systems
We must now describe one important aspect of logical nets ; it is
that part which is closely concerned with perception, and the
sensory systems of organisms.
Figure 7 shows a simple classification system for positive events,
as we shall call it. We believe that this is the basic principle on which
bed
FIG. 7. A CLASSIFYING SYSTEM. This is a simple illustration of a
classifying system with respect to four inputs. This is not of
course the only manner in which such classifying systems can
be constructed.
perception works, even though a very powerful set of economies is
certainly employed in living organisms to reduce the necessity for
complete classification. Indeed, classification is seldom complete; it
is built up in stages involving different sensory modalities. Of
course the same sort of argument applies to our association net or
B-net. All we have wished to show here is the beginnings of an
effective method for the construction of learning systems. We do
not think that this is necessarily the method employed by the
organism, but it is a method in terms of which we can reconstruct
theories of cognition, and this we shall do in later chapters.
LOGICAL NETS 131
The order of presentation of the argument will now be to
proceed from sensory processes, or input systems, to control and
storage systems, and finally to the output systems.
The input system is in some sense a classifying system. This
matter has already been dealt with to some extent elsewhere
(Uttley, 1954), so here the description will be somewhat limited.
Let us conceive, initially, of a large number of 'primitive' inputs.
These are equivalent to the simplest distinguishable elements in
our world. They record, in the form of the firing of, say, cones and
rods, spots of yellow, green, black and white, and so on. They are
very simple in that they merely record, or do not record, character-
istic elements of the environment according to whether or not the
appropriate inputs are stimulated (Price, 1953). From these
primitive inputs, by classification processes, we build up the sense-
data and the physical objects and concepts with respect to our
environment and ourselves. It will later be seen that this picture
of perception is probably over-simplified, and it is probable that
classification, as here depicted, begins at a later stage in the
organization (see Chapters X and XI).
Let us name these primitive inputs 0, &,..., n, or, where we have
to consider very large numbers of them, #1, #2, .-., a^ fa, 62, ..-,
b m , d, - > and so on. We may separate the different sensory modali-
ties by saying that the sets
n m
S at, Z fy, ..., etc.
represent the different special senses, viz. seeing, hearing,
touching, etc. Although this represents a theoretical interpretation
of the model, it obviously entails no difficulty of any sort at the
model level. The set Zai may be made up of elements of the visual
classification system, Sbi made up of elements from the auditory
system, and so on.
In the above manner we can acquire the mathematical means of
defining a classification and control system that may have as many
inputs as we please, and cater for every combination of the input.
It will be capable of counting as many of the conjunctions and
disjunctions of any of the combinations we please by the illustrative
methods already described.
132 THE BRAIN AS A COMPUTER
We shall need, in order to discuss the actual construction of
particular finite automata of biological interest, to have certain
simplifying concepts. The use of molar inputs and outputs has
already been described. (We shall generally use the same letter for
the output as for the input where the output letter is primed. Thus,
if a has a directly connected output then it will be a', b will have b',
and so on.)
The next simplification will be to call any set of counters that
connect any combination of inputs a J3-net. The words S-unit
have also sometimes been used instead of fi-net (George, 1957a,
1957d), the idea being that these fi-nets, in keeping with our use
of molar and molecular stimuli, can occur on either the molar or
the molecular level, and are the organs which, in iterated fashion,
make up almost the whole automaton; they are somewhat similar
to the packages that are used in the construction of digital com-
puters. In practice, we may wish to add a further long term
memory store to the system, but this need depend on no more than
what could be 'tapped' from the looped elements, although, by
applying 'logical' principles, it will be able to derive information
from that 'tapped* input, which will greatly increase its stored
information.
A further word of explanation is here appropriate, although still
couched in general terms. The storage system will derive its
information directly from the input classification and the other
parts of the storage system. These bits of information will be in the
form of events (or, in an ovbious sense, event names) of various
lengths. The central store will then be able to put these events
together to form new events (or event names), as illustrated in a
very simple case, for events of length 2, in Fig. 8. This figure, of
course, shows only a sample of the possible elements and con-
nexions.
The principle is straightforward. An event name of length 2,
A/B (where '/' means 'followed by'), can clearly be stored, as
can event names A/C, B/D, D/B, etc. Now it seems clear that there
is an important relation between A/B and D/B, for example.
Both lead to B, and therefore must be associated. Similarly, if we
set up the association C/J5, then AjC and C/JE taken together
may define an association A/E.
If we can now associate 'words' with event names, and construct
LOGICAL NETS
133
sentences, then we have the possibility of deriving logic and
language. So far, this task of the reconstruction of a complete
language on these lines has not been attempted, although we may
expect to find such attempts being made in the future.
The need for economy in storage space will also demand a
process of generalization that depends upon recognizing similari-
ties among differences and differences among similarities; this is
implicit in a classifying system. This general principle of classi-
fying events, besides enabling recognition to occur, also enables
\
1
A/[
5
By
'E
c
/E
(
i
4
4
1
[
I
I
A/
8
A/
'C
3/C
B/C
)
C/
D
\
\
i'
\
1
L
H
LJ
i
FIG. 8. AN EXTENDED CLASSIFYING SYSTEM. This applies the
classifying principle to events that are already at least of length 2.
Thus the classifying principle permits of drawing inferences by
association. As an illustration, if A IB and BID have the common
element A ID, this may be fired if A IB and B/D have both fired
together or even if they have been fired at any time at all. The
figure only shows a few sample connexions.
reasoning to occur, although here we are not actually suggesting
which of many possible forms the actual associative processes
necessary to reasoning may take in the human organism.
We must also have a motivational system (M-system in the
model language) which, in keeping with the basic 'needs' of the
organism, decrees what is useful to it, and what shall be retained by
the conjunction- and disjunction-counters, and what shall not. In
this respect the equations (and all that has been said so far) are
oversimplified, since there must be added the motivational inputs
134 THE BRAIN AS A COMPUTER
and outputs which fire into all the inner elements of a -B-net.
There is therefore some increase in the complication of the neces-
sary and sufficient conditions for an element to fire.
A 5-unit will exist to connect any subset of inputs whatsoever,
and these units will be elicited in a definite temporal pattern. Let
us consider a definite pattern of events, and suppose the occurrence
of the following combination of stimuli:
abejdki-fridt-abelopq-
or more briefly
' B-D-G-
In fact such patterns will be frequent and in enormous quantities
so let us make up a longer slice of behaviour:
J?--G-JB- T- C/-S- U-K-L-O- C7-S-F-P- U-E-
which might be a short series of discriminable activities, say the
mere recognition of some familiar object. This sort of series should
immediately remind the reader of a Markoff process (Chapter II),
and suggest a whole field of new possible interpretations.
It will be appreciated that many hundreds of counters will, on
the theory, be fired even for such a simple action. Many B-units
will register a large number of conjunctions, and also a certain
number of disjunctions.
It should be noticed that, with the simple use of delay elements,
we can, on our c- and ^-counters, count events that fire as remote
from each other in time as we please. 'Together', therefore, does not
necessarily mean 'simultaneously'.
But there are many complicated considerations that must be
discussed before any progress can be hoped for from the mathe-
matical methods. First, it is essential to try and fix the ideas
implicit in the theory.
Before pursuing our interpretation of the cognitive aspects of
our automata, we should perhaps give a block diagram (Fig. 9) of
the machine we are describing. The cognitive system or control is,
it will be noticed, somewhat similar to (or analogous to) the
cerebral cortex in so far as it is the highest level in the automaton.
We shall discuss the motivational system, the emotional system
(part of the rest of the internal environment) and the memory
system (also really a part of the cognitive system) later, and in the
LOGICAL NETS
135
meantime we shall discuss the cognitive system, or immediate
classification and control system.
The automaton conveniently divides up into a control-system
(this is referred to as a cognitive-system, or C-system at the level of
FIG. 9. THE BEHAVIOURAL MODEL. This shows the fairly arbitrary
distinctions that have been made between the store, the control
and the motivational system. All in the brain is really in storage
except for incoming and outgoing messages,
the model), a motivational-system (M-system), and we may
include an emotional-system (^-system) which is closely related to
motivation, apart from the permanent memory store referred to
above which, as we have already said, is a part of the cognitive-
136 THE BRAIN AS A COMPUTER
system. The classification of inputs and outputs, involving percep-
tion and organized responses to stimulation, will be regarded as
being a part of the control system, as will be the high-speed
memory store.
We shall start by describing the most important part, which is
the C-system. There will be some obvious point in saying that the
C-system is the name of that section of the model which will
subsequently be interpreted as the control or cognitive system in
the automaton.
Clearly, if we restrict ourselves to the memory of the loop
elements of our control system (Fig. 5), then we would have to
face the fact that the number of loop elements available directly
affects the nature of the probability on which the automaton will
operate. Before clarifying this point, let us make explicit the
importance of the conditional probability on which the automaton
will operate.
Let us suppose that a particular 'physical object' using that
term in the broadest sense that philosophers of perception would
use it is represented by a combination of primitive inputs
abcdef, say. We shall call this set A, for short. Let us suppose
further that some number of physical objects B, C, ..., N follow
each other in that order. Then there are relations of an important
kind that connect these physical objects.
The first important sort of relation that our system has to con-
sider is the perceptual one, and this means, in the main, the
problem of recognition. Given some properties a, b, ...,n, what is
the probability of their belonging to some particular set A, say?
This implies the use, by counting as above, of probabilities which
suggest the appropriate set, of which what is sensed at any
instant is a subset possibly, of course, an improper subset.
We think of the operation of perceiving as a definite process of
analysing and classifying the environment ('sampling* is perhaps
the best single word to describe the perceptual operation), and as
being spread over a finite time. It is an ordering process in which
the probabilities vary as the information about the members of the
set increase, wherever that is possible. The tachistoscope on one
hand, and the close analysis with ruler and calipers on the other,
represent two extremes in this regard. Ideally, however, the
process of perceiving the word 'sensing' will be regarded by
LOGICAL NETS 137
some as more appropriate for this seried operation can be
represented by a series of probabilities
tending to 1 in the limit, where ultimately each and every property
of the finite set is identified. In practice, of course, this hardly ever
happens, and we recognize objects (to think now of our inter-
pretation) by small parts of them, or at a glance, in a manner
familiar to those acquainted with Gestalt theory. Roughly speak-
ing, the more familiar the object the more quickly we recognize it,
and this is simply because a certain subset of properties abcd y say,
is nearly always a subset of A. This model will be somewhat modi-
fied later, when we consider problems of perception in greater
detail in Chapters IX and X.
Now the basis of this mechanism is clearly supplied by the
counting and classification system described the model of the
cognitive system. In practice, however, recognition will also
depend on context. All that this means is that the probabilities
associating different elements with different sets must be the
basis of further probabilities associating different sets with each
other. This, of course, will cut across the different sensory modalities.
The automaton's behaviour at any instant clearly depends on
two factors : (1) the current state of the environment, both internal
and external, and (2) the whole past of the organism, as stored in
the memory store. We must, then, conceive of the counting as
leading to responses that are purely classificatory. This storage
operation does not cause overt response, although naturally overt
responses occur as a result of these classificatory responses after
classification (perception) is complete.
All that has been said in this chapter so far is aimed at showing a
method of describing artificial organisms or automata. These
automata are capable of being described precisely in logical terms,
and of being constructed in terms of two-state switches. The
methods so far discussed are quite general, and designed merely to
show the reader that the associations necessary to learning and
perceptions are easily obtainable in such a system.
From this point on, most of the rest of the book is concerned
with bringing such general methods into line with the empirical
facts of behaviour and physiology. This is not to be done by
138 THE BRAIN AS A COMPUTER
writing specific equations for larger and ever larger nets this
would become too complicated but by making the principles of
more complex operations of behaviour clearer, in terms of these
simple associations. Ultimately, no doubt, the more complex nets
must be specified, but this may necessitate the use of a computer,
probably with the help of an automatic coding procedure.
Theory of perception
The theory for the above model for perception is, strictly
speaking, the interpretation placed on the model. In fact, the
theory was formulated first and the model provided subsequently.
The theory of perception here stated, and now to be briefly
described, is molar, and is itself subject to reinterpretation on the
molecular level. It will be seen to be generally adequate as an
interpretation of the net model, and is believed to be consistent
with many of the observable and intuitively known facts of
perception. We would remind the reader again that this model and
theory are intentionally general, and are not yet being discussed in
detail; we are now mainly concerned with illustrating method.
Perception is regarded as being the process of interpreting the
messages that arise from the various sensory sources. This implies
that we should regard the operations of sensing, perceiving and
believing as on a sort of continuum in which the individual is
not necessarily able to distinguish various points or intervals.
The act of perceiving is represented as an organic process of
selection and interpretation. The selection is partly due to the
limits of application of the various senses, and partly due to the
'set' of the individual, which means that the information in the
store (representing his previous experience) will operate in con-
junction with what is momentarily perceived.
Perceiving is thus interpreted as a process of elaboration of
sensory input, where there is a selection from all the potential
stimuli in the environment, and where there is a counter system
(store) for each of the items perceived. The counting, it should be
noted, may well be approximate (Culbertson, 1950), and certainly
receding of the store and other factors mainly concerned with the
economy of storing information, will also arise (Oldfield, 1954).
The responses for this system are classifactory and are themselves
LOGICAL NETS 139
stimuli to the overt response system. We have chosen to describe
this in the terminology of beliefs. We say that perceptual beliefs are
aroused as a result of the categorizing process that perception
serves. These are ordinary beliefs, although distinguished from
beliefs-in-general in so far as they are directly concerned with what
is perceived, whereas other beliefs may be derived, by other
cognitive or logical operations, from what is already stored.
The word 'belief is used here as a theoretical term and in the
behaviouristic manner, although it is hoped that it will be capable
of being interpreted as a formalization of the 'belief ' to which we
refer in ordinary language. To avoid confusion, let us think of
belief as a purely theoretical term which is closely related to a
hypothesis (Krechevsky, 1932a, 1932b, 1933a, 1933b) or an
expectancy (Tolman, 1932, 1934, 1939, 1952). We shall in fact use
the word expectancy for an activated belief. For example, we shall
want to say that there are various beliefs stored at various levels of
generality, and that at any instant an activating stimulus will arouse
some of them, and those aroused are called expectancies. The
arousal of beliefs, as well as the strengthening of beliefs by con-
firmation, will depend on the motivational system as well as on the
perceptual and storage systems.
Motivation
Before completing our general description of the control
system it would be convenient to summarize the role of motivation.
The M-system at the model level, as exemplified by the logical
network, is fairly simple, and in fact needs no more than the
designation of Values' to certain inputs. This particular point will
become clearer after the analysis in the next chapter.
The need for a motivational system in the model is clear if we
want the system to be selective, and since our model is to be
interpreted ultimately as an organism, it is obviously necessary that
it should be selective. In the first place, selection must be on the
basis of survival; those activities which are bad for survival are
omitted, and those which are good are included. Connected with
this basic idea of two sets are many other basic motivators such as
food, drink, sex, etc. In the model these are built-in, as they
represent activities that are instinctive or innate, and thus passed
140
THE BRAIN AS A COMPUTER
from generation to generation by genetic means, and they are
elicited by stimulation which will occur in the appropriate
environment.
We can think of the model as having two sets of motivation
chains made up of loop elements, so that any response which is
followed by a reinforcing or non-reinforcing stimulus will, in
effect, associate that response with either one or the other of the
two sets. This will mean that the C-system will not operate its
counting except in conjunction with the motivational effect of the
FIG. 10. A MOTIVATION LOGICAL NET. A simple example of the
way reinforcement could be introduced into a belief net of the
kind drawn in Figs. 4 and 5.
response. Figure 10 shows a sample M-system (with only two loop
elements) connected to our original C-system. Activity of the C-
system, now modified, is dependent on the outcome of the response.
It is again emphasized that these models are illustrative of the
method, and that alone. In fact, all that is required is that some
stimulus in a conjunction set be necessary to the conjunction. That
extra (though necessary) stimulus can be designated the 'motiva-
tional stimulus'. A simpler example will be given later in this
chapter (see Figs. 15 and 16).
At the level of the molar theory, we shall say that stimuli will
LOGICAL NETS 141
not be effective in eliciting a response unless they are satisfying 2
need. Clearly this is not true of the perceptual system, which
cannot tell whether a need is likely to be satisfied until recognition
is carried through. However, here there is some reason to suppose
that the classifying system of perception is influenced by the
motivational state, at least in the 'choice* of events classified. This
suggests the relevance of 'attention*.
Behaviour may be initiated in some obvious sense by motiva-
tional needs, or it may be initiated by external stimuli which have
the effect of creating a need, and this implies a complication that
our model can easily be shown to cater for. This means that
further input elements presumably from internal sources
should activate the system by firing the inputs initially in a random
manner. After learning has occurred, these internal activators will
be themselves selectively associated with other particular inputs.
The present association system can clearly be extended so that a
loop element will fire until such time as a particular input fires and
stops the loop element from firing further. Figure 10 shows such a
simple system, in which D represents the 'need* stimulus, and C
the stimulus that satisfies the need. For learning to take place we
must now introduce the same counters between D and A, B and C
as exist in our C-system (Fig. 5).
Any system of counters that we have described as a cognitive
system would systematically count everything that occurred that it
was capable of discriminating, unless there was some system for
selectively reinforcing certain events at the expense of others. This
is the principle of motivation, and it is necessary for selective or
purposive behaviour in an automaton.
Now to consider briefly the linkage between the M-system and
the C-system. There are many equivalent ways in which this can
be done, and perhaps the simplest now is to dispense with the
k- and /-elements, and join the wires from the left-hand selector
directly to the conjunction counters, and the wires from the right-
hand selector elements directly to the disjunction counters as far as
excitation is concerned, and the other way round for inhibition.
This is not a vital matter since there are many methods, and these
will model many different processes. One alternative method is
shown in Fig. 10.
We shall not give the logical net equations for the new system,
142 THE BRAIN AS A COMPUTER
for it is obvious that these could be derived as has been shown
previously.
Emotion
In brief, we can say of the jB-system that it is concerned closely
with the M-system, being a signal of different degrees of satis-
faction which the organism is experiencing. It has the job of
facilitating the purely organic aspects of behaviour, but it also has
overt manifestations that make it of importance as an index of the
feelings, etc., which are part of our awareness. The whole problem
of consciousness could perhaps be introduced into the system and
regarded as an extra stimulus response activity (probably con-
nected with the reticular system, see Chapter IX), but we shall
not attempt to deal with this here.
Machines in general do not have either motivational or emotional
systems, simply because they are not normally purposive. However,
there are certain purposive and selective systems in being, and for
them the M-system is vital, even the ^-system is vital, if the
systems are to be in any sense autonomous and are to survive.
As far as the human being is concerned there are various
theories about the effect of emotion on his activities. It seems
certain that they have both a disruptive and a facilitating effect.
The main problem is to decide when one and when the other.
Our E-system could easily be constructed in a manner similar to
the M-system, so there is no purpose in drawing up a network for
it. Its role would be to exhibit a set of specified signals as the
appropriate states arise. Clearly, emotion is a factor that will have
to be considered in any model (and therefore theory) of the
individual; but we shall not attempt to take this argument any
further at the level of our logical networks.
Memory
Something must, of course, be said of memory in the theory and
in the model. It seems reasonable to suppose that there will need
to be at least two different stores, roughly comparable to those in a
digital computer: (1) a high-speed counting store which will be asso-
ciated with perception and recognition, and (2) the more per-
LOGICAL NETS
143
manent store where as much as possible of everything that ever
happens to the organism will be recorded. We would like to make
it plain here that we tend to think of the cognitive operations, such as
'thinking*, as being the process of transfer to and from the stores,
although also involving language. This will be discussed later.
Our molar theories of behaviour tell us that in recall there are
simplifications and distortions of memory that make the remember-
ing process almost one of reconstruction rather than of reproduc-
tion. Bartlett (1932) and others have shown these characteristics in
operation, and they can be seen to be connected with set, attention
I 1
FIG. 11. A STORAGE SYSTEM. The simple principle of storing
binary digits by logical nets. All sorts of variations on the same
theme are possible.
and perception. The storage can be organized in a variety of
different ways and, from the point of view of human organization,
the correct method can only be arrived at by experimentation,
presumably at the neurological level. Our purely molar behavioural
account here must be regarded as limited and suggestive; however,
more will be said on this matter in the next chapter.
We shall now say a little about the possible range of models.
Culbertson (1950) has listed some of the network devices that
could be used, and we shall simply say that a system such as that in
Fig. 1 1 would obviously have the capacity to accept information,
and release that information on stimulation.
It could, of course, also be arranged to circulate the information
144 THE BRAIN AS A COMPUTER
released so that it returned to the store again, if necessary. Such a
net is a simple equivalent of the delay line storage system in com-
puter design. Instead of handling words as impulses in mercury
tubes, the words are handled by sets of elements, and the number
of elements in the set dictate the length of the word handled. It is
an open question as to whether what is remembered is coded as an
instruction connecting sets of input elements, or as a number
indicating the conjunction or disjunction of sets of input elements,
where the actual inputs referred to are localized by the anatomical
location of the store, or both. Matters of this sort can only be
settled by further neurological experiment.
Obviously we could store information in a logical net in a
variety of ways; even without loop elements we could arrange for
chains of elements to circulate information indefinitely, and this
again would be similar to the delay line form of memory store. We
shall next consider one or two examples of hardware automata that
are closely associated with logical net theory.
Flebus
Figure 12 shows the logical net of an input and output classifica-
tion system combined. This was the basis of Stewart's automaton
which he has called 'Flebus'. Stewart's aim in building this auto-
maton was partly influenced by the inverse of the well known
Turing game which was concerned with answering the question:
'Can automata behave like humans'?
Flebus has four input channels, each of which may be in one
of two discrete states. Figures 13 and 14 show the hardware of the
input and output classification system.
The programming of the automata sets up plugboard connexions
between the sixteen output sockets of the input net, and the fifteen
input sockets of the output net, but of course the automaton can be
programmed in a variety of different ways. Stewart then used the
automaton for a series of experiments involving the human
operator, the automaton being used to simulate a number of
different situations, such as the use of binary controls in a binary
display situation, routine checks, fault diagnosis, and so on.
The use of the automaton as a simulator involves further special
input and output material, and the realization of simple logical
LOGICAL NETS
145
functions and stochastic processes that can be made as complicated
as we like.
The automaton has great versatility, and realizes some of the
properties we should expect to find in a human organism, although
FIG. 12. A STIMULUS-RESPONSE NETWORK. A stimulus classifying
and response classifying system. The text should be consulted
to understand its significance.
in a very simple form. One of its most interesting features is that it
was constructed directly from logical net diagrams.
George's models
These models, like Flebus, were built directly from logical nets.
The first model is a direct realization of Fig. 5, and shows a
146
THE BRAIN AS A COMPUTER
r-
r~
D
n m
C B A
FIG. 13. FLEBUS. A network diagram for Flebus (see text).
ROE
L^ LjU, ^ ^p^ T^-L^
h h ^i h ^ ^ h u i
T
+ I
FIG. 14. FLEBUS. A further network diagram for Flebus (see
text).
LOGICAL NETS 147
Darticular classification and conditional probability system. Only
:wo inputs are classified, and the memory is only over six events,
3Ut the model can easily be extended, by the use of additional
elays, to include any number of inputs and any length of memory,
[t can also be extended to deal with temporal sequences as in Fig. 6,
md logical associations as in Fig. 8.
This brief statement applies to the first model made (George,
L956a). The second model was built in units whose logical net
liagram is as in Fig. 5, but whose memory has now been extended
.o something near eighty events. There were some twelve of these
inits available, and they could be connected in any way whatever
:o realize a wide variety of different automata. These automata are
capable of realizing all the characteristics already described, and
:ould be shown to demonstrate many of the characteristics of
;imple learning. Some of the units could be regarded as M-units,
ind thus the effectiveness of any association may be made to
lepend on their firing at some time t.
A third and a fourth model are still under construction, and
hese are intended to be used to model the eye and the visual
ystem, on one hand, and simple learning on the other; they are
>oth designed on the basis of blueprints in logical net form. The
nodels were constructed with the idea of trying to find a workable
ind inexpensive method for constructing large scale automata in
lardware. It is clearly easy enough to draw logical nets, but though
hese are sufficient to illustrate effectively the principles of be-
laviour for a large scale experiment, a hardware system is far
sasier to build than to describe in logical net form.
General
The model and theory we have been outlining from the general
)oint of view can be manufactured in a variety of different ways,
>oth digital and analogue; but the interesting thing about logical
lets is the fact that all the essential features of an organism seem
o be capable of being reconstructed in them in terms of simple
wo state switches. Hence there is a distinct resemblance between
he structure of such a switching system and the nervous system.
This, we have argued, is the way models should be constructed:
vith the theory and the intended interpretation in mind. It is this
148 THE BRAIN AS A COMPUTER
property that places logical nets among the most important of the
list of models of behaviour theories that have so far been created.
In this summary we have outlined a model (or method of model
construction) of the human organism in a form that is still idealized
and contrary-to-fact in many ways, but which can gradually be
brought more into line with the empirical facts as these facts are
yielded by experiment. We have briefly discussed an interpretation
of the logical net model in the form of a molar theory of behaviour,
and this was derived independently as a direct result of molar
behavioural experiments. In constructing the molar theory, how-
ever, we had methodological as well as psychological problems in
mind. We want to advance by slow but careful, and accurate,
degrees towards a model that could be interpreted as a human
organism, and the rest of the book will be concerned with develop-
ment towards this end. The model and the theory need the sort of
flexibility that allow them room for expansion both in detail and on
various levels of description.
A further point about the many-levelled methods employed is
that the theory (or theories) itself could, of course, be formalized.
We think of theories and models being connected in a definite way,
and the process of formalization would be the process of showing
the precise logical structure of the theory. There can be no doubt
that all theories should be capable of formalization, but theories can
be formalized to different extents, and this is where we investigate
the coherence, precision, and logical consistency of a scientific
theory. The logical net is a ready formalization in logical terms of a
behaviour theory, although many other formalizations, all logically
equivalent, are possible. In a sense, indeed, they may not even be
logically equivalent, since the use of theoretical terms in the
theory or theory language is vague enough to allow a variety of
possible interpretations.
We may now summarize the methods briefly. A theory in science
certainly in the behavioural sciences may occur at many
different linguistic levels which represent different sorts of levels of
investigation. Behaviour can be described introspectively, in
molar observable terms, or in molecular terms. This means,
roughly: in terms of private experience, in terms of the behaviour
of the organism-as-a-whole, or in terms of the physiological and
biochemical variables. A complete theory will plumb all these levels
LOGICAL NETS 149
and thus allow workers dealing with all aspects of human be-
haviour to draw on all the available information. These theories
can all have their logical structure and consistency analysed, and
are all subject to confirmation, and with the possible exception of
introspective language, this means empirical confirmation by
public test.
In discussing these methods of theory construction we have
introduced a few empirical statements, usually of a fairly general
character, and we have not tried to show very much in the way of
the detailed predictions and applications that follow from these
empirical statements. Space forbids this, hence we have been able
to give no more than a skeleton theory of behaviour which would,
for any particular application, need to be greatly expanded in
detail, and of course be supplied with the individual constants or
boundary conditions that may be applicable.
The idea behind these methods has been Jiat we should have a
flexible framework which would serve as a scientific tool for
research to encompass the experimental work in progress, and also
be precise enough to avoid the pitfalls of ordinary language; and
yet again, be capable of being used as approximate models for
theories, and to answer questions of varying generality at any time.
Some points from controversy in cognition
Since what has been said so far may seem unduly empty to the
experimental psychologist, it should be added that there are various
questions that are to be discussed with reference to the model-
making methods so far outlined.
The first set of problems comes from learning theory, and
surrounds the nature of reinforcement. The manner of our refer-
ences, so far, to motivation hinting that this is a need-reducing
process of the Hullian kind (see Chapter VI) is intentionally
limited; however, we have also mentioned that 'external* stimuli
can themselves produce needs, and for the time we shall leave open
the discussion as to whether stimuli can be associated, or patterns
of either stimuli or stimuli-responses can be learned without any
reinforcement through need-reduction. This whole matter must
wait, for the benefit of those not familiar with this controversy,
until the end of our introduction to learning theory.
150 THE BRAIN AS A COMPUTER
There are other problems that arise in learning theory that are
obviously not going to be settled by the method of model construc-
tion alone, such as the continuity-non-continuity theory of learn-
ing, and the closely associated matter of discrimination learning
and ordinary learning. These, and our second group of problems
which are concerned with perception, will also be considered later.
The perceptual problems are concerned with the various models of
the recognition process.
In general terms it might be said that a variety of different
models could be constructed to perform the operations of learning
and perceiving, and the difficulty is to decide between them,
although that is by no means the whole question.
So far we have dealt with classification and conditional prob-
ability as if they were essential to the final model, and in some form
this is probably so; but there is no certainty that the problem is as
simple, even in principle, as it has been made to appear up to now,
and later we shall certainly seek to fill in the detail, and modify what
has been previously said. It seems likely, for example, that the
Broadbent concept of a filter will be desirable in some form, and
also possibly a more sophisticated relation between response
activities and the central store.
In this last respect Deutsch's learning theory should be men-
tioned. Broadbent has argued that Deutsch's model we can call
it a model in so far as it seems to be capable of realization in logical
net form, which is to say that it is capable of being actually
constructed has links of elements that allow neatly for a need to
be set up with the result that a certain element or set of elements is
kept live until the need-reducer occurs, whether by being seen,
tasted, or whatever it may be, at which moment the link stops
firing, or is switched off. This is something that lends itself well to
logical net treatment. Figure 10 shows, in simple form, precisely
this principle, whereby stimulation by motivational stimuli would
be capable of activating the system, causing it to search for
appropriate stimulation. It could, of course, also be done by
regarding a particular response as a searching response which
gradually fires the set of relevant inputs.
Figures 15 and 16, which Stewart (1959) calls 'reward type
connecting net' show even more clearly this same type of feedback
characteristic in a response system. At the end of Chapter IX it
LOGICAL NETS
151
will be seen that this argument links directly with what is said
there by Pribram on current neurophysiology.
FIG. 15. A REINFORCING NET. A reinforcing system which illu-
strates the simplest sort of reinforcement.
In Fig. 15 it is assumed that S is an input element, S M is the
motivating stimulus, and R is the output element. If S and R fire
FlG. 16. A STIMULUS-RESPONSE NETWORK WITH RANDOM ELEMENT.
A variation of Fig. 12 (see text).
together and the result is to modify the external environment so
that S M fires, then J will be fired, and the feedback loop will be
152 THE BRAIN AS A COMPUTER
kept active until inhibitory inputs stop it. Figure 16 is a simple
generalization of Fig. 15, and also shows the characteristic of
simple learning.
Probabilistic considerations within the deterministic net-
work
The design of the counting system already outlined is intended
to realize an inductive logical machine or automaton, and it follows,
therefore, that the basis of the network is probabilistic. Indeed, the
method of connecting the counters for scoring and erasing pur-
poses will be a direct influence on the sort of probability that will
be realized by the network. A further influence on probability
considerations will be the number of counters available relative to
the number of events to be counted.
It will be easy to see that such a machine or network as the one
under discussion, even with many more counters, will remember
only the recent past if the number of events it has to count is
large relative to the number of counters. If the number of such
events is relatively small, then a frequency probability of the
Laplacian kind will be the outcome.
In the above connexion careful attention will have to be paid to
various approaches to probability, induction, degree of confirma-
tion and degree of factual support (Carnap, 1952; Hempel and
Oppenheim, 1953).
That our automata will be probabilistic, and may also have the
properties of 'growth', is fairly clear, and these properties must
certainly be considered in the next stages of cybernetic development.
Pask (1958, 1959a, 1959b), Beer (1959) and Chapman (1959)
have considered and built systems that are concerned with learning
and perception, and which have the properties of growth, and
some of these will be referred to again in Chapter VIII.
Chapman's model of a classification system, described briefly
in the previous chapter, is very similar to the logical nets we have
described, but differs in that the degree of connectivity of different
elements of the classification system is a function of the experience
of the system. These growth nets are probably more nearly a
model of what actually occurs in the nervous system, although they
sacrifice the logical description and have a mathematical descrip-
tion in its place. Furthermore, it can be shown that anything that
LOGICAL NETS 153
Chapman's nets can do can also be done by logical nets. This is an
important point in that it suggests that logical nets are an effective
method for description, even if what is described is contrary to
biological fact. However, Chapman's methods are certainly of the
utmost importance to the next development in the subject.
Multiplexing
The method of 'multiplexing', which means the replicating of
messages in a system, could be applied to the nets we have
described. This would increase the probability of their working,
even though the basic components were not always working
effectively. Again, we are not intending to give a detailed analysis
of a multiplexed net system, but it is clear that we can follow up
the principle of the executive and restoring organ (von Neumann,
1952) if we duplicate the network wherever it is possible.
In considering Fig. 5 we can see that a duplication of both the
inputs from a and b to k, with an increase of the threshold of the
^-element to 3, would permit the failure of any one of the inputs
to fire at any instant while still bringing about a correct count.
This is an example which can be applied without much difficulty
to all the other elements ; only the /-elements would be recalcitrant
under such changes, although even these, despite some malfunc-
tioning, would still be capable of keeping a proper record.
Another matter that will receive no detailed consideration is the
use of random elements. These can be used almost anywhere at
any time, and the predictability of the network will largely be
destroyed as a result. Their use in explicit design may be some-
what limited, even when the network is explicitly intended as a
model of organic behaviour, since the fluctuating interference of
the emotional systems on the cognitive system is not a random
matter, but a systematic causal one, and random elements would at
best be a makeshift device, for which a deterministic substitute
should ultimately be found. The indeterminacy of the system
would be sufficiently supplied by the interference between one
system and another, and the attempt to retain proper communica-
tion would be made in terms of multiplexing.
Theory of games
There are many things that might now be said to develop
154 THE BRAIN AS A COMPUTER
strategies in logical nets from their beginnings in Game-Theory
(von Neumann and Morgenstern, 1944; Thrall, Coombs and
Davis, 1954), but we must confine ourselves simply to indicating
the link between Game-Theory and logical networks.
First we should notice that various strategies are related to proba-
bility estimates and guessing behaviour, and apply to behaviour at
the level of uncertain information. This means that Game-Theory
will be of special interest at the initial stages of learning.
The behavioural question is with respect to which strategy will
be employed under various conditions, and the answer would
appear to be that we may work out a best strategy on well founded
empirical evidence, but we also want to see how the changes might
be expected to occur in practice.
The occurrence of beliefs of roughly equal value will give rise to
states of uncertainty, but where equality of beliefs exists that is,
an equality of strength in terms of some motivational principle of
maximum reward-minimum effort (George and Handlon, 1955)
there will still remain the component variables that will generally
differ. An individual will evaluate a particular state of affairs in
terms of giving one sort of variable priority over another, resulting
perhaps in the pessimist's or the optimist's strategy, or in other
variations that reflect the varying experience of individuals.
In short, strategy techniques may represent individual differ-
ences (differences in experience) between the same logical nets;
they are individual constants or boundary conditions in behaviour.
They may be brought about in nets, all of which have the same
starting conditions, as a result of a different segment of environ-
ment being encountered, or they may be due to differences in the
stability characteristics of the net, or both. By stability char-
acteristics we mean the extent to which 'rapid counting' takes
place when environmental conditions change a reinforced to a
weakened connexion. The motivational system hastens the slow
counting change in the C-system, and makes it possible to change
habits quickly. 'Rapid counting' is one way in .which response
choice could be changed very quickly with changed circumstances.
Probably this occurs through the use of language in human
behaviour. By 'rapid counting' we mean literally the same effect as
would occur by stimulation of a counter every single instant over
many successive instants.
LOGICAL NETS 155
In psychology the random activity of a Thorndike cat (a cat
confined in a box but able to escape when it solves the problem of
opening the escape door) is followed by a definite strategy in
escape as a measure of success enters the picture. If we change
the reward conditions slightly we may change the connexions
slightly, which will make the difference between the use of one
particular technique and the abandoning of that technique and the
use of another in its place.
The problem which now has to be described in detail, for any
particular net, is : how does the net acquire the strategies it uses
relative to a particular environment? This again is further described
in terms of computer programming in the next chapter.
A description of Game-Theory in general involves infinite, non-
zero-sum and 7z-person games, and these can be developed in very
considerable detail and rigorously defined (von Neumann and
Morgenstern, 1944). Solutions by algebraic and graphical methods
can be devised.
From the point of view of experimental psychology the theory
of games offers itself as a model of some aspects of human be-
haviour, especially of competitive social behaviour, and we would
expect this to be a part of the very extensive model that will
eventually be needed by psychologists.
As far as this book is concerned, this subject and its ramifications
demand a specialist text and although it will be mentioned from
time to time no attempt will be made to apply its findings as a
model. This applies also to other branches of probability, and
more generally to System Engineering (Goode and Machol, 1957).
The literature on this subject is growing rapidly, but the interested
reader will see more easily the importance of its development, and
its relation to our other conceptual models, in those writings that
are concerned with such topics as the effective computability of
winning strategies (Rabin, 1956; Gale and Stewart, 1953).
We would again remind the reader of the tape automata. It
should be clear by now that we can regard the whole operation of
learning, as well as the other cognitive operations of memory,
thinking, etc., as operations on an input tape which is ruled off
into squares. The output tape is now separated from the input
tape, and we may also introduce a storage tape. The problem of
learning is, then, to place symbols on the output tape that change
156 THE BRAIN AS A COMPUTER
the nature of the input symbols. This can be done as an opti-
malizing process ; the storage tape must record the degree of success
or failure of the whole operation and thus operate selectively on
the choice of symbols for the output tape.
Summary
This chapter follows up the general approach to finite automata
which was started in the previous chapter, and further narrows the
interest to logical net systems.
These logical net systems are then brought into line in a general
way with the generally known facts of behaviour. This means that
it is convenient to consider a general model having an input
classification system, a cognitive system, counters and association
units (which we have called Z?-nets), and storage systems, as well
as a motivational system which selectively reinforces the associa-
tions to which the system is exposed. Finally, some mention is
made of the presence of emotion in the system.
The Braithwaite distinction between model and theory is
utilized here, and we use such terms as S-net with the 'idea in
mind' that it could be interpreted as a belief. Although this belief
should be regarded as a theoretical term, like hypothesis or expect-
ancy in Tolman's theory of learning, it is intended that it could
perhaps be eventually interpreted in the sense of the word 'belief
as we use it in ordinary language, but the whole matter is compli-
cated by the fact that the way we use words in ordinary language
can be too vague to be more than a rough guide to usage in a well-
defined system.
The methods of logical nets are used to illustrate various systems
or units which might be useful to mirror behaviour, especially, of
course, cognitive behaviour, with which we are mainly concerned.
Some models in hardware by the author and Stewart are then
described, and the chapter closes with a brief note on Theory of
Games, which is obviously a conceptual and idealized description
of decision making generalizations.
CHAPTER VI
PROGRAMMING COMPUTERS TO
LEARN
IN this chapter we consider the problem of learning from the point
of view of computer programming. This means the programming
of a general purpose digital computer.
Oettinger (1952) has shown that the EDSAC (the computer at
Cambridge) can be programmed to learn certain quite simple
operations. It is important that in doing so it acts on information
that has not yet been obtained when the original programme has
been stored in it, and thus the behaviour of the computer is condi-
tional on certain events not initially known. Let us give a simple
example of the Oettinger type of programme.
The easiest way to regard the computer as an analogue of the
outside world is to think of the input tape as being the computer's en-
vironment. But since tape-reading on the EDSAC is its slowest opera-
tion, Oettinger has divided the machine into two parts, letting one part
play the role of learning machine and the other the environment.
The description of the learning activities can be interpreted in
terms of a series of shopping expeditions, where the shops are
described by an m x n matrix : The elements <% = 1 if shop i has
article /, otherwise ay =0. Any row of the matrix is a row vector
defining the contents of a particular shop (shop vector), and any
column represents the article and all places where it may be found
(article vector).
An 8 x 7 'stock' matrix
rl
1
.0
1
1
1
1
1
1
1
1
1
1
1
157
1
1
1
o-i
0.
158 THE BRAIN AS A COMPUTER
describes 8 shops selling 7 articles. The m th shop vector is stored
in location m+i in EDSAC, where m is the reference address.
Now the learning machine selects a shop number 4, say, at
random, and forms the address m + ik of the corresponding shop
vector, and from this an EDSAC order C m +i k (C m means contents
of storage location m) which collates the shop vector with the given
order vector. If C order is obeyed, then a^ = 1 if the article is in
stock; if ami = 0, it implies that 4 has not got the article j in stock.
This process goes on until a shop is found with the desired
article. Now the computer stores the information, and also a little
extra information about other articles in the shop besides the one
searched for, and this in turn means that a future search will often
be unnecessary, even if the article has not been searched for
before.
This simple sort of learning has obvious limitations that are
recognized by Oettinger, and he sets out some methods by which
the relative inelasticity of the programme might be overcome. It is
sufficient for our purpose that we can point to the fact that pro-
grammes of a contingent character have actually been constructed.
Somewhat similar programming has been undertaken by Turing
(see Bowden, 1953, and Shannon 1950), where this sort of learning
was involved in the playing of chess.
Shannon programmed a computer to learn chess, but neither he
nor Oettinger paid any attention to the parallel problems of
learning as dealt with by experimental psychologists working on
both animals and men.
In this chapter it is intended to outline a series of programmes for
a general purpose digital computer, showing the problems that
occur in getting the computer to learn for itself. In discussing
computer programmes there is some difficulty that surrounds the
actual terminology in which a computer programme has to be
stated. This varies with each machine, and we shall therefore
represent our programmes in the form of flow diagrams from
which it would be easy to write the detailed programme for any
computer whatever. As a matter of interest, the computer used
for these experiments was the English Electric DEUCE, which is a
medium-sized general purpose digital computer, already men-
tioned in Chapter II.
The difficulties that have been experienced in programming
PROGRAMMING COMPUTERS TO LEARN 159
computers to learn are mainly due to the fact that, in programming
them to play a game like chess, you can assume no background
information whatever; it is the equivalent of a newly born child.
Everything it knows has been told it expressly for the purpose of
playing the game.
Shannon says that the computer lacks 'insight', and in such cases
this is inevitable, since insight can hardly be able to operate over a
single problem considered in isolation. But Shannon went beyond
this ; he said that computers were at a disadvantage because they
lacked 'flexibility, imagination, inductive and learning capacity*.
Now it is certainly true that the form of most general purpose
digital computers is inconvenient for many purposes; nevertheless,
with a sufficiently large store a great deal of flexibility can in fact
be achieved. Imagination we can leave for the moment, but induc-
tion and learning capacities can most certainly be attributed to
them, indeed, given them by virtue of the programme.
A computer does what it is programmed to do, and it can be
programmed to perform inductive operations, and to learn. It is
this that is the main purpose of our investigation.
Programming the computer to play a simple game
In Chapter II we outlined the basic idea of programming a
computer, and now we must consider the problem of programming
it to learn. This will be dealt with in roughly the same historical
order as it has occurred, starting with simple, special cases.
We have already implied that what has been called 'insight'
seems at least to depend upon taking over information from one
situation and using this information in another situation. Or it
may be thought of and this is in essence the same thing as
building up general principles which can be seen to apply to more
than a single isolated case.
The result of this consideration is to make it seem artificial to
programme the computer to play one particular game, such as
chess, or noughts-and-crosses. However that may be, it will serve
as an example to illustrate the method to be used.
The computer starts with empty registers, which means with no
knowledge at all, so for its first game it must be explicitly told what
it has to do. The comparison even with a new-born child is perhaps
160 THE BRAIN AS A COMPUTER
somewhat misleading, for that which is innate in the human is, by
analogy, already built into the computer.
We shall first consider noughts-and-crosses, since it is a simple
and well-known game. The first thing is to number the squares of
what we may call the noughts-and-crosses board, using the
numbers one to nine inclusive, but of course in binary form. This
numbering seems to raise a problem, and the actual choice of the
numbers directly affects the statement of a winning position, or
rather, a won game. There are many ways of carrying out the
numbering, but this turns out to be a matter of no importance
since the computer, provided it is told which game is won and
which lost, will still be able to learn to play the game, regardless of
the numbering system used.
This point about numbering the board state is important in
that we want eventually to programme the computer to learn
anything, and not simply restrict the performance to one particular
game. This means that every game must be capable of being stated
in terms of an array, and that the notion of a 'game' must be
extended to what is usually regarded as learning, the game being
simply to learn what the environment is.
A further point to notice is that, even for noughts-and-crosses,
the computer must be able to discover the results of the games it
has been playing; it must know whether the final position is a
winning or a losing one, for this represents the necessity for
confirmation or disconfirmation in terms of what motivates the
organism.
The computer programme must also provide means for avoiding
moves that lead to a loss, and encouraging moves that lead to a win.
This is the very problem of motivation, and it goes back to the law
of effect. More generally, where games are not necessarily won or
lost, we can substitute some principles of optimalization.
To return to the board state, it will be clear that, for the game of
noughts-and-crosses, this is simply the whole of the sensory field
of the computer, and if we seek generality we must avoid giving the
computer special means of looking at certain situations (e.g.
particular games) which are of no use for other situations. We have,
then, a set of quite general elements, as we shall call them, which
we refer to by numbers, any nine of which represent a noughts-
and-crosses board.
PROGRAMMING COMPUTERS TO LEARN 161
The computer must now learn the tactics that allow it to win,
assuming that it is given direct instructions as to how to select the
elements. It will learn that certain ways of carrying out this process
of selection are called 'winning ways', and others losing ways'.
This, however, implies the existence of concepts in the computer,
and it would be better to say, more simply, that when the number
10, for example, is punched at the end of a game, the moves of that
game are avoided in future; and when the number 11 appears, the
moves are repeated. Number 12 is a draw, and will leave the
"tactical values' unchanged. In one sense the whole process is
quite automatic.
The method of storage must be considered next. Clearly, the
registers of the computer must be used in such a way that the
order in which the moves are made is recorded. Associated with
each order there must be a number, which we shall call the Value
number' (the 'tactical values' referred to above), which increases
or decreases according to the success or otherwise of the particular
play. We can, say, add 1 for a win, subtract 1 for a loss, and leave
unchanged for a draw. We shall not, in fact, need to take the whole
nine moves of a game together and give an evaluation to that;
rather, we shall want to break down the total sequence into
subsequences, say, just three, or five, successive moves, starting
with the opponent's move, followed by the computer's own move,
followed in turn by the opponent's.
Among a number of further points that arise is the necessity to
keep a record of the complete set of moves making up a game, in
order that it will be possible to decide whether the moves are good
or bad. This merely represents the fact that we cannot tell whether
a hypothesis is good or bad (true or false) until we have tested it and
seen the outcome. This process of confirmation is simple in the
game situation, but will be more complicated in general. It is true
that we shall want to regard the business of living in an environ-
ment as being much like playing a game ; and thinking, under these
circumstances, is much like the computer playing a game with
itself, playing both for itself and for its opponent. In this case we
may wish to associate two numbers in the interval (0, 1) with each
sequence of moves, if one number is the probability of one event
following another, and the other number is the Value* to the
organism of this particular sequence.
162 . THE BRAIN AS A COMPUTER
The object of the experiment with simple games is to see if the
machine learns the tactics after being told the rules. There is,
however, rather an arbitrary division between rules and tactics,
and it should be said that rules can, of course, themselves be
learned, provided that the computer is able to watch the game
being played, or that a sample of games is fed into it for analysis
into component values. This implies the use of the computer as a
sequential analyser of a stochastic kind (Bush and Mosteller, 1955),
and since this is so, it is convenient to regard a tactic as a rule for
the purpose of our example.
The rule we will now illustrate is well known in noughts-and-
crosses, but to make it, and our subsequent discussion, clearer we
will select a numbering scheme for our board and play some games.
The board will be numbered in the following rather special way
for purposes of illustration:
834
1 5 9
672
This has the added convenience against which there is certainly
a loss of generality whereby a game won is a game in which
three numbers adding up to 15 are selected by one player before
the other. Indeed, from the computer's point of view, noughts-
and-crosses can be redescribed as a game of playing in turn, the
winner being the first player to select three numbers that add up
to 15.
In terms of the above numbering our rule, then, is to check the
board state to see whether two numbers have already been selected
such that there exists a third number, not yet selected, which will
collectively add up to 15. If so, then this number should be
selected, either to win the game or to stop the opponent winning.
A further problem arises in the course of the game. Since we
wish the computer to learn about its environment, or learn to play
a simple game (which, we have asserted, is the same thing), its
speed will be greatly affected by the slowness of its input and out-
put as compared with its computation speed, to say nothing of
the comparatively enormous delay created by its human opponent's
thought. In practice, therefore, it has been found convenient to
divide the computer into two parts, which we will call a and j8
PROGRAMMING COMPUTERS TO LEARN 163
(Oettinger, 1952), programming a with all the rules and the tactics,
and f$ with only the rules, and letting ft learn the tactics by playing
the games. Figure 1 shows the flow chart for the complete opera-
tion.
FLOW CHART FOR NOUGHTS AND CROSSES PROGRAMME PLAYED
BETWEEN TWO COMPUTERS a AND p
In practice a and p can be two different sets of registers of the same computer.
| Place instructions containing both rules and tactics in a. |
Place the random numbers in the storage elements of p. These represent the
Values* of the combinations of moves made by p. j
_L
[Place instructions containing the rules only in
When the board state is presented to a it fills in a letter previously
vacant according to its explicit instructions. Then transfers records of
board state to ft.
When the board state is presented to p, it first checks whether there are
any two numbers among the winning sets of triads, which have both been
filled by the same computer, and if the third number making up the winning
triad is so far unused it must fill it in. Otherwise it proceeds to the next
step.
p now searches through the appropriate registers to find the maximum value
number and makes the move accordingly. 'Appropriate* here means for
games started by a and reading S/8/3/, that all the registers starting thus
and with next move I, 2, 4, 6 and 7 must be checked. There will be a
convention for cases of equal value numbers. It then transfers record of
board state to a provided the code letter for win draw or loss does not
appear. If they do then proceed to next step.
W, L or D having appeared, p puts I. I or on to every move made in the
game and then destroys the copy of each move that he has made and pro-
ceeds to next game, thus returning an empty board state to a.
J
FlG. 1. FLOW CHART FOR NOUGHTS-AND-CROSSES. This IS a
simplified flow chart for the game played between two computers,
both of which know the rules of the game, while only one knows
the tactics.
We next see a series of games played, taking for granted the fact
that the original randomly chosen set of values was attached to the
registers. These can be stated as follows, where the symbol / means
164 THE BRAIN AS A COMPUTER
'is followed by', and the value tables from which we start have the
last number in each case representing the initial random value.
5/1/1 5/8/4/1/1
5/2/0 5/8/4/2/5
S/3/-4 5/8/4/3/0
5/4/2 5/8/4/6/4
5/6/4 5/8/4/7/-S
5/7/1 5/8/4/9/6
5/8/12
5 J9 1-2
If we assume, for the sake of illustration, a fairly regular pattern
of play in a, then, letting L stand for lost and D for drawn, the
following games may result. Note the convention assumed for
taking the first of two tied value numbers.
5/8/4/9/6/L
5/8/4/2/6/L
5/8/4/9/6/L
5/8/4/2/6/L
5/8/4/6/1/9/3/7/D
After this point the game remains constant for a playing con-
sistently. Exactly the same process occurs for a varying, although
it takes much longer to reach a stable state.
It remains to add that the computer can easily perform the
operations described, and it very quickly learns the important
tactical steps, after which it never loses. One more point of interest
should be noted: the computer never has exactly the same state-
ment of the tactics as a, since a plays on a purely deductive basis
following a rule which is verbal, whereas ]8 carries through the
steps of checking the maximum values from the tables in store. In
practice, of course, this will lead to exactly the same result.
This point is connected with the statement that we should not
yet want to claim the full meaning of 'insight' on the part of either
a or j8, since there is no possibility of taking over a result and using
it in another situation. To grant the circumstances for this to be a
possibility, the computer must be taught at least one other suffi-
ciently similar game, with the record of the noughts-and-crosses
experience still available to it. For these results to be utilizable we
should need the computer to generalize its results.
PROGRAMMING COMPUTERS TO LEARN 165
It can be shown that such generalizations are possible. One
example is offered by teaching the computer to play noughts-and-
crosses and to follow this up by teaching it or getting it to
learn three-dimensional noughts-and-crosses. The learning of
the latter game can be shown to be facilitated by having learned
the former. An extension of this same principle will suggest itself
for all learned material.
A simple explanation of how such a generalization may come
from noughts-and-crosses alone is afforded by considering an
alternative numbering scheme for the board, say,
1 2 3
8 x 4
7 6 5
and then examining the following games:
*/l/2/3/L
*/l/2/4/L
a/l/2/5/L
*/l/2/7/L
It is clear from this short sample that all sequences of moves
which follow the starting move of # will have the general form
xm n(n+4) (1)
if they are not to be losing.
The principle which can now be directly extended to all the
moves of the game is completely general, and eventually states in
the form of (1) a decision procedure sequence. It should be noticed
that the statement of (1) implies the cyclic nature of the number.
Thus, 11 is the number 3.
The ability of the computer to make the above generalization
depends upon the ability to recognize numerical differences and to
state general mathematical forms; this is something which it
must separately learn, unless it is already programmed in.
Auto-coding
The problem of Auto-coding is also of great relevance to our
search for a learning system. The problem can be put in this way:
If we know a simple and sufficiently precise language, we shall
wish to instruct the computer in that language, and to do so we
166 THE BRAIN AS A COMPUTER
shall need an interpreter. For this, the dictionary suffices, so we
build the dictionary into the storage system, and the computer
translates our language into the form of its usual programme.
There is, of course, a wide variety of auto-codes in existence, and
they raise some important issues of relevance to learning.
In the first place, language is known to be closely bound up with
controlling operations, both deductive and inductive. Indeed, we
can illustrate the difference between deduction and induction in
terms of language translation. Where the translation takes place
between two known languages, the operation of translation is
deductive; but when one language is not known, the operation is
inductive.
It should be mentioned that certain 'compiler' auto-codes
like Fortran, the IBM code have a structure very similar to a
formal logical system. Naturally, the possibility of inductive as well
as deductive auto-codes is of importance, since it represents the
fundamental problem of how organisms learn languages.
The scientist is continuously trying to find the appropriate
generalizations about the world he observes, and he could be said
to be translating the language of nature, inductively, into a
language which he already understands. This is, in fact, an almost
ideal example of learning; such work links directly with stochastic
processes and information theory.
The learning situation is exactly mirrored - in a trivial instance
by the computer learning to play noughts-and~crosses, or any
other game. The problem is to construct a dictionary from which
language translation takes place, or to construct a model in axio-
matic form from which deductive inferences can be made. The
interesting point which is now being brought out is that models or
dictionaries or axiomatic systems are all much the same in their
use. Indeed, we are saying, in effect, that models are often, even
usually, verbal.
General inductive programming
Let us use the following notation: A, 5, ..., N will represent
stimuli or input letters, and Q> JR, ..., Z represent overt responses
or output letters. These letters may be suffixed if necessary, giving
a potentially infinite stock of input and output letters. The mode
of generation may be quite general, so that at any instant whatever,
PROGRAMMING COMPUTERS TO LEARN 167
although the number of input and output letters is finite, the
number of letters can always be increased.
We can now state the problem as being one of setting up a
dictionary which relates input to output letters, according values
and probabilities to such relations by virtue of differential rein-
forcement.
Now for every input letter M there will be an output letter Y,
and for every choice of M and Y there will be a probability of
some further input letter N 9 and an assessment of the value of N
is made by the computer. The 'assessment* is not itself an easy
matter to decide in the full scale learning of human beings, but it at
least involves the reinforcement of associations which are in
temporal contiguity with 'pleasurable' outcomes, by designation.
This temporal interval of reinforcement could be graduated and
extended over any number of time intervals. It could also, in the
more complex programmes, be associated with the occurrence of
anticipated outcomes, even where these are remote in time from
the reinforced associations.
It has to be the case that the motives, or some motives, are built
in. For human beings, the main motive is undoubtedly survival of
the organism. For the computer we will normally designate some
input or output letters as positive or negative, motivationally.
The question of whether or not the computer can construct
new goals for itself must be left for the moment, but it will be
returned to after a further discussion of the general inductive
programming procedure.
In practice, inductive programming is best illustrated on the
computer by dividing it into two parts and letting one part play the
role of the environment and the other the organism; in thinking of
the matter, however, it is easier to think of it as a tape that is
punched with the details of the environment and passed into the
computer, and it is with this analogy in mind that we shall consider
the matter. (Figure 2 shows a generalized flow chart.)
We shall have a tape made up of input symbols and representing
the environment, and the problem of the computer will be to
categorize the relationships between the letters on the input tape,
and modify them in terms of its previous experience. For example,
if A is followed by 5 if and only if the computer prints R after A,
then we say that the occurrence of B is contingent on the occur-
168 THE BRAIN AS A COMPUTER
rence of R on the output tape. This means, of course, that the
input tape must be a function of the output tape. This is what
logicians call a contingent relation, and it represents the fact that
what people do may change the nature of the environment in which
they live.
Computer a is stocked with instructions for generating outputs (i.e. (3's
input letters) and responding to p's output letters. The original instructions
for these operations are random.
Computer a records its input letter and responds according to the principles
outlined in Figs. I and 3 of this chapter.
a has to go through the ordered set in storage appropriate to the input
letter (see Fig. 3) and if there is no such event letter it makes either a ran-
dom response, or if there is another event letter similar to the missing one,
it will respond as if that one occurred. This last principle of stimulus general-
ization depends upon the inputs being themselves complex patterns of
letters.
Whichever takes place the result is recorded in a separate storage register.
If a now receives another input letter before a response has been made to
the last letter, it checks blocks I and II of the store (see Fig. 3) and if the
input letter does not occur there then the input letter is put into a tempor-
ary storage and the computer returns to the scanning prior to making
the response still not made to the last letter. If the last letter was involved
in block I or II, then the second input letter would be put directly into
temporary storage without a preliminary check of blocks I and II.
a now associates a new value number with the input-output relation last
processed according to the satisfaction or otherwise subsequently derived.
This also means that a certain range of effect may occur so that the input
before that and perhaps also the one after has its value number changed.
With language in the computer it will also change its description of its
environment as a result of these value number changes.
. i
The computer a is now in a position to process the next input event, and
may if there is a delay before the next input arrives derive the logical conse-
quences of the information already in its storage system.
FlG. 2. A GENERAL FLOW CHART FOR COMPUTER LEARNING. This is
a generalization on Fig. 1 and shows in simplified form a game
in which one computer plays the environment and the other the
organism.
It may also be the case that the machine's response to a particular
input letter will have no effect whatever on the next input letter,
and in such a case the logician will say that the two letters on the
input tape say, C and D are necessarily related.
Quite obviously these are two limiting cases, and in between we
PROGRAMMING COMPUTERS TO LEARN 169
have relations of varying degrees of complexity. Thus, E may
follow F if and only if some combination of R, S and T is printed
on the output tape. This could be regarded as the analogue of the
machine solving a problem; indeed, a scientific problem could be
regarded in just this light as a particular set of relations existing
between input and output letters. The idea of controlling the
environment emerges when the computer is in the position of
being able to anticipate every input letter by virtue of the previous
input letter, and change the next input letter whenever that is
desirable ; this depends directly on the selective reinforcement of
the system.
This is the way in which a computer can learn. It stores in-
formation made up of the occurrence of successive combinations
of symbols or events and, by ascribing probabilities to these
combinations, ensures that a control is maintained, assuming
always that the ability to control the succession of events is in fact
possible.
The storage registers themselves are not fixed in their length,
and this causes some difficulty. Obviously we shall want to store
events of what are sometimes called length three (cf. Tolman's
expectancy, discussed in the next chapter), which means an input
followed by an output followed by an input letter, e.g. A/R/B. But
this may not be enough, since the probabilities associated with an
event of length five, say, are not the same as the product of the
probabilities associated with events of shorter length that make
up the event of length five. That is to say,
p(A/R/B/S/C) ^ q(A/R/B) . s(BIS/C)
where p, q and s are probabilities. In a special case, of course, they
may be equal.
Problem solving behaviour calls for an extension of the length of
events used when the problem is not soluble with events of too
short a length. This implies that there must be means for genera-
ting events of greater length as they are needed.
Statistically speaking, this matter of storage represents the well
known methods of a stochastic type. It is a matter of associating
probabilities with successive elements of a sequence, where these
probabilities are changing regularly as a result of each successive
input. In fact it is probably undesirable that all the probabilities
M
170 THE BRAIN AS A COMPUTER
should change quickly, and there will be some method available
whereby, once a particular relationship is well established with
probabilities approaching or 1, these 'certain beliefs' may be
moved to a separate store, or at least to a set of well defined
registers. At the same time we must use some method of 'rapid
counting* to undo quickly an obviously inappropriate response due
to changed environmental conditions. This might be achieved by
heavily weighted reinforcement, or through language.
All this links up with work that has already been done on
'heuristics* (Minsky, 1959), which demands the use of fairly well
defined generalizations as partial or intermediate solutions.
'Heuristics' here really means analogies (i.e. generalizations) taken
over from one situation and used in another in order to solve the
problem presented by the new situation.
A tactic in noughts-and-crosses can be learned by the differen-
tial reinforcement of moves in a game in which all the moves in a
game lost were scored 1, and all moves in a game won were
scored +1> even though some of the same moves may occur in
either game. This does not matter in noughts-and-crosses, where
the range of possible moves is small, and discrepancies in move-
evaluation are soon worked out; but in a long game like chess it
would take time of astronomical proportions to evaluate every
move in a game, and a similarly excessive period to learn a decision
procedure by such a method. We must therefore look for inter-
mediate or simplifying principles.
Obviously, just these sorts of heuristics, or simplifying prin-
ciples, enter into chess as played by ordinary humans. They have
rules of thumb that guide the strategy or tactics of the game, and
these tactical generalizations could be formulated in an inductive
programme in the same way as in the generalizations which we
have already discussed; but we shall try to show that language leads
to an alternative formulation.
Language for the computer
We now wish to add words X l9 X 2 , ...,X n to our system, and we
wish the computer to have a potentially infinite number of words
at its disposal. This implies that it has the means of constructing
an indefinite number of words. The method, which is learned by
example in humans, may also be so learned by the computer.
PROGRAMMING COMPUTERS TO LEARN 171
The principle of association, by which words come to be
associated with physical objects (or events), is exactly the same as
the manner in which events have already been shown to become
associated with each other. Indeed, it will now be apparent that
our input tape may contain words as well as event symbols, and
furthermore, there is really no need to distinguish these outside
the machine, since the word will associate with an output, say,
and precipitate an action in the same way as an event.
This raises many interesting problems for the programmer.
It can be shown that computers can learn simple languages in this
way, and of course the natural languages for them to use are those
languages which we call 'logical'. They are the logics of empirical
classes and empirical relations (Chapter III), since they are
descriptive and probabilistic. It is from this that ordinary language
can then be derived.
We can see here a clear link between this sort of programming
and auto-coding, although at present virtually all auto-coding is
deductive. This is a matter we shall discuss briefly later, in con-
nexion with an inductively programmed computer changing its
own goal.
The argument about inductive or learning programming seems
to suggest that no distinction, except one for purely linguistic
convenience, need be drawn between words and concepts. The
word 'concept* might be used to apply to the development of a
state, represented by a Markov Chain table in the register in the
computer, up to the stage at which it reaches verbal reformulation
as a result of the computer now having a language with which to
describe everything and anything that occurs to it. This includes
relations between output events, between input events, and be-
tween output and input events. These inputs and outputs must
also themselves include words, for it is now well understood that we
shall want to distinguish between words about events and words
about words.
It should be noticed that generalizations may occur in linguistic
form representing events that may never have occurred in the
computer's experience. This is closely linked to what is called
'imagination', and reminds us that this imaginative process, closely
allied, one suspects, with what is called 'creative thinking', can
most conveniently be handled in language, although, if the tables
172 THE BRAIN AS A COMPUTER
of the computer generated new strings of symbols, it would seem
to be largely an academic matter to inquire whether these were
verbal or not.
A computer that has gone this far can, in principle, surely deal
with the problem of transferring findings from one situation to
another, and thus satisfy a condition which seems to be much the
same as is needed by human 'insight*. We can now bridge the
gulf between the two computers a and j8, where they could be
shown to perform the same responses on different bases. These
different bases refer to the fact that although one computer learns
to do the same thing as the other, it stilll does it on the basis of
tables rather than verbal instructions.
Non-linguistic induction
Earlier in this book we represented the material on which a
computer works as a set of numbers. This means that all the opera-
tions of a general purpose computer are mathematical operations.
From this point of view, games like noughts-and-crosses are
problems of set theory. The same argument exactly applies to other
games like draughts, chess, and even card games, although there
may be additional conditions to be satisfied.
The significance of all this is that we want the most complete
basis for all possible arithmetical operations, and this we find under
the name of primitive recursive functions (Davis, 1958).
Primitive recursive functions are the general class of functions
that include everything that normally occurs in classical mathe-
matics ; the operations of addition, subtraction, and all other mathe-
matical operations can, of course, be exemplified in this way. This
means that if the computer has the power by virtue of being
programmed to carry out any primitive recursive operation, it
would seem that it could do as much as anyone could hope to do
by way of learning.
Changing goals
There has been some argument among cyberneticians as to
whether a computer can or cannot change its own goals. Semantics
are certainly involved here, but in particular terms which will be
explained, it can most certainly be said that a computer can change
PROGRAMMING COMPUTERS TO LEARN 173
its goals. This is, of course, necessary if the model is to be useful
to psychologists interested in learning.
If the computer is differentially reinforced it will perform, with
respect to a certain subset of variables, optimalization operations.
This is like putting survival above all else in a human being; but
these are by no means the only goals, since in the inductive associa-
tive process we can evaluate every association with respect to its
contribution to the optimalization of the basic variables. A simple
example of this is to say that when an event is associated directly
with something obviously good for survival, it becomes thought of
as itself good for survival. We may call these other goals secondary
goals, and these of course will change according to the changing
circumstances upon which the computer is making its inductive
inferences. Similarly, there is no reason why we should not ascribe
specified values to the basic goals, and allow these to change if and
when a secondary goal exceeds the basic goal in value; such things
seem to happen with humans when they are prepared to sacrifice
their lives for some cause.
Cybernetics and learning
Much of what has already been said in this book may be taken
as summarizing some of the results of cybernetic research, and
forging a link between learning and cybernetics. Something more
explicit must now be said on this subject.
In the first place we must consider the relation between the
learning theories, such as those of Hull and Tolman, and cyber-
netic research. It will be remembered that Hull's theory dealt with
stimulus response units (see next chapter) which are strung to-
gether into a stochastic process of the same kind as the one analysed
by the computer. In fact the resemblance goes deeper than that,
because the concept of differential reinforcement that we have used
is very similar to that of Hull's concept of primary and secondary
reinforcement.
In the computer programme we have assumed some such concept
as a primary drive, and further, that initially neutral stimuli take
on this drive, or motivational characteristic, by virtue of their
association with primary drives.
Tolman's theory is essentially the same in its interpretation of
needs and cathexes (this means Values', roughly speaking; see
174 THE BRAIN AS A COMPUTER
next chapter, page 179), where the secondary cathexis that be-
comes associated with an original neutral stimulus is simply an
alternative rendering of what the computer may be said to be
doing. This confirms in part the belief that Hull and Tolman
represent two different renderings of the same system.
Tolman's basic association unit is stimulus-response-stimulus,
rather than stimulus-response and, as with motivation, we might
say that the emphasis has gone away from the habit type of learning
and towards the more sophisticated type where the emphasis is on
the next state, rather than a mere response to a stimulus.
In our computer learning, the same stochastic methods are used,
but we shall not lay heavy emphasis on stimulus-response, nor on
stimulus-response-stimulus, as a 'basic unit', since learning can
be clearly seen to depend upon very complex associations, of
which stimulus-response and stimulus-response-stimulus seem
rather simple special cases; and this is true regardless of the
interpretation we place on the words 'stimulus' and 'response*.
Our computer experiments point to the fact that our methods of
describing learning must be effective. We must consider what our
assumptions (Woodger has called them zero-level statements) are,
and make them explicit and give them an operational definition.
The use of the computer lends further emphasis to this point.
To return to the essentially Markovian (Markov Chain) nature
of learning, it seems clear that the length over which our condi-
tional probabilities must spread is a function of the complexity of
the problem to be solved (or the operation to be learned), and the
extent to which the organism is motivated to learn it, and the
organization of the memory store.
The principles of the input and the output depend, no doubt,
upon a classification principle (Uttley, 1954; George, 19S6a,
1957d), whereas the central problem is that of organizing the
information for storage.
The details of the storage organization have by no means been
worked out in detail, but Fig. 3 shows a suggested scheme of
organization. Programmes have already been designed which
order information such that the most valuable comes out in the
first registers to be scanned, and the ones with high probabilities
come next; this simply means that urgent matters are dealt with
first and habits next. If the input does not demand an urgent
PROGRAMMING COMPUTERS TO LEARN 175
response, but merely elicits a habit response, then it enters into
the bulk of storage where matters are still 'more obviously' being
learned, with the exception that the first set of this large set has
been generalized into 'beliefs', so that some arbitrariness may have
been enacted on the facts. This will not matter if the degree of
arbitrariness is not too great. In other words, it will not matter if
we treat Mr Smith exactly as we treat Mr Brown, provided the
I
VALUE > K
PROBABILITY >H
WHERE K, H CAN BE
THOUGHT OF AS FIXED
CONSTANTS INITIALLY
m
VALUE >K
PROBABILITY <H
UT
VALUE<K
PROBABILITY>H
VALUE < K
PROBABILITY<H
FIG. 3. THE STORAGE SYSTEM. The storage systems may be
regarded as being responsible for ordering stored information.
This figure shows the simplest priorities and there will also be a
variation in degree of generality of information.
difference between them is sufficiently small, so small that we shall
get similar sorts of results from the same response to either.
Finally we come to those matters where learning is still occur-
ring, which will naturally lead to the longest delay in responding.
Those of high value and probability are the most important, but
these variables also partially cloak the other factors of recency and
frequency, except in that value is a direct function of frequency,
and that, among equal values, the most recent will appear as the
top item in the subset. Motivation is represented by built-in
176 THE BRAIN AS A COMPUTER
stimuli, and the development of secondary motivation is brought
about by association.
The pattern of learning is clearly beginning to emerge from
studies of this sort, and it is perhaps not too much to claim that we
now understand how learning occurs (or could occur), although we
do not understand either the biological or the social details
sufficiently well to allow us to make predictions for individuals
beyond a very limited range.
Looking again at what we have said in the light of modern
learning theory, it might be guessed that both stimulus-response
and stimulus-response-stimulus elements occur. The first
represents the 'habits', or events of high probability, where no
emphasis on the next response is needed (since the stimulus-
response connexion has a high probability). In the stimulus-
response-stimulus element, the automatic nature of the response
does not occur, but the 'urgency' (very high value numbers) may
or may not be high. What is important is that much longer seq-
uences may occur, indeed need to occur, for reasonably accurate
learning and problem solving.
It is also interesting that the presence of neither primary nor
secondary motivation is necessary to associate with any novel
input to bring about a response, since the value numbers associated
with all input sequences are relative to the others of the same set,
and thus a response will still be made, although of a random kind.
This brings out the point of trial-and-error learning.
This trial-and-error is subsequently reinforced, and thus
prepares the way for the sort of 'insight' in another sense which
recognizes the appropriateness of a response as a result of selective
reinforcement.
As a result of this we may say that objects subsequently have a
'cathexis* and an 'induced cathexis' (a value imposed by associa-
tion on an otherwise neutral event. See next chapter). But this, as
in Tolman's theory, will be relative to the context in which they
may occur. For the computer, the context is given by events of
greater length that have already a high probability associated with
them. To take a case: for event A, the probability and value num-
bers may be such as to predict not just A/R/B, but A/R/BIS/CI
T/D, or some such longer event.
Generalization will occur if we say that each input is really a
PROGRAMMING COMPUTERS TO LEARN 177
combination of subunits which it surely is in organismic learning
and this means that two sets may be identified if they have
common numbers and are such that no distinction is forthcoming
with respect to one input as opposed to the other. A special case of
this more convenient in the nomenclature of this book is the
simple identification of two different input variables. It will be
noticed that this argument of generalization can clearly apply to
inputs, outpust, or input-output relations, of any length whatever.
Other aspects of learning can easily be explained in terms of
this computer organization, so that 'transfer of training' occurs
simply as a result of generalization over events of length greater
than two.
Memory is such that frequency and recency are necessarily
factors, since this is the way we have ordered the events to be
remembered, subject, of course, to the other conditions of value
and probability.
'Set', by the same sort of argument, depends simply on the
context of events of length greater than two often, indeed, much
greater where the response is made to a stimulus with the
expectation of another stimulus, simply because of its high
probability.
'Learning sets' will be accounted for by saying that a particular
relation that is well learned does not interfere with the same input
letter being associated with a new output, since the first is now of
high enough probability. This means that it would be immediately
responded to were it not for the explicit instruction not to respond
to it. To remember not to respond is thus something that is a
function of the degree of learning; or in other words, the dis-
crimination (as opposed to generalization) can be carried through
better where the probabilities are wholly separated.
This last point is brought out more clearly where the system
works on an approximate basis, and comparison of probabilities is
approximate, and thus glosses over discriminations dependent
upon only a small amount of learning.
In this chapter we have not attempted to bring out the full
significance of computer programming for learning theory, for it
is intended that this significance shall be noticed more fully in
later chapters. It is hoped that, without really taking up in detail
the point of language in the computer, enough has been said to
178 THE BRAIN AS A COMPUTER
indicate the possibilities inherent in this approach. It should be
remembered that many more programmes have been run on the
computer than could possibly be shown here, and much more has
been learned about learning than can now be stated.
Summary
This chapter is really complementary to the last one, and deals
with the whole matter of learning from the point of view of
programming a digital computer.
Contrary to many opinions, the general purpose digital com-
puter can be shown to learn, or behave inductively, if suitably
programmed. The type of stochastic organization needed is
essentially the same as the type of organization used in the logical
net models of the previous chapter.
Although in a short chapter it has not been possible to illustrate
the full range of experiments that have been carried out in com-
puter programming, enough has been said to illustrate the method
and its great potentiality. Programmes have been undertaken over
other games besides those mentioned, and the methods used are
the same. The most interesting points that arise in learning
programmes are connected with the power of the computer to
generalize and to use language. These matters have been discussed
all too briefly, but the possibility of both aspects of computer
programming being greatly extended is fairly obvious.
The second half of the chapter is also concerned with forging a
link between the established theories of behaviour, such as the
learning theories of Hull and Tolman. It is in fact possible to see
that both the Hull and the Tolman theories could be restated in a
manner making them suitable for a computer programme, and
such effectiveness is exactly what Cybernetics needs.
One point comes quite clearly out of the programming of
computers to learn, and that is the fact that there may be a con-
siderable difficulty in dealing with the build-up of input informa-
tion. Learning is a selective process, but so is perception, and we
may expect input information to be put in short term storage while
other information is being handled.
CHAPTER VII
PSYCHOLOGICAL THEORY OF
LEARNING
OUR main aim in this book is to show the part that cybernetics can
play in helping to solve the traditional behavioural or psychological
problems within the field of cognition, and the first cognitive
problem with which we shall deal explicitly is that of learning,
Before we can try effectively to employ logical networks, inductive
computer programmes, or any other cybernetic model, to the
solution of a problem, we must consider what has already been
done in the field, and where solutions are already forthcoming, and
where they are not; otherwise we cannot make the necessary
comparison with what is actually known of human behaviour. We
shall, in passing, be referring to those aspects of learning that have
already been met in previous chapters.
We shall necessarily have to rely on a brief summary of the major
work done in learning, since this is not a text on learning theory as
such. The reader who seeks to develop cybernetic methods in
learning in more detail must do so with a more specialized analysis
of learning. This, of course, applies to the whole of cognition,
indeed, to the whole of behaviour, and on physiological levels as
well as psychological. We shall start with a discussion of the mean-
ing of the word learning*.
'Learning', as Humphrey has pointed out (Humphrey, 1933),
is a recently introduced term. It is not mentioned in the indices
of either Kulpe (1893), Stout (1896), or Ward (1918), nor is it
mentioned explicitly in Baldwin's Dictionary of Philosophy, or
William James's treatise on psychology (1890). Wundt regarded
learning as approximately the same as memorization of words.
William McDougall, in his Outline of Psychology (1923), only once
mentions the word 'learning', where it occurs under the title
'primitive learning'. In fact, of course, the processes were studied
under different names, such as 'memory', 'habit', 'framing', and
180 THE BRAIN AS A COMPUTER
'apperception*. These terms, in so far as they are still used, are
regarded as referring to special cases of learning, developed in
the formative years of the subject; they have now largely
disappeared.
Various attitudes towards learning* will now be noted. Mc-
Dougall himself describes a primitive learning process, among
animals low in the scale of intelligence, as a modification of
present actions through past experience, and he quotes, as an
example, his experiment with crayfish. If some food is placed at
one end of a long trough of water, and the crayfish is put in at the
other end, he will swim towards the food. Now if the trough is
divided into two parts A and JB, so that by A he can reach the
food and by B he cannot, then after some number of trials,
he will always take the path A. This is a particular case of
learning.
Humphrey insists on using 'learning' to apply to behaviour
modification that is useful to the organism (part of the survival
need). A seagull whose behaviour is modified to the extent of
following ships to get food is said to have 'learned'* If, on seeing
a ship, the seagull always flew in the opposite direction, it would
have had its behaviour modified, but would not be said to have
'learned'. In this connexion it is worth quoting Humphrey's own
words (Humphrey, 1933):
A gull, let us say, has learned to fly after the ships as they leave the
harbour. Clearly the learning rests on the fact that the bird is able to
obtain bigger and better meals, and easier ones. That is to say, its energy
intake is more economically effected. If, after finding food behind a
number of ships, it had so modified its reactions that it flew in the opposite
direction whenever a ship appeared, we should hardly say that learning
had taken place.
The special sense in which the word 'learning' is being used
here should be carefully noted. Humphrey goes on to differentiate
between different types of learning, and places them on a con-
tinuum with simple negative adaptation (habituation, or accom-
modation, and tropisms, which are orientating responses and are
known to be mediated by fairly simple physico-chemical means)
at one end, and maze-learning, puzzle-box learning (Thorndike,
1898, 1911, 1932; Adams, 1929; Guthrie and Horton, 1946), and
ape-learning (Kohler, 1925; Yerhes, 1916), in stages of increasing
PSYCHOLOGICAL THEORY OF LEARNING 181
complexity, leading to human learning at the other end. The
conditioned response (Pavlov, 1927) falls somewhere towards the
middle of the continuum.
By a 'conditioned response' we mean here, as before, the
simple associative principle involved in 'classical conditioning*.
The unconditioned response might be salivation at the sight of
food (which is the unconditioned stimulus), and then, when the
food is presented and a bell rings at the same time, the bell may be
called the 'conditioned stimulus'. Conditioning occurs when the
response of salivation is elicited by the bell alone (now called the
'conditioned response'), without the presence of food.
From this starting-point Humphrey goes on to analyse the
whole subject in great detail. So far as our present knowledge of
cybernetics goes, it suggests that the main distinctions are, in fact,
likely to be between 'learning' and 'having learned', where the
learning may vary from trial-and-error to insight, and the 'having
learned' overlaps that which is built in and also that which is
acquired by maturation, or in the course of growth and develop-
ment.
Into the depths of the verbal problems are soon drawn other
terms which are used to refer to modified organic activity. These
terms include 'instinct', 'purpose', 'insight', and 'maturation', and
the whole matter becomes much more complicated. Some attempt
to clarify it can be started by saying that maturation and instinctive
behaviour are usually distinguished from learning.
At a certain level, the distinction may be made between be-
haviour depending on special organic development (of which
Coghill's (1929) salamanders are a very good example) and
learned behaviour. The working out of inherited, relatively fixed,
probably electro-chemically mediated, behaviour patterns (in-
stincts), and behaviour which is in some way modified by external
or internal changes towards the survival of the organism, or
towards a state of homeostasis (Cannon, 1929), demand the closest
attention (Tinbergen, 1951). The verbal distinction between
'involuntary' and 'voluntary' behaviour is in some ways an analogy,
although very limited, to the above distinction.
Now it can be seen that there are large possibilities for con-
fusion in our basic understanding of 'learning', and more careful
definition is necessary. If one turns to some modern definitions of
182 THE BRAIN AS A COMPUTER
'learning' it may be seen that greater clarity has been only partially
effected. Hull states (Hull, 1943, p. 68):
The essential nature of the learning process may be stated quite simply.
Just as the inherited equipment of reaction-tendencies consists of
receptor-effector connections, so the process of learning consists in the
strengthening of certain of these connections as contrasted with others, or
in the setting up of quite new connections.
Hull's work may be taken as one cornerstone of modern learning
theory, and it will need careful analysis. For Hull, 'learning' can
be defined in terms of conditioning, and the problem of learning is
reduced in essence to the problem of reinforcement. However,
before looking more closely at any one view, it is necessary to
continue our survey of definitions a little further.
Hilgard and Marquis (1940) define 'learning' thus:
Change in the strength of an act through training procedures (whether in
the laboratory or in the natural environments) as distinguished from
changes in the strength of the act by factors not attributable to training.
This can be regarded only as a working definition as, of course,
the real difficulty is shelved, since 'training procedures' are not
defined,* nor is the method of observation for distinguishing be-
tween behaviour modified as a result of training or non-training.
The Hilgard and Marquis (1940) definition of Thorndike trial-
and-error learning may also be quoted:
The mode of learning in which the learner tries various movements in its
repertory, apparently in a somewhat random manner, and without
explicit recognition of the connexion between the movement and the
resolution of the problem situation. Tentative movements which succeed
are more frequently repeated in subsequent trials, and those which fail
gradually disappear.
This form of definition leads to the famous law of effect and to a
discussion of reinforcement, and it is fundamental to our inductive
programming.
Three further definitions of 'learning' may be quoted; they are
due to Guthrie, Hilgard and Thorpe respectively. Guthrie's
(1935) reads:
The ability to learn, that is, to respond differently to a situation because of
past responses to the situation, is what distinguishes those living creatures
which common sense endows with minds. This is the practical description
of the term 'minds'.
PSYCHOLOGICAL THEORY OF LEARNING 183
Neglecting the totally unnecessary introduction of the word
'mind', we see that the definition is exactly the same as the implicit
definition of McDougall.
Hilgard's (1948) avowedly working definition reads:
Learning is the process by which an activity originates or is changed
through training procedures (whether in the laboratory or in the natural
environment) as distinguished from changes by factors not attributable
to training.
This, of course, is only a slightly modified form of the Hilgard-
Marquis definition.
Thorpe's (1950) definition is:
The process which produces adaptive change in individual behaviour as
the result of experience. It is regarded as distinct from fatigue, sensory
adaptation, maturation and the results of surgical or other injury.
Separate definitions of 'trial-and-error learning', 'reinforcement'
'latent learning', 'insight learning', 'instinct', etc., are also worth
noting (Thorpe, 1950).
The problem of learning is, plainly, thought to be a central
one for experimental psychology. The difficulty has been to ear-
mark what is essential to learning and what is not, and this may
merely represent the fact that learning is really a more or less
complex process of association units working together, as we
suggested in the previous chapter, and if this is so, this is vital to
the cybernetic approach.
Within the compass of learning there are certain essential
distinctions between different sorts of learning; for example, some
organisms can learn without immediately manifesting their
learning in a changed performance. This is called 'latent learning',
and is very typical of human beings. The fact that some learning
may occur when obviously initiated by purely random behaviour
(trial-and-error learning) does not blind us to the fact that other
learning may show 'insight'. This word does not necessarily mean
something mysterious; it is used here to indicate that what is
learned in one situation, or previously learned in general, perhaps
through language, may be applied in a new or particular situation.
Such refinements and distinctions do not, it seems, invalidate the
essential unity of the concept of learning itself. But it does look as
if learning is dependent on a 'forcing function' or selective opera-
tion such as reinforcement.
184 THE BRAIN AS A COMPUTER
Reinforcement has generally been explained in terms of one of
the following three principles: (1) Substitution, (2) Effect, and
(3) Expectancy, and for most theorists it remains the essential
factor upon which learning depends. Although these three prin-
ciples may appear to be different aspects of some more general
principle, they have not, as yet, been integrated. The principle of
substitution springs from classical conditioning (Pavlov, 1927,
1928; Bekhterev, 1932; et al.\ and a first working definition might
be:
The principle of a substitution states that a conditioned stimulus, present
at the time that an original stimulus evokes a response, will tend, on
subsequent presentations, to evoke a response.
The first important question is that of the generality of the
principle. Pavlov and Guthrie are its principal supporters, but they
differ as to its generality. Pavlov (1927) says that substitution
occurs only under certain circumstances, while for Guthrie
substitution always occurs, and occurs completely. For Pavlov,
the factors determining the degree of substitution are: (1) The
time interval between the conditioned stimulus and the un-
conditioned response, (2) The intensity of the conditioned stimulus
and of the unconditioned stimulus, and (3) The number of repeti-
tions of the stimuli; but these factors are not necessarily regarded
as being exhaustive.
To consider Guthrie first (Guthrie, 1935, 1942; Hilgard, 1948):
it is a general criticism of Guthrie's behaviour theory that it over-
simplifies the facts. The basis of his theory is contained in his two
basic laws :
(1) A combination of stimuli which has accompanied a move-
ment will, on its recurrence, tend to be followed by that movement.
(2) A stimulus pattern gains its full associative strength on the
occasion of its first pairing with a response.
Since these do not allow the necessary predictions, because of
lack of detailed analysis, the laws must be considered inadequate to
explain learning on a sufficiently general basis. We might guess
that it is not that the model is incorrect, but that it is inadequate
by reason of its lack of detail. To put the matter another way,
Guthrie's theory, as stated by him, lacks generalizability. There is
a further objection: it is a principle that does not allow of verifica-
PSYCHOLOGICAL THEORY OF LEARNING 185
tion, nor does it readily suggest further experiment. On these
grounds Guthrie's formulation will be put aside, and provisional
acceptance given to the Pavlov formulation. However, this does
not appear to be a vital issue ; indeed, in a sense it is a sub-issue of
the more general problem of selective learning, which still needs
definition.
Although we appear to be dismissing Guthrie in a somewhat
cavalier fashion, we are very ready to admit that, apart from other
important features, his theory has laid emphasis on the principle
of contiguity as primary and motivation as secondary, and this has
served to draw attention to an aspect of learning that might other-
wise have been obscured. The influence he has had on this score
alone is quite considerable, and can be detected in Estes' model of
learning (1950) as well as in more recent theories of learning such
as those of Sheffield (Sheffield and Roby, 1950; Sheffield, Wulff
and Backer, 1951; Sheffield, Roby and Campbell, 1954) and
Seward (1950, 1951, 1952, 1953).
From the point of view of logical nets this question is one of
special interest. We have said that the motivational system may
initiate response activity and stimulus-response associations may
occur to change the internal (motivational) state of the organism,
but only according to the view stated in the presence of a
secondary or primary reinforcer. If we drop this condition we are
in difficulties in explaining why learning is selective. Even if we
granted the presence of a selective filter, and that some part of that
selection was based on conditions of attention, which was based, in
turn, on the relevance of some stimuli for existing needs, this
would in no way change the basic need for differential reinforce-
ment, although, as we might expect, it would mean that we must
take a broader view of motivation than is implicit in Hull's theory
of need-reduction. The same argument applies, of course, to
stimulus stimulus associations.
We shall leave this knotty point for the moment, and return to
our summary of the principal features of learning theory.
The distinction between Pavlov's and Guthrie's substitution
must now be regarded from the point of view of logical nets.
Consider Fig. 4 of Chapter V, which represents our logical net
model of the conditioned response in its simplest form.
We can see quite easily, in comparing Guthrie's and Pavlov's
N
186 THE BRAIN AS A COMPUTER
notions, that the first question is as to whether we should regard
the association as being set up at once, or by degrees. The answer
is not unambiguous, since our logical net could be interpreted
from either point of view. If we consider the matter from Pavlov's
point of view and ask ourselves whether the time interval between
the conditioned stimulus A and the previously unconditioned
response (the bell and salivation in classical conditioning) makes a
difference to the effectiveness of the associations being made, the
answer is a complex one. We can certainly arrange for events to be
associated directly, however far from each other in time, but we
may expect that pairs of contiguous events are normally associated
during learning. It would therefore seem to be difficult for the
organism to learn the relation between events widely dispersed in
time. This does not mean that, having learned an association, there
may not be considerable delays in the subsequent associations,
although these delays would, according to Pavlov, weaken the
association.
What emerges from this picture is that we have not as yet made
clear the full workings of our automaton, particularly with respect
to its timing, so we shall look further at this aspect of the develop-
ment. In the first place, the designs of Figs. 4, 5 and 6 in Chapter V
are not intended necessarily to accept only single stimuli but,
rather, volleys of stimuli (this matter of volleys could of course be
restricted to peripheral mechanisms in which sensory classification
occurs, although they may take the form of specialized analysers,
or be of a very particular form such as that suggested by Osgood
and Heyer (see Chapter IX), and we may expect that a particular
volley represents, by its size, the intensity of stimulation. If an
event, A say, so represented, occurs, then the subsequent state B
will normally follow quickly, dependent or not on some response
A'* This leads to the belief A-+B, say, where ' > simply represents
the association of an event name A with an event name B such
that we say A implies B, but and this is now vital there may
be many interesting stimuli and responses in the repertoire of the
automaton that occur concomitantly on A *B, and these are what
Guthrie would call 'maintaining stimuli'. These maintaining
stimuli are mostly automatic in themselves but may need to be
given some organization, particularly at the motor classification
level, to permit A->B to occur at all.
PSYCHOLOGICAL THEORY OF LEARNING 187
This argument is important in bearing out Guthrie's points
about an association being immediate and occurring at full
strength, where practice has the effect of organizing the maintain-
ing stimuli. At the same time, the sketchy explanation given is also
consistent with Pavlov's idea that delays in temporal contiguity
affect the efficiency of the association. In other words, beliefs
occur as expectancies in a very complex way, many occurring more
or less together, and where the A part of A-^B may be quite
remote from the B part. Thus, if A occurs, the proper response
may be of the form
where the successful association is only established after many,
even necessary, intervening responses have been made. In other
terminology we could write (1) as
AIICIID...HB
or A I. ..IB
here '/' xneans 'is followed by', and we shall sometimes use '//' to
mean 'is followed immediately by'.
From our assumption (above) of volleys we may see that Pavlov
is certainly justified in saying that the strength of the conditioned
stimulus will be important since, very simply, the more intense
each stimulus is, the stronger will be the association, provided they
become associated at all.
We might next try and compare Guthrie and Pavlov with respect
to motivation. Here we are in agreement with Pavlov in believing
that a motivational system must selectively reinforce the condi-
tioning (associative) process. Guthrie maintains that motivation is
not of primary, but of secondary importance. Unfortunately
Guthrie's position over reinforcement is very vague, and something
like Skinner's in its adherence to operational (sometimes called
positivistic) tendencies (Mueller and Schoenfeld, 1954). In
experimental psychology this usually means that the attempt has
been made merely to restate observed results, with little or no
interpretation, and therefore with little use for theoretical terms. It
is this consideration that hinders a detailed analysis of the situation,
but it does look as if Guthrie and Pavlov could both be talking of
the same logical net, with a difference in interpretation (their
188 THE BRAIN AS A COMPUTER
difference is in their theory language), at least as far as we have
gone.
According to Mueller and Schoenfeld (1954, pp. 368-9),
Guthrie disputed with Pavlov about the importance of pairings in
conditioning, Guthrie insisting upon the importance of the
temporal relation between the conditioned stimulus and response.
The above writers show the doubtful nature of these conclusions,
and though from our logical net point of view the association is
important, it seems perhaps to be less fundamental than that
between the conditioned stimulus and the unconditioned stimulus.
If A-*A' and B-*B' are two unconditioned reflexes, and A is to be
the conditioned stimulus with respect to J3, then A-*B and A-+B'.
But clearly A-*B is false in that, although the association is between
A and B, A will yield the response to B, which is B' y and therefore
what occurs is actually A >B'. This is perhaps the source of a
misunderstanding since, in a sense, A-+B and A-+B' are both
vital connexions that will necessarily go together.
Consider for a moment the case of language in humans : A is
a word whose reference is J5, and the response to the name A or to
the referent B (these are not necessarily identical, hence our use of
(AB) f in our B-circuits) is similar. It seems reasonable, though, to
argue that the 'fundamental* connexion, in some sense is between
A and B and not A and B'.
We cannot take this comparison any further now, but we may
return to their explanations later, in the discussion of anticipatory
responses. Up to now we might say that the differences between
Pavlov and Guthrie are largely due to lack of detailed analysis, but
there is one more point: in order to explain certain aspects of
learning it seems important to make a firm distinction between
items already learned and those being learned, and this, at any rate,
Guthrie does not seem to do.
From the operational point of view, the principles of Guthrie
and Pavlov are virtually indistinguishable, but Pavlov might be
preferred for the reasons stated, i.e. it would appear that the
principles of Pavlov involve the necessary generalizability. On the
other hand there will be the suggestion that this includes only a
limiting case of behaviour.
Before any more can be said about the principle of substitution,
a brief review must be made of the law of effect. This is invoked as
PSYCHOLOGICAL THEORY OF LEARNING 189
a principle of reinforcement, in the context of instrumental
conditioning, where emphasis is placed upon the consequences of
certain activities. One should perhaps start by giving Thorndike's
original definition of this law (Thorndike, 1911):
Of several responses made to the same situation those which are accom-
panied or closely followed by 'satisfaction' to the animal will, other things
being equal, be more firmly connected with the situation so that, when it
recurs, they will be more likely to recur; those which are accompanied or
closely followed by 'discomfort' to the animal, other things being equal,
will have their connexions with that situation weakened, so that, when it
recurs, they will be less likely to occur. The greater the satisfaction or
discomfort, the greater the strengthening or weakening of the bond.
This principle is clearly bound up with 'rewards' and 'punish-
ments', again involving us in the dangers of circularity (Postman,
1947; Meehl, 1950).
We must just remind the reader at this point that the law of
effect is explicitly incorporated in the design of the automaton in
the form of an M- system which is to be interpreted as a motiva-
tional system that selectively reinforces associations in terms of the
law of effect. This fact does not, however, exclude substitution and
expectancy as appropriate principles to explain behaviour, as we
shall see.
The law of effect has sometimes been criticized as being
'circular'. Meehl has argued that the law of effect need not neces-
sarily involve us in any circularity in either of two senses he gives
to the word 'circular'. It is a legitimate form of definition, ana-
logous to Newton's definition of Force, or Hooke's law in physics.
Two versions of the law of effect are quoted by Meehl; one he calls
the weak law and the other the strong law.
The weak law states:
(1) All reinforcers are transnational (a transituational re-
inforcement law states, 'The stimulus S on schedule M always
increases the strength of any learning response'). A definition of
'learning' is needed here.
The strong law states:
(2) Every learned increment in response strength requires the
operation of a transituational reinforcer.
In his discussion, Meehl says that the law of effect is not circular
190 THE BRAIN AS A COMPUTER
in either of two ways that 'circular* can be interpreted, (1) the term
defined in terms which are themselves defined in terms of the
original term, and (2) proofs which make use of the probandum.
He further states that the Skinner Spence type of definition of effect
is clearly immune from these pitfalls. The Skinner version is as
follows :
A reinforcing stimulus is defined as such by its power to produce the
resulting change. There is no circularity about this; some stimuli are
found to produce the change, others not, and they are classified as
reinforcing and non-reinforcing accordingly.
Now we can begin to see the full force of our concession in
avoiding circularity. We are to equate learning with performance
in a positivistic manner, or certainly to regard 'reinforcement* as
applying strictly to performance in a simple stimulus-response
(S R) system; and now one is pushed into the difficulty of explain-
ing the data which come under the heading of 'latent learning* and
'place learning*. Skinner introduces theoretical terms for such
purposes : 'reflex reserve', 'secondary reinforcement', and a distinc-
tion between operant and respondent behaviour. This last distinc-
tion attempts to distinguish between behaviour that is emitted and
behaviour that is elicited.
With these aids, of course, it should be possible to give some
model, although generally Skinner attempts no more than a re-
statement of experimental results. He makes two further points:
that primary reinforcement and habit strength (see page 197) are
not the same, rather it is the patterning of reinforcement that
matters, and also the derived secondary reinforcement. All this
leads to difficulties in assessing the relative value of reinforcers,
and although it would not appear to be circular, it is necessarily
arbitrary, and allows of little or nothing in the way of prediction.
The law of effect itself is a basic issue in all learning theory, and
in some form it seems inescapable.
The third principle of reinforcement is the principle of expect-
ancy, and this is used in the context of instrumental conditioning
to explain the varieties of conditioning known as 'avoidance* and
'secondary reward*. According to the principle of expectancy,
reinforcement must be such as to confirm an expectancy (or
expectation), and the expectancy itself is said to depend on pre-
vious learning. We can say that an expectancy is a theoretical term
PSYCHOLOGICAL THEORY OF LEARNING
191
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192 THE BRAIN AS A COMPUTER
which implies the combination stimulus-response-stimulus, where
the emphasis is 'forward looking* and illustrative of 'purposive*
action.
We must now consider a little farther this central problem of
reinforcement. Broadbent (1958) doubts the validity of primary
and secondary reinforcement as a principle of selection in learning.
Many writers have suggested that novel or strong stimuli are
themselves effective motivators (Berlyne, 1950; Miller and
Kessen, 1952) and there is some neurophysiological support for
this idea (Sharpless and Jasper, 1956).
We would re-emphasize here what we have already said about
these matters, and in particular that in our logical net models we
have assumed that motivation may initiate searching behaviour as
readily as it may itself be built upon selective reinforcement. We
would also want to include here curiosity as a drive, and certainly
we must accept the fact that needs may be set up by conceptual
means. On the associative principle, then, we may expect needs to
occur because of an association with something else that leads to
the organism producing searching activity. This is like saying that
thinking about food will make you hungry, or rather, that it may
do so under certain circumstances, the additional circumstances
being that some need of an organic kind must also exist, although
on its own it would not have led to drive reducing behaviour until
later. It is the association that 'makes the person think about food*
that leads to the production of searching activity.
It may seem that this extension of reinforcement spoils the
Hullian theory, but in fact we would argue that it merely calls for
an expansion.
To take up one particular point made against reinforcement
theory by Broadbent (1958, pp. 245 et seq.), when he asks why the
rat does not learn to go down 'blinds' in maze-running when the
trial as a whole is rewarded, this is, clearly, not to be taken too
seriously, since there are various ways out of the dilemma so
presented. Perhaps the most obvious one is to remember that,
while we may regard the total running of a maze as a trial that may
be reinforced, the rat may well regard each bit of maze as some-
thing that is separately reinforced, and these blinds are of course
non-reinforcing because they stop the rat, however hungry or
curious or both he may be, from moving forward.
PSYCHOLOGICAL THEORY OF LEARNING 193
In fact no great problem really exists here since the selective
nature of learning can only be explained in terms of selective
reinforcement, wherever and however that principle is to be
applied. The problem is, of course, to make the details of its
application clear, and to explain why a degree of stability occurs in
behaviour in spite of the vast range of possible stimulus-response
connexions. It is perhaps over this last point that we must add the
amplifying effect of selection by attention to the mere application
of secondary reinforcement.
Table I illustrates well that the distinction between the various
models of learning proposed is a matter of the theoretical terms
used, and of their interpretation, and we are interested to know
whether this implies a difference in the underlying model. We
add two definitions to those already given; they are by Hilgard and
Marquis.
(1) Heterogeneous Reinforcement. The strengthening of a condi-
tioned response through reinforcement which depends on a
response which does not resemble the conditioned response. This
is a characteristic of reward and escape learning, but not limited
to it. A simple example would be the rewarding of a head move-
ment by the presentation of a carrot.
(2) Homogeneous Reinforcement. The strengthening of a condi-
tioned response by reinforcement with an unconditioned stimulus
which evokes activity similar to the conditioned response, required
according to the substitutional principle. Here, a simple example
would be the salivation of a dog leading to food. It is homogeneous
in that the salivating is something normally connected with food,
whereas in heterogeneous reinforcement, as we have seen, it may
be completely unconnected.
Obviously, crucial experimental tests are necessary to distinguish
the above systems if they are to be taken over in all-embracing
fashion. Brogden (1939) has carried out an experiment that
claims to discriminate between the principles of effect and
substitution.
In this experiment dogs were trained in conditioned response
technique, in pairing a bell and shock stimulus to get conditioned
leg withdrawal response, and rewarded with food when the correct
194 THE BRAIN AS A COMPUTER
response was made. Omission of unconditioned stimulus (shock)
on 1000 trials led to no extinction on conditioned withdrawal.
This may be taken to favour the principle of effect as opposed to
substitution in this situation, but whether on the strength of it one
can be any nearer saying that the effect is more general than
substitution is open to manifest doubts. In fact, one can remind
oneself again that the attempt is to distinguish between different
theoretical terms, and that only. The above table does not disagree
over performance, but only on the constructed theory designed to
explain it.
It will be well to note what is involved here. Different sorts of
experimental situations promote different sorts of behaviour, and
these can be categorized as in the above table. The scientists J s
problem is to find the common elements, and integrate such a set
of elements into a theory which covers each type as a special case of
a general theory; and while as yet this may or may not be possible,
it is certainly necessary at some stage if there is to be a scientific
theory of behaviour. In such experiments it is always being assumed
that individual difference as a variable is cloaked by general
similarity, i.e. that individual variation is markedly less than the
factors in common, in the particular aspect of behaviour being
considered. If this were not so, it would be almost impossible to
have a science of behaviour; or at any rate a deterministic science
in the sense of classical physics or chemistry.
Is it then possible to glimpse, at this stage, some integrative
aspects in learning? Are the explanations of substitution, effect and
expectancy really mutually exclusive? Do they refer to the same
levels of behaviour? In this respect it is important to consider the
comparative factor; have all the experiments been on the same sorts
of organisms? This last point may be important when it is recalled
that, in the early Gestalt Watson differences over insight, and
trial-and-error learning, Kohler's work was largely on apes, and
Watson's on rats. It seems possible that the character of behaviour
is more complex as we ascend the evolutionary scale, and this is
another barrier to generalization.
No adequate statements can really be made until more of molar
behaviour theory has been investigated, but it is instructive to
consider the Hilgard and Marquis table of comparisons further.
According to this table, classical conditioning can be explained by
PSYCHOLOGICAL THEORY OF LEARNING 195
substitution; what, then, is substitution? The definition given by
Hilgard and Marquis (p. 76) is:
A conditioned stimulus, present at the time that an original stimulus
evokes a response, will tend on subsequent presentation to evoke that
response.
In tentatively accepting Pavlov's rather than Guthrie's principle
it is accepted that substitution occurs as a matter of degree, and
stimulus is defined independently of the conditions.
But Hilgard and Marquis try a further, and more adequate,
definition of substitution:
An activity initiated by a stimulus, occurring at the same time as another
activity which results in a response will tend on subsequent occurrences,
to evoke that response.
The penultimate word 'that' in this definition may result in this
being dubbed a special case. Instead, similar (with conditions to be
specified) might be a step towards generality.
This point is brought out, we shall remember, in our logical net
(see Fig. 4, Chapter IV), where a distinction was made between
either the ^'-element or the ^'-element and (-4jB)'-element.
Obviously this network is constructed in terms of the distinction
made independently and proves nothing, except perhaps the
simplicity and the naturalness with which the response to A.B
should be somewhat different from that to A or B alone.
A comparison of the effect principle and the substitution principle
of conditioning might be taken to imply that homogeneous rein-
forcement is a special case of heterogeneous reinforcement.
There is a brief reference to the expectancy theorist in the
phrase, 'learning occurs only if response is part of a behaviour-
route to a goal'. What one knows is that a pattern of performance
takes place, and from this the theoretical term 'learning' is
introduced, and the organism is modified. The expectancy
theorist's description in this case is identical with the other two if
only it is said that, in these very limited conditions, the part of a
behaviour-route is a limiting case, and happens here to be the
whole of the behaviour-route to the goal.
It may be tentatively suggested that the three explanations of
classical conditioning are by no means as different as they may
appear at first sight, encouraging further the notion that it is at the
level of the theory language, rather than at the level of the model
196 THE BRAIN AS A COMPUTER
that differences occur. It seems perfectly possible that a rapproche-
ment can be brought about between expectancy and effect, with
substitution as a special case of either. The real point here is that
when the vague verbal propositions of the various protagonists are
tested by the construction of models, it becomes clear that their
differences are differences of interpretation, or of philosophical
directives that are being brought to bear on the subject. This
belief is further encouraged by the fact that the molar type of
explanation is based on overworked theoretical terms. They are,
in fact, propositions that invite vagueness, and the maximum
interference from the methodological or philosophical prejudices
of the particular theorists and experimentalists.
Hull's theory of learning
In considering Hull's position in reinforcement theory, we shall
draw on his re-stated postulational position (Hull, 1950). There is,
of course, more detail given by Hull than it is proposed to discuss
here, but the basic postulates III-IX which refer to the problem
of reinforcement will be quoted immediately. Hull (1952) further
modified his theory but only to a minor extent and these further
modifications will not be considered here.
POSTULATE III
Primary reinforcement. Whenever an affector activity (R) is
closely associated with a stimulus afferent impulse or trace ($') and
the conjunction is closely associated with the diminution in the
receptor discharge characteristic of a need, there will result an
increment to a tendency for that stimulus to evoke that response,
Corollary (i) Secondary motivation. When neutral stimuli are
repeatedly and consistently associated with the evocation of a
primary or secondary drive and this drive undergoes an abrupt
diminution, the hitherto neutral stimuli acquire the capacity to
bring about the drive stimuli (SD) which thereby become the
condition (CD) of a secondary drive or motivation.
Corollary (ii) Secondary reinforcement. A neutral receptor impulse
which occurs repeatedly and consistently in close conjunction with
a reinforcing state of affairs, whether primary or secondary, will
itself acquire the power of acting as a reinforcing agent.
PSYCHOLOGICAL THEORY OF LEARNING 197
POSTULATE IV
The law of habit formation (sf/js). If reinforcements follow each
other at evenly distributed intervals, everything else constant, the
resulting will increase in strength as a positive growth function of
the number of trials according to the equation,
POSTULATE V
Primary motivation or drive (D). (A) A primary motivation (Z>),
at least that resulting from food privation, consists of two multi-
plicative components, (1) the drive proper (Z>'), which is an
increasing monotonic sigmoid function of h, and (2) a negation or
inanation component (E) which is a positively accelerated mono-
tonic function h decreasing from 1*0 to zero,
i.e. D = D'xE
(B) The functional relationship of drive (D) to one drive condi-
tion (food privation) is: from h = to about 3 hr; drive rises
in an approximately linear manner until the function abruptly
shifts to a near horizontal, then to a concave-upwards course,
gradually changing to a convex-upwards curve reaching a maxi-
mum of 12*30 at about h = 59, after which it gradually falls to the
reaction threshold (sL^) at around h = 100.
(C) Each drive condition (C#) generates a characteristic drive
stimulus (Srf) which is a monotonic increasing function of the state.
(D) At least some drive conditions tend partially to motivate
into action habits which have been set up on the basis of different
drive conditions.
POSTULATE VI
Stimulus-intensity dynamism (V). Other things constant, the
magnitude of the stimulus intensity component (V) of reaction
potential ($$ is a monotonic increasing logarithmic fimction of S.
POSTULATE VII
Incentive motivation (K). The incentive function (K) is a nega-
tively accelerated increasing monotonic function of the weight (w)
of food given as reinforcement,
i,e. # = 1-1
198 THE BRAIN AS A COMPUTER
POSTULATE VIII
Delay in reinforcement (J). The greater the delay in reinforce-
ment, the weaker will be the resulting reaction potential, the
quantitative law being,
J = 1(H*
POSTULATE IX
The constitution of reaction potential (sEx). The reaction
potential (sEp) of a bit of learned behaviour at any given stage of
learning is determined (1) by the drive (Z)) operating during the
learning process multiplied (2) by the dynamism of the signalling
stimulus at response evocation (F 2 ), (3) by the incentive reinforce-
ment (K), (4) by the gradient of delay in reinforcement (J), and
(5) by the habit strength (sH R ),
where S&R =
and F t is the stimulus intensity during the learning process.
Postulates I, II, IX (corollaries), XI, XII, XIII, XV, XVI,
XVII and XVIII are not needed for our examination of Hull's
theory of reinforcement; if needed by the reader, reference should
be made to the original paper (Hull, 1950).
The three well-known questions of Postman (1947) still serve
as a useful 'prop* for a discussion of reinforcement. They are :
(1) What is the agent responsible for reinforcement?
(2) What is it that is reinforced?
(3) What is the basic mechanism of reinforcement?
Wolpe (1950) aimed his solution directly at (3), and was criticized
by Seward (1950) for having oversimplified the problem; he found,
indeed, that Wolpe's theory was lacking in cogency. Seward
returned to an examination of (1) and (2), which appeared to him
to be of first importance. He recognized the many-meaninged
nature of the term 'reinforcement', and he built on Meehl's
(1950) definition to give the following definition:
When a stimulus change -X", following a response R to a situation *S,
increases the probability of R to S, X is called a reinforcer, and its pre-
sentation is called a reinforcement.
PSYCHOLOGICAL THEORY OF LEARNING 199
It will be noticed that this is much more general than Hull's
definition (postulate III), and admirably defines the activity of the
M-system in our logical net (Chapter V).
Let us now proceed to Hull's new system. The most striking
change is the clear-cut separation between learning and perform-
ance. A comparison between Hull's old and new definitions of
both $HR and S&R illustrate the matter.
OLD DEFINITIONS
S H R = (!-
NEW DEFINITIONS
and substituting for K, J, and $H R we get:
sE R = DV (1-10-^)10-^(1-
The resemblance between the old definition of jsHn and the new
definition of sEn is obvious. Omitting e~ ut , and replacing e by 10,
and lastly, put w for W, and the equations are identical. It is clear
that K and J no longer enter the equation for sH R , but they do
directly enter sE R> thus allowing for sudden changes in perform-
ances. Seward has neatly demonstrated this point (Seward, 1950).
Now these brief statements must suffice to show that Hull's
revision has had the effect of making $E R , rather than sH R > the
principal variable affected by reinforcement. This was an attempt
to meet the criticisms of the neo-Pavlovian S R theories made
by the expectancy theorists to the effect that the law of effect
applies to performance rather than to learning. The result, then,
has been to bring the Hull theory much nearer to the Tolman
theory; but we shall be able to see this much more clearly after
our review of Tolman.
For Hull, the basis of learning is still the strengthening of SR
bonds, although the actual relationships between the theoretical
terms which cover the internal variation have now been changed*
It is possible that the problems of latent learning are now more
susceptible to treatment, and the theory has probably gained in
generality and flexibility. However, there is still the question of
testing the theory, and that will have to be done before any
200 THE BRAIN AS A COMPUTER
detailed judgment can be made. One might guess a priori that no
adequate definition of a theoretical term such as &HR can be given
as a function of N alone. It suggests an unlikely simplification, of
the type associated with Guthrie's theory.
Furthermore, Seward has pointed out that it is at least unlikely
that the present place of J and K in the definition of $ER is
adequate. Indeed, one can go further and question whether such a
linearly related system of theoretical terms can adequately mirror
the complexities of even relatively simple organisms' performances,
under all circumstances, with anything approaching the necessary
degree of approximation. The attempt seems thoroughly worth-
while but, with all its clarity and conciseness, the theory is still
open to objections on the grounds of vagueness. The particular
interpretation that one gives to 'response', for example, seems vital
to the acceptance of the basis of the theory, and in particular, the
definition of sHR depends crucially on precisely what constitutes a
trial, and so on.
Seward (1950) sees the difference between the Hull and Tolman
theories as primarily a difference between the habit-builder
(rS G ) and a 'mobilizer of demand' (Tolman, 1932), 'cathexis'
(Tolman, 1934), or 'progression readiness' (Tolman, 1941). On
the other hand, Meehl and MacCorquodale (1951) describe the
ultimate non-verbal difference between Tolman and Hull as
dependent on the notion of 'response'. In fact, to put it another
way, the difference could be stated simply as: Tolman's theoretical
terms are more central than Hull's. We shall maintain that the only
difference is in the theory language, and not in the model at all.
Before we discuss Tolman's expectancy theory, we must
remark that a formalization of Hull's earlier theory of behaviour
has been undertaken by Fitch and Barry (1950) and although we
cannot discuss this formalization here it takes Hull's theory one
stage nearer to the sort of precision we need, for it is a model of the
process implied by the learning theory and, although applied to
the older Hull theory, it makes it easier to see what sort of blue-
print is explicitly entailed by Hull's theory language.
Tolman's theory
Tolman's system will now be briefly described. His work has
not been systematically stated nor, as yet, put into postulational
PSYCHOLOGICAL THEORY OF LEARNING 201
form, although recently MacCorquodale and Meehl (1951) have
proposed a provisional set of postulates for it.
Let us first outline Tolman's theory in simple terms. The core
of his theory, and the equivalent proposition to reinforcement,
is the setting up of an expectancy; this is a central theoretical term.
Tolman himself talks in terms of strip maps, and it is clear that
some sort of internal mapping is, in fact, envisaged, although as
Spence (1950) has pointed out, this map-control-room vs. telephone
switchboard way of comparing Tolman and Hull is merely a
matter of colourful metaphor, and not relevant to a genuine com-
parison.
The important points have been impinged on by MacCorquo-
dale and Meehl (1954). They point out that there are certain
important aspects of behaviour which are not necessary to an
expectancy theory, including 'Gestalt-configural stress', 'per-
ceptual field stress', 'discontinuity in discrimination learning', and
perhaps more surprisingly, the distinction between 'learning and
performance'.
The essential difference claimed for Tolman's theory is in the
fact that it is an SS, rather than an SR, theory. Tolman's system
anticipates increments in learning other than by an S-then-J?
sequence actually run off in performance. The basic definition of
expectancy has previously been quoted, and here we shall state the
preliminary postulates, as suggested by Meehl and MacCorquo-
dale, for the introduction of an expectancy postulate. These are
essentially tentative. The logical net model can, of course, be
equally effective in dealing with SS as with SR relations.
p. 1. Mnemonization: The occurrence of the sequence S^R^
S% (the adjacent members being in close temporal contiguity)
results in an increment in the strength of an expectancy (S^R^S^).
The strength increases as a decelerated function of the number of
occurrences of the sequence. The growth rate is an increasing
function of the absolute value of the valence of S 2 . If the termina-
tion by S% of the sequence (S^ >R ) is random with respect to
non-defining properties of S^ the asymptote of strength is <
relative frequency of P of *S 2 following S^R^ (i.e. a pure number).
How far this asymptote is below P is a decelerated function of the
delay between the inception of R^ and the occurrence of S z .
o
202 THE BRAIN AS A COMPUTER
p. 2. Extinction: The occurrence of a sequence S^-^-R l9 if no-
terminated by #2, produces a decrement in the expectancy if th<
objective iS 2 -probability has been 1*00, and the magnitude of this
decrement is an increasing function of the valence of S 2 and the
current strength of (S^R^S^. Such a failure of S% when P has beer
= 1 is a disconfirmation provided (SjR-^S^) was non-zero. For casei
where the S 2 -probability has been <1*00, if this objective prob-
ability P shifts to a lower P', and remains stable there, the expec-
tancy strength will approach some value <P' asymptotically.
p. 3. Primary stimulus generalization: When an expectancy
(SiR^S^ is raised to some strength, expectancies sharing the Ri anc
*S 2 terms and resembling it on the elicitor side will receive some
strength, this generalization strength being a function of the simila-
rity of their elicitors to S v The same is true of extinction o:
osyw
p. 4. Inference: The occurrence of a temporal contiguity S%S*
when (SiRiS 2 ) has non-zero strength, produces an increment ir
the strength of a new expectancy (S^S*). The induced strength
increases as a decelerated function of the number of such contigui-
ties. .The asymptote is the strength of (S^^S^) and the growtt
rate is an increasing decelerated function of the absolute valence
of S*. The presentation of 3 without S* weakens such an inducec
expectancy S^R^S*. The decrement is greater if the failure of S*
occurs at the termination of the sequence S 1 -^R 1 --^S 2 than if i 1
occurs as a result of presentation of S 2 without S* but not follow-
ing an occurrence of the sequence.
p. 5. Generalized inference: The occurrence of a tempora
contiguity S 2 S* produces an increment in the strength of ar
expectancy S^R^S* provided that an expectancy S^R^^ was ai
some strength and the expectandum S 2 ' is similar to $2. The
induced strength increases as a decelerated function of the
number of such contiguities. The asymptote is a function of the
strength of S^RjJS^ and the difference between S% and 2 '. The
growth rate to this asymptote is an increasing decelerated functior
of the absolute valence of S*.
p. 6. Secondary cathexis: The contiguity of S% and S* when S*
has a valence |V| produces an increment in the cathexis of S 2
The derived cathexis is an increasing decelerated function of the
number of contiguities, and the asymptote is an increasing decele-
PSYCHOLOGICAL THEORY OF LEARNING 203
rated function of |V| during the contiguities, and has the same
sign as the V of S*. The presentation of S 2 without 5*, or with S*
having had its absolute valence decreased, will produce a decrement
in the induced cathexis of 5 2 .
p. 7. Induced elicitor-cathexis: The acquisition of valence by an
expectandum 3 belonging to an existing expectancy (^i^?i5 2 )
induces a cathexis in the elicitor S I9 the strength of the induced
cathexis being a decelerated increasing function of the strength of
the expectancy and the absolute valence of S z .
p. 8. Confirmed elicitar-cathexis: The confirmation of an expec-
tancy (*S r 1 72 1 *S f 2 ), i.e. the occurrence of the sequence (S l -^-R I -^S 2 )
when (5 1 J? 1 iS f 2 ) is of non-zero strength, when S 2 has a positive
valence, produces an increment in the cathexis of the elicitor S^.
This increment in the elicitor-cathexis by confirmation is
greater than the increment which would be induced by producing a
valence in 5 2 when the expectancy is at the same strength as that
reached by the present confirmation.
p. 9. Valence: The valence of a stimulus S* is a multiplicative
function of the correlated need D and the cathexis C* attached to
S* (applies only to cases of positive cathexis).
p. 10. Need strength: The need (D) for a cathected situation is an
increasing function of the time-interval since satiation for it.
Upon present evidence, even basic questions of monotony and
acceleration are unsettled for the alimentary drives of a rat, let
alone other drives and other species. There is no very cogent
evidence that all or even most 'needs' rise as a function of time
since satiation, although this seems frequently assumed. Even the
notion of satiation itself, in connexion with 'simple* alimentary
drives, presents great difficulties-
p. 11. Cathexis: The cathexis of a stimulus situation S* is an
increasing decelerated function of the number of contiguities
between it and the occurrences of the consummatory response.
The asymptote is an increasing function of the need strength
present during these contiguities. (There may, however, be some
innately determined cathexis.)
p. 12. Activation: The reaction-potential S^R of a response J? x
in the presence of 5 X is a multiplicative function of the strength of
the expectancy (SJR^S^ and the valence (retaining sign) of the
expectandum. There are momentary oscillations of reaction-
204 THE BRAIN AS A COMPUTER
potential about this value $ER, the frequency distribution being at
least unimodal in form. The oscillation of two different S^R'S
are treated as independent, and the response, which is moment-
arily 'ahead' is assumed to be emitted.
Add to this the fact that Tolman regards 'Maintenance Schedule 1
(M), 'appropriate goal object* (<?), 'mode of stimuli' (5), 'type of
motor response 5 (R), 'cumulative numbers of trials' Z(OBO),
'pattern of preceding maze units' (P), as the set of independent
variables. The equivalent intervening variables are, 'demand',
'appetite', 'differentiation', 'motor skill', 'hypotheses' (which he
later called 'expectancies'), and 'biases'. The relation of the
independent and intervening variables is a function of 'heredity',
'age', 'previous training', and 'endocrine, etc., states'. Finally,
there is 'performance', which is a complicated function (generally
non-linear) of these three sets of variables.
Tolman regards his intervening variables as in need of defining
experiments. The trouble here is that it does not appear possible
to apply the usual form of linear experimental situation to define
variables that will generally be non-linear. It is probable, rather,
that the so-called intervening variables should actually be regarded
as full logical constructs, as Tolman himself now seems to suggest
(Tolman, 1952).
Now a comparison of Hull's theory with Tolman's shows that
there is, in fact, precious little difference between them. Indeed, it
is possible that the theories are interchangeable, provided a suit-
able interpretation is given to the word 'response' by the SR
school. If, however, they insist on interpreting this as an effector
event, then it does seem to constitute a definite non-verbal
difference (Meehl and MacCorquodale, 1951; MacCorquodale
and Meehl, 1954). From the cybernetic point of view our suspicion
is again that the differences are at the level of the theory language;
it is the same sequence of events, S^R^-S^-R^- th at i fi being
dealt with, only the one takes SR, and the other S-RS, as the
basic unit.
Tolman's system, generally, is a molar behaviourism, as is
Hull's, but it tends to emphasize purpose in the theory construction
in a way that Hull's theory does not. In Tolman there is no direct
use of reinforcement, and in place of it we find the notion of
expectancy based on sign-learning (cf. expectancy and effect earlier
PSYCHOLOGICAL THEORY OF LEARNING 205
in this chapter). The strength of Tolman's theory can be seen most
favourably in three situations: (1) Reward-expectancy, (2) Place
learning, and (3) Latent learning.
Tinklepaugh's (1928) experiments with monkeys are a classical
illustration of (1). A monkey saw a banana placed under one of two
containers, and was then taken away. On returning later he showed
accuracy of choice. When a lettuce was substituted for the banana
in the monkey's absence, he exhibited searching activity on his
return.
The place-learning experiments, of which MacFarlane's work
(MacFarlane, 1930) may be regarded as typical, tend to show that
the actual process of running a maze is not a chain of S R acts,
but involves a knowledge of the maze-as-a-whole a sort of
insight. Place-learning is exemplified by an organism learning to go
to a particular spatial location X, say, regardless of the route taken.
Latent learning supplies perhaps the strongest experimental
evidence in support of Tolman's position as opposed to the older
Hull theory (Blodgett, 1929; Tolman and Honzik, 1930), and this
will be reviewed separately.
A further experiment carried out by Krechevsky (1932a, 1932b)
must suffice as an example of the type of hypothesis theory that is
characteristic of the expectancy or S-S theorist, as opposed to the
S-R theorist.
This particular example of Krechevsky's work is an analysis of
individual rat performance. The experimental situation involved
the training of rats to discriminate between a path containing a
hurdle and an equally lighted path containing no hurdle. A multiple
discrimination box was used, and the performance was documented
in terms of number of errors, number of right turns, number of
left turns, and number of terms in keeping with an alternating
scheme. On statistical analysis, it seems that any response occur-
ring above 73 per cent would almost certainly be a non-chance
factor. The graph (Fig. 1) shows the cases of greater than 73 per
cent response rate very clearly, and is therefore thought to con-
stitute evidence for 'hypotheses'.
Krechevsky (1933a, 1933b) also avers that 'bright' rats use
spatial hypotheses predominantly, whereas 'dull' rats are more
prone to use non-spatial hypotheses (e.g. visual, in the particular
experiment). Control rats appeared to be neutral in this situation.
206
THE BRAIN AS A COMPUTER
Krechevsky (1935) farther reports that the number of 'hypotheses
used by rats is decreased in discrimination learning. In the argu
ment regarding bright and dull rats there exist the seeds of possibl
circularity in an objectionable sense.
4O
PROGRESS OF POSITION AND HURDLE HABITS
50
60
70
80
90
IOO
Chance
Chance zone limit
/ Hurdle habit
/ Right position
habit
5
Days
8
FIG. 1. EVIDENCE FOR HYPOTHESES IN A RAT. The rat was trained
to discriminate between two paths only one of which contained
a hurdle to be surmounted. The solid line represents the per-
centage of errors made on successive days, while the broken line
represents the right-turning response of the subject. It should be
observed that the right position habit occurs with a frequency of
from 70 to 100 per cent during the first 6 days of training. It then
approaches a frequency that could be attributed to chance.
This suggests that the rat was guided by the hypothesis that a
right turn would solve the problem. This 'spatial hypothesis'
was finally given up in favour of the correct 'non-spatial hypo-
thesis', which in fact means that the correct path is the one with
the hurdle. (After Krechevsky.)
The main fact about Krechevsky's work that will be of import-
ance is the relation between learning and performance. Inevitably
the process is to observe performance, and make inferences abou
learning, and here the notion of hypotheses does, in fact, appear tc
fit very well.
Some attempts have been made to decide between S-R and S-
PSYCHOLOGICAL THEORY OF LEARNING 207
theory at the experimental level. Two examples will probably be
sufficient illustration (Humphreys, 1939a, 1939b).
Humphreys carried out an experiment on eyelid conditioning
in humans. Conditioned discrimination was thought to be more
rapid when subjects knew which stimulus of a pair was to be
positive, which negative, etc., rather than when experience was a
necessary prelude to prediction. Humphreys showed that a
random alternation of reinforcement and non-reinforcement led to
a high level of conditioning, and a greater resistance to extinction
than if reinforcement was 100 per cent.
He assumed that changing hypotheses accounted for this and,
using humans in a study of verbal expectations, he appeared to get
corroborative results. The actual study involved showing two
lights, one at a time, and when one light was switched on, asking
the subject whether the other light would follow or not. Two
groups were set up, and the first group was always shown light 1
followed by light 2, while the second group had a random distribu-
tion of light 2 or not light 2 after light 1 . The second group guessed
at chance level which, so far, was to be expected. The next part
was the extinction of these responses, and this was seen to be much
quicker in the first group. These experiments seem to favour an
expectancy theory; in fact, the resemblance to Krechevsky's
'hypotheses' will not be overlooked.
To return to the comparison of Tolman and Hull, one or two
tentative statements may be made. Tolman tends to place emphasis
on the organism dominating its environment, while for Hull,
emphasis is placed on the environment's domination of the
organism. It is only a matter of different emphasis, but this
difference can be traced back to the differences in philosophical
directives accepted by their two viewpoints. They are modern
variations on the well known mechanistic vs. teleological contro-
versy in biology, and their positions have been modified to such an
extent they have arrived at situations which differ by only a very
little, if at all.
Partial reinforcement, latent learning and some other
variables
Before it is possible to complete an assessment of molar theories
from a cybernetic point of view, it is essential to consider some of
208 THE BRAIN AS A COMPUTER
the other principal variables and theoretical terms in the molar
psychological field. It is intended to start with 'partial reinforce-
ment', and to make considerable use of the summary made by
Jenkins and Stanley (1950) in the discussion. For reference
purposes it might be convenient to give a working definition of
'partial reinforcement'.
Partial reinforcement = df. Reinforcement which is given on
only a certain percentage of trials (or following responses). Thus
the limiting cases are: total 'reinforcement' 100 per cent, and no
'reinforcement' per cent.
In partial reinforcement, interest will be centred on a brief
summary of the experimental evidence, and a more detailed study
of the suggested theories. Platonov is one of the first experimenters
credited with partial reinforcement experiments. In one series of
his experiments a conditioned response was maintained by
application of the unconditioned stimulus on the first trial only of
each day. Pavlov, Wolfle and Egon Brunswick carried out early
experiments in this field, and Egon Brunswick was led to his
interesting probability theory of discrimination (Brunswick, 1939,
1943, with Tolman, 1935),
The most important experiments would appear to be those
carried out by Skinner, and since in this sort of work it is not
humanly possible to investigate each and every case separately for
slight variations in design it will be assumed that a certain degree
of generalizability is possible, and Skinner's work will be regarded
as, largely, typical. At this point it is important to notice that, to
him, the operations are the principal concern, and not such theo-
retical terms as 'reflex reserve', which are invoked to explain them.
Skinner's experimental work is on rats. The first experiments
(1933) compared lever-pressing performance following a single
reinforcement, and following 250 reinforcements. He found that
the relationship was, at least, not a linear one.
The actual performance demanded of the rats was that of lever-
pressing, and the reinforcement was the pellet of food received
from the apparatus.
Using essentially the same lever-pressing apparatus, Skinner
has shown two different sorts of partial reinforcement. The first,
which he calls periodic reinforcement, involves the use of rein-
forcers at standard intervals of time (Skinner, 1938). This implies
PSYCHOLOGICAL THEORY OF LEARNING
209
a constant amount of reinforcement per unit of time, and leads to a
constant response performance. Over a considerable range, Skinner
found a roughly constant response rate of 18 to 20 responses.
From this is derived the notion of 'extinction ratio'. (Extinction
ratio = df. the uniform number of responses per reinforcement.)
This is supposed to be a measure of learning under varying condi-
tions of drive. Parenthetically, it may be noticed that the greater
maintenance of response-rate observed in partial reinforcement is
2OO
ISO
IOO
50
FOLLOWING 25O V
REINFORCEMENTS "
'FOLLOWING A SINGLE
S RE!NFORCEMENT
TIME ONE HOUR
FIG. 2. EXTINCTION OF LEVER PRESSING BY RATS. The graph
illustrates simply the different amount of responding after one
and after 250 reinforcements.
accounted for by Skinner simply by employing a theoretical term,
'reflex reserve'.
In Skinner's second type of partial reinforcement, which he
called 'reinforcement-at-a-fixed-ratio', the pellet is delivered after
a standard number of responses, instead of after a standard interval
of time, and the result is a very high response-ratio, the extinction
ratio changing from 20 : 1 in Skinner's first type I situation, to
200 : 1 in this. Two sets of graphs will illustrate these well-known
results.
210
THE BRAIN AS A COMPUTER
This work does require some explanation, but before this is
discussed we must devote some attention to more general con-
siderations in the design of partial reinforcement experiments,
'Frequency' and 'pattern* may be seen to be at least two of the
most important variables, i.e. continuity of reward and regularity
of reward are the variables that appear to be most important, and
15 20
Time (one hour) Time (daily one-hour periods)
FIG. 3. RESPONSES WITHIN ONE AND WITHIN REPEATED SESSIONS
OF PERIODIC REINFORCEMENT. In the left-hand figure, the situa-
tion was one in which a pellet of food was delivered every 3, 6, 9
and 12 min. respectively. The more frequent the reinforce-
ment the more rapid the rate of responding. In the right-hand
figure is shown the cumulative record over several of the rats
depicted in the left-hand figure.
this has been illustrated by Skinner. However, there are two kinds
of experimental situation which need to be distinguished: (1) those
where the responding is independent of the experimenter and of the
environment, circumstances which cover both types of Skinner's
conditioning, and called, after Jenkins and Stanley, 'free respond-
ing', and (2) experiments where trials are involved, and there is
control of opportunity to respond, e.g. mazes, multiple-response
PSYCHOLOGICAL THEORY OF LEARNING
211
situations, etc. (this is referred to as 'trial responding'). (1) and
(2) differ with respect to a time schedule. The following table
o
0.
u_
o
o:
UJ
m
s
o
48 I
576
384
192
ONE. HOUR
ONE HOUR ONE HOUR
FIG. 4. RESPONSES WITH REINFORCEMENT AT A FIXED RATIO.
Responses from individual rats reinforced every 48, 96 and
192 responses. The point of reinforcement is indicated by the
short horizontal lines.
(Jenkins and Stanley, 1950) is useful in distinguishing the various
cases.
Variations
of
reinforcement
Situation
Free-responding
Trials
Simple Alterna- Multiple
response tive responses
response
Time
Regular
Irregular
Periodic reinforce-
ment
Aperiodic reinforce-
ment
Time variation not ordinarily
used
No. of
responses
Regular
Irregular
Fixed ratio rein-
forcement
Random ratio rein-
forcement
Fixed ratio reinforcement
Random ratio reinforcement
212 THE BRAIN AS A COMPUTER
It will be noted in these experiments that initial training has
always been on reinforcement, and only subsequently has partial
reinforcement been introduced. Keller (1940) carried out an
experiment in this field. A group of rats were continuously re-
inforced for one period, and then were split into two groups, one of
them being subjected first to continuous and then to periodic
reinforcement, and the other group being given the same reinforce-
ments, but in the opposite order. Using resistance to extinction as
a measure, the second group was far superior for the first five
minutes only.
Apart from these difficulties, and suggestions of further com-
plexity, there are other problems too detailed to enumerate, such
as inter-trial interval, massed and spaced training, and the complex
relationship between number of trials and number of reinforce-
ments. For example, a group that has been partially reinforced can
be compared with a continuously reinforced group, with respect to
number of trials or number of reinforcements, but not both.
Further, there is the variability of response-strength at the end of
learning to be considered, in comparing resistance to extinction in
continuous and in partially reinforced groups. These, of course, are
only the major aspects of the problem.
One point worth noting especially is that made by Jenkins and
Stanley, that there is a marked skewness in various response sets,
especially with respect to extinction, which implies that the use of
many standard statistical methods is invalid.
However, to put it concisely, it may be said that the problems of
partial reinforcement may be placed under five headings: (1) Ac-
quisition, (2) Performance, (3) Maintenance, (4) Retention and
(5) Extinction. As far as acquisition is concerned, the general
findings are that there is little apparent difference between the
continuous and the partial groups, although the former appear to
have a slight advantage. The same state of affairs appears to pertain
in (2), (3) and (4), and it is only in extinction that a serious reversal
is apparent. Here the partial group were significantly ahead of the
continuous group. These results, briefly stated as they are, require
explanation. How are they explained by molar psychologists?
In the first place there are certain, as it were, sub-difficulties.
Skinner's work on reinforcement at a fixed ratio (see Figs. 5, 6
and 7) shows oddities in graphing that appear to call for explana-
PSYCHOLOGICAL THEORY OF LEARNING 213
tion on three scores: (1) the very high rate of responding, (2) the
delay after reinforcement, and (3) the acceleration between rein-
forcements. Skinner explains these by saying that each lever-
pressing in the early part of a run acts as a secondary reinforce-
ment (this is a very important principle that requires further
analysis). (2) is explained by the 'negative factor' associated with
reinforcements, and the weakening of what Skinner calls the
reflex reserve, and (3) is a function of (1) and (2). This sort of
explanation by appeal to theoretical terms and functional relation-
ships between them is typical of molar theory, and is often difficult
to test. It is these interrelated theoretical terms that we are hoping
to model more adequately by the use of logical nets. It should be
mentioned in passing that Trotter (1957) demonstrated a major
weakness in Skinner's experiments by showing that 'responses' are
arbitrarily defined, and that semi-responses made by the rats were
simply not counted.
It is not clear that a straight application of S~R theory could
account for partial reinforcement. The fact that a reward
strengthens a response, and omission of reward weakens it, would
be insufficient to account for partial reinforcement, since it would
fail to account for the greater resistance to extinction following
partial training. Skinner, Sears, and Hull have formulated explana-
tions in terms of secondary reinforcement, although Sears pointed
out that the definition of response could be widened to meet the
difficulty, and that our treatment of units of behaviour may be at
fault. This may be true, but it does not lead to an adequate
explanation of the behaviour. Miller and Dollard (1941) have
suggested that greater resistance to extinction may be expected to
occur when unrewarded behaviour is ultimately followed by a
reward, and their argument is essentially based on a gradient of
generalization.
Mowrer and Jones (1943) accept the fact that a response
removed in time more than 30 sec from a reward is not rein-
forced, and yet they accept an explanation in terms of Perin's
'temporal gradient of reward', even though intervals far above
30 sec have been found efficacious.
Jenkins and Stanley (1950) make this comment on the above:
It would seem that some mechanism of the response-unit variety is
operating, otherwise, behaviour could not be maintained when reinforce-
214 THE BRAIN AS A COMPUTER
ments occur only once in nine minutes, or every 192 responses. A temporal
gradient restricted to strengthening only behaviour occurring not more
than 30 seconds before reward is, at best, an incomplete account. A
temporal gradient may well be one of the factors interacting with several
others, but clearly it cannot explain many of the findings that Mowrer and
Jones fail to mention.
Sheffield and Tenmer (1950) have compared the acquisition,
and extinction, of a running response under the escape and avoid-
ance procedures, and point out that extinction practically always
involves a change in the cue patterns, present in training, while
escape training does not permit the conditioning of the conse-
quences of failure to respond. Thus, correctly, their theory predicts
greater response strength for escape procedure in training, but
greater resistance to extinction following avoidance conditioning.
The modern Hull interpretation of partial reinforcement would
appear to depend wholly on secondary reinforcement, and, in this
context, it will be of special relevance to refer once more to the
work of K. W. Spence. Spence (1947, 1950, 1951, 1952) has made
the assumption that the gradient of reinforcement is a special case
of the stimulus generalization gradient. He goes on to place
emphasis on the vital nature of secondary reinforcement. Now
secondary motivation (III (i) in Hull's newer postulate system) is
said to arise when neutral stimuli are repeatedly and consistently
associated with the evocation of a drive, and this drive undergoes
an abrupt diminution. Secondary reinforcement (III (ii)) occurs
when a neutral receptor impulse occurs repeatedly, and consis-
tently, in close conjunction with a reinforcing state. The secondary
reinforcing is the fractional antedating goal response TSG, and this
is apparently conditioned, in the Hull view, to the after effects of
non-reinforcement in the stimulus compound, during training.
Sheffield (1949) goes on to argue that in extinction following
partial reinforcement the stimulus situation, by virtue of general-
ization, is more like conditioning that after 100 per cent reinforce-
ment. In extinction, as opposed to conditioning, the cue pattern is
changed greatly for the 100 per cent group, but is reinstated for the
partial reinforcement group.
It is, perhaps, enough at this stage to have isolated partial rein-
forcement, and noted that explanations can be offered by the
representatives of both Hull and Tolman, and also by Skinner,
PSYCHOLOGICAL THEORY OF LEARNING 215
that the differences are not very marked, albeit perhaps it may be
thought that Hull's is the most cogent form of explanation.
In terms of logical nets the problem of partial reinforcement can
be highlighted in an interesting way. We may ask the direct ques-
tion: will the automaton which we have so far outlined (Chapter
V) exhibit the properties manifested under partial reinforcement?
The answer appears to be 'yes', subject to a condition to be stated.
We shall assume that we are dealing with single stimuli inputs,
and that reinforcement is occurring only on 1 trial in n\ then the
belief which is confirmed is that reinforcement will occur in every
72th trial, hence the process of disconfirmation will take longer to
occur and the response rate will vary with respect to the belief
acquired and the value attributed to the stimulus.
Clearly, a stimulus may be made more valuable by its relative
rarity; the conjunction-count will therefore be greater for a rare
(though valuable) stimulus than it will be for a regular stimulus ;
but to achieve this end we must assume that the degree of need-
reduction is greater when the stimulus is more infrequent. It is
easy to see that this can be arranged in a logical net system in many
different ways.
Latent learning
In the subject of latent learning, now to be briefly considered,
there is a difficulty that does not wholly apply to partial reinforce-
ment. There is, indeed, a doubt as to whether latent learning
actually takes place or not that is, within the definitions framed
by some workers, and both Maltzman (1952) and Kendler (1952),
in criticism of Donald Thistlethwaite's summary of latent learning
(1951), were suspicious of the evidence. Maltzman suspects the
statistical evidence in the Blodgett design, and regards the criterion
for 'latent learning* as inadequate, and he proposes an alternative
interpretation. The Haney design is also criticized.
It would be as well to enumerate the designs for these types of
experiment before following up the Maltzman-Kendler comments.
Thistlethwaite classifies latent learning into four groups:
(1) Type I. The Blodgett variety, in which the rats are given a
series of unrewarded, or mildly rewarded, trials in a maze, and
then a relevant goal object is introduced before further trials take
place (Blodgett, 1929).
216 THE BRAIN AS A COMPUTER
(2) Type II. The organisms are allowed to explore the maze
prior to a trial in which a relevant goal object is used (Haney
type, 1931).
(3) Type III. Organisms (rats), which are satiated for food and
water, are given trials in a maze, the pathways of which contain the
goal objects for which the animals are satiated (Spence Lippett
type, 1940).
(4) Type IV. Organisms (rats), either hungry or thirsty, are
placed in a maze with relevant and /or irrelevant goal objects. Rats
are then satiated for formerly desired goal objects, and deprived of
the previously undesired goal object (Kendler type, 1947).
Further, the term 'latent learning' has the twofold historical
usage:
(1) Learning not manifest in performance scores.
(2) Learning that occurs under conditions of irrelevant incen-
tive.
Returning to the question of existence, Maltzman has claimed
that type I and type II (Blodgett and Haney types) do not reveal
latent learning, and can be explained in terms of the Hull and
Spence theory of reinforcement. It will be noticed immediately
that there are two quite separate points here. Maltzman's argument
appears to be that since there is improvement in performance in
the unrewarded period, then any distinction is invalid, and he
questions the statistical significance of the results. Later, however,
it appeared to him that there was some confusion over the defini-
tion of latent learning, resulting apparently from the lumping
together of the two separate propositions that: (1) latent learning
is not revealed, and (2) the phenomenon revealed can be explained
in terms of the Hull-Spence theory of reinforcement. No one, it
should be noted, is averring that latent learning is not explicable
in Hullian terms.
The Haney design is the one in which a group of hungry rats
were permitted to explore a 14-unit T-maze for 4 days (18 hr
per day), while a control group spent the same amount of time in a
rectangular maze. In this first part of the experiment neither group
was rewarded with food in the maze. Then both groups were run,
hungry, in the T-maze for 18 days, and rewarded one trial per day.
PSYCHOLOGICAL THEORY OF LEARNING 217
The experimental group, having been allowed to explore the T-
maze, had of course been able to acquire knowledge which had
been denied to the control group, but since there was no statistical
difference in performance, the result actually shows that learning
can take place without a reward. There is, however, a point here,
in that performance is taken to imply learning, and it is therefore
presumed that it is possible to identify this in a negative sense.
Without bringing out the points of Kendler's criticisms of Thistle-
thwaite in full, it may be said that there exists the usual doubt that
the existence of latent learning is supported by his experiments,
for he claims that these include all the stated conditions of latent
learning, and yet do not show that it takes place.
Kendler does make a point of logic which is of interest to us. He
says of both the Blodgett and the Tolman-Honzik experiments that
they led to the conclusion that maze performance did not neces-
sarily mirror maze learning, and he makes the point already
mentioned, i.e. that in comparing the food and no-food groups,
performance is taken as a measure of learning, whereas the same
level of performance does not necessarily imply the same level of
learning. This is a serious point, but it is possible that performance
can be taken to be the same as learning if, and only if, the motiva-
tion and reward-value of the incentive are equivalent. This is
precisely the reply that Thistlethwaite makes, and it is also implied
in Tolman's writing. The important point is whether or not
motivation can be sufficiently controlled, and the burden of proof
for this lies with the experimenters. Thistlethwaite's replies to the
criticisms of Kendler and Maltzman are of interest (Thistlethwaite,
1952). He comments initially that reference to experimental
evidence should end controversy. This is obviously over-optimistic
in practice, since the results of experiments are rarely so precise as
to allow of only one interpretation. His comment on the exclusion
of untestable hypotheses is laudable, but not clear cut. He, more-
over, appears to consider that the burden of proof, in the matter of
Kendler's criticism of his so called logical point, lies with Kendler,
and with this it is, of course, impossible to agree.
The next step is a brief re-consideration of the theoretical inter-
pretations of latent learning. The first point is that reinforcement
may be introduced (i.e. defined) in such a way that it is always
necessary to every performance, or that it may be independently
218 THE BRAIN AS A COMPUTER
defined, and thus may or may not be relevant to the behaviour
under discussion. The particular convention adopted commits us
to one of two very different interpretations of reinforcement; the
first being Hullian in type, and the second Tolmanian. The posi-
tion seems to be that if the hypothesis that reinforcement is
necessary to all learning is granted, then it is necessary by defini-
tion, and the next step must be to show, by operational methods if
possible, that such a definition is consistent with the observable
facts. This would indeed appear to be an embarrassment to the old
Hull S-R theory, but it is important to note that Hull's modified
theory (Hull, 1950) might be said to make an explanation easier.
There always remains, of course, the possibility that suitable
sources of reinforcement may be found; for instance, in the
Blodgett type experiment, curiosity and escape are, at the least,
such possible sources. There is no need here to summarize this
work in detail, as this has already been admirably done by Thistle-
thwaite (1951); it will therefore be sufficient for our purpose if a
general statement is made.
Tolman's theory would appear to have no special difficulty in
giving an account of latent learning, since it does not demand an
iS-then-jR type behaviour; and although latent learning is an
embarrassment to Hull's older theory, his modified theory (the
modifications, one presumes, were brought about to cater for this
very effect) can be made adequate by freeing both J and K from
'habit', i.e. by differentiating more sharply between learning and
performance, the gap can then be bridged.
Other problems of learning
We shall now move away from the established theories of
learning and, in considering some problems of learning theory with
which these theories were not primarily concerned, see if our
finite automaton can deal with them.
As far as latent learning is concerned, our automaton will, like
Oettinger's programme (see Chapter VI), show just this
characteristic, as indeed can any system with storage. The interest-
ing question is as to whether we should regard latent learning as
Russell (1957) does, and interpret it for the machine as 'unre-
warded experience put to use later on*. As far as logical nets are
concerned, this involves a decision as to whether or not every bit
PSYCHOLOGICAL THEORY OF LEARNING
219
of information is recorded if and only if, say, it satisfies a need. Is it
a matter of secondary reinforcement or not? This is perhaps less
important than it once seemed, but we shall continue to suppose
that information is not retained unless associated in some way with
reinforcing activities; the question is really as to how remote the
association can be.
Matrix representation of logical nets
We have already mentioned the use of matrices to represent
logical nets. Unfortunately there do not seem to be important
matrix properties which would allow us to restate the theory in
terms of groups and other abstract algebraic forms; however, for
the purposes of clarity of exposition, it is convenient to state the
obvious fact that a matrix A made up of the numbers, 0, 1 and 1
can completely define the structure of any logical net; for example,
Fig. 4 (Chapter IV) has a 'structure matrix', as it may be called, as
follows:
(1)
fO
1
1
1
I 1
1
-1
1
1
1
-1
1
1
,0
o.
The form of such structure matrices is always
O A B
focal
000
(2)
where the blocks are of input, inner and outer interconnexions.
The rows and columns are of course made up of elements A, J3,
-' N :
It is also clear that for each moment of time these connexions
may be live or dead, which means that a matrix composed of O's
and 1's accompanying a structure matrix (sometimes called a
220 THE BRAIN AS A COMPUTER
'status matrix') completely defines a logical net and its history.
Such status matrices in one form have already been discussed in
Chapter IV. Now we wish to add a further matrix, which we shall
call a .B-matrix, to add to our collection. This is mainly so that we
can quickly refer to the associations or beliefs that occur in any
logical net and let this matrix show the cumulative state of the
associations, so that a positive number in any position a^ designates
a belief that will be effective if any of its components fires, while a
negative number in that position designates a belief that will not
fire unless all the components are present.
This particular B-matrix is consistent with the B-nets we have
previously defined, but it should be emphasized that this particular
arrangement depends solely on the connexions, and the manner in
which they are chosen. This point will be seen to be of the utmost
importance when we consider the problem of extinction. This is
perhaps also an appropriate moment to make the point that we are
not committed to one particular form of connexion; the problem is
simply to make the connexions define the .B-matrix so that
they are consistent with all observed behavioural phenomena.
In what follows it will also be seen that if A and B have occurred
together more often than A and C, then when A is presented
B is assumed, by which we mean that the automaton will respond
with AB' and not AC 1 . In the same way ABC 1 is elicited when
ABC occur together more often than all proper subsets of ABC.
Retroactive inhibition
Consider the following three lists of stimulus response con-
nexions.
List 1 List 2 List 3
A-B A-D M-N
C-D C-L O-P
E-F E-B Q-R
G-H G-J S-T
I-J I-H U-V
K-L K-F W-X
and now consider the change in the JS-matrix when List 1 is
successfully learnt. Let us suppose, for simplicity, that the only
B's affected are in the first row of the matrix, and if there is an
PSYCHOLOGICAL THEORY OF LEARNING 221
increment of 1 for each occurrence, then after n trials (let us
suppose that n is fairly large) the matrix will read:
/n n ... n\
/ ... \
\0 O ... OS
(3)
Now it is clear that there will be a great difference in the nature
of the subsequent matrices according to whether list 2 or list 3 is
next used. Let us suppose they are represented by the second and
third rows respectively of the B-matrix, then they will appear
exactly the same in that, after r trials, they will have the form of the
matrix above, with either the second or third row filled with r's ;
but whereas in the case of list 2 the presence of the r's will be
completely ineffective in producing response until r>, in the
other case it will be effective as soon as r>0.
The reasons for the above are quite simple. The probability of a
particular stimulus is given wholly by the previous experience of
the system as reflected in the counting devices attached to the
classification system. Thus, for associations like .4-5, given A there
will be a response B and therefore not Z), whereas M will be
responded to immediately by N since it has no other association.
The above argument, which simply says that a conditional
probability system of the type we have defined will lead to retroactive
inhibition, can be given two different interpretations in practice,
according to whether or not it refers to the use of conditional
probability in recognition (or perception) itself. In the perceptual
case, the tied nature of associations giving the probabilities could be
said merely to cause confusion as to the identity of the object per-
ceived since, to put it simply, there would be many different physical
objects with many of the same properties. Alternatively and if
one has to choose, this seems the more likely it is the relation of
consecutive perceived events (already composed of many sub-
properties) that become confused simply because they are similar
in that some part of an association is already tied to another event.
The present discussion has been straightforward, but we must
now turn to a more complex and more interesting question.
Granted the above argument is correct and this merely assumes
that a conditional probability operates in a particular inductive
222 THE BRAIN AS A COMPUTER
manner what are the means by which we can predict closely
related phenomena? Let us first consider 'transfer of training'.
Transfer of training
Transfer of training is merely a way of describing the empirical
fact that similar tasks have a degree of 'carry over'. It is a comple-
mentary fact to retroactive inhibition, and has been neatly sum-
marized by Osgood (1949) in a simple geometrical model.
From the point of view of our machine model it is easy to see
how transfer would occur. The interesting fact is that it could be
either of the two well-known principles : (1) By virtue of some large
task involving whole sequences of events, where two sequences
had many common pairs, or (2) By virtue of stimulus generaliza-
tion, which means that two sequences of events are treated as the
same, or as being two subcases of some more general relation; this
depends on the fact that our conditional probability machine will
be capable of deriving consequences, by inductive and deductive
processes, from the relations that are observed through its per-
ceptual processes.
The first explanation is self evident, but the second needs some
elaboration. We should note, though, that here we have a case in
which what have appeared as two rival explanations could both be
appropriate to a learning machine; furthermore, they smack of the
sort of distinction that might be made at the 'habit level' in the
first case, and the more 'cognitive level* in the second.
Stimulus generalization
A further discussion of our second method in which transfer of
training takes place means that we must look again at stimulus
generalization. This, and the fact that certain events are classified
together as if they were identical, must be a characteristic of any
system, and it means that differences are either intentionally
neglected or not observed. The only situation in which such
generalization could be revealed or discarded would be one in
which the outcome of the generalization was unexpected or
undesirable, and this would be revealed in its effect on the motiva-
tional system. Need-reduction would fail to take place, and the
necessary condition for registering a conjunction count (a positive
association 'to be encouraged') in the machine would not occur.
PSYCHOLOGICAL THEORY OF LEARNING 223
Now it is obvious that what has been said does not tell us what
any particular automaton will generalize with respect to, at any
time. In so far as it is general, it will depend on set and value for the
organism. Set is merely the fact that the probabilities associated
with perception will interact with knowledge of context, which is
simply saying that the probability with respect to the perceptual
process is never independent of its place in the temporal sequence
of events; it is the conditional probability over the larger interval
that will lead the organism to expect some particular outcome to its
responses (this will particularly depend on the machine's use of
language). Value will arise in so far as different stimulus response
activities will be associated with different degrees of need-
reduction (change in state of motivational system, or rather, rate of
change). This matter is obviously complicated, and no further
discussion of it will occur here.
We must also bear in mind that the automaton will have the
capacity to draw logical inferences, and again we can illustrate the
principle only by saying that within the machine two pairs of
events may be seen, or perceived, to be independent. Consider the
following scheme of events involving A 9 B, C and D, where the
same letters primed imply organismic responses to the molar
stimulus of the same name:
A/B (4)
and
C/D (5)
and let us suppose again that * / ' means 'is followed
by'-
Now suppose B is always followed by C. This means that the
relation B/C is a necessary relation, necessary, that is, for the
organism; it still remains a problem to confirm that A/B or C/D
are necessary relations. A/B /C/D, as we should now write it, is a
slice of behaviour that involves one necessary relation with or
without the other two relations being necessary, and this means
that the conditional probability for BjC must be 1. This necessity,
and indeed the probability for the other purely contingent relations,
may be said to be dependent upon, or independent of, some
response on the part of the organism. We can substitute
224 THE BRAIN AS A COMPUTER
* / for * // ', thus including the word 'immediately' if
we wish, then we can write the necessary and contingent relations
AUX'I/B//Y'1/CIIZ'HD (6)
and
(N')AI/N'//B//N'//C//N'f/D (7)
respectively, where ( ) is the universal operator taken from the
lower functional calculus, and N f may range over all possible
responses in the organism.
The above interpretation is simply that of a typical Markoff
process, where the sequential conditional probabilities are stored
with stimulus and response letters.
The process of generalization arises whenever two subsets have
common letters. Thus abcdefg and abcdefh are common members
of the set abcdef, and if we write A for this set, it is easy to see that
if g and h are properties that, while possibly recognized, are
independent of the outcome of the response, they may lead to
generalization. Indeed, such set-theoretic inferences can be
drawn on any of the relations existing in the store.
We can now state once more that it seems plausible to add a
permanent store to the simple counting device with its temporary
storage system. A logical net can be drawn in pencil and paper, or
built in hardware as in a general purpose computer, wherein
information in temporary storage will at some time, and according
to certain conditions, be transferred to the permanent storage. What
are these conditions? One might guess that there are two sorts, and
that they interact with each other: (1) Where the degree of con-
firmation is high, and in particular (2) Where the association is at
the habit level. This last phrase, 'habit level*, can be the source of
much discussion, but what is intended here is that there are certain
relations that involve no interference, and association is actually
known. The problem here is to know the correct response for some
desired outcome; the system apparently does not know it inexor-
ably until some number of trials have taken place, and this may
reflect the presence of random elements in our connexions. We
are, indeed, merely drawing attention to the fact that the learning
process which is perhaps dependent on the temporary store
is different from the learned process, which is dependent on the
PSYCHOLOGICAL THEORY OF LEARNING 225
permanent store. This is exactly the same problem that arose when
we were considering the programming of computers to learn.
The distinction is usually drawn between temporary and per-
manent storage registers in digital computer design, and although
it is not obviously necessary in uneconomical automata, it is
precisely through economy of space and elements that this distinc-
tion comes about. Here it is suggested that all the counters are in
multi-stage storage, and some small subset of all the counters is
used for all actual counting. When associations have passed a
certain level of count (all of which are in agreement), then no
further counting will occur, and the production of the stimulus
elicits the response. The recurrence of a doubt about an association
would then renew the counting process. Such a counting and
transfer arrangement is very simple to reproduce in our network
terms or in a computer. Confirmation of this distinction is con-
siderable, and one special case must be quoted, that of 'learning
sets'.
Learning sets
Various experiments have been carried out on learning sets, and
results of an apparently inconsistent type have sometimes been
discovered. It appears, however, if we may generalize, that with
overlearning, interference from retroactive inhibitions is wholly
overcome. This implies that our matrix (1) applies only to the
learning period, and that the first row of n's is replaced by zeros
after some finite time t.
What is now the basis of this transfer? It seems plausible to say
that transfer will take place when all the counters, or counting
capacity, of the machine will be used up, it being assumed that
there is only the possibility of a finite count taking place. We might
guess that value has a bearing on this, and it would doubtless have
the effect of merely filling up the counting elements more quickly
where greater value-for-the-organism occurs. At any rate the
finite automaton will have just this property of a finite set of
counters and can be given the property of precisely discharging its
probability into a permanent store after the counters are filled up.
Let us now look a little deeper into this matter. Suppose A/B
(or A\X'\E) is a well-learned association, we must be careful to
remember this means that some response, X' say, is appropriate
226 THE BRAIN AS A COMPUTER
to A to produce satisfaction 5, where A represents the letter A in
list 1, and X' the utterance of the letter B from the same list. Now
learn list 2, and we have the association A/Y'/B where Y' re-
presents the utterance of D. Now when A occurs during list 2 one
might expect that X' would be the response, and this would indeed
be so were it not for the fact that some rule intervenes. This rule is
the experimenter's instruction which occurs and is stored, and this
granted that the first list has been learnt sufficiently to ensure it
being taken off the temporary store replaces the belief derived
from the previous direct learning.
The above explanation depends upon one very important fact,
which is that the effect of a verbal instruction can completely undo
a 'certainty* relation, and is far more effective than a count that
arises through direct acquaintance with the environment. This
argument depends upon the distinction between description and
acquaintance, and yet we shall certainly wish to argue that lan-
guage is learned by the same associative process (by counting) as
any other learning activity. The implications of this very important
point go deep, and demand an analysis of language in the auto-
maton, and this cannot be undertaken here. Let it suffice that
there is every reason to suppose that, while language signs are
associated with their referents in the same way as all other signs,
when a coherent set of signs is learnt and a language therefore
known, the effect of utterances in that language can be different
from a direct experience of an event, in that it will bring about a
large and quick change in the count. It is as if another person's
large experience (count) were transferred to the listener's storage
where, subject to certain other considerations of confidence, it will
have the effect of concentrated experience.
The rule can only operate on the permanent store where it itself
is stored, and this reflects the fact that any attempt to pursue this
course before the transfer has taken place will cause precisely the
interference of retroactive inhibition.
It should be emphasized that what we are trying to do here is to
build up a precise machine a blueprint from well-understood
principles for constructing switching devices, keeping within the
fairly well-validated evidence from experimental psychology.
Clearly, it is the hope that such automata that fit some of the facts
of experimental psychology can also be shown to fit others for
PSYCHOLOGICAL THEORY OF LEARNING 227
which they were not explicitly designed, and other tests should be
suggested from which psychological experiments could be
designed. This attempt is no more than a beginning to the process,
which is necessarily very complicated.
In the matter of learning sets, James' (1957) results suggested
that the order of presentation, as well as the nature of the stimulus,
will materially alter results. This one might expect to be the case
in a finite automaton, given only that they had already built up a
fair number of beliefs (associations and generalizations) ; ' it
follows that no simple automaton could exhibit this behaviour,
which is an extension of stimulus generalization, wherein sets of
associations and relations what we commonly call theories,
hypotheses, or general beliefs are already effective.
It will generally be the case that, after a longish period of time,
the automaton will acquire many different scores in its S-matrix.
The only problem that now arises for a matrix such as
nn ... n
/ ...,\
... S I
ww ... w
where n, r, s, ..., w>Q, is involved if the components of the J5's
in the later rows have common components with the 5's of the top
row. For the input matrix this will cause confusion in the recogni-
tion process; but for the 5-matrix this will not cause confusion,
even though there are components in common, unless events that
are incompatible occur together, and this, presumably, would
make nonsense of all processes.
We should notice that, to explain learning sets, we assume that
after n trials the information (now learned) is transferred to a
permanent memory store, and that the reason that a new response
to a stimulus already in store does not occur is because there must
also be the rule (experimenter's instruction) in store, and this is
effective in suspending the original count.
Two questions have to be considered here. The first is the
nature of the memory store used by humans, and its reproduction
in the machine, and the way the selective process of perception
works with the memory store in the first place.
228 THE BRAIN AS A COMPUTER
We shall say that the facts observed and the rules under which
these facts are observed (the experimenter's instructions) are
coded economically from the initial stage of the experiment. The
events being coded for store are effectively infinite, and we may
therefore expect that gross abbreviations occur. These will occur,
' according to our empiricist viewpoint, in terms of the effectiveness
(value) of the coding in previous cases. Having said so much, it is
easy to see how this as well as many other oddities comes
about as a sort of artefact, in that the coding was too abbreviated
to allow a success, due to the need for more information than such
a situation normally demands.
Thus, to take a simpler case as an example, if you show a subject
a simple diagram such as a black square on a sheet of paper, he will
probably remember the words 'black square', and in a future
recognition test he will easily pick out the figure from a group of
such figures if it is the only black square of about the correct size.
If, however, you ask him to choose from a set of black squares he
will probably fail. This is partly because he may find it difficult to
code the actual size if he is not allowed actually to measure the
square, and partly because he will not have stored anything more
than a rough visual estimate which is inadequate in the subsequent
fine test. Essentially the same thing would certainly occur with a
machine that coded its perception as 'arrow pointing to the right',
and then applied that rule directly in the new situation when facing
the opposite way. The conceptual contamination situation of
Piercy's (1957) is more complex than this, and depends on the
inability to carry through what is a fairly complex transformation.
The possibility arises in this case, therefore, that the capacity to
reason logically has also failed. Certainly we can easily show that
people are not able to draw simple, logical conclusions in easy
mathematical or logical puzzles. Here, it is more in the nature of a
geometrical puzzle, and failure to see what is required is the cause
of coding into storage the wrong information.
This whole question raises difficulties for our machine design
because, if our explanations are correct, then the fault is a very
high level and complicated one, very closely related to the nature
of the machine's experience. But if we put the machine in an
environment where somewhat similar operations are ordinarily
performed (the natural process of turning around in a room), then
PSYCHOLOGICAL THEORY OF LEARNING 229
the economy of coding would soon necessitate a coding habit that
would be adequate in the difficult Piercy conditions. Random
elements would be introduced into a realistic machine so that
there would be a certain percentage of blockages to ordinary
reasoning, and this would account for both sorts of error, the
ambiguity over axes (stimulus generalization) remaining, as
Piercy suggests, the cause of more errors in the one direction than
the other.
Two consequences of interest follow from the above. It seems a
clear prediction that if Piercy had instructed his subjects in a
simple routine method for retaining the information necessary to
the successful performance of his task, then he would have elimi-
nated errors. The error is clearly one of performance, which
could be remedied by learning. Secondly, the relation of percep-
tion to memory is thrown into relief, and the question of the
selective memorizing of perceptual processes is clearly connected
with experience. This last point becomes more obvious when it is
realized that a machine without the earlier similar (but also
different) experience would not have made the Piercy errors,
because the making of the error, on our hypothesis, depends on
having learned to do something different from what is now
demanded. This point relates it to the other matters of stimulus
generalization and retroactive inhibition already discussed.
We also see from what has been said that it does not in the least
matter what memory storage system we use for this machine; any
one would yield the same results, since it is not in the storage
method but in the selective coding that the error occurs.
These few samples must be sufficient to show the methods of
application of finite automata theory to learning theory, as com-
pared with its use in giving an effective model for existing learning
theories.
We must remind the reader that molar psychological theory
and this is what we have so far discussed with respect to learning
is a particular example of what is called 'black box theory', the
essential principles are to give a predictive account of the be-
haviour of the black box under a range of different conditions,
without opening the box to see the internal mechanism. However,
the use of theoretical terms makes it clear that we shall need, for
the purpose of constructing effective theories, at least to guess at
230 THE BRAIN AS A COMPUTER
the internal mechanisms, and this will later be supplemented by
an actual study of the mechanisms under the name 'physiology*.
We have only been able, in spite of the lengthiness of our present
chapter, to outline some of the principal examples of learning
theories, controversies over theories, experiments and controversies
over experiments; and there are other theories especially the
mathematical ones and many other experiments, that should be
carefully considered by the reader in this context (Estes, 1950;
Bush and Hosteller, 1955 ; et al}.
Extinction
We will now consider the problem of extinction from the cyber-
netic point of view. Here it will be easier to follow the argument if
we illustrate a succession of stimuli by a status matrix wherein
rows represent a succession of times, o> ft., .> t n > and the columns
represent the set of elements and whether they fire at any particular
instant or not. Unfortunately we cannot conveniently represent in
one matrix the current firing state and the cumulative past history
of the automaton; fo simplify the discussion we shall therefore
leave the cumulative matrix out of the discussion and, unless
otherwise stated, it may be assumed that the cumulative state is
positive if the particular combination making up the element's
firing has more often fired together than not. To illustrate the
point, let us say that if x and y have occurred together more often
than not, then the firing of x receives a response as if both x and
y fired.
Broadbent, writing on this subject and describing Uttley's
(1955) explanation of extinction, concludes that it is inadequate,
and that therefore the problem of extinction requires more than
the storing of conditional probabilities. This argument is not
necessarily true and should be restated in the form that if extinc-
tion is inadequately catered for by Uttley's explanation, then this is
only inadequate for his particular version of a conditional prob-
ability system.
We consider it extremely important to make it clear, even at the
risk of boring repetition, that whether or not Uttley's particular
model is correct, conditional probabilities are not necessarily in-
correct on that account. There are a number of different ways of
PSYCHOLOGICAL THEORY OF LEARNING 231
computing conditional probabilities, not just one, and the possible
inadequacy of Uttley's explanation does not necessarily imply the
inadequacy of conditional probabilities.
Broadbent's description of Uttley's explanation is based on a
series of tables, and we shall briefly consider some of them.
The first one takes the following status matrix form for inputs
X y Y and Z, which are represented by the first three columns,
and X.Y, X.Z and Y.Z, which are represented by the last three
columns :
'1 1 1 0\
110100
110100
100100
101110
101010
1 1 1 1 I/
In this matrix it is assumed that a short finite number of associa-
tions for all the desired pairings is enough to illustrate the method
basic to the argument.
Now the first thing we should notice about this matrix is that it
represents a particular set of logical nets in the same way as we
have described it in Chapter IV.
The second thing is to realize that we could have changed many
of the items in the present matrix and still have preserved our
logical net representation and, indeed, our conditional probability
principle. This point can be quickly illustrated. If X had been
regularly paired with Y it must have taken on a positive count for
X. Y. If this is so, then the counter for X.Z could be either or
m after m associations of X and Y. Either is possible, and either
will depend or may be made to depend upon whether or not
the associations are 'reinforced*. The next point in the example
given, taken from Broadbent, is that it appears to be assumed that
X and X.Z are different stimuli, and that ifX/Y fails through lack
of reinforcement, or through the failure of Y to occur (these might
be the same thing), then it is assumed that X.Z/Y is unaffected.
But again this simply depends on whether or not the firing of the
elements X.Z and X have the independence which they could
easily be given, and which could equally easily be granted.
232 THE BRAIN AS A COMPUTER
The following matrix illustrates an alternative conception of the
conditional probability* net:
/I 1 1 0)
110100
110100
100100
100100
100100
\1 0)
Here the failure of X to elicit F is really independent of the
presence of X, and depends merely on the decaying association
of X and F, which itself could account for extinction; and indeed
we could always account for it by firing a stimulus of any kind and
at any time with an inhibitory association.
This last point brings out another matter that we should bear in
mind. The lack of need for an inhibitory activity to account for
spontaneous recovery, disinhibition and, in general, extinction,
does not in any way mean that the concept of inhibition is unneces-
sary. Here, in the light of empirical evidence, especially from
neurophysiology, Occam's razor is inappropriate; it is simply
failing to pay attention to the probabilities implicit in the empirical
evidence.
Leaving this aside, and returning to logical net or finite auto-
mata and the conditional probability explanations of extinction,
brings out again the failure of Uttley's model to fit the plausible
empirical evidence suggested by Pavlov. But again, of course,
there is no problem in general; we can easily arrange for our
system to fit the facts. Extraneous stimuli can be made quite
ineffective, as in the second matrix (above), and in many other
possible matrices representing a whole set of finite automata.
What we are saying here does not deny that Broadbent may be
right in believing that Uttley's theory of learning may need
supplementing by further principles; indeed this is likely to be so.
One further principle is that suggested by Broadbent himself: the
principle of the selective filter; but what is important to notice is
* A conditional probability machine can be defined in terms of connexions
where each connexion is defined by a fraction m\n where n is the total number
of occurrences and m the number of favourable outcomes, but this system can
be constrained or differentially weighted in any way we choose.
PSYCHOLOGICAL THEORY OF LEARNING 233
that the effects described can be quite easily accounted for without
going beyond conditional probabilities.
The foregoing is an excellent example of the value of a methodo-
logical analysis and of the reduction of a problem, in part, to a
mathematical form. From what has already been said about logical
nets it is obvious that one could be constructed with the desired
properties, and that the problem of learning, indeed of all cogni-
tion from this point of view, is the mathematical problem of
whether or not there exists a set of matrices that satisfy each and
every piece of empirical evidence and are at the same time con-
sistent with each other. Such a net is precisely the conceptual
description for which we are searching.
Our last task in this chapter will be to give a brief interpretation,
in terms of finite automata, of those terms in cognition which have
not already been sufficiently discussed. Various terms such as
'taxis*, 'kinesis', etc., do not obviously need interpretation; and
'instinct' can be taken to refer to those beliefs, or associative
connexions (J5-nets), that are built into the system. A 'displacement
activity* would seem to be an example of an activity that involves
the blocking of a particular response in such a way as to return the
pulse into some other response channel, rather than merely
stopping and destroying it. A 'releaser' is a stimulus for a built-in
belief or association; 'imprinting' (see Russell, 1957) is the
acquisition of detailed basic behaviour from experience; and so on.
There are many other terms in common use in learning theory
(see, for example, the glossary of terms in Hilgard and Marquis,
1940), and it should be possible to reinterpret each and every one
in terms of our own finite automaton, and to carry through this
programme rigorously. It is confidently hoped that the reader will
now understand what the process entails, for it is not the intention
in this book to carry through the programme in detail.
Summary
This chapter has tried to state the principal features of learning
theory without dwelling especially on some of the narrower and
more sophisticated discussions that have taken place in the very
recent past. It has not been intended for the experimental psycho-
logist in its summarizing detail of such standard behaviour patterns
Q
234 THE BRAIN AS A COMPUTER
as latent learning, partial reinforcement, as well as in the main
discussion of primary and secondary reinforcement; indeed, more
detail has been included than would be necessary for him. This
extra detail is for the benefit of those other scientists interested in
cybernetics but unfamiliar with learning theory.
We have also tried to show in this chapter the connexion be-
tween logical net models and learning theory, and we have tried to
emphasize that our models are capable of reconstructing a whole
range of behaviour, and that we are still trying to discover the
effective method for reconstructing behaviour that is now fairly
well authenticated. The argument is that our method of recon-
struction will facilitate our understanding of the material itself,
since it is consistently argued that science is not merely the
collecting of empirical data.
Much of what is stated in this chapter should now be considered
from the point of view of the methods of the previous three
chapters.
CHAPTER VIII
BEHAVIOUR AND THE NERVOUS
SYSTEM
So far we have discussed the properties of finite automata and
their relation to some part of cognition ; now we should try to say
something of the nervous system and its established properties.
This is where the trail narrows, since automata are essentially
conceptual systems, and when we apply them to the task of model-
ling behaviour, one problem we presumably have to face sooner or
later is to make comparisons with the human organism, and this
means primarily the nervous system. It should be clearly under-
stood that while this is ultimately necessary if automata theory is to
be biologically useful, it could be argued that the maximum
utility of automata theory at the moment lies in its application to
the modelling of molar behaviour. However, some brief survey of
neurophysiology will, in any case, be suggestive for future applica-
tions in the subject.
In our logical net models we have talked of elements or cells
which clearly could be interpreted as neurons, and for many
purposes this is desirable. McCulloch (1959) when challenged as
to the use of a two-state switch to represent a neuron, admitted
that something like an eighth order differential equation was
necessary to describe a neuron's behaviour. But this is only true at
one level of description, and we are happy to model at least
initially the neuron at an altogether simpler level, while at the
same time bearing the more complex levels in mind.
The nervous system, we shall say, is a complex switching
system made up of neurons which are special cells for the purpose
of quickly reacting to and communicating changes in the environ-
ment, both internal and external. Even amoeba and simple multi-
cellular organisms react to environmental change, and in the
latter case certain specific cells have been developed for the purpose.
As we go up through the various species, through the inverte-
235
236
THE BRAIN AS A COMPUTER
brates and vertebrates, it is possible to detect an evolving pattern of
complexity. The spinal cord with its increasing modification at the
head end, and the developing complexity of the specialized
receptors, are indicative of the trend. Then with the primates we
have increasing complexity with the development of a highly
specialized brain, and different layers in the 'control* centre itself;
the cerebral cortex being divided into fairly well localized areas
concerned with 'controlling' or 'integrating' specific functions in
the body.
Nerve cell membrane potentials
Action potentials
[May be graded and decremental ]
[or all-or^npne and propagatedj
Transduced potentials
[From external event^j
Internal response potentials
"From antecedent actlviry]
within the some cell J
Sawtooth
Local
Spike
Polarizing Depolarizing Polarizing Depolarizing
FIG. 1. THE TYPES OF NERVE CELL MEMBRANE POTENTIALS.
A neuron is a specialized cell with an especially high degree of
irritability and conductivity. There are, of course, various neurons
in the nervous system, motoneurons, short connecting Golgi type
II neurons, bipolar neurons in sensory nerves, and so on. These
neurons may differ from each other greatly in size and sensitivity,
and straight away we can see that our logical nets cannot be identi-
fied literally with an actual nervous system, since all the elements
of the automaton are basically the same, and this must at least
imply a many-one relationship with actual nervous systems
(Bullock, 1959).
Whether nerves have myelin sheaths or not is something that
does not -enter into automata theory, but neither do any of the
BEHAVIOUR AND THE NERVOUS SYSTEM
237
particular characteristics of a physio-chemical kind; this matter of
the chemistry of the nerves will shortly be discussed, since with
the development of chemical type computers this whole subject is
put into fresh relief. This is perhaps of special interest in view of
the efforts of Pask (1959) and others to show that a growth process
can be mimicked in a manner not wholly different from that
involved in the regeneration of nervous tissue.
We can think of the gross divisions of the nervous system as :
FIG. 2. SPONTANEOUS ACTIVITY IN A GANGLION CELL as revealed by
an electrode inside the soma or body of the nerve cell. The spikes
are about 10 mV here and are followed by a repolarization, then
a gradual depolarization the pacemaker potential which at
a critical level sets off a local potential. This in turn usually rises
high enough to trigger a spike but is seen here several times by
itself.
(1) the spinal cord; (2) the myelencephalon, including the medulla;
(3) the metencephalon, which includes the cerebellum, pons, and
part of the fourth ventricle; (4) the mesencephalon (the midbrain,
including the colliculi of the tectum) ; (5) the diencephalon, which
includes the thalamus, hypothalamus, optic tracts, pituitary,
mammillary bodies, etc. ; and finally, and perhaps most important
to an understanding of human behaviour, (6) the telencephalon,
which includes cerebral hemispheres, olfactory bulbs, and tracts
and basal ganglia.
The spinal cord itself carries tracts running up and down its
238
THE BRAIN AS A COMPUTER
Synapical region
-Terminal ramification
FIG. 3. FACILITATION AND DIMINUTION. An ultramicro-electrode
inside the nerve cell of the cardiac ganglion of a lobster recorded
first the synaptic potentials resulting from the burst of five
arriving impulses from one presynaptic pathway and then those
BEHAVIOUR AND THE NERVOUS SYSTEM
239
length, and these are nerve fibres or white matter, while the cells
or grey matter are the core of the spinal cord. Figure 2 shows a
typical cross-section of the spinal cord with incoming, or ascending,
OLIVARY BODY
PROSENCEPHALON
.MESENCEPHALON
CEREBELLUM
METENCEPHALON |
PONS<VAROLl)J
MYELENCEPHALON
.PARS CERVJCAUS
ENCEPHALON
BRAIN
PARS THORACALIS
PARS LUMBALIS
PARS SACRALIS
FIG. 4. THE NERVOUS SYSTEM. A general schematic diagram of
the principal parts of the nervous system; these are severed to
show more clearly where they are in relation to the rest of the
system.
and outgoing, or descending, nerve fibres at every level, and
represents the reflex arc of input output activity.
Closely associated with the spinal cord is the autonomic nervous
system. This is responsible for the control of the internal organs
such as the heart, lungs, pancreas, etc., and is made up of two parts
called the sympathetic and the parasympathetic systems, the
240 THE BRAIN AS A COMPUTER
sympathetic chains, so called, lying along the ventro-lateral aspects
of the vertebral column. The parasympathetic system emanates
from the midbrain, medulla and pelvic nerve, and is comple-
mentary to the sympathetic system in its control; they act together
like the two reins controlling a horse. The whole autonomic
system is represented in the cerebral cortex, and is clearly closely
associated with emotions and motivation. Here, lack of space will
not allow us to say very much about this system.
For the benefit of those for whom it is unfamiliar, it is perhaps
worth saying that the various divisions of the nervous system,
TRACT OF GOLL
TRACT OF BUROACH
DORSAL SPINOCE
FASCK3JU
.RUBROSPINAL TRACT
TRACT
iNTRAL CEREBROSP/NAL
FASCICULUS
FIG. 3. TRANSVERSE SECTION OF SPINAL CORD. This diagram
shows the principal tracts in the white matter of the spinal cord;
the grey matter lies in the centre, and the tracts on top (at the
back of the cord) travel upwards, while those at the side and at
the bottom (at the front of the cord) travel downwards.
mentioned above, are to be investigated with respect to their
function. This means that we are bound to use their names, and
these become unwieldy and ugly. It is hoped that, with the aid of
the figures shown and bearing in mind that almost every part of
the nervous system is made up of collections of neurons called
nuclei the reader will find it easy to follow. The names of the
nuclei will usually illustrate their positions. The thalamus offers a
good example for illustrating this point, being sometimes described
in terms of its surfaces which are called dorsal (uppermost),
ventral (underneath), medial (central) and lateral (sideways),
BEHAVIOUR AND THE NERVOUS SYSTEM 241
although the nuclei of the thalamus include the anterior nucleus,
the medial nucleus, the paraventricular nucleus, the intralaminar
nuclei, the lateral nucleus, the posteromedial ventral nucleus, the
lateral ventral nucleus, and so on, each part of the thalamus having
a specific position relative to the whole and to the closely related
structures called the metathalamus, subthalamus, epithalamus
and, most important of all, the hypothalamus.
The thalamus and hypothalamus are very important to our
behaviour picture, and they have connexions with the visual and
auditory systems through parts called the lateral and medial
geniculate bodies respectively. They are also rather complicated
anatomically, being surrounded by various other nuclei and tracts
of fibres in a somewhat complex arrangement. The main points
that might be borne in mind to help the reader new to neurology
are: the thalamus is centrally placed, as is the hypothalamus, and
surrounds the third ventricle which is part of the canal system of the
brain carrying the cerebrospinal fluid in which the brain is bathed.
A large collection of fibre tracts from the spinal cord (called the
'internal capsule') runs up to the cortex outside the thalamus,
dividing it off from the ventricular nuclei and caudate nuclei.
These two bodies with the amygdaloid nuclei make up a large part
of that part referred to as the basal ganglia, and constitute the chief
organ between the thalamus and the cerebral cortex.
Figure 6 shows a transverse section through the brain, Fig. 7
shows the external surface of the brain, and Fig. 8 shows a
'phantom* of the striatum. It is hoped that this note and these
figures will help to orientate those readers unfamiliar with the
maze of the nervous system.
Our problem is to relate these structures to fairly specific func-
tions. We know that this cannot yet be done, but we can say some-
thing about the function of the various parts involved, and make
some guesses as to how they may be related to our automaton.
But before we try to elucidate this major problem, let us turn
again to the basic factors of nervous tissue, particularly the chemis-
try of nervous function and the synapse.
Chemistry of the nervous system
R. S. Lillie is a name that springs readily to mind when we
think of early attempts to construct chemical models of the nervous
242
THE BRAIN AS A COMPUTER
Outer layer of durameter
Inner layer
Sub dural space
Arachnoid
/Sub-arach. tissue
Cingulurtr
Pia mafer
Fronto-occ fasc.
Body of caudate nucleus
Base of corona radiata
Stria
'Insula
Septum
lucidum
Fornix 1
Connexus
Superior longitudinal
fasciculus
Sub-thalamlc
nucleus
Optic
Basis peduncle
Substantia ni<
Dentate gyrus
Olivary body
Tail of caudate
nucleus
-Tapetum
Inferior longitudinc
fasciculus
Hippocampus
.Collateral sulcus
Trigeminal nerve
Eighth crania! nerve
FIG. 6. A CROSS-SECTION OF THE BRAIN. This section is cut in a
plane parallel to the plane of the face. It shows the white fibres
of the internal capsule (INTCAJPS in the figure) spreading out
and separating the tail of the caudate nucleus from the central
part of the thalamus and the central canal system. The lenticular
nucleus (L.N.) also lies outside the internal capsule.
BEHAVIOUR AND THE NERVOUS SYSTEM
243
system. His model was built some years ago, and was a fairly simple
one. It consisted of an iron wire which had been immersed first in
nitric acid and subsequently in sulphuric acid and water, having
the property, if stimulated at one end, of firing off an impulse
which travelled along the length of the wire, and destroying the
thin film of iron oxide that separated the iron from the acid.
Lillie's model was able to imitate, to some extent, the proto-
plasm and its surrounding medium, and the special problem of the
semi-permeable membrane that divided one from the other. This
Central sulcus or
fissure of rolando
Frontal lobe
Parietal lobe
Fingers
Head
Eyelids
Cheeks
Jaws
Lips
Occipital looe
^Temporal iobe
FIG. 7. THE CORTEX. This diagram of the outside of the external
surface of the cerebrum shows some of the principal cortical
areas with some of the principal functions that are associated
with these areas named against them.
semi-permeability allows some substances to go through it and not
others. On the other hand, from the point of view of physiology it
was clearly unsatisfactory, not only in that it was a model that was
quite different in its chemical action from that of the living nerve,
but also in that it lacked one very important property that nervous
tissue was known to possess : that of resealing itself after firing, so
that a new impulse could follow after the refractory period, which
is the short delay following the firing of a neuron, during which
time it is either totally or relatively insensitive to further firing.
244
THE BRAIN AS A COMPUTER
It has been known for a long time that the train of depolarization
that effectively connects one end of a nerve fibre with the other
Pytomen
Amygdaloid'
Pallidus
(C)
Part II
FIG. 8. Part I. Phantom of striatum within the cerebral hemi-
sphere. Part II. Form of striatum of left side, (a) Lateral aspect;
(b) anterior aspect; (c) posterior aspect.
depends upon the characteristics of semi-permeable membranes,
and that the nerve's firing of impulses, and the transmission across
BEHAVIOUR AND THE NERVOUS SYSTEM 245
the synapses, is accompanied by electrical and thermal changes;
the details of the chemistry are still elusive, however, and the
problem is thought of as existing in a background of great com-
plexity, even though our knowledge of the process has been steadily
increasing since the concept of the action current theory of the
nerve impulse itself, which is only 100 years old.
Before proceeding to a description of what is now being
attempted in the field of nerve chemistry, it is necessary to restate
briefly what has become known as the Ionic Hypothesis (see
Hodgkin, 1951, 1957; Eccles, 1953). This hypothesis is aimed
primarily at giving an account of how nervous functions are
chemically explained. The nervous impulse is to be thought of as a
wave of electrical negativity that travels without decrement along
nerve fibres.
The nerve itself is an extended cylinder of uniform radius, filled
by a watery substance called axoplasm, and bathed in an ultra-
filtrate of blood. These are separated from each other by a very
thin membrane of lipid-protein structure. This membrane has
special electrical properties that make it highly resistant to the
passage of ions.
It is thought that the resting membrane is readily permeable to
chloride and potassium ions which move across the membrane
solely by diffusion; yet the reaction of the membrane to sodium is
much more selective, at least in that these ions are removed from
inside as soon as they appear. What has been called a 'sodium
pump', assumed to be incorporated in the membrane itself, is
responsible for this. The pump derives energy from metabolic
changes within the fibre, and keeps the internal concentration of
sodium at a level of about 10 per cent of the external concentration.
Glutamic and aspartic and isethionic acids provide a high
internal concentration of impermeable anions which, together with
the sodium concentration, make for a potassium gradient of
twenty to fifty times more inside than outside the membrane, and
about the opposite for chloride ions.
At room temperature the resting membrane potential E is
given in terms of potassium and chloride concentrations by the
following formula:
E = RT/F log Ki/Ko = RT/F log Cfc/Cfc
246 THE BRAIN AS A COMPUTER
This is the potential in Donnan Equilibrium where RT and F are
constant and the logarithms are to the base e.
At room temperature this equation can be rewritten in micro-
volts
E = 58 logics/Kb
and the outside would be around 85 mV to the inside; this keeps
the gradients for potassium and chlorides in a state of equilibrium.
If the resting potential is now diminished by the application of
electric currents, the membrane immediately becomes highly
permeable to sodium ions. This is said to be due to a 'sodium
carrier mechanism' which has a feedback that proceeds until the
potential across the membrane approaches that of a sodium
electrode, creating a reversed potential with the inside positive to
the outside. As the peak is reached the sodium carrier starts to
decline, the process is reversed, and the nerve fibre returns to its
resting state.
A large number of experiments have been carried out to confirm
the truth of the Ionic Hypothesis, and much confirmatory evidence
has been forthcoming, although a certain amount of detail,
particularly about the sodium pump, is still lacking. The refractory
periods of nerve fibres have been studied and can be shown to be
consistent with the above account which, while thought to be
basically correct, is still lacking in detail and not effective in a way
that is sufficient for cybernetic purposes.
There is much more to be said about this field, and the interested
reader should refer to specialist literature on the subject (Eccles,
1953; Beach, 1958; Shanes, 1958; Tower, 1958).
Before leaving the chemistry of nerves altogether, it will be very-
useful to the cybernetic view to have a short comment on this
same work from a different angle.
A new set of experiments has been carried out by a group of
chemists with the object of trying to understand the chemistry of
cell membrane formation.
Work has been in progress for some years on the nature of
organic membranes, and something must be said here about the
advance that has been made.
The Ionic Hypothesis had assumed the presence of lipid mem-
branes between the inside and outside of a nerve, and protein or
BEHAVIOUR AND THE NERVOUS SYSTEM 247
lipid films have been used between two liquids to model this
membrane. The problem of studying these interfaces between
aqueous liquids depends on being able to study the electrical and
optical properties of the surfaces in question.
Saunders (1953, 1957, 1958; Elworthy and Saunders, 1955, 1956)
has designed and built an apparatus for studying diffusion pro-
cesses and photographing them at the membrane. From this work
it was discovered that lecithin sols (a complex chemical colloidal
substance derived from egg yolk) formed stable membranes
between liquids, and that these membranes could be further
strengthened by injections of serum albumen sol at the actual
interface between the liquids.
A more sensitive apparatus was then built by which it was
possible to measure the surface forces that existed at the boun-
daries of the lecithin sols and water. The next step was to study the
effects of various inorganic salts such as potassium and sodium
chloride on these surface forces and, as a result, suggestions were
made as to the formation of actual cell membranes. With an
intracellular fluid sufficiently rich in phosphatides, and with a little
calcium and some lecithin, the lecithin was thought to be stabilized
to the monovalent metal salts by soaplike substances, probably
lysolecithine (also derived from egg yolks). By contact with fluids
of higher calcium content, a calcium-lecithin complex film is
formed which becomes fixed and relatively insoluble by absorption
of proteins and insoluble lipids.
It was later shown that the appearance of the film surface force
was related to the stability of die lecithin sol, and that a wide
variation of stability to salts can be achieved by altering the ratio
of lysolecithins to lecithin in a mixed sol of the two phosphatides.
Various other experiments on the properties of the viscosities,
stabilities to salts, and haemolytic activities have been carried out,
and there is current research on the electrical properties of lecithin
membranes and their permeability to electrolytes.
The results as a whole show that our knowledge of cell mem-
brane formation has taken a large step forward. It is even to be
hoped that the next year or two should see the completion of a
chemical picture of the membrane formation process, and the
diffusion properties that operate in nervous and other organic
tissues. In the meantime we have the power to produce artificial
248 THE BRAIN AS A COMPUTER
cells that could be used in a computer system in the place of relays.
This much is clear in principle, and work is afoot now on the
practicability of actually carrying through such an undertaking.
This brief account of certain aspects of the chemistry of the
nervous system is included for heuristic and orientating purposes,
but its importance for cybernetics may be very great indeed, since
an effort is now being made to produce what Beer (1959) has called
Fungoid Systems, and what may be thought of as chemical or
ultimately, it is hoped, chemical-colloidal computers (Pask, 1958).
The main importance of chemical computers for cybernetics
lies in the fact that, unlike the digital computer, they exhibit the
properties of growth in direct fashion, and this is something that was
bound to be needed sooner or later in our biological modelling.
The nervous system
Turning again to the general properties of the nervous system,
we must note that the properties of the synapse are very important,
and we do not yet know sufficient to enable us to build models with
absolute certainty; but the synaptic junction clearly plays a vitally
important part in our neurophysiological theory of behaviour, both
in the classical sense as a junction station and in the modern sense
of Hebb (1949) with the development of synaptic knobs. We
should mention here the many attempts to build electrical models
of neurons (e.g. Taylor, 1959), but while such a study is useful, it
does not come quite within our purview.
Apart from the chemical mediation of the spike potential or
nervous impulse, there are other factors which are well known about
the neuron; it has a critical intensity that fires it and this property,
realized in our logical nets is called the "threshold. Another pro-
perty that is accepted in the logical nets, which is in keeping with
the facts, is the all-or-none law, which states that when a nerve
fires it fires 'completely* or not at all. The after-potentials (changes
of excitation immediately after the main excitation) that follow the
spike potential are not mirrored in our model, nor is their physio-
logical function wholly clear.
There are many further properties of neurons, such as their
relative and absolute refractory periods, but these will not be
discussed further here. It might just be mentioned that the fact
BEHAVIOUR AND THE NERVOUS SYSTEM 249
that there is some delay, an instant, in the logical nets can be
taken to be an analogue of the refractory period. But let us turn to
the synapses.
The synapse is a functional junction between neurons such that
transmission between neurons takes place across the synapse.
Transmission between neurons may also occur through ephaptic
transmission (Eccles, 1946), which means directly across the
membranes of adjacent neurons.
There are two currents, the anodal and cathodal in nervous
transmission, and these can cause successive states of inhibition
and excitation in ephaptic transmission. However, in synaptic
transmission unlike the ephaptic case there is no final inhibi-
tory impulse following the excitatory, and thus the resting fibre
which is the other side of the synapse can build up a considerable
potential. There are local potentials at the synapse which makes the
firing of the resting fibre contingent on the relation between the
potentials in both neurons in the chain. Sometimes, when an
impulse is not itself sufficient to arouse the resting fibre, summa-
tion of local impulses from the same source in quick succession, or
from two different sources having close contiguity on the synapse,
will effect temporal and spatial summation respectively, either of
which may then be sufficient to fire the resting fibre.
It is probably because some summation is necessary to fire
neurons that the conduction of a nervous impulse will travel in one
way only across synaptic junctions. The reasons for this are
anatomical in that the synaptic junction is ordered in having
many one and never one many relations; there are also delays at
the synapse.
We can see that spatial summation is easily realized in logical
nets, but temporal summation requires that there be at least two
elements operating together, and is thus really a contrived kind of
spatial summation. However, here there is some evidence that
temporal summation in nerves is in fact due to the occurrence of
reverberatory circuits, and not merely to the summing of local
potentials from the same source, in which case our analogy is a
close one. The same argument, somewhat extended, leads to the
phenomenon called recruitment.
The inhibitory function of nerves can occur either directly,
when two stimuli act antagonistically, or when one follows the
250 THE BRAIN AS A COMPUTER
other after a delay, a delay which is too long for temporal summa-
tion to occur. Again, in our logical net model, inhibitory endings are
assumed so that an impulse travelling along a fibre will be specific-
ally inhibitory or specifically excitatory. In Chapman's growth
nets (1959) it is possible to have the same nerve fibre carrying
either an excitatory or inhibitory impulse, and this seems likely to
be nearer to the physiological facts.
Let us next consider some of the classical work of Sherrington
(1906) and his co-workers on the nature of excitation and inhibi-
tion in collections of neurons joined together into a network,
which is certainly how we wish to view the total organization of
the nervous system.
It is well, in the first instance, to regard the central nervous
system as a distributed network of more or less specialized tissue,
and as working together as-a-whole. The parts will work autono-
mously under certain circumstances, but the whole system cannot
be assumed to be the simple sum of the working of its parts ; in
fact it may be expected to exhibit characteristics which are both
non-additive and non-linear.
The cortex might be regarded as having a controlling influence
on sub-cortical and spinal nerve tissue, differentiated in something
like hierarchical layers. As Sholl (1956) puts it:
The cerebral hemispheres of all vertebrates are hollow cylinders of
nervous tissue with a ventricle for the cavity. At first they are only
associated with impulses arising from the olfactory organs but, in the
higher vertebrates, connections are developed so that impulses arising
from all the sense organs are transmitted to the forebrain and interact
there to control the behaviour of the animal.
Methodologically, we have to make the classical findings (or
interpretations) of anatomy, histology and physiology fit with tie
findings from work on the EEG, the organism-as-a-whole
behaviour studies, work on brain injuries, electrical stimulation
studies, ablation studies, and so on.
However, Sherrington's approach tells us something like this
about the human nervous system: the nervous system has a
property of excitability, and it is organized into networks in living
organisms in such a way that its behaviour appears to take the form
of an interconnected hierarchy of reflexes. The notion of a reflex,
of a simply connected input output system, may, of course, be an
BEHAVIOUR AND THE NERVOUS SYSTEM 251
artefact of our method of isolation. A simple example is that of the
spinal reflex. If we stimulate an afferent nerve the impulse travels
to the spinal cord and, with a synaptic junction, is transferred to an.
efferent nerve (here we assume the Bell/Majendie law which
distinguishes motor and sensory nerves). The number of inter-
nuncial or 'shunt* neurons involved may be quite large. Similarly,
specialized receptors may be involved but we shall not immedi-
ately consider the extra complexity this implies. The 'segmental
reflex', as it is called, is the simplest reflex of the nervous system
that is readily available.
The theoretical terms 'central excitatory state' (c.e.s.) and
'central inhibitory state' (c.i.s.) are at the heart of Sherrington's
theory, but before discussing them let us consider some observable
data from which these theoretical terms were derived.
We directly observe, in the muscle nerve preparation, excitability
of the nerve and a change of excitability as a result of electrical
stimulation. We also observe the properties of relative and absolute
refractory period and due to our ability to measure the velocity
of nerve conduction we can, by arithmetical subtraction, observe
a delay in segmental reflex (in the more complicated reflexes called
'reflex latency') which are assumed to represent synaptic delay.
Directly observable also are the properties of 'spatial summa-
tion' and 'temporal summation' of nervous impulses, and the
'threshold' of nervous tissue as a way of measuring the sensitivity
of nerve cells; all these we have already mentioned.
The notion of spatial summation requires some comment. If
two afferent nerves are stimulated, and both play on the same reflex
centre, summation takes place, and reflex responses take place
which would not occur in response to either stimulations acting
alone. An example of this phenomenon is that of tiUalis anticus.
Changes in collections of central neurons may last as long as 15
msec, and Sherrington assumed that a subliminal stimulus set up a
c.e.s., and that a further stimulus might then be additive and fire off
the efferents. 'c.e.s.' is here playing its role as a theoretical term,
and it is interesting to note that it must take care of delays up to
20 msec.
Lorente de No's (1938a, 1938b) work on this problem shows
that in a single central synapse, summation of subliminal stimuli
can be demonstrated over an interval no longer than 0-5 msec.
252 THE BRAIN AS A COMPUTER
However, de No believed that c.e.s. can be taken to mean (opera-
tionally) delay involving several internuncial neurons intercalated
between sensory fibres and anterior horn cells, thus accounting for
the longer delays assumed by Sherrington. This allows of more
enduring responses than can be accounted for by this setting up of
internal excitatory circuits.
Eccles's work on electrical states at synapses has suggested a
model for synaptic delay and summation. To build these synaptic
phenomena requires, largely, the ordering or organization and
control of systematic detail (see Creed et aL, 1932; Erlanger and
Gasser, 1937; de No, 1947; Eccles, 1953). It will suffice here to add
that the majority of synaptic connexions considered were of the
boutons terminaux type, and the development of these may be
correlated with states of the organism-as-a-whole. Furthermore,
boutons terminaux apparently exist in abundance in the cortical
areas, though there are histological difficulties with respect to their
staining.
Next, the notion of 'central inhibition* must be dealt with. In
the decerebrate cat the crossed extensor reflex can be inhibited or
blocked entirely. In view of the time relations involved, Fulton has
suggested the ventral horn cells as the seat of the inhibition.
Sherrington showed that the knee jerk was inhibitable, and it was
used as an index of c.i.s. That inhibition (operationally, this is the
suppression of normally elicitable reflexes when they are elicited
contiguously with certain other reflexes) is observed is clear, but
theory is more concerned with the explanation of why it takes place.
There are in fact many theories, and we shall take as examples
those of Gasser and Eccles. Gasser believes that the internuncial
circuits normally involved in the now inhibited reflex have a
greatly heightened threshold and become relatively unresponsive.
This is not wholly dissimilar in essence to the explanation of Creed
et aL (1932) when the competition for the final common path led to
selective changes of excitability in one centre. By final common
path (f.c.p.) we mean simply the final response path that decides
the behavioural act. They point out that when an antidromic
volley travels up motor nerve fibres to motoneurons, the excitation
is thought to disappear from those neurons, and this accounts for
the long duration of inhibitory effects produced by a contralateral
volley.
BEHAVIOUR AND THE NERVOUS SYSTEM 253
They summarize the properties of inhibition in the following
way:
(1) Centripetal volleys in ipsilateral nerves normally excite
contractions of flexors and inhibit extensors, while centripetal
volleys in contralaterals have the opposite effect.
(2) Inhibitory processes in motoneurons can be graded in
intensity.
(3) Summation of inhibition may be produced by successive
volleys on one or more afferent nerves.
(4) Inhibition is antagonistic to c.e.s. and may slow down the
build-up of the c.e.s.
(5) c.e.s. and c.i.s. are mutually antagonistic.
(6) c.i.s. undergoes a progressive and spontaneous subsidence.
It should be noticed that no evidence was dealt with by these
writers for inhibition other than with motoneurons.
In the descriptions of inhibition by most early writers we find
little reference to the chemical means by which this is achieved,
although Eccles (1953) has something to say by way of summary
on this matter.
It is already clear that the notion of the reflex arc in isolation is
somewhat artificial, and that reflex activities occur together in a
very complicated manner. In the first place there is the competition
for the final common path, the competition that occurs for the
control of motoneurons, and thus of all movement patterns.
Direct inhibition is explained in terms of hyper-polarization of
the neuronal surface membrane. Indeed it is now thought that
during a period of hyper-polarization there is the need for a larger
post-synaptic potential to activate the self-regenerating sodium
carrier, and there is much evidence to support such a view.
Eccles goes further than this, and explains more complicated
and more prolonged inhibition in terms of hyper-polarization, and
the theory has been developed that this inhibitory synaptic
activity is a function of a specific transmitter substance liberated
from inhibitory synaptic knobs.
However, we have agreed to leave the development of the
chemical aspects of nervous function outside our range, and it
254 THE BRAIN AS A COMPUTER
must suffice to say that there is an increasing awareness of the
workings of the inhibitory activity which is so necessary to
account for the gross activity of the nervous system, and that it is
possible to guess at a plausible form of explanation of 'central
inhibition', whether it be direct or indirect. The really important
point is that it does take place.
Before leaving the subject of inhibition we might consider for a
moment its relation to logical nets. It will be remembered that we
assumed merely two sorts of nerve terminations, served by identical
fibres carrying identical impulses, except of course for the indivi-
dual differences among fibres, which is something we have not
considered in our logical nets. This, of course, can be met in many
ways by using many pathways together to make up a volley of
impulses, or by changing the idealized nets to fit the facts more
closely. From tide behavioural point of view this last demand is not
obviously necessary.
Inhibition is therefore brought about in a logical net by direct
stimulation of a neuron (we shall now use the word neuron, as we
are placing the nerve interpretation on these models), or by altering
the effective threshold of a neuron by retaining the record of some
previous firing. This means that something very like a classical
neurological picture is really subsumed in the construction of
nerve nets. What perhaps is more interesting is the manner in
which the differences between the two can subsequently be met.
It would be easy to show in logical nets two neural chains carrying
impulses for a final common path, and the manner in which these
chains can be regarded as antagonistic, so that the path is given to
only one chain at any particular time.
The next stage in the classical theory involves the types of
reflex which are elicitable in the central nervous system, e.g.
postural, flexor, extensor, intersegmental, etc. For illustrative
purposes the classical experiments by Sherrington on the spinal
cat should be sufficient. As a result of this work we have explana-
tions given in terms of convergence, final common pathway
(f.c.p.), occlusion, after-discharge, reflex centre, etc.
It is assumed that the co-ordinated activity of muscular action
is the result of overlap in reflex fields, made possible by the
convergence of afferent and internuncial paths on to one efferent
f.c.p. Occlusion, in particular, takes place as a special case of this
BEHAVIOUR AND THE NERVOUS SYSTEM 255
overlap when two afferent nerves, simultaneously stimulated, fire
off a high percentage of the same motoneurons. After-discharge
is regarded as a function of internuncial delay paths. The discus-
sion of the remainder of the reflexes introduces no essentially new
idea: they may all be explained in terms of the principles already
referred to.
So far we have built up a conceptual picture of the nervous
system as a complicated network like a telephone exchange, in
which reflex activity is the element we have inherited, and the
selectivity of the reflexes is made dependent on the inhibition of
these networks at synaptic junctions. Both excitation and inhibi-
tion are summable, and they may interact in complex ways which
are partly determined by the anatomical organization of the
nervous system.
In modern neurology, more and more, the concept of the reflex
is being replaced by the simple graded servo or feedback system
(neural homeostats), but while we shall review some of the grosser
evidence, it must be remembered throughout how little we know
of the more intimate and detailed connexions in the nervous
system.
Information theory and nervous impulses
It is well known that information theory is used to describe
possible nervous activities, and the appropriateness of such
descriptive means is obvious enough.
The most evident point about the nervous system and its trans-
mission is that the code is, basically, a simple one, being of the same
pulse no-pulse kind that is used by computers. It is a morse code
with dots only, and thus of a binary form, based on the all-or-
nothing principle of nerve transmission.
It is also easy enough to guess that the intensity of stimulation
clearly a necessary variable is correlated with frequency of
discharge of impulse along afferent fibres, and such a factor
automatically suggests the occurrence of summation, where
relative economy of fibres occurs entailing manyone and one
many relations from cells to fibres and fibres back to cells. It is
partly because of this that temporal and spatial summation are
such essential features of nervous activity, and the thought follows
256
THE BRAIN AS A COMPUTER
naturally that inhibition will be included in the means by which
integration takes place.
Rapoport (1955), Sutherland (1959) and Barlow (1959),
among many others, have considered the problem of coding with
respect to the visual system, and their work will be discussed
further in Chapter X.
The implication that all parts of the nervous system, as well as
the whole organism, could be studied from the point of view of an
information system is clear, for the brain is indubitably an
information-receiving, transmitting and storing system; but these
FIG. 9. LOGICAL NET FOR FIRING THROUGH A CONSTRICTION. The
figure shows one simple way in which an input can be fired
through a channel which has less fibres than there are inputs and
yet an input event can still be reproduced correctly as an output.
facts, apart from being useful in the construction of molar models
of organic behaviour, do not help substantially in unravelling the
intricacies of the function of complex nervous tissue. What it
achieves, in conjunction with other cybernetic methods, is an
almost ideal behavioural model as a basis for neurophysiological
comparison.
A further point should be made with respect to the importance
of many one relations mentioned above. This seems to occur
commonly in the nervous system, and involves a mapping of a set
of impulses from a set of neurons on to many fewer nerve fibres and
vice versa. This is well known to occur in the visual system, among
many other parts of the nervous system, and leads to the firing
through the restriction of the visual pathways. Figure 9 shows the
fairly straightforward logical net principle that could be used to
mirror just this sort of thing.
BEHAVIOUR AND THE NERVOUS SYSTEM 257
What is important about this is that the splitting up of nerve
impulses into a sequential train of pulses makes it necessary to
reaccumulate that train in part or whole at some later time, and
this requires precisely the operation of summation.
Broadbent (1954) has shown that the operation of the ear, in
accepting information simultaneously presented to it, is itself
sequential. The implication is that the auditory system is able to
store information prior to its being dealt with centrally, and this is
precisely what must be implied by passing information through a
constraint.
So far we have only dealt with the elements and their simple
organization into a network, we must now look for a while at what
has been discovered about the brain itself. Here we shall simply
select certain relevant features from various points of view, and
indicate in each case, what sort of equivalent logical net organiza-
tion would be possible and plausible. In this next section, it will be
borne in mind that we can think of the logical nets originally
described in Chapter IV as being very high speed in their function
and thus being influenced by whole volleys of impulses rather than
single ones alone. This implies a statistical type of description for
a large network, and such statistical models have already been
discussed to some extent (Beurle, 1954; Rapoport, 1950a, 1950b,
1950c, 1950d, 1955; Sholl, 1956). In any case they will become
essential as our logical nets increase in size, as indeed they must if
they are to mimic in any useful way the human brain.
We shall also bear in mind that as the search for neurological
models becomes more urgent, our problem will be to discover how
the nervous system is actually wired. There is no reason to doubt
the ease with which nets can be drawn that will perform the
necessary behavioural functions, but in order that they may be
scientifically useful ultimately, we shall wish to draw the nets with
only particular information flow, which have the right dimensions
as regards numbers of elements used, and which can also perform
the necessary function in the same manner as the nervous system.
With these ideas clearly before us, let us look at some of our
information on brain analysis.
Our subject-matter is so vast that the best that we can hope to do
here is to give a brief summary of relevant work. This means that
the more detailed analysis of neural transmission, and detailed
258 THE BRAIN AS A COMPUTER
work on certain chemical aspects of neurology, will not be further
considered; but even after putting these aside, there remains an
immense bulk of neurological data which would fill many volumes,
and we can discuss here only selected aspects, selected always with
one eye on the ultimate interests and needs of the cybernetician.
Before discussing the rest of the nervous system let us look at
some more diagrams that will help in our terminological problem.
Figures 10 and 11 show the inner and outer surface of a cerebral
hemisphere with names and also numbers (Brodman, 1909) that
indicate its general topography. Brodman's numbers were based
on histological distinctions, and these are now known to be in-
adequate on these grounds, but are convenient to retain purely as
spatial coordinates.
Methodology
The first question of importance is that of methodology in
neuroanatomy and neurophysiology, and this will be discussed
immediately. The anatomist can contribute an enormous amount
to our knowledge of neurological function, as has been pointed out
by le Gros Clark (1950). But there are certain limitations that need
to be observed; the general topography of the nervous system may
not in itself be a good guide to function. The histological staining
techniques, used on mapping fibre connexions in the brain, have
also had considerable doubts attached to them.
The mapping of the cortex, however, is now considerably
advanced, thanks to specialized silver techniques, intravital
methylene blue, neuronography, electrical stimulation, and the
methods involving experimental lesions and accidental brain
damage. Le Gros Clark has noted that the blood vessels, and their
mapping, is especially important to neurology since it supplies a
clue to the degree of metabolism, and hence to function. It is
interesting to note, in this respect, that the cortical arteries, being
confined to the cortex and immediately subadjacent to the white
matter, can serve the purpose of cerebral lesion; for example, if the
pia mater is stripped from the area to be studied, a lesion is effected.
For an account of the histological features of the brain, reference
should be made to Ramon y Cajal (1952) and Sholl (1956).
The method of neuronography, devised by Dusser de Barenne,
and used by him and McCulloch ( Dusser de Barenne and McCul-
BEHAVIOUR AND THE NERVOUS SYSTEM
259
loch, 1937, 1938, 1939; Dusser de Barenne, Garol and
McCulloch, 1941 ; et al) has been very useful in the mapping of
direct neural connexions. The application of filter paper soaked in
strychnine sulphate to one cortical locus leads to 'strychnine
spikes' occurring at certain other loci.
Marginal portion
of circular s.
role
Isth of gyi
-fornicatus
cuneus
^Occipital pole
Parolfactory
area
Temp,
pole
Fasciola cinerea
FIG. 10. CENTRAL SECTION OF CEREBRUM. The section is cut in a
plane at right angles to that of the eyes and approximately
bisecting a line joining the two eyes. The numbers refer to
Brodman's areas (see text).
The central assumption of neuronography is that there exist
direct connexions, without synapses, between the two areas in-
volved. There is a high correlation between anatomical detail and
neuronographical records, where corroboration has been possible,
but against this must be stated the evidence of Frankenhauser
(1951). As Frankenhauser points out, the above work in neurono-
graphy implies that the absence of spikes in a given region excludes
the existence of direct pathways. He strychninized the olfactory
260
THE BRAIN AS A COMPUTER
bulb, but was unable to find any spikes in regions where many direct
pathways from the olfactory bulb are known to exist. He feels,
therefore, that the negative implications of neuronography are
unjustified.
Electrical techniques
The method of electrical stimulation of nerve tissue has also
been criticized from time to time, especially with respect to
Temporal pole
Tf-Occipital
FIG. 11. EXTERNAL SURFACE OF CEREBRUM. This figure shows
more of the names for features of the cortex and also gives some
of the numbers for Brodman areas mentioned in the text.
spreading effects on the surface of the cortex; other workers in this
field (Gellhorn and Johnson, 1951), however, have defended the
method with some cogency.
Another source of information with seemingly enormous
potentialities is the Electroencephalogram (EEG), and an assess-
ment of the various methods adopted here is far more complicated
than in the case of anatomical localization, histology, neurono-
graphy, or electrical stimulation.
Darrow (1947) inferred that the relative failure of the EEG to
BEHAVIOUR AND THE NERVOUS SYSTEM 261
contribute much to the field of psychology may be from one of two
reasons: either the code of the EEC is simply not understood, or
the EEG gives, not an integrated cortical record, but a record of
subsidiary homeostatic processes. This failure would appear to be
certainly partially due to the first cause, although from a
physiological viewpoint some guesses have now been made at the
code. For the second point, it may be true that the EEG does give
a homeostatic picture, and homeostasis is to be thought of as a
fundamental characteristic of neural activity.
Hill (1950) has given an assessment of the EEG in its relation-
ship to psychiatry, in which he points to the fact that EEG
characteristics are as typical of an individual as, say, his finger-
prints, or his I.Q. What is of special interest is that many of the
individual differences exhibitable on the EEG may disappear on
suitable chemical, or physiological, stimulation.
Burns (1950, 1951, 1958) has studied carefully the levels of
response from electrical stimulation, and his results are consistent
with those found by Albino (1960) in ablation experiments. It is
clear that different strengths of stimuli do in fact elicit quite
different sorts (or levels) of response.
Burns' work was on isolated cortex, and his results were thought
to be caused by chains of neurons which, when they all become
fired under strong stimulation, become refractory. Similarity, he
found that repeated strong stimulation of cortex gave rise to bursts
of responses which may last for as long as an hour after cessation of
stimulation.
Some of the summarizing characteristics of the EEG work noted
by Hill are:
(1) Attention and increased cerebral activity are associated with
low voltage and fast activity, while relaxation and decreased
cerebral activity are correlated with high voltage and slow activity.
(2) 'Emotional tension* changes EEG patterns.
(3) Hypothalamic activity influences cortical rhythms.
(4) Amplitude of waves in a rhythm is a rough measure of the
number of cellular units taking part in its production.
(5) Hill thinks, more speculatively, that the constant pattern of
the EEG reflects maturation of the brain in terms of functional
organization.
262 THE BRAIN AS A COMPUTER
With respect to (3), Henry and Scoville (1952), in a discussion of
suppressor bursts from isolated pieces of cortex (they were con-
sidering patients who had had frontal lobotomy performed, which
also involved undercutting of areas 9 and 10, and the orbital gyri),
considered that the fundamental rhythms of the brain emanated
from the hypothalamus.
The whole question of the value of the EEG as a research
technique is of immense complication and demands specialist
consideration. The volume of work already produced on the EEG
is enormous, nevertheless it is probable that nothing has yet been
discovered which critically affects the behavioural picture.
All afferent volleys to the cortex set up an initial surface positive
wave (Eccles, 1953) which is restricted to the cortical region in
which the volley terminates; the wave form may be complex,
although this is not true for single afferent impulses. It has been
suggested that the initial positive wave is caused by the synaptic
excitatory action of afferent impulses generating post-synaptic
potentials on the deeper parts of the apical dendrites and the
bodies of pyramidal cells.
It should be added that there is some evidence that reverbera-
tory circuits from the thalamus contribute to the later stages of the
responses to afferent stimulation in the cortex.
In such terms it is worth considering the nature of the a-rhythm.
It is thought to be due to impulses travelling in closed, self-
exciting chains.
More recently, Eccles has suggested that the a-rhythm is
due to circulation of impulses in closed self-re-exciting chains, the
idea being that it is due to the low intensity bombardment during
states of attention.
Stewart (1959), taking a more cybernetic view of the problem,
has suggested that the a-rhythm and the other brain rhythms are
due to the inevitable periodicity of a finite automaton, and that it is
something we might expect from the very construction of any finite
automata.
Even more recently Kennedy (1959) has proposed that the
a-rhythm may arise from mechanical oscillation of the gel of
the living brain and not from the synchronization of neural activity,
except very indirectly.
it rmi<jt hf* aHmittftH that tliiQ whnl^ matter
BEHAVIOUR AND THE NERVOUS SYSTEM 263
further investigation, especially since it offers clues of a fairly
definite kind for the designers of artificial brains.
We must now say something of the functions associated with
gross anatomical divisions of the brain.
The myelencephalon
The myelencephalon or medulla is relatively simple; it is simply
the joining point of the spinal cord to the higher brain levels. It is
composed of groups of cells or nuclei, and is the point of exit and
entrance for many of the pairs of cranial nerves.
It is probable that the medulla is a relay station for the autono-
mic nervous system since it contains certain nuclei which directly
affect autonomic function, and yet there is evidence of cortical
representation of autonomic function, and therefore its role is
probably an integrative one allowing partial classification. The
words 'relay station* which we will use from time to time are
meant to suggest little more than the fact that certain locations are
on the direct paths between different parts of the brain, although
the presence of nuclei suggests that there is some switching
function to be performed there.
The metencephalon
The metencephalon, which consists of the cerebellum, pons and
a part of the fourth ventricle, is something like the cerebrum in
that it consists of grey matter on the surface with white under-
neath, the rest being largely nuclei. Problems of cerebral localiza-
tion also occur (Fulton, 1949), but for the purpose of our precis it
is sufficient to indicate its principal areas, which may be called
ventral, dorsal, anterior and posterior respectively.
The semi-circular canals, utricle and sacule, send fibres to the
ventral portion, while the spinal cord supplies fibres to the
anterior and posterior portion. The dorsal portion, or neocere-
bellum, as it is sometimes called, has connexions with the pons and
the frontal lobes of the cerebral cortex.
The pons itself forms the ventral part of the metencephalon, and
is composed of fibres that leave the cerebellum and return to it,
after crossing the ventral surface of the hindbrain. Other nuclei
264 THE BRAIN AS A COMPUTER
and fibre tracts both ascending and descending make up the
rest of the pons.
The cerebellum is almost certainly concerned with co-ordinating
motor activities, and it is known that injuries to the cerebellum
will destroy muscular co-ordination. The pons is probably con-
cerned with the association of motor activities, and since the tri-
geminal nerve has its'nuclei in the pons, it may be supposed it is
closely concerned with the sense of touch, and movement of the
face and mouth.
The mesencephalon
The mesencephalon or midbrain connects the forebrain and
hindbrain. This is probably a motor reflex centre in part, with
ascending and descending tracts. The tectum, which forms part of
the midbrain, has a sensory function involving the four colliculi, so
called. The superior colliculi have already been thought of by Pitts
and McCulloch (1947) as a possible feedback centre for the opera-
tion of visual scanning.
The inferior colliculi are concerned with hearing, and the
colliculi generally again qualify for the vague description of relay
centres.
The reticular system
This is perhaps an appropriate moment to describe the non-
specific neural mechanisms, especially the system called the
ascending reticular system.
If the central reticular core of the brain stem is stimulated then
there is a change of cortical electrical activity which is closely
associated with attention. Jasper (1958) has recently given a fairly
loose definition of the reticular system in the following terms :
... the reticular formation, extending from the thalamus down into the
medulla, is represented by all those neuronal structures which are not
included in the specific afferent and efferent pathways.
The development of our knowledge of the reticular system is
extremely relevant to our understanding of the problem of
attention and alertness, and also perhaps of consciousness.
These studies have developed from an interest in spinal reflexes
BEHAVIOUR AND THE NERVOUS SYSTEM 265
(Magoun, 1958), and to an interest in the allied function of non-
specific brain mechanisms.
Olds and Milner (1954) have shown that direct stimulation of the
central reticular core of the brain stem exhibited some of the same
electrical changes in the cortex as occur in waking from sleep, or on
the sudden alerting of an individual. This leads to the replacement
of high voltage slow waves and spindle bursts in the EEG record
by low voltage fast discharges (Moruzzi and Magoun, 1949).
Lesions of the ascending reticular system caused sleepiness in
animals, and stimulation caused wakefulness.
As well as peripheral sources of input to the reticular system
there are also projection fibres from the cortex to the central
brain stem (Jasper et al.). Also projecting to the central brain
stem, are the associated areas of frontal, cingulate, parieto-occipital
and temporal cortex, and the sensory and motor cortical areas.
One implication of this work is that the excitation of cortical
sensory areas is insufficient by itself to induce arousal or cause
sensation.
A further set of results shows that afferent transmission is also
aifected by these non-specific central states.
Morrell and Jasper (1955) have been able to demonstrate, in
terms of conditioning, that the blocking of the a-rhythm as a
conditioned response is a method for the study of temporary
connexion formation in the brain. At the beginning of condition-
ing, a generalized blocking reaction occurs which, with repeated
conditioning, becomes more specific, and restricted to some local
cortical area. There is a general activation and blocking prior to
any learning operation.
Consciousness can perhaps be seen to be emerging from this sort
of work, although as Jasper (1958) puts it:
The stream of our consciousness is only a minute sampling of the multi-
tude of simultaneously active cells and circuits in the complex machinery
of the mind.
Much, even most, of the function of the reticular system is
probably still unconscious, and it is the ascending reticular system
that is probably primarily concerned with consciousness. Attention
is probably a further differentiation of the generalized arousal
mechanism, where there is little doubt that generalized arousal is
dependent on activity within the mesencephalic and caudal
266 THE BRAIN AS A COMPUTER
portions of the diencephalic reticular system. As far as attention is
concerned Jasper (1958) says:
The fact that the thalamic reticular system seems to possess a certair
degree of topographical organization relative to its cortical projection!
may provide a neurophysiological basis for the direction of attention.
It is interesting that the most important cortico-fugal projection*
seem to arise from areas not primarily sensory in function
They are the frontal, cingulate, temporal and parietal areas anc
area 19.
The implication is perhaps that these elaboration areas are the
places where consciousness enters the picture; and the integrative
process of the brain is possibly to be regarded as a multistage
process, and one in which the reticular system may be thought tc
play a central part.
It has been noticed (Delafresnaye, 1954) that moderate activity
in the reticular formation of the brain stem is correlated with fasi
asynchronous EEG recordings, and also correlated with alertness
and attention. Lesions of the reticular formation lead to slo^
synchronous EEG recordings, and unconsciousness or somnolence
Lindsley (1951) has actually suggested a theory of excitation basec
on activation of the reticular system, and more generally, it has
been concluded that the reticular system was vital to skillec
voluntary acts, and to memory and intelligence. The effect oJ
stimulating the reticular areas at increasing intensities has been tc
lead through a progression from alerting to searching, and then tc
flight.
The limits of variability of cortical organization (Lashley, 1947
are a matter of 'individual differences', 'species differences', etc.
and therefore the generalized suggestions made here must neces-
sarily be particularized for different species, and ultimately for '<
particular individual.
Much current work is going on in the field of the reticulaj
system, much of which must be taken to modify the neuror
psychological theories of Hebb, Lashley and others. From the
point of view of our own approach, we should seek to give inter-
pretation to the reticular system as bearing closely on the M-
system or motivational system and the closely related jB-system oi
emotional system, and the relation of both these to the C-system
No more than this will be said at the moment.
BEHAVIOUR AND THE NERVOUS SYSTEM 267
The diencephalon
The thalamus and hypothalamus, the optic tracts and retinae,
the pituitary, mammillary bodies and third ventricle make up the
diencephalon.
The main interest for behaviour theory, with the exception of
visual perception (see Chapter IX) lies in the thalamus and hypo-
thalamus.
The thalamus is thought of as another relay station, the principal
one in the brain, and it is made up of various nuclei.
Thalamus and hypothalamus
The thalamus is embryologically old compared with the cerebral
cortex, which has been modified in a series of extensive ramifica-
tions. The thalamus (Fulton, 1943) appears to be best viewed as
an end station in the forebrain of sensory systems of the body. The
geniculate bodies appear to be connected with the special senses.
Its associative functions are cortico-diencephalic and intra-
diencephalic. It has seven principal afferent tracts, and is con-
nected with the adjacent mass of the hypothalamus. Anatomically,
the thalamus may be divided into three groups of nuclei with
(1) subcortical connexions, (2) cortical relay nuclei which transmit
impulses from somatic sensory systems and the special senses, and
(3) its association nuclei.
Lesions of the posterior third of the ventral nucleus cause transient
cutaneous impairment, and rupture of the thalamogeniculate
artery 'causes' paresthesia and hyperesthesia. Starzl and Magoun
(1951) suggest, as a result of studying the cat's thalamic projection
system, that it is organized for mass thalamic influence on the
association cortex.
It has been generally assumed that the hypothalamus is con-
nected with the emotional aspects of behaviour. However, the
anatomy and physiology of the hypothalamus is, like the thalamus,
closely associated with cortical areas. Its main divisions are
(1) periventricular region, (2) pre-optic region, (3) lateral region,
(4) rostral or supraoptic middle region, (5) tuberal, infundibular
middle region, (6) caudal, or mammillary region. The existing
knowledge of the hypothalamus is somewhat mixed but, as le
Gros Clark (1950) has said, much of the most recent development
268 THE BRAIN AS A COMPUTER
on 'psychosomatic' medicine has surrounded a study of the
hypothalamus. The work of Philip Bard (1934) and Masserman
(1943) on 'sham rage' is now well known, and needs no further
comment here; le Gros Clark's survey continues the same line of
thought. Lesions of the hypothalamus are still considered to be
closely related to the 'emotional* aspects of behaviour, as well as to
the autonomic nervous system. The hypothalamus is probably
central to any 'total' theory of behaviour, but does not contact
the more restricted aspects of 'learning' to quite the same
extent.
However, a few words in summary on the hypothalamus may be
suggestive for purposes of general development (Le Gros Clark,
1950):
(1) The hypothalamus is situated in the base of the brain, and
has the cerebral peduncles immediately behind, and the optic
chiasma in front; it is also, of course, close to the pituitary which is
an outgrowth of the hypothalamus.
(2) Its considerable blood supply suggests high metabolic
activity, and the hypothalamic pituitary connexions are again
emphasized.
(3) In submammalian vertebrates, the supraoptic and para-
ventricular nucleus is fused in a single mass which suggests a close
functional connexion.
(4) The hypothalamus has a motor pathway from the posterior and
lateral hypothalamus into the brain system (possibly autonomic).
(5) The medial thalamic nucleus projecting to the granular
cortex of the frontal lobe might suggest a railway station function.
(6) The Mammillo-thalamic tract (bundle of Vicq d'Azur)
connects the thalamus and hypothalamus.
(7) There are fibres derived from the globus pallidus running
from the subthalamus to the hypothalamus, and this, perhaps,
implies partial basal ganglionic control of the hypothalamus.
(8) The frontal cortex has (possibly autonomic) fibres direct to
the hypothalamus.
(9) The fornix, en route from the hippocampus to the mammil-
lary bodies, is a large afferent tract to the hypothalamus. The
fibres from the MammiUo-thalamic tract to the anterior nucleus of
the thalamus, and to the cingulate cortex, form a closed circuit. It
BEHAVIOUR AND THE NERVOUS SYSTEM 269
may be that the hippocampus is not only olfactory (as will be
emphasized later; Scoville and Milner, 1957), and the mammillary
bodies are probably relay stations. This last is of special interest in
the now well-known possible role of cerebral prolongation at
cortical level.
(10) The frontal lobe is a projection area for the hypothalamus.
(11) Lastly, it can be tentatively restated that the hypothalamus
is to be regarded as a relay station under cortical (and striatal)
control. This is especially related to autonomic function, and also
plays an integrated part in normal cerebral function; it is, indeed,
probably connected closely with reverberatory circuits.
The telencephalon
Under this term we subsume the olfactory bulb and tracts, the
lateral ventricles and basal ganglia and, rather especially, the
cerebral cortex.
Very generally we can divide the cerebral cortex into the four
areas which are duplicated, one in each hemisphere. These areas
arecalled(l):Frontal(especiallyareas4,6, 8 11, 44 and 45), (2) Pari-
etal (especially areas 2, 3, 5 and 7), (3) Temporal (especially areas
38, 39, 40, 41 and 42) and (4) Occipital (areas 17, 18 and 19). It has
been suggested that the broad function of these areas is that the
frontal lobes are integrative and the posterior portions concerned
with relatively specific motor functions and also motor elaboration
functions, the speech areas, areas 44 and 45, being specialized
regions. The parietal lobe is concerned with sensory control and
sensory elaboration, the temporal with speech recognition, musical
recognition and generally with memory, while the occipital areas
are specialized for vision and visual elaboration.
Within the compass of this very general statement there are
problems about the relation between the two cerebral hemispheres
which are by no means fully understood, and this makes all
subsequent analysis of the function of specific areas somewhat
tentative. The notion of cerebral dominance is of the first import-
ance neurologically, and although there is some evidence that left-
handed people are right hemisphere dominant, the whole problem
is much more complex than this suggests. This matter is very
important for comparative neurology since animal experiments
270 THE BRAIN AS A COMPUTER
seem to show that bilateral ablation is often necessary to produce
impairment of specific function whereas in human beings this may
often be produced by unilateral ablation. Clearly the human brain
is more specialized and their equivalent cerebral areas are not
merely mirror images of each other.
The cerebral cortex
We must now turn to a more detailed study of the cerebral
cortex and, of course, the closely related neural structures of the
immediately lower levels. In this discussion it is the cerebral
hemisphere, particularly the cerebral cortex, the study of the
Brodman areas and their function, cytoarchitectonics, the alleged
suppressor areas, and the reticular system, etc., which are of the
first importance. This involves the basal ganglia and other parts of
the nervous system viewed as functions of the control of the
cerebral mantle.
In discussing the cortex we should note the recent terminology
that has been suggested by Pribram, Jasper and others (1958).
The Paleocortex or allocortex is phylogenetically older, and
includes the hippocampus (Ammon's Horn and the dentate
nucleus), the pyriform lobe, and the olfactory bulb and tubercle.
The Juxtallocortex includes the cingulate gyrus, presubiculum and
fronto-temporal cortex. The non-cortical tissue of first importance
includes the amygdaloid complex, the septal region, thalamic and
hypothalamic nuclei, as well as the caudate and mid-brain reticular
formulation. The isocortex, or neocortex, is further divided into
Extrinsic and Intrinsic areas. The extrinsic have projective fibres
from the thalamic relay nuclei and fibres from outside the thalamus,
while the intrinsic project solely from the thalamic relay nuclei to
the isocortex.
There is some evidence that the extrinsic fibres are closely
connected with the different behaviour functions of peripheral
receptor mechanisms, and the intrinsic are concerned with
discrimination, which is known to be affected by removal of
posterior intrinsic cortical areas.
It is necessary now to select carefully our analysis of the struc-
ture and function of the cortex with an eye to behaviour theory and
automata construction. We shall first consider the function of the
BEHAVIOUR AND THE NERVOUS SYSTEM
271
frontal lobes (Stanley and Jaynes, 1949; Hebb, 1945, 1949;
Fulton, 1943, 1949; Shell, 1956).
Cytoarchitectonically, the frontal lobes are part of the isocortex
Septa!
Optic chic
Arcuate nucleus-
FIG. 12. THE FIGURE SHOWS THE CORTEX and its extrinsic and in-
trinsic thalamic connexions. FX is Fomix, HP is theHabenulo-
interpeduncular tract, IP is the Interpeduncular nucleus, MB
is the Mammillary bodies, M T the Mammillo-thalamic tract, to
the olfactory tubercle, TEG the midbrain Tegmentum and CA
the Anterior Commissure.
and are stratified in five layers. An outstanding feature is the
presence of giant pyramidal cells in area 4. Furthermore, it is
interesting to compare the smaller pyramidal cells of 6 with those
272 THE BRAIN AS A COMPUTER
of 4, and also with 7 in the temporal lobe. Campbell (1905), it may
be noted, did not differentiate areas 6 and 7. Area 4 is usually
regarded as a motor area, with giant pyramidal (or Betz) cells in
layer V. It may be subdivided into 4A (leg), 4B (arm), 4C (face),
for superior, middle, and inferior parts (Vogt, 1919). Variation is
only apparent in the size of the pyramidal cells, and it is note-
worthy that, in man, area 4 is largely concealed in the central sulcus.
For a comparative study reference should be made to Bucy (1944).
It is probable that the motor areas of the frontal lobe are not
immediately vital to the behaviour picture ; what, however, may be
of importance is the strip region between areas 4 and 6 which is
known as 4s, a suppressor area (Marion Hines, 1936). Area 6 is
similar to area 4, without the pyramidal cells in layer V.
The subdivisions of 6 refer to buccal and respiratory muscula-
ture. Area 8 is also motor in function (transitional cortex which has
extensive extrapyramidal projections to the striatum, thalamus
(latero-ventral nucleus), subthalamus and tegmentum. It also
possesses another suppressor area, 8s. Areas 9, 10, 11 and 12
(orbito-frontal cortex) are sometimes referred to collectively as the
frontal association areas.
Cytoarchitectonically these are vastly different from areas 4 and
6. There are, for example, no motor cells in layer V. As regards
function, 13 and 14, in the near orbital region, have been ear-
marked as respiratory and olfactory areas by Walker (1938).
Generally it is probably true to say that cytoarchitectonic
analysis, with its extensive staining methods, has not yet reached its
limits, and its contribution has been largely in its divisions of
cortical areas in terms of cellular structure. One needs to supple-
ment this knowledge with knowledge of the frontal areas derived
from psychological experiments, neuronography, and so on. Here
one must draw on the work of Fulton, Stanley and Jaynes, and
many others.
(1) The frontal lobes may be divided into the orbito-frontal
cortex (projection area of dorso-medial nucleus of the thalamus),
9, 10, 11, 12, as well as 13 and 14 on the orbital surface.
(2) The cingulate gyrus (24) ; the projection area of the antero-
medial nucleus of the thalamus.
(3) Broca's speech area 44 and 45.
BEHAVIOUR AND THE NERVOUS SYSTEM 273
Area 24 has an. antero-medial connexion which, in turn, has a
projection from the mammillary bodies, thus the hypothalamus is
linked with the cortex. The antero- ventral and antero-dorsal nuclei
project to areas 25 and 29. The dorse-medial nuclei are stationed on
hypothalamic, and orbito-frontal, projections.
The hypothalamic-frontal connexions imply a connexion
between autonomic function and the cerebral cortex, and the
methods of neuronography have well illustrated this. The integra-
tion of autonomic responses probably takes place in the frontal,
particularly in the orbital, surfaces. Evidence on these points
comes from leuchotomy cases, as well as from neuronography.
There appears, indeed, to be considerable overlap (Fulton, 1949)
of autonomic and somatic function in cortical areas in the frontal
lobe.
It is necessary now to pass on to the consideration of the
behavioural aspects of the frontal lobes, and the correlation
between somatic function and behaviour, and one is forced to
concede straight away that there are serious problems to be faced.
(1) There are, as yet, insufficient behavioural checks on
neurological findings, and contrariwise, neurological methods are
not yet sufficient.
(2) The difficulty of finding homologous areas in different
species.
(3) The difficulty of individual variation within the species.
(4) The complex problem of individual differences in learning.
This may dominate the actual neural model with respect to neural
patterns.
(2) and (3) have been built up to a great degree by the work of
Clark and Lashley (1947), and bear on matters of localization.
The function of suppressor areas, as described by Stanley and
Jaynes, is to relax all striate musculature, raise the threshold of the
precentral cortex, and reduce, or disrupt, after-discharge of the
motor cortex. It is also of immediate interest that all the suppressor
bands connect directly to the caudate nucleus, although it must be
admitted that the very existence of suppressor areas is open to
some doubt and, in view of this, they will not be discussed
further.
274 THE BRAIN AS A COMPUTER
Kluver's classical experiment, involving bilateral frontal ablation
in a monkey, is concerned with the monkey's reaction to the
stimulus of the sight of a grape. He will pick up the grape and begin
to move it towards his mouth, but if he is then shown a second
grape he will drop the first one and pick up the second. This
process may go on until the monkey is surrounded by grapes,
having eaten none (Kluver, 1933). It need hardly be added that
this cannot be reproduced in the normal monkey. One is
reminded, parenthetically, of the behaviour of very young
children.
A large number of such experiments are quoted and compared
both by Fulton (1949) and Stanley and Jaynes (1949), and men-
tioned by Hebb (1949), and we shall now gather together their
results on the effect of frontal ablation.
(1) The increased food intake factor (Hyperphagia).
(2) Alterations in emotional and social behaviour as exemplified
by the experiment of Jacobson, Wolfe, and Jackson, who found
that two previously excitable chimpanzees were persistent, and
benign, in a delayed reaction test, even in the face of repeated
failure. Both had bilateral ablation of the frontal region. Ward
(1948) found that unilateral or bilateral ablation of area 24 (cin-
gulate gyrus) in four monkeys led to a profound change in the
animals* emotional and social behaviour, while other workers have
been able to observe no such changes.
Arnot (1949), in presenting his theory of frontal lobe function,
re-emphasized the now well-established fact that changes in social
behaviour take place. Arnot saw the frontal lobe function as one
involving the persistence of emotional states, chains of thought,
motor activities and motor inhibitions. This will certainly be seen
to fit some of the facts well.
(3) Thirdly, there is the fact of hypermobility (sometimes also
inertness is observed) following on bilateral ablation of the
frontal region. This has been specifically demonstrated by Ruch
and Shenkin (1943) on bilateral ablation of area 13 of Walker, and
on no other part of the frontal cortex, and has been confirmed by
Fulton, Livingstone and Davis (1947); Mettler (1944), however,
failed to confirm it. He found that hypermobility follows bilateral
ablation of area 9, or the pre-motor areas. It is also interesting to
BEHAVIOUR AND THE NERVOUS SYSTEM 275
note that vision apparently plays a major role in the sensory control
of hypermobility. Kennard, Spencer and Fountain (1941) found
that enucleation of the eyes, occipital lesions, or even darkness,
reduced the total amount of activity in monkeys.
(4) According to Settlage, Zable and Harlow (1948), there is a
difficulty in 'habit reversal' in an *either-or* test, which is sub-
sequently reversed for the correct response. In the view of these
workers there is a marked difference between the reversal patterns
of the frontal animal, as opposed to the normal. There exists a
perseveration of the non-reinforced habit shift in the normal
monkey.
(5) There is intellectual loss sometimes observed, and finally
(6) We should mention that there is normally a general change in
motivation.
In another report, Harlow, Meyer and Settlage (1951) discuss a
study they carried out on the effects of extensive unilateral lesions
in a group of monkeys. They also used another group of monkeys
(there were four in each group) who had both unilateral lesions
and destructions of lateral surface of contralateral prefrontal
region. A control group of four was also used. They found that
there was almost complete loss of function in the 'delayed re-
sponse* situation, even though medial and orbital surfaces of the
frontal lobe were intact. They also found that generalized response
was affected in the prefrontal monkey.
Some interesting comparable results were found by Blum,
Chow and Blum (1951) on the Macaca mulatto., in the auditory
dicrimination habit and the delayed reaction test (auditory and
visual clues used). Blum noted that the mid-lateral destruction
caused serious impairment, whereas ventro-lateral or dorsal
destruction caused only slight impairment. It was noticeable, too,
that the total amount of destruction seemed important in the
mid-lateral case.
(5) Seriatim problems involve poor performances in 'frontal'
monkeys. Jacobson's experiments (1931, 1935, 1936; Jacobson
and Elder, 1936; Jacobson and Haslernd, 1936; Jacobson, Wolfe
and Jackson, 1935) are illustrative of this. He had two chim-
panzees and gave them six months training in (a) delayed reaction
tests, (b) problem boxes, and (c) stick and platform problems.
276 THE BRAIN AS A COMPUTER
The Problem boxes, of which there were two types, involved in
the first instance a simple, single operation, such as pulling a rope
or rod. The second operation had a more complex combination
box, in which a rope, rod and crank had to be operated in a
particular order to open the box. Both animals were operated on,
and at first one frontal area was removed in each, the areas involved
being 9, 10, 11 and 12. The animals were subsequently tested for
three months, and then the second frontal area was removed, with
apparently no change in behaviour. However, between the first
and second operations there were, in fact, certain not easily
observable changes that Jacobson (1931, 1936) described as
'frustrational behaviour' (e.g. when unrewarded in discrimination
or delayed reaction tests if the wrong choice was made), and the
presence of 'temper tantrums'. After the second operation there
was a complete lack of emotional expression, and the chimpan2ees
appeared to be unworried by failure. After the bilateral ablation,
the chimpanzees failed the double stick and platform test. In
Jacobson's work it appears that the anterior parts of area 24 were
destroyed, and that the orbital surfaces, on the other hand, were
left intact.
The next experiment is concerned with Lashley's conditioned
reaction problem, a type of discrimination problem in which two
stimuli are presented, and one is conditioned with respect to some
other feature of the environment, e.g. black and white cards were
presented, and food was given for response to the black card.
Normal animals learnt this easily, but the 'frontals' failed in a
thousand trials. The delayed reaction problems are of various
forms and reference should be made to the original work for
further details (Jacobson, 1931, etc.). The results are fairly con-
sistent. Jacobson found delays up to 2 min in normal
monkeys, and also found that the responses were, at worst,
destroyed by bilateral ablation; at best, delays of some 3 or
4 sec were obtained. Campbell and Harlow (1945) have
found that by certain devices, such as increasing the time interval
after operation, and time intervals between trials, longer delays
could be obtained.
One confirmatory experiment was carried out by Chow, Blum
and Blum (1951) in which they used monkeys (Macaca mulatto)
with bilateral parieto-temporo-preoccipital ablations. Subse-
BEHAVIOUR AND THE NERVOUS SYSTEM 277
quently there was removal of the frontal granular cortex. Tests
and observations of sensory states and abilities in discrimination
(vision, somesthesis, audition) were made before and after the
frontal operation, and the conditioned reactions and delayed
responses in the monkeys were listed. The effects of additional
prefrontal ablation on the four monkeys were, as interpreted by
the experiments: (1) Decrease in visual activity in one monkey,
and restriction of visual field in another; the other two were
apparently unaffected with respect to sensory defects. (2) Deficient
retention was observable in two monkeys, and deficient discrimina-
tion with respect to temperature and roughness in two. There
appeared to be no failure in visual discrimination. (3) There was a
decrement on the conditioned reaction problem. (4) Three of the
monkeys failed completely on the delayed response, and the fourth
was considerably poorer. (5) There was a general increase of
activity in all the animals.
One further inference made by these workers is of interest.
They discuss the occurrence of 'fringe activity* in the cortex, and
imply that a model of cortical activity must include the notion of
dominant and recessive controlling factors overlapping. Such
cortical overlap is very suggestive and consistent with a conception
of the cortex as a functional mosaic, which may account for the
variable results so often found after repeated stimulation of the
same cortical 'point* even without differences of strength of
stimulation.
Sholl (1956) believes the frontal lobes are the seat of co-ordina-
tion and fusion of the incoming and outgoing products of the
several sensory and motor areas of the cortex and we may guess
that the frontal lobes are probably simply storage areas, from the
computer point of view, and although these storage areas are
probably primarily concerned with the higher level integrative
activity, it is also likely that they participate in the networks of the
cortex, having effects of a variety of kinds on other particular
activities such as autonomic function and emotional changes. The
speech areas, of course, are specific but can still be regarded as
storage registers. This sounds ridiculously simple, but it is a fact
that, from the whole vast amount of experimentation so far per-
formed, little more could be said in a general way as a pointer to
frontal lobe function.
276 THE BRAIN AS A COMPUTER
The Problem boxes, of which there were two types, involved in
the first instance a simple, single operation, such as pulling a rope
or rod. The second operation had a more complex combination
box, in which a rope, rod and crank had to be operated in a
particular order to open the box. Both animals were operated on,
and at first one frontal area was removed in each, the areas involved
being 9, 10, 11 and 12. The animals were subsequently tested for
three months, and then the second frontal area was removed, with
apparently no change in behaviour. However, between the first
and second operations there were, in fact, certain not easily
observable changes that Jacobson (1931, 1936) described as
'frustrational behaviour* (e.g. when unrewarded in discrimination
or delayed reaction tests if the wrong choice was made), and the
presence of 'temper tantrums'. After the second operation there
was a complete lack of emotional expression, and the chimpanzees
appeared to be unworried by failure. After the bilateral ablation,
the chimpanzees failed the double stick and platform test. In
Jacobson's work it appears that the anterior parts of area 24 were
destroyed, and that the orbital surfaces, on the other hand, were
left intact.
The next experiment is concerned with Lashley's conditioned
reaction problem, a type of discrimination problem in which two
stimuli are presented, and one is conditioned with respect to some
other feature of the environment, e.g. black and white cards were
presented, and food was given for response to the black card.
Normal animals learnt this easily, but the 'frontals' failed in a
thousand trials. The delayed reaction problems are of various
forms and reference should be made to the original work for
further details (Jacobson, 1931, etc.). The results are fairly con-
sistent. Jacobson found delays up to 2 min in normal
monkeys, and also found that the responses were, at worst,
destroyed by bilateral ablation; at best, delays of some 3 or
4 sec were obtained. Campbell and Harlow (1945) have
found that by certain devices, such as increasing the time interval
after operation, and time intervals between trials, longer delays
could be obtained.
One confirmatory experiment was carried out by Chow, Blum
and Blum (1951) in which they used monkeys (Macaca mulatto)
with bilateral parieto-temporo-preoccipital ablations. Subse-
BEHAVIOUR AND THE NERVOUS SYSTEM 277
quently there was removal of the frontal granular cortex. Tests
and observations of sensory states and abilities in discrimination
(vision, somesthesis, audition) were made before and after the
frontal operation, and the conditioned reactions and delayed
responses in the monkeys were listed. The effects of additional
prefrontal ablation on the four monkeys were, as interpreted by
the experiments: (1) Decrease in visual activity in one monkey,
and restriction of visual field in another; the other two were
apparently unaffected with respect to sensory defects. (2) Deficient
retention was observable in two monkeys, and deficient discrimina-
tion with respect to temperature and roughness in two. There
appeared to be no failure in visual discrimination. (3) There was a
decrement on the conditioned reaction problem. (4) Three of the
monkeys failed completely on the delayed response, and the fourth
was considerably poorer. (5) There was a general increase of
activity in all the animals.
One further inference made by these workers is of interest.
They discuss the occurrence of 'fringe activity' in the cortex, and
imply that a model of cortical activity must include the notion of
dominant and recessive controlling factors overlapping. Such
cortical overlap is very suggestive and consistent with a conception
of the cortex as a functional mosaic, which may account for the
variable results so often found after repeated stimulation of the
same cortical 'point' even without differences of strength of
stimulation.
Sholl (1956) believes the frontal lobes are the seat of co-ordina-
tion and fusion of the incoming and outgoing products of the
several sensory and motor areas of the cortex and we may guess
that the frontal lobes are probably simply storage areas, from the
computer point of view, and although these storage areas are
probably primarily concerned with the higher level integrative
activity, it is also likely that they participate in the networks of the
cortex, having effects of a variety of kinds on other particular
activities such as autonomic function and emotional changes. The
speech areas, of course, are specific but can still be regarded as
storage registers. This sounds ridiculously simple, but it is a fact
that, from the whole vast amount of experimentation so far per-
formed, little more could be said in a general way as a pointer to
frontal lobe function.
278 THE BRAIN AS A COMPUTER
Cortical stimulation
Penfield and Rasmussen (1950) have carried out extensive
research in the cerebral cortex in the course of cranial operations on
a number of patients suffering from epilepsy. One of the important
reminders they give is with respect to the facts discovered initially
by Sherrington and Graham Brown on reversal of response, and
the allied problem of facilitation. These are worth stating in
operational form.
If point A on the precentral gyrus is stimulated and produces
finger flexion, then the same response may be elicited considerably
anterior to A, say at J3, whereas direct stimulation of B would not
in fact produce finger flexion. Reversal of response can be elicited
similarly by stimulating a point B to elicit extension, then stimu-
lating A, producing flexion, and continuing to stimulate in turn
points at short intervals downward along the precentral gyrus.
Flexion will follow each stimulus up to and including point 5.
Anomalous results of the same kind may be found in the motor
cortex when a point C, say, apparently changes its function to a
wrist movement instead of a finger movement.
Summation, after-discharge, inhibition, etc., were all elicited by
cortical stimulation, and it is of interest that Sherrington and
Brown regarded inhibition as more characteristic of the cortex
than excitation.
Temporal and parietal areas and motor-sensory cortical
areas
Information on the cortical areas other than the frontal lobe are
of some considerable interest. The areas 17 and 18 of the occipital
lobe are rather especially connected with visual function, and
these will receive further consideration in the next chapter. The
temporal and parietal lobes will now be briefly discussed.
Penfield (1947) associates the 'dream states' of Hughlings
Jackson (1931) with the temporo-parietal areas under the name
'psychical seizures'. Penfield and Rasmussen (1950) consider that
the temporal area, while including auditory and vestibular
representation, . is primarily devoted to 'memory* and 'sensory
perception*. As far as perception is concerned it is assumed to
depend, in part, on memory; but with epileptic discharge in only
BEHAVIOUR AND THE NERVOUS SYSTEM 279
one temporal area and the resulting confused hallucinations, a
'false memory* becomes involved. Thus perceptual illusion results
in part from disturbance in one temporal area. If, as Penfield and
Rasmussen have pointed out, a patient had epileptic discharge
in a single remaining lobe, then the faulty 'perceptions' could
not be corrected. Faulty perceptions, it should be added, are
not always corrected when there is another healthy lobe
available.
It is emphasized that the temporal areas are not distinct, or
clearly delimited, from their surround, so that there appear to be
involved: hearing, vestibular function, speech and hand skills,
visual and smell functions. Temporal lobectomy (involving only
the lobe) does not normally involve serious memory defects (Pen-
field and Rasmussen, 1950), although sometimes interference with
the optic radiations affects the patient's vision. Indeed more
recently, Milner (1958) has shown some specific memory loss
depending on the side of the lobectomy.
Marsan and Stoll (1951) report that the temporal pole is
frequently the focus of epileptic discharge; using neuronography,
conduction of electrically induced after-discharge, and evoked
potentials, they investigated subcortical structures in monieys and
found the pulvinar-lateral nucleus, septal-fornix, hypothalamus,
basal ganglia and thalamic reticular system all had thalamic
connexions.
Especially interesting from the behavioural point of view are
the studies of temporal lobectomy (Riopelle, Alpher, Strong and
Ades, 1953; Chow, 1952, 1954; Meyer, 1951 and 1958) on learning
sets (Harlow, 1949).
The simple problem confronting a monkey, say, is to discover
which of two covers is concealing food; they can transfer then to
other such covers in a single trial. Meyer describes this in terms of
freeing the monkey from trial-and-error behaviour we shall, of
course, be tending to think of this in terms of the transfer from
one store to another (Chapter IV), but let us see what the con-
nexion with the temporal lobes is. Very briefly, the normal monkey
accumulates knowledge (generalizations) while the temporal
monkey seems to find each problem a new one, indeed he does not
form learning sets.
From the cybernetic point of view this last is one of the most
280 THE BRAIN AS A COMPUTER
interesting results since it suggests the possibility, at least, that the
temporal areas contain precisely the storage registers associated
with material that has been learned, mostly in the form of general-
izations. Other experiments have been carried out confirming these
results (Meyer, 1958) and aimed to distinguish the factors of
retention and acquisition, both of which were found to be affected.
Scoville and Milner (1957) showed, that in human, bilateral
medial temporal lobe resection extensive enough to damage the
anterior hippocampus and hippocampal gyrus, results in persistent
impairment of recent memory. On the other hand neither the
bilateral removal of the uncus and amygdaloid nucleus nor uni-
lateral temporal lobe removal affects recent memory. It may be
concluded that the hippocampus and hippocampal gyrus are
therefore important features in recent memory. At the same time it
would be rash to say they were actually the registers directly
concerned yet they may supply a source of registers concerned
with recently acquired data which are essential to the learning
process, and thus of course vital to the formation of learning
sets.
Milner and Penfield (1955) performed partial temporal lob-
ectomy on two human epileptics. They extirpated the hippo-
campus, hippocampal gyrus, uncus and amygdaloidal nuclei in
the dominant hemisphere.
There was evidence of damage to the opposite hippocampal
area; there was also a deficit in recent memory but without any
change in I.Q., reasoning, etc. Tests given showed that immediate
recall was unaffected, but that there was a total loss of information
after 5 min, and this also obtained for recognition and recall,
for verbal and non-verbal material.
A third patient without non-dominant hippocampal damage did
not show these memory effects.
There is further evidence to substantiate these findings. Lashley
was apparently influenced by Hughlings Jackson in a fairly extreme
way when he showed, in a series of experiments, the surprising
ability of the cerebral cortex to recover from all sorts of insult, and
as a result he moved away from the older concepts of cortical
localization to a much more functional view.
General conclusions on the temporal lobe must include Pen-
field's (1947) work on temporal stimulation, which generally
BEHAVIOUR AND THE NERVOUS SYSTEM 281
elicited relatively precise, familiar, visual scenes in the patient.
Penfield and Rasmussen are quoted:
It would seem, also, that the original formation of the memory pattern
must be carried out from a high level of neural integration, for a man
remembers the things of which he was conscious and especially the
substance of his own reaction to them. The same was true of memories
evoked by stimulation. They were usually composed of familiar elements,
at least to the same extent as dreams are.
The general conclusion on the temporal lobe at this stage is that it
involves a fairly high degree of neural organization in the form,
presumably, of some sort of synaptic patterns. Naturally these
relatively stable patterns (whatever their detailed form may take)
are primarily associated with memory and perception.
The parietal area appears (Penfield and Rasmussen, 1950) to be,
largely, an area involving elaboration of certain functions; for
instance, the superior parietal area may be associated with hand
and foot movements, and the inferior parietal area with speech
'elaboration'. The parietal area here referred to lies directly
behind the postcentral gyrus. The arguments are, generally, induc-
tions made from operative surgical cases of parietal removal, from
both the dominant and non-dominant hemispheres. One example
concerns a patient who had a large cortical removal from the non-
dominant parietal lobe. He had no sensory disturbances in the
opposite arm, but found difficulty in manipulating this hand in
tasks set him. He also had difficulty in dressing himself, as the left
arm was to a large extent ignored.
Lashley (1950), in discussing memory in terms of nervous
function, drew the following conclusions:
(1) It seems certain that the theory of well-defined conditioned
reflex paths from sense organs via association areas to the motor
cortex is false. The motor areas are not necessary for the retention
of sensori-motor habit, nor even of skilled manipulative patterns.
(2) It is not possible to demonstrate the isolated localization of
a memory trace engram anywhere within the nervous system.
Limited regions may be essential for learning or retention of a
particular activity, but within such regions the parts are function-
ally equivalent. The 'engram' is represented throughout the
region.
(3) The so-called associative areas are not storehouses for
282 THE BRAIN AS A COMPUTER
specific memories. They seem to be concerned with modes of
organization and with general facilitation or maintenance of the
level of vigilance. The defects which occur after their destruction
are not amnesias but difficulties in the performance of tasks which
involve abstraction and generalization, or conflict of purposes. It is
not possible as yet to describe these defects in the present psycho-
logical terminology. Goldstein (1939) has expressed them in part
as a shift from the abstract to the concrete attitude, but this
characterization is too vague and general to give a picture of the
functional disturbance. For our present purpose the important
point is that the defects are not fundamentally those of memory.
(4) The trace of any activity is not an isolated connexion be-
tween sensory and motor elements. It is tied in with the whole
complex of spatial and temporal axes which forms a constant
substratum of behaviour. Each association is oriented with respect
to space and time. Only by long practice under varying conditions
does it become generalized or dissociated from these specific co-
ordinates. The space and time co-ordinates in orientation can, I
believe, only be maintained by some sort of polarization of
activity, and by rhythmic discharges which pervade the entire
brain, influencing the organization of activity everywhere. The
position and direction of motion in the visual field, for example,
continuously modifies the spinal postural adjustments, but a
fact which is more frequently overlooked the postural adjust-
ments also determine the orientation of the visual field, so that
upright objects continue to appear upright in spite of changes in
the inclination of the head.* This substratum of postural and tonic
activity is constantly present, and is integrated with the memory
trace (Lashley, 1949).
I have mentioned evidence that new associations are tied-in
spontaneously with a great mass of related associations. This
conception is fundamental to the problem of attention and interest.
There are no neurological data bearing directly upon these prob-
lems, but a good guess is that the phenomena which we designate
as attention and interest are the results of partial, sub-threshold
activation of systems of related associations which have a mutual
facilitative action. It seems impossible to account for many of the
*It has been drawn to my attention that in fact mistakes in orientation will
in fact occur under certain circumstances with a change of inclination of the head.
BEHAVIOUR AND THE NERVOUS SYSTEM 283
characters of organic amnesias except in such general terms as
reduced vigilance or reduced facilitation.
(5) The equivalence of different regions of the cortex for reten-
tion of memories points to multiple representation. Somehow,
equivalent traces are established throughout the functional area.
Analysis of the sensory and motor aspects of habits shows that
they are reducible among components which have no constant
position with respect to structural elements. This means, I believe,
that within a functional area the cells throughout the area acquire
the capacity to react in certain definite patterns which may have
any distribution within the area. I have elsewhere proposed a
possible mechanism to account for this multiple representation.
Briefly, the characteristics of the nervous network are such that,
when it is subjected to any pattern of excitation, it may develop a
pattern of activity, reduplicated throughout an entire functional
area by spread of excitations, much as the surface of a liquid
develops an interference pattern of spreading waves when it is
disturbed at several points (Lashley, 1942). This means that within
a functional area, the neurons must be sensitized to react in certain
combinations, perhaps in complex patterns of reverberatory circuits,
reduplicated throughout the area.
(6) Considerations of the numerical relations of sensory and
other cells in the brain make it certain, I believe, that all of the cells
of the brain must be in almost constant activity, either firing or
actively inhibited. There is no great excess of cells which can be
reserved as the seat of special memories. The complexity of the
functions involved in reproductive memory implies that every
instance of recall requires the activity of literally millions of
neurons. The same neurons which retain the memory traces of one
experience must also participate in countless other activities.
Recall involves the synergic action of some sort of resonance
among a very large number of neurons. The learning process must
consist of the attunement of the elements of a complex system in
such a way that a particular combination or pattern of cells
responds more readily than before the experience. The particular
mechanism by which this is brought about remains unknown.
From the numerical relations involved, I believe that even the
reservation of individual synapses for special associative reactions
284 THE BRAIN AS A COMPUTER
is impossible. The alternative is, perhaps, that the dendrites and
cell body may be locally modified in such a manner that the cell
responds differentially, at least in the timing of its firing, according
to the pattern of combination of axon feet through which excitation
is received.
This statement, by one of the greatest authorities on the neuro-
logical foundations of behaviour, seems worthy of mention in this
context even though it is being used here mainly to underline the
intrinsic complexities of the nervous system.
The above statement of Lashley's could have been made more
comprehensive if it had not been for the lack of an adequate
background model; for example, the search for a memory, in the
above terms, shows a compartmentalized attitude to a theoretical
term that is incompatible with the sort of philosophical analysis
and cybernetic model required here.- As a result, although it is not
possible to accept wholeheartedly Lashley's conclusions at any
rate at all levels the neurophysiological evidence put forward by
Lashley remains vital. The six points he makes are largely con-
sistent with the notion of a logical network whose reverberatory
activity may be short-circuited by cells from any particular area
without destruction of the network.
The principal implication, from this, is to drop the notion of a
cortical area whose function is controlling only, and of the circuit
that can only be controlled from a particular localized area. It
may be controlled, normally, from one cortical area, but it may be
amenable to control from any point in the network. Looking back
over the reports made by Lashley and his associates on their
extensive neurosurgical experiments, it seems that if one assumes
a network that involves many anatomical layers, and which fires
off circuitously, and in more than one way, then the sort of
destruction carried out by Lashley would produce precisely the
results that he found.
If the existing neurosurgical results are coupled with those of
Penfield and Rasmussen, Milner, Scoville, and Milner et al., on
stimulation of the temporal areas, they complete the suggested
picture of a network, where the 'elaboration' areas may be
assumed to play an important part in the integration of networks.
It can well be seen that the age-old argument about movement-
patterns and musculature and their cortical representation is
BEHAVIOUR AND THE NERVOUS SYSTEM 285
partly a verbal problem and partly an organizational one. What is
represented is some part of a network which is directly a function of
all the body musculature. In short, the cortical neuron is not in
control of a particular muscle, but may be connected with one or
more networks which initiate specific muscular activity. Thus
cortical localization takes on a rather new significance.
The programming of computers to learn suggests that informa-
tion may be changing fairly quickly in the central nervous system.
At least, if it is true for the nervous system that the continuous
recording of information is necessary as it seems to be in a
computer programme then this, too, would account for the
results derived by Lashley.
We must also ask at this stage how the nervous system represents
information if it can be moved quickly from location to location,
as it does from register to register. We shall leave the answer to
this question until the end of the next chapter.
Aphasia
We cannot complete even a cursory survey of neurology and its
relation to behaviour without a brief mention of the very extensive
field of language and speech disorders. We can at least outline the
terminology used:
There is a certain specific set of complaints concerned with loss
of recognition. This is collectively called 'agnosia', and it may be
visual, auditory and tactile. On the motor side the name 'apraxia'
is given to loss of ability to do things this implies loss of habits
like tying a necktie and so on, even though no paralysis may be
involved.
Aphasia is used to describe language disorders in the brain,
both sensory and motor, and a wealth of different sorts of problems
are involved.
To take one typical example, a patient may have motor aphasia,
and he may know what he wants to say, and be able to write this,
but be quite unable to say it. The implication being that transfer
into the output has somehow been destroyed. From the point of
view of neurophysiology the problem is one of strict localization
versus non-localization (Goldstein, 1939), although it seems likely,
as Head and Jackson have suggested, that it is actually a matter of
286 THE BRAIN AS A COMPUTER
'degree of localization'. Visual recognition has been connected with
area 18 and visual reminiscence with 19 ; area 39 for reading language ;
area 7 for tactile recognition; Wernich's area in the temporal lobe
for speech recognition; area 38 for musical recognition; and so on.
From the cybernetic point of view it looks as if one would get a
series of similar effects in an ordinary digital computer if particular
instructions were obliterated; e.g. if the transfer to output 1
instruction were missing, the information could only be put out
through output 2, say, and this parallels motor aphasia. The same
effect might be achieved by cutting the wire carrying the informa-
tion to output 1. These analogies are natural ones to adopt and
suggest, perhaps, not so much a crucially high degree of localiza-
tion since a computer can place the same information in different
registers, and can be multiplexed in order to offset the effects of
destruction but a measure of localization with effects brought
about by partial destruction of a fairly specific kind. This seems to
mean, in view of the neurophysiological evidence, a fair measure of
localization as far as 'area* is concerned, if not actual 'points'.
With this we must conclude this brief survey, and in the next
chapter we shall turn to more specific attempts to model the ner-
vous system and some aspects of its function.
Summary
In this chapter we have attempted to give some idea of the
range of knowledge of neurophysiology, and sufficient anatomy to
follow the argument. It has not been intended as a chapter for the
neurophysiologist, but rather for the experimental psychologist
with a fair knowledge of the nervous system. We have also tried to
fill in enough extra explanatory detail to make it intelligible to the
reader interested in cybernetics, but with little or no knowledge of
the workings of the nervous system.
It is clear that the nervous system divides into sections or units
that can be broadly correlated with behavioural function, and we
have now arrived at a stage where the correlation has to be made
much more detailed. The way we are advocating that this should
be done is through the development of a series of models in paper-
and-pencil and hardware which will help us to gain a clearer idea
of nervous function.
BEHAVIOUR AND THE NERVOUS SYSTEM 287
It should be added that this chapter should be read in especial
conjunction with the next chapter, since one of the later sections
of that chapter summarizes the most up-to-date views on neuro-
physiological function as outlined by Pribram. This could well
have come at the end of this chapter, where it would certainly be
relevant; nevertheless it seems reasonable, in the light of other
considerations, to defer it.
CHAPTER IX
THEORIES AND MODELS OF
THE NERVOUS SYSTEM
IN this chapter we turn our attention to more general ('molar')
models of the nervous system. We start with what are explicitly
theories, but which are perhaps best regarded as models, or at
least preliminary blueprints for models.
This chapter attempts to form a sort of link between the physio-
logical evidence of the previous chapter and the idealized or con-
ceptual system dealt with earlier.
It may appear inadequate and even inept to the physiologist
that cyberneticians and other model builders should proceed by
steps to the reconstruction of physiological models for human
behaviour, but it seems to be the fact that it is quite impossible to
effect the transformation in one step, and this means that we must
make the most of every analogy and clue that offers itself in what
will undoubtedly prove to be a slow and lengthy process.
We shall start within the realm of neurophysiology, with the ad
hoc model suggested by Pavlov. This is built around the notion of
a conditioned reflex (see Chapter VIII, page 181).
Fundamental to Pavlov's neurophysiological theory comes the
notion of 'excitation' and 'inhibition', but his use of these terms,
particularly 'inhibition', is different from that of Sherrington and
most of classical neurophysiology; here it is made to refer to actual
conical processes of a gross kind, without reference to the state of
individual synapses. He further assumes that the cortex is an
analyser upon which the whole of the muscular, etc. systems of the
organism are mapped.
The cortex, and probably also the subcortical ganglia, are
assumed to have the property of plasticity, which refers to relatively
permanent neural changes.
It is as well to remember that the Pavlovian neurophysiological
theory is essentially a mirror of classical conditioned response
288
THEORIES AND MODELS OF THE NERVOUS SYSTEM 289
theory, and the conditioned response is assumed to be the funda-
mental unit of nervdus activity. The actual formation of the
conditioned response involves the establishment in the cerebral
cortex of a connexion between the centre of the conditioned
stimulus and the centre of the unconditioned stimulus.
The actual cortical processes pictured by Pavlov took place in
phases. Afferent stimulation set up an excitatory process at a
definite point of the cortex, diminishing with the distance from
the point of origin. The second phase is one of recession and
concentration at the initial point. The picture is then supple-
mented by a further series of theoretical terms which try to make
for consistency between theory and observation, and we find
introduced the notion of (neural) induction. As the cortical process
subsides at any point, it may be succeeded by the opposite process
which is called 'induction*. Negative induction intensifies inhibition
under the influence of preceding excitation (induction comes about
in a relative way, due to relative change of threshold, in a manner
analogous to the fatigue theory of after-images) ; positive induction
intensifies excitation following inhibition.
The conditioned reflex is assumed to be set up in the following
way: excitation set up by neural stimulus at A irradiates from A
and will be concentrated at some other point B which is the focal
point of the unconditioned stimulus. Thus, to speak metaphori-
cally, a sort of channel is set up between A and B in such a way
that drainage takes place from a 'weak* to a 'strong' centre.
Generalization next follows, from the fact that excitation at B
will be aroused by A, or excitation at some near centres A' y A" y
A'" y etc., all very similar to A, Inhibition arises if B is extinguished
by presentation of stimulus without reinforcement. Internal
inhibition is really the name for this last process, as opposed to
external inhibition which involves the contemporaneous eliciting of
a different unconditioned response with the conditioned stimulus.
Other manifestations of inhibition are in the form of inhibitory
after-effect and disinhibition. Inhibitory after-effect is generaliza-
tion of inhibition. Furthermore, inhibition can be removed
temporarily under the influence of foreign stimuli, and this is
disinhibition.
The presence of generalization in the theory implies the presence
of differentiation and of conditioned inhibition, which is a particular
190 THE BRAIN AS A COMPUTER
:ase of differentiation. There is also one further kind of internal
nhibition, known as inhibition of delay, which involves a condi-
ioned response followed after an interval of the unusually long
ime of 2 or 3 min by an unconditioned response.
Following some concentrated experimental work by Krasna-
jorsky there exist some experimental generalizations which we
hall call the Krasnagorsky generalizations:
(1) The more the conditioned stimulus resembles the stimulus
>riginally inhibited (extinguished or differentiated), the more
asting is the inhibitory after-effect.
(2) The more the conditioned stimulus resembles the inhibitory
timulus, the stronger is the inhibitory after-effect, granted equal
ime intervals.
(3) Secondary inhibition of all conditioned stimuli applied
fter inhibitory stimuli increase gradually, achieves its maximum
fter a dozen or so seconds, and then diminishes.
(4) The more times the inhibitory stimulus is repeated, the
tronger and more lasting is the inhibitory after-effect.
(5) Secondary inhibition of active conditioned stimuli imping-
Qg upon the same analyser as the inhibitory stimuli is stronger and
nore prolonged than the inhibition of stimuli impinging upon
>ther analysers.
With all that has gone before there exist some further assump-
ions about the nature of the cortex itself. The cortex, in fact,
>ecomes viewed as a mosaic of points in states of relative inhibition
>r excitation, and this introduces one or two more notions.
Capability is the term used to denote the fact that different cells
tave different degrees of excitability, and the application of more
ban top excitation brings out protecting inhibition.
The phase of equalization is defined as the condition when both
trong and weak conditioned stimuli evoke an identical conditioned
esponse.
This brief summary of the rather vague Pavlovian model
llustrates the principal points made and the general methods
dopted, which should be sufficient for our present purpose.
Let us now consider some criticisms of the Pavlovian theory.
(1) First it should be said that the cortical picture is generally
ague, idealized, and somewhat removed from experimental fact.
THEORIES AND MODELS OF THE NERVOUS SYSTEM 291
Pavlovian excitation and inhibition are essentially inferential
processes, and should be broken down into their constituents.
Much of the model is also remotely metaphorical, e.g. the notion of
drainage.
(2) More specifically, irradiation is non-demonstrable in the
simple form suggested by Pavlov. Neuronography techniques
(de Barenne et al.) have demonstrated great variability in spread
of excitation; Brodman areas 5, 17, 18 and 19 show virtually no
spread, while spreading effects in other areas are by no means as
simple or symmetrical as is suggested by Pavlov.
(3) Pavlov assumed that conditioning was an explicitly cortical
process, and the apparent conditioning of de-corticate animals
(even though difficult to obtain) by Ten Cate (1923), Culler and
Mettler (1934), and others suggests a revision of the idea that
cortical integrity is essential.
(4) For Pavlov, the term 'inhibition* is at least different from the
term 'inhibition' which implies synaptic inhibition in the classical
neurophysiological theories. From comments 2 and 3 it is clear
that Pavlovian inhibition, which refers to a quasi-permanent state
of the cortex, is not a model with much empirical support, although
it is not alone in this respect.
(5) In the classical theory we have action by contact in the
sense that neurons fire neurons in a more or less precise manner.
Neither Pavlovian irradiation of excitation or inhibition behaves
quite in this manner, although they could perhaps be made to
conform to this extra constraint, particularly by using the Lorente
de No hypothesis of closed chains of cortical activity; but again
this might be difficult to reconcile with the specific usages of
Pavlovian terms.
(6) From Konorski's (1948) viewpoint the most important error
of a fundamental kind is the assumption, deep-rooted in Pavlov,
that excitation and inhibition are not only essentially cortical
processes, but that both the excitatory state evoked by application
of an active conditioned stimulus, and inhibition evoked by
application of an inhibitory conditioned stimulus, are localized in
the cortical centre of the stimulus. This leads to the total omission
of the reflex arc (not necessarily a bad thing) and, more dubiously,
it leads to concentration on unspecified states of excitation and
inhibition which irradiate or concentrate, summating or restricting,
292 THE BRAIN AS A COMPUTER
etc., and above all, it is not committed to particular neuron
chains.
The point made by Konorski is that different states can be
introduced at a cortical centre merely on the grounds of whether or
not a stimulus is reinforced.
(7) Another difficulty remarked upon by Konorski is that of
making sense of the notion of 'indifference states' that exist be-
tween centres of excitation and inhibition.
Now we shall summarize the further developments of Konorski's
arguments against the background of the internal inconsistencies
in the Pavlovian model:
Firstly, there is the vagueness in the distinction between excita-
tion and positive excitability, as there also is between inhibition
and negative excitability. The notions of positive and negative
excitability refer to states (more or less permanent) of cells, as
opposed to the processes of excitation and inhibition. An example
of the confusing manner in which these terms have been used is the
establishment of differentiation which may be followed by an
increased conditioned response, thanks to the permanent influence
of positive induction from the inhibitory focus, in spite of the fact
that it is also said that positive induction can be brought about
only by inhibition. Another example of the confusion appears in
the proposition that the administration of bromides increases the
size of the conditioned response and of the positive induction
evoked by the concentration of inhibition. When we go on to read
that a wave of excitation caused by an extraneous stimulus
may summate with the excitation of a conditioned stimulus,
whereas a wave of excitation may 'wash away* the inhibitory
excitability of a given point and leave a temporary state of positive
excitability, the confusion increases, and the versatility of these
theoretical terms becomes embarrassing.
A further assertion of the theory, which is attributable to Piet-
rova and Podkopayez (see Pavlov, 1927), is that which says that
irradiation is immediate with very strong or very weak stimuli,
and is delayed until the stimulus has ceased with medium stimuli.
This assumption is not verified, and (particularly if we add the
Pavlovian notion of top inhibition) it leads ultimately to an explana-
tion of internal inhibition by two quite separate mechanisms:
THEORIES AND MODELS OF THE NERVOUS SYSTEM 293
concentration of excitation and negative induction, or irradiation
of excitation and top inhibition, and these processes appear to be
opposed. Here again the theory is confused.
There are many other details of internal inconsistency, for
example, the problem of sleep as explained by internal inhibition
is open to criticism. Furthermore, other writers before Konorski,
such as Beritoff (1932), have noted defects in the Pavlovian
model. But probably enough has been said here to show that, at the
best, it is not adequate, for although it has indeed been of consider-
able service in the past, it is no longer sufficiently useful as a model
for cybernetics or behaviour theory.
Konorski's model
We will now consider what appears to be a useful integrative
step, the Konorskian model (1948), which represents the Pavlovian
theory in a Sherringtonian guise.
Konorski's first point is that plasticity is a concept central to all
neurology and behaviour theory, and he suggests that it is a
property of the intact organism-as-a-whole. He gives some
interesting examples of the properties of plasticity, e.g.
(1) The application of a certain combination of stimuli (here we
include an individual stimulus in the term combination) tends to
give rise to a definite plastic change, the repetition of the combina-
tion leads to 'cumulation' (i.e. an increase in this change), and this
cumulation, like the law of effect, has certain limiting properties.
(2) If the combination of stimuli, which is the cause of the
plastic change, is not applied, this change suffers regression, etc.
These propositions represent, of course, generalizations from
observations of behaviour in the organism-as-a-whole, and it is not
easy to demonstrate the neurological correlates. The best-known
theory of neural growth is probably that of Aliens Kappers
(Kappers, Huby and Crosby, 1936). He proposes that new neural
connexions are established by growth of neural processes. They
grow after stimulation in such a way that if two cells are simul-
taneously excited, the resulting ionization is assumed to direct the
growth of axons towards the cathode, and dendrites towards the
anode, and thus sets up new synaptic connexions. This idea has
been used by Holt (1931), and Hebb (1949) has re-stated the
294 THE BRAIN AS A COMPUTER
position that a Kappers-growth is morphologically impossible,
and has not, in fact, been observed over any large distance, but
remains a possibility over small distances which, in Hebb's own
treatment, is all that would be necessary.
Konorski's integration starts from the assumption that the
simplest and best-known type of plasticity is the conditioned reflex,
which involves the setting up of new functional relationships
between concurrently excited groups of nerve cells. Konorski calls
the centre of the conditioned stimulus the 'conditioned centre',
and the centre of the reinforcing unconditioned stimulus is called
the 'unconditioned centre 5 . These centres may or may not be
cortical, but they will normally involve the cortex. The connexion
between these centres, unlike the Pavlovian centres, is assumed to
be extremely complex, and involves a number of intermediary
stations or internuncial centres. Konorski substitutes for the 'top
capability* of cortical cells the classical notion of occlusion. The
occlusion, which involves the diminution of the strength of two
stimuli, say, when their sum is far too strong for the effector
system, is assumed to occur in the unconditioned centre. This
form of modification has been extensively carried out throughout
Pavlov's work, with the aim of increasing internal consistency.
Now there is one important extension of the Pavlov theory
that needs to be considered before we can adequately summarize
the Konorskian revision. With respect to plasticity, the classical
conditioned response is not considered to be the only mechanism.
The classical response, or conditioned responses of the first type,
must be supplemented by conditioned responses of the second
type; this has been referred to as 'instrumental conditioning' in
some of the psychological literature. The data, which are well
known to psychologists, need not be repeated here. The various
examples of type II conditioning were enumerated in Chapter
VI: (1) reward, (2) escape, (3) avoidance, and (4) secondary
reward, involving us (Hilgard and Marquis, 1938) in the principles
of substitution, effect, expectancy, etc.
Konorski takes a type II experiment and infers from it that
unconditional stimuli can be divided into two categories: those
which by reinforcing the animal's movement cause it to perform
the movement spontaneously, and those which by reinforcing the
movement cause it to perform an antagonistic movement. He calls
THEORIES AND MODELS OF THE NERVOUS SYSTEM 295
these positive unconditioned stimuli and negative unconditioned
stimuli, respectively.
It should be said in the first place, with regard to the changes
suggested by Konorski, that there is at least a doubt as to whether
the conditioning terminology is usefully taken over to describe the
whole of nervous activity. It seems that the classical conditioned
response is a special case of the general associative processes in-
volved in the central nervous system, and that whether or not we
regard type II conditioning as a type of conditioned response is
purely a matter of terminology, and therefore not one of the
greatest importance to our cybernetic modelling.
There are certainly some aspects of the changes in notation
made by Konorski that seem to fit the facts better, in that a definite
gain appears to have been made in breaking down some of the
theoretical terms by our increased observation. The phenomenon
of generalization of excitatory conditioned reflex seems perhaps
better accounted for by the notion of partial cortical overlap, for
which there is some evidence (Liddell and Phillips, 1951; Lilly,
1958).
The notion of 'occlusion', which acts as a limiting mechanism in
the top value of conditioned reflexes, seems a more satisfactory
theoretical term than the 'top capability' of cortical cells, if only in
so far as we thereby attain an integration with classical theory.
This last remark, of course, is generally applicable to the Konor-
ski revision, which is to be commended on the grounds of integra-
tion in scientific theory, and the achievement of the use of the same
theoretical terms and formulations as classical theory. Much, also,
of the internal inconsistency of Pavlov has been remedied, with the
result that the confusion over inhibition, negative excitability,
etc., has now largely gone. The new statement about the formation
of the inhibitory conditioned response is now explained in terms of
the contemporaneous excitation of the conditioned centre, with
fall of excitation in the unconditioned centre. Also, the observable
fact of increase of the excitatory conditioned reflex concurrently
with the inhibitory reflex seems more adequately explained by
summation of the excitatory conditioned response and the excitato-
inhibitory response, with facilitation predominating.
But whereas Konorski has supplied a necessary criterion for
conditioning and thus, perhaps, for all learning in the notion
296 THE BRAIN AS A COMPUTER
of plasticity, his particular idea of how this may take place is
perhaps, in the light of the latest neurophysiological work, not
wholly plausible.
He assumes that there is an emitting centre where the stimulus
to be conditioned is centred, and a receiving centre for the
unconditioned stimulus, and potential connexions between these
centres which involve growth and the multiplication of synapses.
This bears a relation to the theory proposed by Hebb, but with
this difference, that it seems to fall foul of the evidence on cortical
localization from experiments in cortical ablation by Lashley and
others, evidence which suggests something a little more subtle in
the actual organization of these cortical centres. This model, as
well as Hebb's, at least lacks experimental verification as it stands.
Eccles (1953) assumed, in his explanation, that two knobs were
necessary for the synaptic excitation necessary to generate an
impulse. He also assumed that the same neurons could contribute
to different patterns of nervous activity involved with a concept of
cortical overlap, for which there is some empirical evidence.
In his explanation of conditioning Eccles starts from the reflex
arc, and then assumes that the conditioned stimulus causes the
discharge of afferent impulses along a particular pathway, where
they converge on neurons also excited by the impulses in the
collaterals from the afferent pathways of the unconditioned
stimulus. Synaptic facilitation is caused by the post-synaptic
potential, and leads to impulses being set up in otherwise unaffected
neurons, and there is an increased sensitivity of those synaptic
knobs that are most used. Here we see a close parallel to Hebb's
basic assumption of the development of neural connexions.
From this area so affected we generate a spatio-temporal pattern
of impulses that link the conditioned and the unconditioned
stimulus. And for this purpose Eccles draws a particular 'neuronaP
net, as he calls it, which shows just how this interaction could take
place (Eccles, 1953, page 221 et seq.).
The models that are considered here are all rather generalized,
and neglect the more recent and more detailed analysis of parti-
cular nervous areas; especially, they neglect the work on the reti-
cular system, and the latest research of an electrical kind. This is
no defect in the theories considered, since their value lies in the
fact that they were built as descriptions, however elementary, of
THEORIES AND MODELS OF THE NERVOUS SYSTEM 297
the nervous system, and they can be translated into cybernetic
terms.
It is of interest that the building of cybernetic models to mirror
these models of nervous activity depends on making the model
precise, and at the same time acts as a check on its functional
accuracy.
From what has already been said in earlier chapters it is clear that
a finite automaton can easily be constructed to carry out the
activity of a Konorski or Eccles type model, but equally it seems
certain, for reasons which are partly based on the economy of cells
and partly on further neurophysiological evidence, that these
models are still nothing like a precise model of what occurs in the
actual human brain.
The ethologists
Ethology is closely bound up with behaviour and with the
models for that behaviour and rather like much of molar experi-
mental psychology has tended to construct theories and models
using any available analogue whatever (Thorpe, 1956; Lorenz,
1950; Tinbergen, 1951; et al.). Ethology is the study of animal
behaviour, carried out in the main by zoologists and primarily
from a comparative point of view.
We shall not here attempt to summarize the various fields of
ethological modelling and experimental activity, since much of it
overlaps what has been said in this and the previous chapter.
Pavlov and Konorski have been reviewed, and although Pavlov's
theory is now largely rejected, Konorski's grew from it, and this in
turn has led to many other theories such as those of Hebb (1949),
Pringle (1951) and Eccles (1953), which have received careful
consideration in ethological circles.
Indeed, it is increasingly realized that cybernetics is a source of
models for theorizing in neurophysiology. Pringle's model, in-
volving the coupling of oscillators which show properties of lock-
ing and synchronization, is typical of the cybernetic approach,
even though not carried out under that particular name.
Hebb will be considered more fully later in this chapter and in
the next, in the background of perception, but his theory, too,
tends towards the cybernetic, and falls short of being so classified
u
298 THE BRAIN AS A COMPUTER
only in the degree to which it is effective. It is not mathematical as
are those of Shimbel (1949, 1952), McCulloch and Pitts (1943),
Minsky (1954) and many more that have been constructed, and by
the same token it is not wholly precise. Also, it depends upon the
concept of closed active circuits of the kind suggested by Lorente
de N6, as well as the idea of neurophysiological growth suggested
by Kappers and others, and both these suggestions, especially the
first, are open to some doubt, even though it is difficult to imagine
how learning in the nervous system would be possible without at
least one of the two concepts.
Lashley's theory
There is a theory of nervous function that has been proposed by
Lashley (1929b). Some indication of Lashley's ideas was given in
the previous chapter, and here we shall simply append some of the
principles that Lashley regarded as important even necessary
to any models of the nervous system.
In the first place, generalization is thought to be an essential
basic property of neurons, and one dependent on the integrity of
the cerebral cortex, without which the organism loses the necessary
capacity to adapt to a changing environment.
Such generalizations, according to Lashley, must occur in the
visual system where the fixation of points varies, and thus occasion
stimulation of many different retinal cells, although we are aware
of a single object only. This is assumed to involve a memory trace
which is a property of the whole nervous system.
The cortex was regarded by Lashley as being a set of resonators.
He further assumed the interference of different sensory excitations
which would lead to modification of ordinary, isolated, sensory
stimuli.
He also believed that cortical neurons were in constant activity,
and that complex patterns of interaction were the basis of integra-
tion. This view is, of course, intended to be in opposition to one
that regards external events as mirrored in the nervous system by
specific, and relatively isolated, pathways.
This particular conclusion is one we should bear in mind when
trying to construct economical finite automata, since it seems
certain that such a view is fundamentally correct ; in fact it may not
THEORIES AND MODELS OF THE NERVOUS SYSTEM 299
be inconsistent (Hebb, 1949) with the concept of specific pathways
and neuron circuits being connected with different learned items.
Lashley proposes four types of integration in the cerebral
cortex: (1) the selective patterning of excitation, (2) sensitization
to pattern anticipation, (3) stimulus equivalence, and (4) con-
vertibility between temporal and spatial patterns. Some of these
matters directly affect perception, and they will be discussed later
in Chapters IX and X; in the meantime we shall consider a
specific problem of learning and the nervous system; one that was
dealt with especially by Hebb. This is the problem of early and late
injuries.
Early and late brain injuries
This is doubtless a matter of considerable importance both to
the behaviour-theorists and to the neurologists, and the evidence
will be summarized briefly.
Penfield and Rasmussen (1950) are of the opinion that there is a
marked difference between cortical destruction in youth, and
cortical destruction later in life (see their work on the use of speech
'elaboration' areas, p. 222). Hebb's summary states the essential
points (1949, p. 289 et seq.). I.Q. is generally far more affected by
brain injury early in life than by equivalent injury in adulthood.
One interesting point, made by Hebb, is that the 'Binet' type test
shows least well any change in I.Q. after brain injury (except for
the relatively specialized speech areas) since the nature of such
tests is not sufficiently fine a probe. Obviously a greal deal of the
argument here depends on the nature of the term 'intelligence', and
this term, as used in most test situations (especially Binet-type),
includes much that depends on memory function, general experi-
ence, etc. If the injury occurs early in life, the necessary generalized
functions will not be sufficiently developed; if later, then the
logical (neural) nets set up will by-pass the injured areas. The
inference is that much cortex may be needed initially for making
the network which, later, can be retained by far less cortex. The
implications for automata construction are very significant, and
suggest an important distinction between learning and having
learned. However, there may well be two factors (the hereditary
and the experiential) which contribute towards 'intelligence', and
the problem here is to guess what light it throws on neurophysio-
300 THE BRAIN AS A COMPUTER
logical function. It could be that a certain set of neurons may be
included in a network, all the cells of which are necessary to the
initial assembly, and that destruction of a part may, in general, lead
to a by-passing of the missing parts, but not to the destruction of
the network. This is, roughly, the Hebb view, and it has the ring
of credibility.
Of the hosts of further experiments on different cortical areas
and their total or partial destruction, we would mention here
Sperry, Stamm and Miner (1956), who showed that the corpus
callosum was necessary in cats for the transfer of training of a
tactile discrimination from the left paw to the right. Since the work
of Olds and Milner (1954), Bursten and Delgado (1958) and
others have done a great deal of work showing that direct stimula-
tion of the cortical areas had a reinforcing effect on behaviour.
There has also been some work on the function of the lateral and
medial geniculate bodies.
Adding to the enormous amount of work already done, each
new publication in this subject brings more enlightenment; even
while this is being written some new evidence may have taken us
a step further. But in the whole body of the knowledge we have
acquired in this field there is still nothing which denies the very
general view that the brain is an extremely complex switching
system, the details of which will take us many years to unravel.
In absolute terms, the sum total of our present information is
indeed large, but it is small relative to what we wish to know. We
can see, however, the possibility of applying the principles of
classification and conditional probability to what we know.
The visual cortex could certainly be viewed as a visual classifica-
tion system; other areas could also be regarded as classification
areas (association areas) with respect to input information from
the other special senses. This means that the greater part of the
brain could feasibly be thought of as being made up of a set of
storage registers. Information is clearly transferred in complex
fashion from point to point, and the system as a whole is suffi-
ciently 'multiplexed' to make it fairly certain that loss of particular
neurons does not necessarily stop the activity normally associated
with particular cortical areas.
It would seem unreasonable to regard the cortex as being wholly
pre-wired, as is a finite automaton, in terms of logical nets; but
THEORIES AND MODELS OF THE NERVOUS SYSTEM 301
when viewed in terms of growth nets, or growth processes, we can
see the possibility of formulating an appropriate blueprint.
Consciousness even (Culbertson, 1950) has been analysed in
logical net terms, and this is a significant indication of the use of
cybernetics. Even if we reconsider the problem of human activities
in terms of their nervous systems, we can still supply models
appropriate to the task, at least in principle. From this point of
view the complexity of electrical and chemical-colloidal changes is
unimportant, although to neglect such evidence would ultimately
prove to have been extremely foolish.
There is nothing by way of evidence in this or the previous
chapter which goes against the idea that the brain is appropriately
viewed as an enormously complicated computer system even if
both digital and analogue. Indeed, when viewed in this light, there
are no results of electroencephalography, cortical destruction, or
electrical stimulation that should occasion any surprise whatever.
All that is derived from neurophysiology is a series of clues to the
blueprint we are looking for. At the moment, the scent can hardly
be called warm, but already we can see the sort of results that
might be expected from a cybernetic point of view.
In the digital computer, we think of the routine behaviour as
being carried out in terms of a programme that places the instruc-
tions inside the storage and then automatically operates on the
data usually numerical according to the nature of the instruc-
tions.
This could equally mirror the human activity, except of course
that the human is not generally operating on a fixed set of special
instructions ; in certain cases, though, he may be, such as where he
is following an exact set of instructions in his job. But generally he
will be told the desired end-result, without being given an explicit
method for reaching that end-result, and then he must scan his
storage system for information that allows him to proceed to the
end state. He will also be subjected to further inputs while working
on a programme, which means that he has to have storage space for
future programmes necessitated by these inputs, which may also
modify present programmes. Obviously the human differs from
the digital computer as normally used in this respect.
It is for the above reason that we tend to think of our computer
analogue with a functionally interdependent input tape and output
302 THE BRAIN AS A COMPUTER
tape. These tapes work in one direction, and are associated with
instants of time. In such an automaton it is, of course, now essential
to have a storage system, and the store we would envisage is
precisely the sort of general storage arrangement described in
Chapters V and VI. The problem of human organization is thus
the same as the problem of organization of stored information,
apart of course from showing how the concepts, etc., are built up
inside the storage system in the first place.
The implication is clear that the human brain is primarily a
storage system, and it is connected with the immediate processing
of input data from the main sensory sources. This still leaves a
variety of questions about the manner in which the storage is
effected, and this is the great problem for future physiological
psychologists.
Let us now consider some of the other approaches to our
problem. Incidentally, in so doing we shall be led back to the
problem of conceptual models.
Beurle's model
Beurle (1954a, 1954b) has suggested a theoretical model for
aspects of neural nets (Sholl, 1956), for which he considers a
whole set of units with the following properties: (1) They are
connected in a non-specific manner which can be described
statistically; (2) Active units can excite inactive units by means of
immediate connexions; (3) Over a period of time, summation of
excitation occurs; (4) When the summated excitation exceeds a
certain 'threshold* value, the unit becomes active; (5) There is a
'refractory period 5 after firing before a unit takes any further part
in neural activity.
Beurle predicted many interesting properties from these
assumptions, and he used a further assumption similar to that of
Chapman, in supposing that a threshold is slightly diminished
with each firing.
The assumption of random connectivity is one that can be
introduced into logical nets, from which starting point, by growth,
or by the non-use of pre-wired connexions, the specific logical nets
can be derived. Beurle's block of units is thought to be similar in
some respects to the cerebral cortex, and there is little doubt that
some extension of this kind is necessary to bring the Uttley type of
THEORIES AND MODELS OF THE NERVOUS SYSTEM 303
model into line with the neurological facts; such an extension
could be easily achieved.
A somewhat similar viewpoint to Beurle's was expressed by
Turing in an unpublished paper on 'Intelligent machinery', in
which he was able to show that a randomly connected network with
experience could take on a specific form.
Ashby's model
In returning to Ashby (1947, 1948, 1950, 1952, 1956a, 1956b)
we are coming full circle with respect to cybernetic models which
purport to bear some resemblance to the brain.
The Homeostat has already been discussed in Chapter IV.
Ashby has also set down his design for a brain in a separate book;
the theory, being essentially mathematical, proposes that step
functions are appropriate descriptions of a feedback system which
has the necessary property of ultrastability.
Stewart (1959) has pointed out a difficulty in the application of
such 'homeostatic* principles to the brain:
The number of moves needed as a stable field is achieved increases as a
roughly exponential function of the number of degrees of freedom of the
system. For large systems, it is therefore essential to increase the prob-
ability of stability by some means.
This difficulty may be overcome by having a number of ultra-
stable systems a 'multistable' system and Ashby has designed
such a model.
More recently, Ashby has proposed a theory of cybernetics
which depends on the notion of transformation and permutation
groups. This represents a form of description that has some ad-
vantages at a purely functional level, and indeed such a description
could be regarded as an alternative to a logical net description,
since logical nets can easily be dealt with as a branch of matrix
algebra, as we have seen, and such sets of matrices have, in certain
cases, group properties which bear a similarity to the suggestions
made by Ashby. But here we are heading right away from the
neurological, and are back wholly in the realm of finite automata.
Hebb's cell assembly and Milner's mark n cell assembly
Hebb's (1949) cell assembly is a hypothetical structure ob-
viously intended to be understood as a conceptual nervous system.
304 THE BRAIN AS A COMPUTER
It is made up of a collection of cells which are closely associated as a
result of learning. The learning involves the firing of a set of cells
which may be originally in a fairly randomly organized state.
Cells excited in the visual cortex (area 18) are actuated by some
visual stimulus A, say, and this set will have many cells in common
with the assembly activated by other visual stimuli J3, C, D 9 ...
These cell assemblies, through fractionation and recruitment, or
growth, become differentiated and highly organized. In the future,
sequences (a 'Phase Sequence') of cell assemblies occur, mirroring
the activities of perception and learning.
Hebb's system will not be discussed here; for a detailed discus-
sion reference should be made to Hebb's writing. Some mention
of Hebb's system is also made in the next chapter, but the main
point is that his system is too versatile as it stands, and although
it is similar in many ways to the sort of logical nets we have been
describing, it has needed a good deal of modification.
In Hebb's Cell Assembly four factors determine whether or not
a cortical neuron fires. These four factors are: (1) The number of
impulses bombarding the neuron from all sources for the few
milliseconds during which temporal summation is assumed to
take place ; (2) The strength of the synapses, which is a function of
recurrent firing; (3) Whether or not the neuron is refractory, and
(4) Neural fatigue.
Hebb's system starts in random form but learns much too
quickly to be a realistic model of learning in organisms ; but this
rate of learning can be brought into line with the facts by use of
inhibition (cf. Chapman's model).
Milner (1957) assumes that cell assemblies and phase sequences
occur subject to the neural postulate as suggested by Hebb. Figure
1 shows the Milner assumptions in network form.
He first assumes that there are neurons with long axons with
cortico cortico connexions, and neurons with short axons with
local inhibitory connexions. Through facilitation from the non-
specific projection system cortico-cortico transmission is made
possible, and thus one neuron may fire some ten or more neurons,
and these ten may themselves each fire ten or more. The idea is
that neurons with long axons fire the neurons with short axons in
their neighbourhood and, as more of the short axon cells fire, more
inhibitory neighbourhoods come into being.
THEORIES AND MODELS OF THE NERVOUS SYSTEM 305
Figure 2 demonstrates the next point, which is that recurrent
inhibitory connexions are assumed to occur whereby a cell A fires
and inhibits B, C and ), but not itself. This means that by firing
A we are protecting it from inhibition, and this will affect equili-
brium activity in the cortex by the setting up of re-exciting path-
ways. Eventually adaptation brings about a lowering of firing.
In these terms we can undertake to look again at the manner in
which a stimulus A leads to a response C and to a further stimulus
B. (These letters do not apply to the letter names for the cells in
Fig. 2.) Milner says that a cell assembly, after being under direct
FlG. 1. A NETWORK FOR MILNER'S CELL ASSEMBLY SYSTEM. This
net has the simple property of exciting one element and at the
same time inhibiting the neighbouring cells (see text).
control, is under indirect control for some minutes, and A has
either latent or active trace associations with B and C. The word
'priming* is used to describe the lowering of threshold that follows
the stimulation of a cortical cell by an afferent impulse; the effect
is supposed to last only a few seconds. The sensory projection areas
of the cortex are final distribution centres for sensory impulses,
and the organism ignores stimulation if the cortex is already very
active. But if the cortex is not very active, and the stimulus is very
strong, then the activity of the cortex will be significantly changed.
Learning is presumed to occur because sets of neurons once
306
THE BRAIN AS A COMPUTER
fired together are assumed to refire together. Selective excitation
occurs much as in the original cell assembly; however, there is
assumed to be a fringe of uncertainty, which means that the total
pattern of cortical activity is not determined by a single stimulus.
Phase sequences may be fired by internal as well as sensory means.
Finally, Milner assumes that recruitment comes from priming,
"^^r^
FlG. 2. A NETWORK FOR MILKER'S CELL ASSEMBLY. This net shows
cells which when fired inhibit their neighbouring cells. This
figure is closely comparable to Fig. 1.
and that perceptual overlearning implies ease of linking assemblies.
Now motivation affects learning and rate of responding, and it is
assumed that arousal systems are cholinergic, that motivation and
emotion are correlated, and that novel stimuli are more potent
than ordinary stimuli in arousing activity.
This model of Milner's is ingenious, and is not lacking in
physiological plausibility; we shall see that the basic ideas, or some
THEORIES AND MODELS OF THE NERVOUS SYSTEM 307
of them, are incorporated into the Pribram model which is
described in the next section.
Pribram's theory outline
The penultimate section of this chapter will be devoted to a
recent summary by Pribram (1960) of the world of neurophysio-
logy. His most interesting summary is selective, and really
amounts to the outline of a theory almost of a model. It is of
special interest to us because of its strong cybernetic leanings.
Pibram's first point is that brain tissue has intrinsic rhythms, and
although the cerebral cortex may be said to be quiescent without
input, it is easily aroused to prolonged activity, and this may be
taken to imply a complex memory process. In the intact organism,
the spontaneous discharge of receptors maintains a certain level of
cortical activitjrl
In recent years, of course, this spontaneous activity has been
increasingly thought of as occurring in the reticular system.
The second, and perhaps the main point of Pibram's view is
that the reflex arc is increasingly being thought to be replaced by
the closed loop circuit elements, feedback units or homeostats, and
indeed evidence for the feedback unit is now growing rapidly!
Granit (1955) and Galambos (1956) have shown that the optic ancl
otic systems respectively have efferent activities originating in the
receptors that can be directly modified by the central nervous
system. Thus, the assumption of sensory and motor nerves made at
the beginning of the previous chapter must, like the concept of
the reflex arc, be modified to some extent by these new ideas.
To generalize the stimulus-response or reflex arc is now the
problem, and Miller, Galanter and Pribram (1959) have suggested
a unit they call a TOTE. The letters TOTE stand for test-
operate-test-exit. The tote sequence is a basic neurological unit; it
represents a sort of servo-operation, and one which suggests
graded responses in organization, in opposition to the all-or-none
law of nervous function.
Steps taken in the direction of graded response mechanisms are
exhibited by the recent discovery of graded dendritic potentials
(Li, Culler and Jasper, 1956; Bishop and Clare, 1952).
It is of interest that these graded response mechanisms were
308 THE BRAIN AS A COMPUTER
discovered during an attempt to establish the source of potentials
recorded on the EEG. Their significance is by no means fully
understood, but Pribram himself has suggested that they play
some part in the test step of the TOTE sequence. Somewhat
similar graded responses are also observed in the interaction
between the cortex and the reticular system.
Pribram describes the work on the reticular system and the
diencephalic structures as leading to a new concept of what he calls
the 'concentric nervous system', the system built from the inside
outwards. The system, which contains further homeostats in the
form of respiratory control, food intake control, and so on, is near
the midline of the ventricular system.
Hebb (1955) and Olds (1959), among others, have emphasized
the drive-regulating aspect of the reticular system, but drive itself
is now thought to be composed of many components, such as:
(1) selection, (2) activation and (3) equilibration. The resemblance
here to a servo-control system is obvious, and of course the
implication is clear that the type of need-reduction theory of
motivation suggested by Hull is only a part, in reality, of the total
motivational process, and that at this level the motivational system
can act by 'conceptual* means which is something that we had
anticipated on other grounds.
The limbic system, which is the name for the structures on the
innermost edge of the cerebral hemispheres, have been closely
associated with motivational and emotional behaviour, and there
have been suggestions that this system has associations with
memory.
One of Pribram's main hypotheses is that the limbic system
regulates the disposition of organisms, and this it does by the
use of neural homeostats.
The frontal intrinsic mechanism, he believes, is like the posterior
intrinsic mechanism in being loci sensitive to and partly deter-
mined by experience in their representations, the big problem
being the timing of the pattern of firing. The intrinsic repre-
sentational process is hierarchically organized, and is sensitive to
variations in circumstances, provided that these variations are not
overly abrupt. The posterior systems are primarily related to the
major projective systems, and are organized to select the invariant
properties of receptor stimulation.
THEORIES AND MODELS OF THE NERVOUS SYSTEM 309
The frontal mechanism is primarily related to the limbic
formations of the endbrain, which are organized to enhance con-
stancies of state which, in turn, are dependent on the biased
homeostats of the brain stem core.
The posterior intrinsic mechanism is reinforced completely
when the organism is fully informed, and the frontal intrinsic
mechanism is reinforced completely when the organism is fully
instructed. Pribram suggests that attention is given to instructions
until conditions are met. The first reinforcement is through the
identification of the similarities among the range of differences,
and the second is through the fulfilment of intentions. This seems,
as Pribram says, very different from Hull's need-reduction
principle, but it could be that only a slight modification is necessary
to make the two come together, and indications of the sort of
changes we are looking for are not far to seek. In the first place, we
are fairly sure that need-reduction is not a simple or linear process,
and that conceptualization comes into the picture. There is also the
probability that curiosity may be acceptable as a drive that is to be
reduced, and by virtue of which generalizations and classifications,
both perceptual and conceptual, take place. All this is built upon
Hull's admittedly oversimple, but very useful, concept of need-
reduction.
In summary, Pribram suggests that a hierarchical process in the
nervous system is necessary and sufficient for reinforcement to
occur and, using Mackay's (1956) idea, it is suggested that selective
modification interacts with representation. A unique match will
stop the searching process, which has proceeded by successive
probabilities.
There are two stages to problem solving. The first stage is to
gain information, and the second is to order and utilize that in-
formation. The posterior and frontal intrinsic systems are thought
to be responsible, and are concerned, in the first case, with
differences between past and present invariance in stimulation.
The frontal intrinsic areas, through the limbic system, are sensitive
to differences between past and present and dispositional states of
the organism.
All this is achieved by multi-linked homeostats attempting to
attain ultrastable dispositional states; these connect directly
with the limbic system of the endbrain, and so control the biases
310 THE BRAIN AS A COMPUTER
of the central core of the brain stem, while others control the
ordering of the behavioural processes and sequences of actions.
Homeostats are assumed to abound in the internal core of the
brain stem, and there is a modality nonspecific activating system
that is directional, with drive components in a generalized, specific
sensory and hedonistic form. Changes in the activating system,
through graded response mechanisms, modify homeostats in their
area. The graded response shows a change in excitation in the
nervous system and this, with signal transmission, suggests to
Pribram the usefulness of the models of Kohler, Lashley and
Beurle. In Pribram's own words:
Reinforcement by cognition, based on a mechanism of hierarchically
organized representatives, dispositions and drives regulated by multi-
linked and biased homeostats ; representational organization by virtue of
graded, as well as all-or-nothing, neural responses; spontaneously
generated, long-lasting intrinsic neural rhythms; organisms thus con-
ceived are actively engaged, not only in the manipulation of artifacts, but
in the organization of their perceptions, satisfactions and gratifications.
This quotation reminds us again that the gulf between empirical
descriptions and conceptual analyses is very narrow indeed. We
are not to be thought of as either stating facts or as theorizing, for
the two go together; and Pribram's ideas, when clarified by
semantic and cybernetic analysis, will be found to be very close
to those that are being put forward in this book.
One more thing should be said before leaving Pribram: the
particular emphasis on Lashley and Kohler is indicative of the
link between the cruder mechanisms of the past and the better
integrated mechanisms of today. This does not, of course, mean
that materialistic thinking was wrong even assuming the present
trends are correct but rather that models have become more
sophisticated and slightly less simple.
Cybernetic models in general
The brain is clearly a vastly complicated system, and there is an
obvious naivety doubtless irritating to a neurophysiologist in
such statements as, 'just a switching device', 'the eyes are like a
television scanning system', 'the brain is a complex digital (and ana-
logue) computer', and so on. Let us, then, put the whole matter in
another way.
THEORIES AND MODELS OF THE NERVOUS SYSTEM 311
A great deal of progress has been made in neurophysiology and
neuroanatomy by thinking of the brain and the nervous system as
a telephone exchange system ; and although a great many objections
have been made to this analogy, it has had its uses. However, with-
out pressing analogies into literal descriptions, we may say that the
concept of computers is also a useful one for, of course, through
finite automata, we can make our computer any way we like.
Growth nets (Chapman, 1959) may eventually be the appropriate
description of models which would serve as bases for descriptions
of the nervous system. For the moment, it would be a considerable
step if we could see some relation between the particular finite
automata outlined in Chapter IV, and what has been said of the
actual nervous system.
The principles involved were classification, stochastic storage,
conditional probabilities, generalization, and of course the
existence of built-in systems. Feedback is taken to be implied by
the organization, which is essentially an elaboration of an input-
output system with complex storage, and with modification of
response-tendencies through experience. At the highest level we
have the problems concerned with symbolic representation of
input output events. This problem of language represents without
doubt one of the big challenges for the future.
While emphasizing once more that finite automata even those
in logical net form are not necessarily to be interpreted as
actual nervous systems, it is clear that such a relation would be
desirable.
Von Neumann (1952) has hazarded the guess that 'neural pools'
may occur in the nervous system which are similar in form to the
restoring organs which he has described; these might be used for
maintaining accuracy in those parts of the nervous system where
analogue principles apply.
Kleene (1951) makes our purpose clear when he describes his
own neural nets in the following manner:
These assumptions are an abstraction from the data which neurophysio-
logy provides. The abstraction gives a model, in terms of which it be-
comes an exact mathematical problem to see what kinds of behaviour the
model can explain. The question is left open how closely the model
describes the activity of actual nerve nets. Neurophysiology does not
currently say which of these models is most nearly correct ...
312 THE BRAIN AS A COMPUTER
Rashevsky (1938), Householder and Landahl (1945), and
others of the school of mathematical biology, have tried to
apply the methods of mathematical physics directly to biology,
and therefore represent yet a further attempt in the direction of
cybernetics.
Sholl (1956) has discussed the quantification of neuronal
connectivity, as has Uttley (1955) and other writers since.
A different approach to the problem has been made by Coburn
(1951, 1952) in what he describes as the 'Brain Analogy', in
seventeen postulates. This model keeps close to the facts of
conditioning, and has the advantage of being precise in form, and
capable of being translated into logical nets. The relation to actual
neurology is slight, but nevertheless it has the advantage of being
in keeping with some of the facts. As a model it is a step in the
direction of the mathematical models of learning mentioned
earlier.
We (George, 1957, 1958, 1959, 1960) may now summarize a few
of the tentative interpretations that are implied by our own
investigations. Broadly speaking, our C-system is to be identified
with the cerebral cortex and basal ganglia; the input is identified
with the special senses, merging into the cortex and the C-system.
The M-system is surely to be identified with the effects of the
internal organism, making use of the reticular system, on the
thalamus and hypothalamus. The jE'-system is identified with the
hypothalamus and the autonomic system. These ideas are, of
course, crude, and need to be refined.
In the first place we must regard the nervous system as having
special purpose and analogue systems (both built-in and chemical),
to which our logical nets are only an approximation.
The storage systems make up the bulk of the cerebral cortex,
and the problems are largely of the special function of particular
sets of registers and their mode of operation. It is not difficult for
the reader to take the next step and envisage the range of possible
models which might next be described with an eye to experiment.
However, more will be said on this matter in the final chapter of
the book.
We shall turn in the next chapter to an analysis of perception,
and we shall perform the analysis from a cybernetic, a molar
psychological, and a neurophysiological point of view, together.
THEORIES AND MODELS OF THE NERVOUS SYSTEM 313
Summary
In this chapter we have taken our neurophysiological discussion
one stage further. Apart from Pribram's summary of the contem-
porary neurophysiological situation, the chapter is largely con-
cerned with more conceptual models of the nervous system which
are not intended to have anything like complete and immediate
verisimilitude. This in itself brings out clearly, and yet again, that
in science, models and theories that mirror precisely, or make
precise predictions of events, cannot always be immediately built;
and this is the reason why conceptual and logical models are so
useful, even necessary, to our theory construction programme.
Although we have not explicitly discussed Hebb's cell assembly
theory, we have mentioned many aspects of it. It is, in any case,
one of the best known of neurophysiological theories, and it is
hoped that Milner's modification of the cell assembly theory as
described in this chapter has been found intelligible.
The work of Pavlov and Konorski is not always easy to read,
because of the rather ugly nomenclature, but nevertheless it was
thought important that their views should be summarized.
We have given little more than a mention to the work of the
ethologists, and readers interested in the work of Tinbergen,
Lorenz, Thorpe and others may feel that we have hardly done
them justice. The reason for this, as for the brevity of comment on
many other closely related topics, is simply that this book has
to be kept to a reasonable length ; no biologist, at any rate, will be
ignorant of the very useful work in this field done by ethologists.
CHAPTER X
PERCEPTION
CHAPTER VII dealt with some of the traditional problems of what
has been called 'learning' and while it is necessary to 'break-down'
our analysis of behaviour into such terms as 'learning' and 'percep-
tion', we must bear in mind that we are doing so with some deal of
arbitrariness. A precise definition of either term is very difficult to
phrase, and since we may assume that the reader is fairly familiar
with what occurs between the covers of books on perception, we
shall not attempt anything approaching a careful analysis or
formalization of the term. In the meantime we can at least say
that 'to perceive' is something more than 'to sense' and something
less than 'to know'.
The majority of psychologists have given full approval to the
position taken up by Hebb (1949), who believes that one of the
big problems of modern psychology is to find large scale relations
between psychology and physiology.
In perception, this attitude led directly to Hebb's efforts to
initiate the job of reinterpreting physiologically the evidence
collected within psychology; indeed, Hebb's evidence has helped
to demolish the arguments stemming partly from Lashley's
work that the behavioural facts of perception cannot be repre-
sented by any sort of specific neurophysiological processes. There
is, in fact, no evidence to support a denial of the possibility of
specific behavioural acts being directly correlated with specific
states of the nervous system, neither is there any evidence to
support a field theory of neurology of the type suggested by
Kohler (1940). At the same time we have seen that too narrow a
mechanistic view has had its particular difficulties. The writer has
no wish to minimize the value of Gestalt theory, but it must be said
that it never was a complete theory, and useful concepts such as
'wholeness' that it has formulated have now been more or less
incorporated into the body of scientific behaviour theory.
314
PERCEPTION 315
Osgood and Heyer (1952) have done much, as did Marshall and
Talbot before them, to suggest a more satisfactory link between
physiological states and introspectively-given perceptual data, and
this connexion will be followed up. These present tendencies are of
importance to a general account of the visual system in its percep-
tual as well as in its sensory aspects; the figural after-effect has
been of special interest in this respect.
The figural after-effect is simply the effect of one perceptual
configuration on another. If you look at an open line circle on a
piece of paper, and then look at a square on another piece of paper,
where the square falls on roughly the same area of the retina, then
the square is liable to be severely distorted. This distortion is
fairly systematic in character, and has been extensively studied
(Kohler and Wallach, 1944).
The use of the optic chiasma, which is the point in the optic
system where the nerve fibres from the left eye cross over to the
right visual cortex, and vice versa, has been a standard method of
distinguishing central from peripheral visual phenomena. With
this method, after-effects of the after-image kind can be shown to
be primarily peripheral and thus, presumably, a function of
physiological correlates in the retina, or eyeball, itself.
The non-peripheral effects such as the figural after-effect, and
the closely related plateau spiral effect, are of interest since they
involve the 'higher interpretative' levels of the central nervous
system. The lateral geniculate body has an uncertain status in
these matters, but the main problems are thought to be cortical.
The Plateau spiral should be rotated with the subject fixating
its centre, and as a result it may seem to unwind towards or away
from the subject. If it is stopped, there follows an apparent move-
ment in the opposite direction.
In the closely connected problems of perception of movement,
apparent and real movement are intimately associated with each
other, as is the pendulum effect, which is immediately related to
apparent movement (Hall, Earle and Crookes, 1952) where the
form of the apparent movement observed was directly dependent
upon the extra clues, which were auditory, in the form of rhyth-
mical clicking. Most of those subjected to these conditions formed
the impression that they were observing the movement of a pen-
dulum.
316 THE BRAIN AS A COMPUTER
Kendon Smith (1952) has pointed to some of the difficulties
that are involved for Osgood and Heyer's (1952) theory in ex-
plicating some of the more dynamic central visual effects, and
Deutsch (1954) has also raised objections to the theory. These
will be discussed more fully in the next chapter.
Deutsch's (1953) work on the spiral is also relevant. He found
that intermittent illumination of a static spiral gave an effect of
'apparent rotation', and also (often) gave after-effects similar to
those associated with an actual rotation. Of course, it is not
difficult to imagine that our sensory apparatus records certain
external events and, if certain cues or clues are suppressed, that it
cannot distinguish different situations that depend solely on
observing those certain suppressed cues. Thus 'apparent 1 and
'real' movement are visually the same, and only contextual clues
would distinguish them, through inference. This leaves open the
question of central after-effects, but the writer believes that here is
a case where an explanation of the effects depends, in the first
instance, on giving a physiological account in terms of the eye, the
lateral geniculate body, and the visual cortex, and leaving the
obviously interpretive effects (e.g. the rotational aspect of the
recorded after-effect) to the other cortical areas.
This is surely where central interpretations are a function of
experience in the form of beliefs and expectancies.
Throughout this kind of interpretative work the problem is to
deal with different levels of neural tissue as well as different levels
of explanation, although the process is in fact a function of the
organism-as-a-whole. It does not seem possible to talk of un-
interpreted recordings (and their manifold effects) in the visual
system alone, and then of their interpretations in various cortical
areas, such as area 17 alone, the occipital areas alone, or the
cortex-as-a-whole. However, in some respects we can recon-
struct a set of models and theories with these crude distinctions
in mind.
There are many problems in perception yet to be solved, and it
will surely be a most fruitful field for amalgamated work by
perception-psychologists, sensory-physiologists, neurologists, etc.,
for their experimental results are of extreme relevance to each
other. We have already summarized briefly the very considerable
(but still very inadequate) evidence that has been collected by
PERCEPTION 317
neurophysiologists and other biologists in general, but the mole-
cular approach to perception as such has been only lightly touched
upon. Nevertheless, it will be more useful at this point to turn to
the molar approach.
Boring (1952) holds a view that regards perception as related to
the constructed space of science on the one hand, and the subjec-
tive space of the observer on the other. Boring is interested in
invariance among the variables that range over both sorts of space.
He restates some of the well authenticated data, e.g. that perceived
size is positively correlated with change of distance in free bino-
cular vision, sufficient of the normal clues being present. If these
normal clues are inadequate, perceptual size depends more and
more on retinal size, and less and less on 'object-size'. This sort of
relationship, which has been emphasized by Thouless (1931) in his
work on phenomenal regression, poses no serious problem, since it
is the way one would expect an inference-making organism to
respond under such circumstances. Similarly, reduction-screens
are simply a means of reducing some or all the cues to the holding
of a correct belief with respect to some object, or more generally,
some stimulus.
Boring sees the problem as partly a semantic one when he says
that a six-foot pole close at hand and one a hundred yards away
are such that the far pole 'looks just as big although it looks
smaller*. There is no paradox here; it simply reflects the ambi-
guity of the word 'looks', which may mean either 'look in the
sense of by-literal-retinal-equation', or 'look in the sense of
believe'.
One problem left untouched by Boring is that of the relation of
size and distance when celestial distances are involved. Here, no
doubt, we need the same sort of generalization as was effected by
Konig and Brodhun on the Weber Fechner law (see p. 333). The
relation between size and distance is approximately linear up to
some limits, but over a sufficient range it would seem to have a
much more general relation where phenomenal size falls off much
less quickly with distance.
The question of constancy has made the perception of the moon
a matter of special interest, and writers have used data on it for
and against both empiricism and nativism. There is also the
interesting relation between the degree of size-constancy and the
318 THE BRAIN AS A COMPUTER
angle of viewing (Holway and Boring, 1941) which is characterized
by the well-known case of the 'horizontal moon*.
The inoon near the horizon appears much larger than the moon
at the zenith, and Holway and Boring seem to show that this
depends on the elevation of eyes in the head. This may be a
function of non-Euclidean dimensions of perceived space, or it
may be a function of experience, either in the central or the
non-central sense, or it may even be a function of these factors
together.
The vast number of experiments on the constancies (see, e.g.
Woodworth, 1938) have, of course, their own intrinsic interest, but
apart from that, they seem to the writer to support the empiricist
view of perception and should therefore themselves be explained in
terms of experience. This is not, quite obviously, to deny the
immediate and essential dependence on the organization of the
visual system, but it does seem unlikely that the visual system
works independently of the inferential (probably cortical) processes.
The general evidence is surely against such a wholeheartedly
nativist interpretation.
The general emphasis must be placed on the organism-as-a-
whole, and ordered, experimentally determined, theoretical
processes, such as the phase-sequences of Hebb, which are near to
the best perceptual reconstructions available in molar psycho-
logical theory.
To return, though for a moment only, to the question of size-
perception, which serves to illustrate the scientific problem of
perception, Gibson (1950) has suggested some conclusions that
place him on the side which views objects as primary, and sensa-
tions as secondary.
This dualism, which both Boring and Gibson accept, has
certain difficulties, but the question of the primacy of the object or
the sensation is one to which it is difficult to ascribe any signifi-
cance. It is a matter of theory-construction technique and not of
empirical fact.
One of the dangers we have to face in the piecemeal reconstruc-
tion of perception is the fact that these various problems of size-
perception, apparent movement, and so on, are not sufficiently
independent. There can be little doubt, for example, that motiva-
tion modifies perception, and the danger is that we seek explana-
PERCEPTION 319
tions for part processes that are only explicable when the organism
is treated as a whole.
The distinction between appearance and reality is better made
as a continuous series, or degrees, of interpretation rather than as
a dichotomy. The difference emphasized is that between seeing
(with a high degree of interpretation) and seeitig (with the mini-
mum interpretation). This is useful, and doubtless on the right
lines, but inadequate for some of our more subtle purposes.
Cybernetics and perception
Now we must describe some of the general principles that have
been adduced as a result of regarding certain biological systems
from the point of view of cybernetics.
It was Hayek (1952) who first suggested that the method of
human perception was dependent upon a classification system.
This suggestion was followed up by Uttley (1954, 1955), who
built, as mentioned earlier (pages 112-114), a model of a classifica-
tion system wherein he assumed a certain set of primitive proper-
ties, <z, b 9 ...,#, which could be partitioned into subsets of these
properties 1, 2, ..., n at a time. This is the same essential principle
on which the input of the digital computer operates, and it seems
to be essential to the human visual system (as well as to the other
special senses) in one form or another.
Such a classifying system is consistent with our knowledge of the
empirical world, which we divide up into classes and properties,
and which is precisely a reversal of the process ascribed by us to
the special senses. Later, we shall give some account of the human
visual system, and our account will rely from the start on the
concept of classification. From this starting point we must
consider the need for more specific perceptual structures.
A human nervous system must obviously include a storage
system in some form. It is clear that without the ability to record
previous experience no human being could behave in an intelligent
manner, and that part of perception called recognition must
depend upon a comparison with what has already been stored. This
question has been analysed by Culbertson (1956), who showed
that memoryless automata could, in fact, exhibit what seems to be
intelligent behaviour but this does not change our view, quite
320 THE BRAIN AS A COMPUTER
apart from the evidence from introspective (or retrospective)
events which we can 'consciously remember'.
Many different methods of storage have been constructed in
hardware, including chemical storage systems. These different
systems can be utilized to produce certain sorts of results in
conjunction with certain types of input, and a direct investigation
can thus be made of the central nervous system with the idea of
discovering which methods are most plausible, neurophysio-
logically. There is some neurophysiological and behavioural
evidence on this point that suggests the use of at least two different
sorts of storage, perhaps in a primarily chemical form, and operat-
ing in a manner similar to the registers of a computer. At the very
least, a short term and a long term storage must exist.
Uttley's conditional probability machine (1955) has some of the
inductive capacities required for recognition, and in Bristol a
computer has been built capable of exhibiting the same properties
(George, 1958; Chapman, 1959). But before we discuss these sorts
of systems further, let us return for a moment to the more general
molar questions.
We must ask ourselves the cybernetic question : Are the problems
of perceiving size and movement and the problem of constancy
made clearer by recourse to our models, whether in hardware or,
more especially, in logical net form?
We have already started to outline our approach to problems of
perception, where we think initially of perceiving as occurring on
the basis of classification. To proceed with the argument to the
next stage we must further develop the basic assumption of
classification.
It is clear that the normal human being receives information
from his environment which is of a continuously varying kind,
involving considerable redundancy (Rapoport, 1955; Barlow, 1959),
and also coming from a wide variety of sources. This stream
of information, coupled with the organism's responses, are the
events that represent behaviour in an environment, where each
event has a certain specifiable probability relation with every
other event.
We shall say, then, that the occurrence of a sign will give a
definite expectancy with respect to other signs or stimuli that will
influence the process of recognition or perception. Further to this,
PERCEPTION 321
there are differently weighted probabilities that will be applicable
to certain combinations of stimuli at any instant, in terms of which
the process of recognition will operate. These probabilities are
weighted not only by frequency and recency but also with respect
to their value for the organism, both in urgency and extent. But let
us start from a consideration of the peripheral elements.
Different sensory endings account for different sorts of classified
inputs, since nerve transmission, while varying with strength of
stimulus, remains qualitively the same for varying sensations. Thus
it seems likely that nerve endings are each specifically sensitive to
some sort of definite effect, such as heat and cold. This indeed
grants, in part, the argument by Sutherland (1959) which points
to the need for specific stimulus analysers.
Similarly, the process of hearing seems to depend on peripheral
analysers, with recognition depending on the terminal areas of the
cortex becoming specifically associated with different parts of the
cochlea. To take another example, the retina is specifically related
to different points of area 17 by some set of transformations
through the restriction of the optic nerve, which makes temporal
and spatial summation necessary, and thus sets up a correspond-
ence between points of the retina and points of area 17.
We are not at present concerned with peripheral mechanisms
which mediate the sensory process, nor with the precise mechan-
isms at the central nervous level which distinguish between,, say,
the length of a contour line and its shape; this matter will be
discussed later. Many theories and models are already in existence,
but we are primarily concerned with the handling of the signals as a
key to the perceptual act, on the .assumption^ that the process of
classification is somehow possible.
The fundamental process of visual perception can now be said
to be that of recording patterns of discriminable inputs in area 17,
using certain unspecified devices, such as the time interval
between the onset and cessation of streams of stimuli, and so on.
But let us now give some consideration to the nature of classifica-
tion in machines.
The machine design
The idea of photoelectric cells, cathode ray oscillographs, radio
transmitters and receivers, etc., naturally occurs to the builders of
322 THE BRAIN AS A COMPUTER
sensory equipment for machines. Uttley (1954) has shown that we
can have a display of photosensitive cells so that any particular
shape interposed between them and the light playing on them will
fire whatever cells are placed in the shadow. This, and many other
methods, could be used to record shapes, and the proper recording
of the particular cells so fired, against the previous experience of
the machine, will lead to appropriate responses in terms of a
general classification and control system (George, 1956b, 1957d).
There is no doubt that any system of pattern recognition will
have the difficult job of accounting for that recognition even when
the pattern in question is transformed in various ways. As
Selfridge has pointed out (Selfridge, 1956),
... faces as visual patterns are subject to magnification, translation,
intensification, blurring, and rotation, and they remain the same faces still.
It is the search for a system that preserves certain invariances
under transformations that will model accurately the recognition
process. Such recognition is clearly dependent on learning, since
we can only classify the details in terms of information already
acquired, or possibly previously built in.
Selfridge describes a visual model made up of photosensitive
elements that are clustered towards the centre, and which record
1's where inputs occur and O's where they do not occur. The
machine then maximizes its 1 -count and this causes a movement of
the system in such a way that the objects tend to fall on the
greatest density of photosensitive elements; this is obviously a
type of retinal model we should bear in mind.
A more general theory along similar lines was designed by
Pitts and McCulloch (1947), in which they pictured the recogni-
tion system as being made up of two mechanisms that preserve the
appearance of an object by pattern, in spite of transformations, by
achieving an invariance in terms of a process of averaging.
Neurologically, the group transformation is centred at the
superior colliculus, and the general theory depends on the exten-
sion of the idea of reverberatory circuits. Perhaps the most obvious
field of investigation to suggest itself to the mathematician is that
of transformation groups and conformal representation, where
retinal figures are transposed from one coordinate system to
another, and the question remains as to the nature of the appro-
priate transformation.
PERCEPTION 323
All this is about the nature of the retinal recording and the
transference of that record to the area 17, or some higher visual
centre, but our chief concern at the moment is with what happens
after that, even though the two stages cannot be wholly separable.
Some attempt to separate the two processes occurs in Price's
writings (1953), where he distinguishes primary from secondary
recognition. Most discussions of pattern recognition have been
with respect to primary recognition; in this section, however, our
analysis is mainly directed at secondary recognition, with the idea
of showing its influence on primary recognition. The whole
relationship is certainly relevant to semantic difficulties over the
word 'perception', and to the disputes between nativism and
empiricism.
Primary recognition is, roughly, the process of recording a
shape or property, such as redness, or roundness, while secondary
recognition is the process of classifying it, or of putting an inter-
pretation on it. Price says:
When one sees a red object in a good light, one recognizes the redness of it
directly or not at all. Familiar colours, shapes, sounds, tastes, smells and
tactual qualities are recognized immediately or intuitively, when one
observes instances of them. But when I see a grey lump and recognize it
as a piece of lead, this recognition is indirect ...
This distinguishes the primary (direct) from the secondary
(indirect) process. It seems, though, that they differ in degree
rather than absolutely, and in our model we shall suggest that one
process grades over into the other.
We have already suggested a brief terminology dealing with the
sort of situation that involves perception and learning. We acquire
beliefs about the nature of reality, and we act on these beliefs when,
for our model, we mean the word 'belief to be understood as a
theoretical term linking the input to the output; it is at least some
part of that link where the output may not be in fact enacted. Thus
the process of perception is one of interpreting, in the light of the
organism's experience (making use of its storage system), the
stimuli that are selected from all of the potential stimuli. The
resulting response to this classificatory act becomes the stimulus
for a resulting action, if such action is necessary. This means that
the arousal of a perceptual belief leads to the awareness of some
object or event in the immediate environment, and this itself may
324 THE BRAIN AS A COMPUTER
be party to a whole series of events that have previously been
associated in a temporal pattern.
It is in this way that selection of stimuli takes place, since the
occurrence of one event, correctly perceived, will lead the organism
to ascribe some probability to the next event likely to be perceived,
in the light of its knowledge of its own response, and the prob-
abilities of such sequential relations, inductively collected from
previous experience. This is surely directly responsible for what is
called set in psychological literature.
Let us return to the actual identification of such objects or
events as occur in the neighbourhood of the organism.
We have partitioned sets of receptors
such that at any instant there are collections of receptors, generally
from each partitioned set, that will be firing. At any instant, there-
fore, we shall record a finite string of symbols, say:
a^a^b^c^ (2)
and this means that counters of the classification system (that
record every possible combination of all the inputs or so we
shall assume for the time being) will alter with each instant. Thus
all combinations of the subsets of the string (2) will have 1 added
to their count, and then the machine itself will respond by some
classification in terms of what this count implies in terms of its
experience. More precisely, we shall say that physical objects, for
example, are never recognized by all their characteristics at once,
and we shall argue that the probability of some physical object A,
with respect to the existence of some subset of its characteristics,
has a definite probability value to be ascribed to it.
We are saying that a, b, c, ... are the elements of primary
recognition, and that lengthy combinations of these strings are to
be called, for simplicity, A, B, C, ... where A, for example, might
stand for (2), and where A, B, C, ... are the elements of secondary
recognition.
Empirical classification in terms of classes or properties
The above system can now be given a more precise treatment,
and to avoid typographical complications we shall talk of a,b,c,...
PERCEPTION 325
and A,B 9 C> ... without the use of suffices, as sufficient for demon-
stration purposes.
The machine has a classification system wherein the world is
divided up into classes of properties, and these properties can be
subdivided into indefinitely many subsets. Some classes will be
those of colour, size, shape, brightness, noisiness, etc., and size, for
example, can be further divided into length, width, height, and so
on, whereby a particular object may be classified by reference to its
impression: X classifies Y as short; or by reference to an actual
measurement: Y is five feet four inches tall.
Under this general procedure we have subsumed different visual
recognition processes, from a momentary exposure under a
tachistoscope at one end of a sort of continuum, to a lengthy and
detailed analysis, including the measuring of its dimensions, at the
other end, here perhaps involving tactile as well as visual recogni-
tion.
To recognize an object, we have to recognize its properties
it may be said that an object is its full set of properties and
normally we will recognize some subset at any instant; we shall
therefore, whenever it is possible, take as many instants to perform
the recognition as is necessary for us to be reasonably sure of its
success, ascribing the object to our classification according to its
height, weight, colour, shape, and so on. In any instant the
probability of its being one object rather than another will be
computed purely on the basis of frequency.
At the moment we are not considering the effect of temporal
context. If, then, we classify properties adghjk, there may be two
different physical objects that have these properties, such as
adeghijklnp and abdghjklo, and we can decide the matter in prob-
ability terms by reference to the past count. So if we call the first
string B and the second C, we can say that the probability of jB,
given adghjk, is p lt and the probability of C on the same basis is
q v and now^> 1 >^ 1 implies B, whereas $i>pi implies C.
If we now take the next instant and add the property 1 alone,
we shall change the absolute but not the relative probability. The
further addition of properties enp will decide against C and
strengthen the probability of B against all other possibilities, giving
it a value 3 , say. Theoretically, this process can go on until a
value p n is achieved, carrying all the properties of B, and thus
326 THE BRAIN AS A COMPUTER
having the value 1. So we have the possibility of a series of
probabilities pi, p%, ...,p n with respect to some object which tends
towards the limiting value of certainty. We shall call these steps
'categorizing responses' of which the last is called the 'final
categorizing response* (F.C.R.). In fact, we are normally content
with something far less than a ^-value of 1 for an F.C.R., and
indeed we have to be, either because we simply are not permitted
by time (or space) to see all the properties, or which is more
usual because we are fairly sure, knowing only a few properties,
that we know what the object is, due to the temporal context of the
situation. In effect, this means the weighting of the set-theoretic
conditional probabilities by the probabilities of temporal ex-
pectancy.
The counting system
The counting system has already been described in Chapter IV,
where it depended (although it need not have) on the use of closed-
loop elements that fire themselves and continue to fire until
stopped by some inhibitory input. A chain of conjunction-counters
can be built that will record the frequency of occurrence of any
combination of inputs, or properties, whatsoever; and disjunction-
counters that will fire when some part of a combination fires but
not all of it. Thus, the counters for a and b fire conjunctively if a
and b occur together, and disjunctively if a or b occurs alone. In
fact events of any length, either positive, negative or mixed can
easily be counted by a simple logical net, using a classifying system.
Motivation is clearly a vital condition for the firing of counters,
and this is assumed to be occurring in the perceptual process.
Combinations have not only to occur but must satisfy, in some
sense, the organism or at least be connected to satisfactions
for the process of counting to take place. Satisfactory associations
are broken down by this disjunction-counting when a certain
response leads no longer to satisfaction, but instead, to pain. This
all depends on certain stimulus response connexions being already
built into the machine. Taken in terms of isolated instants, we can
use the calculus of empirical relations (see Chapter III and
Chapter XI) for that seems to describe adequately the perceptual
process as a Markoff process, in effect, although other relations
besides temporal ones could be involved.
PERCEPTION 327
The temporal order
So far, in any classification system we have discussed, we have
only been concerned with the case of the instantaneous classifica-
tion of subproperties to some total set of properties. We have
mentioned, though, that it will not generally be necessary to make
categorizations, or classifications, in terms of such instantaneous
states alone. This is so because there is a temporal order of things
such that when a stimulus S^ occurs, we may respond with
response R 2 when the expectation is that S$ will follow. Indeed,
our counter systems for the cognitive process, built on the same
principle as for perception alone (George, 1956b), predict pre-
cisely the probability of one event following a particular response,
in the same manner as some subset of properties is the basis for
predicting the total set of properties. Thus if S l has occurred 100
times and has been followed by S$ 85 times when the response R 2
has been made, we only need a record, by the use of counters, to
tell us the probability of S z following S f 1 , granted that the response
R 2 was made. Clearly^) = 85/100 in this particular case.
The calculus of empirical relations is a method of computation of
beliefs that the organism holds merely on the basis of classifying
and counting. It is an interpretation of the inductive formula
c(h> e) = p. Here c means the degree of confirmation, which is
given by the probability^, in favour of hypothesis A, by evidence e.
The sequential categorizing responses of a set of instants in the
process of perceptional, p%, ...,p n includes as a particular case the
tests to confirm a scientific theory or hypothesis, e.g. the perceptual
process can be thought of as all or as a part of the series.
ci(hi 9 ei), c%(hz, 02), ..., c n (hn, e n ) (1)
Such a system, we shall remember, can be represented by nets, and
may in fact be considerably weighted for recency as well as fre-
quency, apart from the fundamental requirement of value through
reinforcement.
This very brief account of an inductive logical machine is
addressed here primarily to the problem of perception, and the
central role of secondary recognition. It is felt by the writer that this
approach to the problem is one that should be made prior to
attacking primary recognition.
By now we should have seen enough, peripheral receptors apart,
328 THE BRAIN AS A COMPUTER
to ask ourselves the basic question: would a system built on the
lines we suggest exhibit all the properties we want?
It is evident that there is no problem for simple differences in
size. Granted that we have a receptor mechanism that is able to
record anything at all, it may be expected to show differences in
the area recorded, and the simplest manner in which this might be
expected to occur would be by counting. The problem here seems
to be primarily peripheral, and we shall return to it in more detail
later.
The real problem is that of size and distance. Is our machine
going to say, 'A six foot pole close at hand and one a hundred
yards away are such that the far pole looks just as big although it
looks smaller*? If we assume that we have some peripheral
receptor which registers a 'retinal size', then it is easy, by simple
geometrical considerations, to show that such retinal sizes are
quite different for the two poles. Obviously, therefore, two factors
enter into the second part of the apparent 'paradox' that suggests
that they look the same. It is the context of the process, and our
previous experience as represented in our storage system, or in the
storage system of the machine, which allow the equivalence. The
recognition that it is a pole is said to evoke a particular pattern
a-^a^a^a^ say, and the peripheral mechanism gives a difference of
size, but other cues which the classification mechanism will record
are cues in the form of lines of perspective, other objects, and so
on, all recognized and with a stored knowledge of their sizes and
their 'significance* for size. This again encourages a belief in the
empiricist's interpretation of perception.
One group of experimentalists working primarily in the field of
perception and called the Transactionalists (Kilpatrick, 1953), are
strongly empiricist in bias. They have been able to show that the
interpositioning of stimuli between the stimulus under considera-
tion and the eye, will alter the interpretation placed in the size of
the distant object. This is so if the nearer object bears (size apart)
a relation to the further object that supplies a clue (usually false)
as to the further object's distance.
They were also able to show that the relative brightness of an
object has an influence upon its apparent size; the reason is to be
found in the experiential fact that brighter objects are generally
nearer to the observer. The Transactionalist arguments for a
PERCEPTION 329
perceptual theory have not sufficient definiteness to suggest an
immediate model, but their general findings are very suggestive
for the sort of cybernetic model we have in mind.
Any object, according to transactionalist theory, derives at least
a part of its nature and comprehensibility from its participation in
a total situation. Such a present transaction which constitutes
the essence of perception has its roots in the past experience of
the individual, and its implications necessarily extend into the
future. The world of phenomenological experience is a world of
significances provided by such transactions. These significances,
resulting from past transactions, are 'externalized* by the perceiver
as the basis of his present and future action. The philosophical
theory of transactions will incidentally be found in Dewey and
Bentley (1949). A brief statement, and a discussion of its applica-
tion to perception, are given in a series of articles by Cantril,
Ames, Hastorf and Ittelson (1949). See also Ittelson and Cantril
(1954). For a more general application to the phenomena of the
Ames demonstrations see Lawrence (1949a, 1949b).
The problem of the context and the transaction of perception is
clear in terms of our set-theoretic model, though of course this
does not of itself guarantee the correctness of that model. However,
this matter will be pursued later, and for the moment we will return
to our more general understanding of perceptual problems
indeed, to our particular perceptual problems and ask, as an
example, why the 'moon illusion' occurs.
The answer seems to be that the conditions for perceiving the
moon as enormously large are lacking, both in our immediate
perception of it (there are no cues) and in our previous experience
(there are no clues. We shall use the words 'cue' and 'clue'
throughout in these senses). The fact that primitive people had no
conception of astronomical sizes and distances, and that Anaxagoras
was cruelly persecuted for saying that the moon was larger than
the Peloponnesus, is an indication that perception here does not
follow the form of perception in our immediate vicinity.
Let us next consider movement in perception. Since successive
retinal patterns occur somewhat displaced from each other,
relative to a retinal datum and a conceptual datum which will
allow for eye movements and head movements, we may expect to
record a 'moving object', and indeed our idea of a moving object
330 THE BRAIN AS A COMPUTER
depends precisely on this sensory (not visual alone) fact of succes-
sive stimulation of a pattern which retains its identity. This is to be
explained in terms of the peripheral receptors, and we can thus
concentrate immediately on the difference between apparent and
real movement.
We may expect that, subject to certain restrictions in the form
of cues that allow the classification system to infer 'apparent
movement', such a system alone will be unable to distinguish
apparent from real movement. This implies that it is the clues
from storage, and inferences made in terms of the subject's know-
ledge of the overall position in which he is placed, that make the
distinction possible. Confirmation of the above argument may be
found in the Pendulum Effect.
It is perhaps clear by now that the machine system, as thought of
in the precise designs of finite automata, will be almost wholly
committed to an empiricist form of explanation, where the cues
and their immediate bearing on objects in the instantaneous sensory
field, although often supplying information for recognition, are
themselves dependent for their efficacy on previous associations.
Further to the above, we can see that we should seek to explain
constancy by the same sort of explanatory process as that already
suggested. The co-operative working of the sensory classification
and the control system is certainly the source of such effects, and
the main interest for us must lie in showing the more precise
nature of the models suggested as a result of the more detailed
experimental data.
We say, then, that constancy is concerned with the contextual
situation where our stored knowledge directly influences the
results achieved by our classification system. Again we see the need
to specify more precisely the range of possible workings involved.
We also have words like 'attitude' which represent the influence
of the store in an anticipatory way (possibly with contamination
from emotions) on the anticipated occurrence. In ordinary lan-
guage we might say, 'I had an attitude of suspicion because I had
been duped that way before. Instead of -4->jB, A was presented
and yielded C, so now I am uncertain (suspicious) of the outcome
with respect to the stimulus A, and so on.'
We shall be careful to distinguish between constancy in this
contextual sense, and the continuous identity of a physical object
PERCEPTION 331
moving through space, where the identity might be dependent
upon characteristics in the peripheral receptors ; or both these and
the storage's interaction with the sensory classification system.
The effective stimulus in perception
Another problem of importance in perception is that of the
nature of effective stimulus variables. Boring (1952) takes up the
point raised by Dewey as to what constitutes an effective stimulus
a matter which has also been emphasized by transactionalists.
The problem of any stimulus response system is to identify the
stimulus. Boring says of this :
He (Dewey) was right, for the effective stimulus is not an object but a
property of the stimulus-object; some crucial property that cannot be
altered without changing the response, some property that remains
invariant, for a given response, in the face of transformations of other
characteristics.
This problem can be treated in many ways ; indeed, the whole
question of an appropriate language for descriptive purposes is
brought back at this point. There is a certain vagueness over the
words 'object' and 'property of the stimulus-object* in the above
quotation that calls for further discussion. It seems that both
objects and properties of objects may act as stimuli, and what, for
that matter, is an object but the total set of its properties? Cer-
tainly, though, it is often the case that the stimulus is a relation
(perhaps usually an invariance relation), and certainly it is a
distinct problem to establish the identity of an effective stimulus.
It is often the case that, in an environment of potential stimuli,
one has to wait for the response in order to make an induction
about the nature of the stimulus. Our search for a (public) science
is conducted partly by laying down laws such that, given all the
potential stimuli and the state of the organism, we shall be able to
say which will be effective stimuli, in terms of either the con-
temporaneous state of the organism (which includes all its experi-
ences in the form of an end-product or resultant vector), or by
knowledge of the experience of the organism. For theoretical
purposes this matter is a sophisticated end-product rather than a
relatively crude initial problem.
Our method of discussing properties of stimulus variables must
332 THE BRAIN AS A COMPUTER
be in terms of the objective properties of the stimuli ; the process of
making a stimulus effective is the problem of behaviour. The study
of these objective characteristics is not of special relevance to the
present discussion, although it is vital to the nature of the per-
ceptual theory one arrives at, and therefore to the sort of models we
shall construct. The objective properties are those of physical
distance, size, shape (or form), brightness, colour (certain refrac-
tive and reflective properties of materials), relative perspectives,
groupings and so on and so forth.
Such laws as those set down by Wertheimer (see Woodworth,
1938) are of great relevance at this point, as is the whole work of the
Gestalt school, although we must be careful to distinguish the
actual (or physical) charcteristics of potential stimuli in so far
as they are knowable other than by someone's perceptions from
the effective stimuli and interpretation, which are a function of the
organism's interaction (or transaction) with its environment. Thus
Wertheimer J s laws of perceived movement which show a perceived
relationship between similar things, or things moving with
similar speeds, etc. (see Boring, 1942), and more obviously, the
division of the stimulus-field into figure and ground, and so on, are
part of the activity of the organism; and binocular vision, flicker
fusion, inferences, and so on, become part of the essential features
of perception. Gradients, texture gradients, indeed gradients of all
kinds (including, on a different level, the physiological gradients of
C. M. Child) are part of the method or language of description of
the organism's activity, the activity of classification, categorization
and, in general, that of response.
It is as well to remember here the non-sensory figures of Hebb
(1949), and the research that appears to show that there are various
possible interpretations of sensori-motor activity. There may, for
example, be motor activities which are not the direct result of
causal stimulation; indeed, many people have suggested that it
would be incorrect to regard the sensory and motor components of
the reflex arc as, in any sense, mirror-images of each other. One,
for example, may arouse (or partially arouse), while the other may
direct, and not merely respond, in a manner already discussed in
Chapter IX where we described Pribram's homeostatic type of
control. Our models will certainly be capable of mirroring these
facts, as a careful reading of Chapter V will already have revealed.
PERCEPTION 333
Psycho-physics
The essential connexion between the objective state of affairs and
the subjective is covered by the field of psycho-physics. It should be
noted here that explicit assumptions are made that connect
stimulus and sensation; for example, the Weber Fechner Law can
be stated:
R = K log SI So
where S is the stimulus, R is the sensation, and S is the smallest
stimulus which leads to sensation. The adequacy of psycho-physics
clearly depends upon the degree of precision of the fit between the
parameters of stimulation and the parameters of sensation. There
are examples in the psycho-physical field, such as quality control,
where the fit does not always seem sufficiently good for the purpose
in hand. But now, the method of testing the validity of the psycho-
physical methods becomes important, and this line of approach
will not be continued further. The problems are clear enough (in
one sense at least), and much experimental work needs to be done
in this field to clarify more completely the status of psycho-physics ;
its methodological vagueness is a direct function of the mindbody
problem.
The psycho-physical methods, which are the methods of constant
stimuli, single stimuli, limits, sense-ratios, reaction-times, etc., are
essential to the design of experiments with respect to the sensory
modalities. The general form of all psycho-physical experiments
can be characterized:
R =/(0, b, c, d, ...n ... t...x,y,x)
where a, b t c, ... refer to specified aspects of stimuli; ... x, y, %
refer to specified conditions of the organism; R means response;
n is the number of presentations and t is time. The precise speci-
fications of the variables in this equation are, as Graham (1952) says,
matters for further research and theoretical analysis.
Many books could be written on the diverse and widely ranging
subject matter of this chapter. It is not our aim to review, as might
a textbook, all the details of the variables and problems of percep-
tion. Our aim, rather, is to illustrate the cybernetic application to
it by selected examples, and to seek generalities that will help us
towards a general theory of perception.
334 THE BRAIN AS A COMPUTER
To summarize this section, we may say that what is being
emphasized, when questions are asked about the nature of the
effective stimulus, is the fact that there is a selective process
operating, and that what is effective in stimulating the organism is
dependent not only on what appears in objective space at any
moment, and the configuration in which it appears, but the state
of the store which, in conjunction with previous stimulation,
introduces states of 'set*.
What about the complex configuration which has been the
subject of investigations by the Gestalt theorists? This is a matter
we must consider, but here at least there seems to be a case for
considering what is normally regarded as a perceptual problem
(as opposed to a sensory problem) after our discussion of receptor
mechanisms.
Form perception
We shall now consider the problem of form perception in terms
of the models that have been suggested. Deutsch (1954) has
suggested the six main facts that a theory of 'shape recognition*
as he calls it must explain:
(1) Animals can recognize shapes independent of their location
in the visual field. It is not necessary to fixate the centre of a
figure in order to recognize it, nor need the eyes be moved around
the contours of a figure.
(2) Recognition can be effected independently of the angle of
inclination of a figure in the visual field (this means the tilt of an
image in two dimensions, and not the tilt of the figure in depth
such as occurs in shape constancy experiments).
(3) The size of a figure does not interfere with the identity of
its shape. This, of course, does not hold at the extremes of size for
reasons which seem sufficiently obvious.
(4) Mirror images appear alike. Both rats and human beings
tend to confuse these. This would appear to rule out any 'template*
theories of shape recognition, according to which, a contour is
rotated in two dimensions until it coincides with one of the many
patterns already laid down. But such a superimposition cannot take
place in the case of mirror images, and no room is left, therefore,
for this particular type of confusion.
PERCEPTION 335
(5) Visually primitive organisms such as the rat and the octopus
find it hard (perhaps impossible) to distinguish between squares
and circles. This does not seem to be a limitation imposed by the
peripheral characteristics of the optical systems, but appears to
be a more central defect, as these organisms can distinguish shapes
which dirt far more alike geometrically. This type of evidence tends to
cast doubt on theories which base themselves on the angular
properties of figures.
(6) These abilities, which appear to be mediated by the striate
cortex, survive the removal of the major part of it. It is therefore
reasonable to suppose that this ability to disentangle shape is
common to all parts of the striate area, and that one part of the
striate area is not essential in helping the next one to operate.
Deutsch feels that this would tend to rule out notions based on a
scanning process. It is difficult to see how a regular scan could be
maintained in the presence of extensive damage. Further, any
system which requires the fixation of the centre of a figure so that
it coincides with the centre of the visual field must also be ruled
out. The ability is maintained even where there are extensive
scotomata of central origin.
We should notice that, of this list, we might question the truth
of (1), at least in the initial stages of perception (Hebb, 1949), and
there may be doubts about Deutsch's inference in terms of (6).
Furthermore these six points lay no claim to completeness, but
they are suggestive as a general starting point.
Culbertson (1948), Rapoport (1955), Deutsch (1955) and
Selfridge (1956), among others, have suggested models for systems
that would be capable of carrying out the task of form recognition.
Culbertson has used logical nets for describing his own system
of shape recognition; he in fact suggested some effective, although
probably biologically implausible, form abstractors for the
purpose.
The first abstractor is a translator, which simply passes an
image from one set of elements to the right, say, to an adjacent
set, and on, indefinitely, across a surface, and in particular where
the surface is a cylinder, around its face.
The second abstractor is a rotator which is made up of two disk-
shaped arrays between which is a cylinder. This device is able to
336 THE BRAIN AS A COMPUTER
rotate any pattern indefinitely. Incidentally, both the translator and
the rotator would be easy for the reader to draw, using the logical
nets of Chapter V.
Dilators and expanders can be constructed to make the image as
large or as small as we please. Then we have the image centring
system, and all these taken together in an appropriate combination
can be shown to be sufficient to process a shape for the purposes of
recognition. It is of interest, too, that the whole form abstraction
system requires only 2 x 10 7 elements and the reaction time of the
whole net is less than a quarter of a second.
The possible objection to this model of Culbertson's is, of
course, Deutsch's point (4), which puts the argument against
straightforward 'template* techniques.
It seems certain, to answer Deutsch's first point, that whereas
image centring may not be necessary later, during the learning of a.
perception, it may be absolutely necessary.
Rapoport has constructed his perceptual model partly in terms
of logical nets and partly in terms of information theory. This all
implies that one must start with fairly idealized ideas about how the
nervous system works. Rapoport regards the retinal photoreceptor
layer as a 'mosaic that could be specified by, say, spherical polar
co-ordinates, and uses the shortest refractory period of all the
cells as his unit of time ; then the effective mosaic at each instant,
which is the time-unit, is uniquely specified.
Now let us assume that each instantaneous state of the retina is a
potential message, which means that for n receptors there will be
2 n messages. If the photoreceptors were all independent of each
other, and if in the rth instant the probability of firing the fth
receptor was given by pi, and if we said, by analogy with Laplacian
probability, qt = 1 p^ then the information content of the source
would be given by
H =
and if pi = for all i,H n bits per message.
Now to consider what value n, the number of photoreceptors,
might have. Cajal has suggested n = 10 8 , and Fulton has sug-
gested that 10" 3 is about an average refractory period. If the
independence of the receptors is maintained we can conclude that
the production of information in the retina is at 10 11 bits per second.
PERCEPTION 337
This result is far too large, judging by all our other evidence of
human capacities for reaction to visual stimulation.
The next step, then, is to consider as does Rapoport the
possibility of regions sending messages, where the actual number
of photoreceptors firing in each region constitutes the message.
This gives us a more complicated expression for H\ and then we
can consider the interaction of the elements in the regions, which
will make our expression for H more complicated still.
Physiologically, we have a lot of evidence that suggests that the
retina is highly organized, and that there is a great deal of inter-
dependence in the successive states of the visual field. Looking at
an object under normal circumstances, we will generally see it from
various slightly different angles successively. This implies a high
measure of redundancy in the retina, and it is this redundancy
that enables the visual system to operate at well below the level of
what is suggested by the formula derived (above) by Rapoport.
The next problem is to consider the information as to the state
of the visual field, as exemplified by successive states of the retina.
We know that there is a bottleneck effect which operates between
the retina and the representation of visual events in the cortex,
possibly in area 17, in much the same way as they were originally
at the retinal level. This bottleneck suggests not only lost informa-
tion but, what is more important, the method by which information
is selected. The extent of the bottleneck as suggested by Polyak is
that 10 8 photoreceptors map on to 10 6 ganglion cells, which implies
a ratio of 100 to 1 on the average. This average covers a range of
1 to 1 at the fovea, to many hundreds to one in the periphery of the
retina. The reintegration of information at the end of a bottleneck
is characteristic of the nervous system and depends on temporal
summation.
Sir Henry Head's distinction between epicritic and protopathic
vision, and the nature of these connexions, suggests that detailed
vision of the cones presents no serious bottleneck; the bottleneck
applies only to the protopathic or generalized visual states, re-
cording only crude characteristics of change of brightness.
Rapoport's model does not consider the distinction that is raised
by the difference between epicritic and protopathic vision. He
addresses himself rather to the general problem of transmission of
information with minimal loss.
338 THE BRAIN AS A COMPUTER
The system of minimizing the loss of information involves the
suitable choice of a code. The reader will know that codes can be
constructed for various purposes and, to take cognizance of the
epicritic protopathic distinction, two sorts of codes, at least, seem
to be necessary for the visual system. One must retain detail, and
this will be easiest at the region of least bottleneck. The other
must try and retain as much information as possible, while
maximum attention will be given to speed of signal. The mere
recording of movement and so on for peripheral photoreceptors,
and great detail in the areas of great acuity.
This problem of the appropriate coding suggests the need for
detailed anatomical knowledge. In the lack of this we can construct
neural or logical networks as models, and consider what code
should be used for systems that are nearer the known structure of
the optical system.
Rapoport and Culbertson have suggested models that have a
fair measure of realism and can be suitably coded to transmit
information in the manner necessary to retain as much information
as possible.
Selfridge's visual pattern recognition model
In the Selfridge (1956) model an original image made up of
90 x 90 O's and 1's is transformed into a secondary image by one of
three operations. The secondary image itself may be transformed a
number of times. After the image has been transformed by the
operations, the Ts left in the image are counted. A typical original
image is transformed sequentially showing the secondary images
at each step.
The final count is then compared with the numbers stored for
that particular sequence under the various symbols. If, after a
number of sequences have been run on an image, the counts check
sufficiently well with the stored distributions of symbol 1, say, the
computer may identify that image as symbol 1.
It is not supposed that the operations mentioned are an exhaus-
tive set. They are of three kinds, and they are all local and isotropic.
The first, local averaging, replaces each datum by an average of the
neighbouring data. In this way, inter alia, it eliminates granular
noise, isolated Vs in a field of O's, and isolated O's in a field of Ts,
emphasizing local homogeneity. The second operation, local
PERCEPTION 339
differencing, replaces each datum by an average of the logical
differences of the neighbouring data, thus emphasizing local
discontinuities and tending to sharpen contrasts, edges, and
corners. The third operation, 'blobbing', replaces each relatively
isolated conglomeration of 1's by a single 1.
Many kinds of visual features cannot be handled by these parti-
cular operations; for example, this model cannot distinguish a capital
Cfrom a capital U. The latter may be merely the former rotated to
an angle of 90 degrees, and all the operations are isotropic.
The kinds of things the model could recognize have been
deliberately restricted because the digital computer was small and
slow. Even though it had 65,000 bits accessible within 10 micro-
seconds, and five times that many in slightly longer, it still took
as long as 15 minutes to process an image.
It can be seen, though, that the operations are powerful enough
to detect and count critical points. They are actually powerful
enough to compute some measure of curvature.
Other kinds of operation will occur, as Selfridge says, to the
curious. One can, for example, project along any direction, which
will reduce any two-dimensional set of data to a one-dimensional
set, or one can 'thin', i.e. change the exterior 1's of an image to
O's, so long as one does not alter the topological connectivity.
Furthermore, it is not necessary that the final data reduction be
counting. The topological connectivity might be stored instead.
The instructive part of the Selfridge machine, however, is not
the particular sequences of operations it uses to recognize symbols,
but the way in which it hunts for good sequences. Every sequence
is good or bad according as 4 the numbers, which are obtained by
applying two images, tend to differ consistently for different
symbols. The essence of learning, it seems, lies in having the
computer recognize the pattern of good sequences. At the begin-
ning it selects sequences in a random fashion, but as soon as some
of the sequences are 'seen' to be better than others, it fashions and
tests new sequences that are like the successful ones (this is
precisely the sort of thing we suggested in Chapters V and VI).
The concept of similarity of sequences is built in, and is governed
merely by a matrix of transition frequencies. All the sequences to
be tested are fashioned, in the Monte Carlo manner, by this matrix
of transition frequencies, which is initially flat. As soon as a
340 THE BRAIN AS A COMPUTER
successful sequence appears, its transition frequencies are used to
bias that matrix, which then represents a hypothesis about (the
pattern of) good sequences. This hypothesis can be tested by
using it to build up new sequences, and discarding or accepting it
and them according as they prove useless or useful.
It is not maintained that this method is necessarily a good way
of choosing a sequence, but only that it should work better than
ignoring all the knowledge of die kinds of sequences that have
worked in the past.
Deutsch's visual model
Deutsch has suggested a paper and pencil model for shape
recognition. It is made up of a two-dimensional array of elements
joined to the retina, such that a contour falling on the retinal
elements will fall on the equivalent elements of the array. Further-
more, as each new retinal excitation arrives, so a pulse will be sent
down the 'final common cable' (f.c.c.) as well as exciting its
neighbour. This system is like Culbertson's in effecting a transla-
tion of the figure so that, with a rectangle, there will be a set of
pulses fired into the f.c.c., and then another set will be fired as it
comes into coincidence with the opposite side. In this way the
brain can receive information about the length of sides and also of
shape. On the other hand, it depends upon the brain being able to
make temporal distinctions, and this receding in terms of time
seems to demand a clock, which may not be too implausible.
It should be mentioned that Sutherland (1959) has suggested the
possibility that the coding should be done in terms of intensity,
and this notion is one that will be used in a further partial model
which we shall outline at the end of this chapter.
Hebb's model for perception
There are many cases of perceptual models which are on the
borderland between molar and molecular theories, Hebb's, like
that of McCulloch and Pitts for pattern recognition, is primarily
intended to give a plausible physiological account.
Of Deutsch's six points, the most obvious one which affects
Hebb's theory, and which a theory of shape recognition must
explain, is that of scanning. Deutsch argues that a careful perusal
PERCEPTION 341
of the contour lines surrounding the figure is unnecessary, whereas
Hebb, with supporting evidence from von Senden (1932) and
Riesen (1947) believes that the learning of shape perception in-
volves the process of counting corners, or more generally, of
fixating successive points on the outline of a complex pattern.
This successive fixation process is the basis of the cell assemblies.
This argument is perhaps especially important at the time of
learning to perceive, but is less important in adult perception,
which may be the reason for the apparent disagreement here.
Let us consider Hebb's theory a little more carefully. In the
first place Hebb assumes that connexions from the primary visual
projection area in the brain are originally random. The thresholds
at synapses are supposed to vary in a random way from moment to
moment as a function of recency of firing of a post-synaptic nerve
cell. By repeated firing of particular sets of retinal cells the prob-
ability of the same cell assembly being fired is increased.
The possibilities of this theory are not perhaps clear, but
Taylor has constructed a model which helps us to see what the
implications of Hebb's theory are. This is one of many instances
where it is useful actually to build a hardware system to mimic a
theory.
The arguments against Hebb, mostly stated by Sutherland
(1959), are that while the scanning of contour lines during the
learning of the shape of a figure is all right for figures of equivalent
size, this theory does not account for recognition without eye
movement.
Now although Collier (1931) and others claim to show that such
recognition is possible without eye movement, there are in fact
two difficulties. The first is to ensure that all eye movements have
really been eliminated; and the second is that eye movements may
be only necessary to the learning and not to the recognition process.
During learning the figure may have to be brought into standard
positions by scanning, but after learning, the barest sample of the
figure is usually enough for recognition purposes, even though in
practice there is, of course, still the availability of eye movements
for confirmation of the identity of a figure.
Certainly Sutherland's arguments against the generalized
approach to perceptual models are only partly effective, and this
can be seen again in his criticism of Uttley. Sutherland has argued
342 THE BRAIN AS A COMPUTER
that Uttley's system does not lend itself to generalizations other
than from a subset to those sets of which it is a possible subset.
Now it is obvious that this is not necessarily true, since it is easy
to arrange for generalizations to depend upon the notion of similar
sets, which similarity is defined in terms of so many common
elements. Sets with different elements can also be identified with
respect to having a common resultant, and so on. This sort of
argument has really no bearing on the relative advantages of
regarding specific analysing mechanisms as against general
systems.
At the same time, Sutherland produces much relevant evidence
to support the idea that we should not wholly overlook specific
analysing mechanisms.
The fly-catching behaviour in newts seems certainly to depend
on specific analysers (Sperry, 1943), and the work of Sharpless and
Jasper (1956) and Hernandos-Peon, Sherrer and Jouvet (1956)
supports clearly the idea of ordered sensory processing.
In the experiment of the latter group, peripheral blocking on
the part of a cat was inferred when a cochlear potential to clicks
was completely inhibited by the sight of a mouse. It was suggested
that this might be a function of the reticular formation.
While accepting the fact that a too complete adherence to
general principles in perception is probably false to fact, it would
seem unwise to go as far as does Sutherland in supporting what he
sees as the only alternative. In fact, of course, it is not a matter of
alternatives, but rather of modifying a general approach to fit the
particular experimental facts that Sutherland so ably presents.
A model for perception
Let us next consider an outline necessarily abbreviated of
a suggested working model for the study of human perception. It
is a model that is being constructed at Bristol, and although it may
need much modification, it is hoped eventually to connect the
retinal model to a sufficiently large storage system, and so make a
detailed analysis possible (George, 1959b, 1960b).
We will take the retinal model first. This will obviously be
mirrored by an array of elements in duplicate, both mapped onto
the inside of a roughly spherical shell. For practical purposes, and
to clarify the argument, we can think of it initially as a single array
PERCEPTION
343
that may be set out in any plane whatever. The particular shape
and its duplication we shall at first regard as incidental to the major
properties we shall be interested in mirroring, although clearly this
will have the effect of temporarily eliminating matters dependent
upon binocular vision.
In this single array we may label the elements as the elements of
a square matrix, and we will make some tentative suggestions as to
(a)
(0
FIG. 1. VISUAL NETWORK ELEMENTS. l(a) shows an element that
fires when stimulated. l(b) a network (three elements) that fires
when the input is fired and not after, and when it stops firing
(on-off element) and l(c) shows an element that does not fire
when it is stimulated (off element).
what properties such a matrix must have to carry out such func-
tions as shape recognition, colour vision, and various other visual
functions that are, at least partly, determined by the retina.
Figure 1 shows a sample of some of the elements that the retina
might contain. Figure l(a) shows an element which fires steadily all
the time it is stimulated. Figure l(b) shows an on off element that
fires with a change of stimulation, either as firing stops or as firing
344 THE BRAIN AS A COMPUTER
starts. Figure l(c) represents an element that fires whenever it is not
being stimulated. Cells which fire only at the outset or cessation of
stimulation may be said to be a special case of the on-off element;
they will be called 'on* and 'off' elements. The type of Fig. l(a) will
also be called 'on' elements. Let us assume, to begin with, that
these elements are randomly and densely packed all over a square
array. The outputs from these elements will be assumed to run
across the surface of the array and funnel through one point called
the 'blind spot'. It should be borne in mind that the use of words
like 'blind spot' is intended to remind us of the functional analogy
with the human retina, without necessarily committing us to the
statement that it is in any sense exactly the same. On-off elements
and the like may be capable of being mirrored in many different
ways, and we are not intending, at this stage, to be committed to
biological verisimilitude.
Let us now suppose that the fibres that are led away through the
blind spot are connected to a classification system, and we will also
suppose for the moment that every fibre from every retinal element
is connected to the storage system directly and called by its retinal
name. A retinal name is used here merely for our own naming
purposes, and for retinal names we shall use, as before, the letters
A, B > ..., N, and combinations of these letters.
If we now place a figure, such as a solid triangle, against the
retina so that its projected shape fires those cells that lie inside its
boundaries and not those that lie outside, then a certain set of
retinal on-elements will be fired and its complementary set will
remain unfired. The off -elements will not fire (be inhibited) inside
the triangle, but the on-off will, of course, have fired.
Suppose now that the set fired is recorded in a storage system
that is attached to the classification system. Here, each output from
the classification system has a storage set so that it is fired, and
stores the information each time a set of pulses is received, as well
as giving off responses. The particular set fired we shall call the
'triangle' set; if fired again it might be said to produce the identical
response with the one originally elicited; but by the nature of the
connexions in the storage system it will be seen that the whole of
the triangle set will not subsequently need to fire on every occasion
for the same response to be elicited as was originally elicited.
At this point we will temporarily change our description of the
PERCEPTION 345
operation to a simple set-theoretic description, since this is what is
implicit in our classification and storage system. This means that
any subset of the total triangle may be able to elicit the triangle
response. What will in fact decide this matter will be the extent to
which subsets in the past, assumed to be samples of the triangle
subset, have been responded to 'without mishap'.
This last point requires some elucidation. If our recognition is
to be effective it must be able to tell us whether a particular subset
is a sample of a certain larger set or not. If, according to a prob-
ability measure, it is 'said to be* a sample of some particular set,
then confirmation of this can be achieved through the prolonged
sampling of the sets in the visual field, or by acting on the assump-
tion of correct identification^ and then observing the subsequent
outcome of the whole context of some piece of behaviour to
discover whether or not there is any discrepancy. Naturally, such
a probabilistic system will be liable to error. But more of this later.
We must now look again at the retina itself and discover its
limitations. The first and most obvious is that if we project on to
the retina another triangle which is slightly larger or smaller than
the one already 'learned 1 , it may fire no element in common with
the first set; we may therefore ask why there should be any
similarity between the first set and the second.
To answer this objection we can introduce the notion of scanning.
To make the new triangle elicit many of the same responses at the
level of the subsets, we must arrange that the contours of the figure
which is presented to the retina are scanned, and to do this we must
effect a gradient across the face of the retina such that the retinal
centre (or central area) will move along the contour lines. This
means, of course, that already we have destroyed the random
nature of our retina.
Before discussing how this might be achieved we should men-
tion that, to conform with the facts of eye movements, there must
be a certain oscillation of the eye around whatever line is being
fixated. This is in keeping with the results of experiments on. the
fixated eye, and has the effect of keeping the on-off elements on
the contour lines firing steadily, and so transferring a total outline
of the figure to the classification system. But this, of course, is
insufficient to elicit the same subset of responses from the classi-
fication system, and it is here that we must add the condition of
346 THE BRAIN AS A COMPUTER
scanning; indeed we might guess that the fact of eye movements is
a direct result of the scanning operation of the eyes. Even in the
fixated eye it is supposed that scanning cannot be wholly sup-
pressed, and it appears to show slow 'damping' properties.
At any instant that the retina is stimulated by the presentation
of a figure, there will be a localized centring response that moves
the figure towards the point of maximum excitation. Should it
happen at any instant that there are a number of equi-excited points
at equi-distance from the centre of the retina, then those eye
movements which occur even in the resting state, partly through
slow 'damping', will immediately bring one point into the maxi-
mum place and so cause movements along the contour lines to this
local maximum. As the maximum is reached, so the feed-back
effect is diminished to a minimum, thus causing the next point to
become a maximum. This is simply because the feedback causing
the movement increases with distance from the retinal centre, as
well as with intensity of stimulation. This means that the scanning
of a figure will proceed indefinitely unless or until the tendency to
scan can be removed by the storage which suppresses the scanning
operation, although the suppression is never so complete that no
incipient scanning movements in the form of eye movements are
observable. The question of this storage control must be left for
the time.
Figure 2 illustrates the point of the feedback which leads to
scanning. The effect of centring and scanning need not be achieved
exactly as we have described it, since there are many ways in which
such a mechanism could effect a scan of a field with differing
potentials, and such that a point of maximum becomes diminished
as it travels across a graded scanner, setting up new maxima and
thus producing further movement. What is important at this level
of cybernetic analysis is that we can see how to construct a system
in electronic form that would have this sort of ability.
Two important points should be noted in passing; firstly the
gradient across the retina may divide into two parts, the part that
brings the figure on to the central area of the retina, where in fact
the sense of movement gives way to sense of detail, and the
movement that still remains on that retinal area sensitive to detail
but which now is necessary to the actual scanning operation. It is
not being suggested here that two separate mechanisms are
PERCEPTION
347
necessary for this, though there is some biological evidence that
this is so. The evidence is, crudely, that peripheral photoreceptors
have more many-one connexions (perhaps a measure of feedback
strength for centring) with their bipolar cells than do the more
central photoreceptors; yet eye movements will still occur when
the whole figure is within the virtually rod-free area. This is
clearly a matter that can only be decided by further experiment.
Our second point is that classification and storage are not
necessarily effected in a single stage. It seems indeed likely that
FIG. 2. CORRECTOR. The figure illustrates the very simple
principle involved in making correcting movements with respect
to a stimulated point.
classification proceeds by stages in a hierarchical fashion, with the
the first stages being retinal and the final stages being cortical.
This last point is closely concerned with another important fact.
It is being suggested that the visual (and other sensory systems)
are primarily set-theoretic in their mode of operation. This implies
that a particular concept, such as a corner or line, or a figure like a
triangle, must involve the sequential firing of closely related subsets
of elements. If this is so, then the nature of the classification system
in however many stages it may occur will use an astronomical
number of elements, since it must take account of every possible
figure as well as every actual figure. This suggests that we should
also be able to show a method for self-classification.
A system that has the necessary properties of self-classification
has in fact been designed (Chapman, 1959). It is simply a system
that constructs its connexions as those connexions are needed, or,
more properly, as a function of the times that they have fired
together, the actual firing of the subsets increasing their prob-
ability of firing in the future. Chapman's system will become
relatively stable when the majority of the environment has become
familiar, and his model should be regarded as representing the
growth of the classification process with learning.
While Chapman's system in no way precludes the possibility of
some fixed connexions being built in genetically, or through a
process of maturation it does not require that the classification
system be fully connected. From a logical point of view, Chapman's
model is illustrated by Fig. 5 (Chapter IV) where it is necessary to
have some storage registers available to increase and decrease the
sensitivity of connexions as a result of their frequency of use. In
the logical net system, however, it is necessary to have all the
connexions initially made before the sensitivity can be changed,
and this may be neurophysiologically undesirable.
This whole question of appropriateness of description is bound
up with the concept of growth. Chapman's 'growth nets' have
advantages which suggest that their potentialities should be given
detailed investigation. This is itself bound up with the present
trend in cybernetics, which is towards the manufacture of models
using chemical and chemical-colloidal fabrics. A chemical self-
classifying system is one that is envisaged, and it is hoped to
build such a system in the near future.
Figure 3 shows a logical net that will clearly fire a specific pulse
code down the optic nerve where, we shall be tempted to say, the
code represents a specific characteristic, such as colour. This, of
course, sheds very little light on the biochemical states of the retina
which produce the different codes, but something of value may
come of such an analysis even here, since we can construct two,
three, or more basic sets such that their mixture, coming from two
or three different types of 'colour' element spread throughout the
retina will produce a coded input at area 17 that represents the
various spectral colours. It is easy to see how the process might be
carried through, and this immediately suggests a certain range of
experiments (see a similar method outlined in Landahl, 1952).
PERCEPTION
349
What is the distribution of the colour elements on the retina
such as to be able to reproduce the Benzolde Brucke phenomenon,
or the Purkinje phenomenon, both of which are changes in the
hue of spectral colours with a change in the level of illumination?
The Purkinje phenomenon in particular shows that, as light
increases from zero, the blues appear first and the reds last. These
various effects have been observed with colours on the human eye
(Granit, 1947, 1955; Wilmer, 1946). Here, if anywhere, our
analytical device shows through clearly, since we shall certainly
want to substitute a more analogue, ultimately chemical, model for
the logical net model of the retina.
FIG. 3. CODED INPUT. A logical net which fires if and only if it
receives an input of the form 101, where 101 is an ordered event
of length three involving firing, non-firing and firing of A in that
essential order.
There are obviously a vast number of questions that we should
now start to ask of our model, especially on the lines of: can it do
this, or that? We should expect it to be able to pfoduce effects
already observed, or now capable of being observed, in the human
eye, but it is necessary now to bear in mind the nature of the
storage and the nature of motivation. We must also just mention
the matter of dimensions.
Suppose the optic nerve contains about one million fibres
(Stewart, 1959), and they act in the binary fashion we have
assumed, then a complete classification system of the form shown
in Fig. 5 (Chapter IV) would call for 2 1 .oo,ooo elements, which is
clearly ridiculous. Actual estimates have suggested 10 12 as some-
THE BRA1JN AS A UUMFU IfcK
thing like an upper bound for the whole of the central nervous
system, so we can immediately see the need for incomplete classi-
fication, whether or not that classification is self-selecting.
Jacobsen (1951) has estimated that the optic nerve would have
to be fifteen times larger for the nerve fibres to be used as in-
efficiently as they are in the ear. This is again an economy in the
nervous system, achieved by incomplete classification. This whole
problem of redundancy and economy in nervous organization is
one that will repay the most careful study in the future (Barlow,
1959); it is of course essential in bringing our conceptual models
into line with the biological facts.
Our present problem about the nature of the storage system is
simply as to whether we should postulate many different types of
store, or not. Certainly it is tempting to suggest that the storage
arrangement of Fig. 5 (Chapter IV) refers to the learning process,
and that the information so learned is then moved on to some more
permanent store; but while this can be shown to be possible with
a logical net system, it offends our need for economy in the brain
model. At the same time we do envisage the classifying and storage
system occurring in stages, so that visual classification may itself
occur at various levels and, at the highest level, information will be
stored and associated from the visual, auditory, and indeed all the
special senses, as well as from the internal organs.
The above storage system has of necessity the property of
working on the basis of weighted frequencies, so that where the
number of occurrences are less than the number of available
storage elements, the response is a function of a Laplacian prob-
ability. If the alternative state holds, then the probability is
weighted for recency. When we add the motivational system to the
storage, we immediately add the differentiation factor of 'value*
into the building up of the storage. If we wish to separate Value*
from the probability of occurrences, we can do so by keeping a
duplicate set of storage elements ; but this, in general, and in the
interests of neuro-economy, will hardly be plausible.
Since it is not our primary interest here to discuss storage
systems in logical net models, we shall cut short this particular
discussion. They have been mentioned only in so far as they are
clearly bound up with vision.
Before we leave the matter altogether we must mention again
PERCEPTION 351
the problem of language. This is only just beginning to be studied,
and it will obviously prove extremely complicated since it should
go some way to focus on the overlapping interests of logicians,
semanticists, philosophers and psychologists, as well as biologists.
All that can be said here is that a system of labelling can be
associated with objects perceived, actions made by the automaton
itself, and relations between the two. This association can be
achieved by an automaton in exactly the same way as we have
already described for learning shapes. The problem is largely
bound up with the gradual reconstruction of human language with
respect to human environment, such that a whole syntax can
eventually be reconstructed. For our purpose here it is important
to note two very crucial facts. Language, while apparently invol-
ving an astronomically high number of elements, will also have the
effect of allowing the automaton to use linguistic generalizations
as a succinct store of information. This implies that in the human
brain there must be the possibility of operating by an over-
riding control of ordinary associations as a result of language. This
could be taken as an argument for a separate store for linguistic
generalizations, as distinct from the storage system so far discussed,
and to some extent this must be so. It seems likely, indeed, that this
extra storage works with information from the storage elements al-
ready referred to, so that conceptual operations can be performed.
These operations will include deductive and inductive inferences,
and will also include what we call 'imagination', since it will be
possible to initiate firing of the storage elements from inside the
store, and not just by sensory control alone.
This matter of language is almost certainly directly connected
with vision in the human being, since the words (concepts) such as
'line', 'corner', 'curvature' and so on, will all arise as a result of
associating words with particular sensory experiences. It can be
seen from this that certain familiar figures will immediately
produce the response of naming, and certain words such as 'corner',
'line', etc., will be aroused in the storage, and a small sample may
be enough for the response 'triangle', or 'square', on an almost
instantaneous sample of the environment. This is in accordance
with suggestions about the perception and recognition of shapes,
and the learning of this perceptual process, which goes back to the
work of Hebb (1949).
We shall now return to some of those problems of the visual
system that might be regarded as relatively independent of the
central organization, bearing in mind that we have already had
occasion to realize that many of the visual acts we perform are so
completely bound up with the brain-as-a-whole that they cannot
be studied adequately in isolation.
Let us then briefly consider some of the functional details of our
model of the visual system so far suggested in outline. It must be
emphasized that the purpose here is not to try to give great detail
since our main purpose is methodological but merely to say
enough to allow the reader to see how the process might be
continued.
We will first consider what is known as the 'figural after-effect',
which we described at the beginning of this chapter. This has
been explained by Osgood and Heyer (1952), using the model of
the visual system suggested by Marshall and Talbot (1942), by
reference to an excitation that was set up along a double contour
line that brought about a wedge of excitation in area 17. The
wedge of excitation was an approximate integration of separate
excitations whose maximum was assumed to represent the line
'actually seen' by the individual. The superposition of a second
line, after two minutes' fixation of a point near to the first line,
caused the second line to be displaced to a position further away
from the fixation point. This was thought to be the result of the
relative 'fatiguing' of the cells, caused by continued firing in the
period of fixation, leaving the second line falling on an area which
is below the resting state of excitation of the rest of the retina. The
two curves of excitation are superimposed, and the maximum is
simply moved away from the position it would otherwise have
taken up.
In our own retinal model of the last section, exactly this state of
affairs pertains, although not designed for. After the initial
excitation there is a decrement in the excitation curve due to the
falling off of the on-element's firing, except at the edges of the line.
This conforms with the assumption we made in discussing scan-
ning, when we said that the points of maxima died away on being
reached, leaving another maximum for the eye to move on to.
The eye, being fixated by central control alone, still shows limited
movement, and the excitation for the equivalent part of the visual
PERCEPTION 353
cortex must fall below that of the surrounding retinal elements;
cortical representation and the figural after effects could be
accounted for exactly as in the Osgood and Heyer model. The
reason for the fall of excitation with fixation could most easily be
accounted for by saying that at the central retinal point the off-
elements are in excess of the on-elements, and when the on-off
fall below a critical level, the state of excitation becomes less at this
focal point than in the surrounding areas. This could also be
accounted for in a variety of other ways, one of which is mentioned
below.
It need hardly be said that this is by no means the only way in
which the scanning operation can be made effective, and the
biological plausibility of the explanation should now be seriously
considered. The off-effect has been regarded by Granit (1947) as a
release from inhibition, which suggests that the off-elements are
elements that fire in the resting state and therefore, with an area that
is stimulated, the off-fibres might be regarded as being inhibited.
This problem of the diminution of excitation with a fixated eye
accounts, on the Marshall-Talbot hypothesis, for figural after
effects, and requires further consideration. It is something that
seems to be quite necessary to an explanation of the functioning of
the eye, and perhaps represents the same physiological fact that is
called 'fatigue*. This could, of course, be accounted for by con-
sidering a decrement in the on-elements, where more and more of
the cells cease to fire with increasing stimulation. A logical net
can easily be drawn to represent this state of affairs.
The points so far mentioned also link up with evidence on the
formation of contours in the visual system. The Werner effect is
shown in a simple experiment where a black disk is presented on a
white background, quickly followed by a black ring whose inner
radius is exactly the same as the radius of the disk. This causes loss
of ability to see the disk if the ring is presented sufficiently quickly
after the disk. The Werner effect is thought to obtain because the
contour of the disk is not formed before the same contour is used
in the ring, and so the black disk is suppressed altogether. This fact
is certainly one that would occur in our model, provided it is
arranged that the horizontal cells of the retina are functionally
interdependent in their connexions with the on-off elements on the
periphery of a figure, and this again can easily be arranged.
354 THE BRAIN AS A COMPUTER
The degree of stimulation, of course, can be achieved by fre-
quency of firing, as well as by the number of elements that fire, and
both will be expected to occur in our model.
In this same connexion one might seek to explain the a-
rhythm by appeal to the synchronous firing of the off-elements, or
at least some of them. We should here seek to relate the character-
istic waves with the observed frequency and amplitude of the cells
themselves. In much the same way we would try to replace the
coded elements suggested in Fig. 3 for colour vision by codings
that represent a direct function of the frequency and amplitude of
the primary colour waves.
In a similar way we may expect to find an explanation of contrast
effect. With two adjacent black and white patches there will be a
maximum difference in excitation, since in any case all the on-
elements will fire, and immediately next to this will be an area with
a minimum number (zero) of on-elements firing. The change here
from a maximum to a minimum will thus be maximal. This effect
could clearly operate in the same way for complementary colours,
and it should be possible to work out a code that shows precisely
the necessary relations between neighbouring areas to achieve this
end. The contrast effect will be further emphasized by the hori-
zontal cells which fire elements in the surrounding black areas, and
not at all in the white areas, as we have already suggested above.
So much for the present outline of Cybernetics and perception;
some more general suggestions will be made about these matters in
the next chapter.
Summary
This chapter has tried to give a brief integrated account of
perception, taking into the account the physiological and philo-
sophical evidence, as well as the experimental psychological evid-
ence.
There is some repetition of our earlier discussion, in Chapter V,
of the methods of classification and of the perceptual models based
on classification.
Uttley, Deutsch, Selfridge, Culbertson, Rapoport, McCulloch,
Pitts, and others, have formulated models for perception which we
have briefly considered, and a new model is suggested that incor-
PERCEPTION 355
porates some of the characteristics of these other models, as well as
the model of the visual system due to Osgood and Heyer.
A little general discussion has also taken place with respect to
the well-known psychological evidence on perception. The
evidence we take to be well-known includes constancy, after-
effects and after-images, perception of space and, of course, the
perception of forms which is so essential to recognition. It is to
be remembered that, while it is truly necessary to show how
recognition can occur under conditions of minimal cues, it can
also, and does normally, occur under conditions permitting of a
vast redundancy of information from many different sensory
sources.
This chapter is directly continued in the next one, which con-
tinues to deal with the perceptual problem.
CHAPTER XI
PERCEPTION AND THE REST OF
THE COGNITIVE FACULTIES
THIS may be an appropriate moment to summarize some of the
advantages and benefits that cybernetics has to offer in the analysis
of perceptual and cognitive problems.
In the first place we are, of course, to understand 'cybernetics'
as implying effective methods, and not merely as the construction
of hardware models or the programming of computers. This means
that much of experimental psychology is already included in the
field of cybernetics. In a narrower view, however, we may expect
to find value coming from the simulation of all aspects of the ner-
vous system and human behaviour.
In particular, we need more computer programmes to illustrate
learning, which is crucially connected with the organization of the
storage system, and this eventually includes recognition, recall,
and every aspect of cognition including perception.
The primary problem for the future of cognition, and one which
has been much neglected so far, is that of language; and language
is also capable of analysis by computer methods.
At the same time as we need to simulate by digital and analogue
computers, we also need to build models of different parts of the
nervous system. These models may be at various levels of general-
ity; some need to simulate its electrical activity, some its chemical
activity, some the relations between neurons, and so on. While we
can hope to simulate much of the structure and organization of
human behaviour, we also need to do the same thing for other
organisms. We also need to build models that modify their own
structure, or grow and change, as well as the models that are pre-
wired and only change functionally.
Finally, we need to build our models of every kind of fabric,
from electronic and other physical systems to chemical and
chemical-colloidal ones.
356
PERCEPTION AND REST OF COGNITIVE FACULTIES 357
This is the search, and it carries a promise of which experi-
mental psychologists have only recently become aware.
We shall now return to a reconsideration of some of the problems
of perception and cognition, with an eye to making the conceptual
models, so far discussed, more nearly meet the experimental facts
of human behaviour.
Perceptual models
The particular outline of perceptual models and the eventual
set of suggestions made in the last chapter, suffer from many
doubts and possible defects. Two of the most prominent ones
surround the question of eye movements, and the necessity for a
scanning operation as a preliminary to recognition.
Let us first consider the problem of eye movements. Work by
Riggs, Ratliff, Cornsweet and Cornsweet (1953) lends credence to
the claim that figural after-effects of various kinds do not depend
upon eye movements and this was suggested as a result of using
contact lenses, which allowed the figures perceived to move with
the movements of the eyes.
While it is not certain that by such means all relative eye move-
ment is eliminated, it is certainly minimized. Bearing in mind
Deutsch's (1956) objection to the Osgood-Heyer model for figural
after-effects, we might feel that the attempts to model either these
or other related perceptual phenomena are on the wrong track.
Deutsch's argument is simply that eye movements are not
essential to the figural after-effect, and that the Osgood Heyer
model depends on an interaction of the normally distributed
excitations in the visual cortex. But, he argues, if such excitations
can summate over such a wide visual angle, how are two lines
normally discriminated, as they are known to be, in terms of a
much narrower retinal angle?
The problems so posed can be 'solved* or 'resolved' in a number
of ways, none of which is immediately and completely testable.
In the first place, if eye movements are not necessary to these after
effects, then the distribution of excitation of a single stimulus line
(double contour line) will tend to be very narrow indeed, and thus,
apparently, greatly reducing this possibility of summatory effects.
Indeed, we know that no effect will occur unless a further condition
358 THE BRAIN AS A COMPUTER
is introduced, namely, that the inspection figure must be mapped
on to the retina for some period of not less than one minute, and
preferably two minutes. The implication is that the spread of
excitation which is necessary to the summatory effect is derived
only under conditions of steady stimulation. George (to be pub-
lished) has carried out an experiment which is aimed at settling
this point, and the results are, to say the least, encouraging. By
taking two vertical lines at varying distances apart, and at varying
distances from a fixation point, it was found that, after steady
fixation for one minute, the ability to discriminate between the two
lines had entirely vanished; at least, many subjects significantly
many subjects claimed that this was so. This appears to justify
the argument that, with spread of excitation under 'fatiguing*
conditions, summation will occur and discrimination will be lost.
There are other theoretical suggestions that could be made to
overcome the Deutsch objection, but in view of the apparent
success of the first tentative suggestion, the matter need be
pursued no farther. The only weak link in the logical chain is that,
under the ordinary conditions of figural after-effect, eye move-
ments certainly do occur, and the spread of excitation that seems
to occur with fatigue has not been shown to occur independently of
eye movement. This will not greatly concern us now, though, since
the occurrence of a summatory spread of effect certainly seems to
take place normally, and it is rather too much to ask us to believe
that it will not also occur in the eye when all movement is elim-
inated if figural after-effects still occur. The doubt is as to whether
all eye movements are really eliminated, or whether the spread of
effect occurs anyway. The two points are by no means mutually
exclusive, but the second seems to be true in any case.
Now let us look for a moment at the scanning operation of the
eye. This is one way in which similar figures in different retinal
locations could be brought into positions of comparison. If this is
to be ruled out by elimination of eye movements or scanning
movements, even during learning, then we will have to use some
other indicator of retinal position, such as one conveyed by tem-
poral coding (Deutsch, 1955; Dodwell, 1957). There are some
difficulties with this idea as we have already remarked, and the
Culbertson model achieves its coding by having the equivalent of
retinal scanning more centrally placed. It seems that either way
PERCEPTION AND REST OF COGNITIVE FACULTIES 359
could be effective, and further evidence (not yet published), casts
further doubt on the idea of scanning that we have suggested, and
that was previously suggested by Hebb (1949).
This might be said to be one major point which can only be
settled by further experiment, since there is plenty of evidence
that, from the purely conceptual point of view, any of these
models might suffice. An alternative that, as far as the writer is
aware, has not been taken very far, is that the retina, as a classifying
system, might simply represent the relations between sets of
points, so that the stores may indeed receive subsets that have no
element in common, and yet use the same word such as 'triangle'
or 'circle* to describe them, because they bear certain char-
acteristic and similar relations to each other.
The principle suggested is exactly that by which we represent
different families of curves in Cartesian coordinates, so that any-
thing of the form ax+by+c = represents a straight line, three
such lines represent a triangle, a form such as xP+y* = a 2 would
represent a circle, and so on.
It is not being suggested that the nervous system converts
geometrical patterns into sequential patterns exactly in the
Cartesian, or even the projective manner; but some such a principle
would overcome the need for postulating scanning eye movements
as necessary to recognition during the learning period.
It is not intended that this matter should be pursued further
here, for this would need exploratory construction of new models,
combined with new research on the physiology of the visual
system, while this book is endeavouring only to summarize what
has been done to date.
As far as this particular problem is concerned, we cannot rule
out the more central theories which might account for the effects
to which we refer as 'movement after-effects' and 'figural after-
effects'. As an instance, there is something to be said for regarding
the set to move the eyes which indeed might not actually need
the eye movement itself, although generally it would be accom-
panied by it as setting up a central storage state such that, when
the movement is stopped, the actual physical stimuli will make
relative movements in the opposite direction. To put the matter
crudely, this means that if the movement was to the left, the lines
will be discovered persistently to the right of the anticipated
360 THE BRAIN AS A COMPUTER
position. Wohlgemuth (1911) has demonstrated many of the
properties of the movement after-effects, but little has been
suggested by way of explanation. One approach may be to try to
develop the Osgood Heyer theory, and we shall do this shortly.
Another way is to assume that the Osgood Heyer effects are
negligible, and that the matter should be centrally explained.
This last question naturally suggests that we should look at figural
after-effects from the same point of view. Could figural after-
effects be explained more plausibly in a central manner? Although
we cannot discuss the matter in detail here, it is essential that
we look again at the basic process by which contours are formed
in the visual cortex. The results of Werner (1940) and Fry and
Bartley (1935) make it clear that there is an intimate relation
between contour formation and perception of brightness of
surfaces. It is also known from the work of the Transactionalists
that brightness and size are interdependent, and there is the
possibility that the figural after-effects represent the work of
central interpretation, where a figure becomes distorted as a result
of the subject seeing the test and inspection figures together as a
meaningful whole, even though they do not overlap.
One piece of evidence that bears on this last suggestion seems to
imply the opposite (George, 19S3c), for when the test and inspection
figures were actually superimposed for a particular case, the result
was the opposite to what our suggestions above would lead one to
expect. However, this case is not really a parallel, since we are not
suggesting that they should appear as one pattern, but rather that
the effect of the inspection figure is to present a certain space, and
that when the test figure is presented, the test figure 'is distorted
accordingly.
A real possibility is that when an inspection ^figure ^f two
unequal circles, say, on either side of a fixation point is seen, they
are seen as three-dimensional, and therefore the one which is
smaller distorts the spatial framework (as centrally interpreted)
and this would naturally result in the equal squares, say, of the
test-figure being seen as unequal. The difficulty, here, is that this
same figural after-effect can be derived with other figures that do
not readily lend themselves to interpretation in three-dimensional
terms.
A more sinister thought of course is that it is both the Osgood-
PERCEPTION AND REST OF COGNITIVE FACULTIES 361
Heyer effect and the interpretative effect occurring together that
causes the many after-effects. But we shall not pursue that
possibility any further at present.
Perception of movement, as we know from work on actual and
apparent movement, depends upon sequential contour formation,
but the fact that apparent movement occurs reminds us that the
actual discrimination between contours is a function of successive
stimulation.
D
FIG. 1 . FIGURAL AFTER-EFFECT. If the eye fixates the dot half way
between the two squares at a distance of about eighteen inches
and then after about 30 seconds is transferred to the dot immedi-
ately below, the left-hand circle can be seen to be smaller
than the right.
When we have solved the problem of visual perception to the
extent of providing a model of discrimination of brightness,
constancy, etc., we can tackle the problems presented by clinical
psychologists (Zangwill, et aL). In the meantime their findings
such as that destruction of parts of the optic radiations seem to
destroy constancy, perhaps by way of brightness discrimination,
which was also destroyed are valuable as contributing to our
present model, and a reminder that all these things are closely
interdependent.
362 THE BRAIN AS A COMPUTER
Movement after-effects
Let us now explicitly address ourselves to the problem of move-
ment after-effects. The problem is as to whether the Osgood-
Heyer model is sufficient to account for these effects as well as for
the figural after-effects. It should be noticed that Osgood himself
(1953) has applied the model to the case of apparent movement.
He suggested that two contour lines interact when their peaks are
mutually shifted. Indeed, the same sort of explanation could be
used to explain movement itself, although presumably it would
only be necessary to do so in the case of the fixated eye. Either way,
the idea is that the two excitation distributions interact in such a
way as to produce a single moving peak in apparent movement,
while in actual movement the peak is already an integrated one
FIG. 2. THE PLATEAU SPIRAL. This figure has been used to
produce movement after-effects in the eye (see text).
from a single source, or if a series of lines, from a series of sources.
In the case of apparent movement, the problem of the Osgood-
Heyer model is again simply to explain how summation takes
place here, and not when two lines are discriminated. The answer
in the fixed case of the figural after-effect seems to be, as we have
already said, that during the fatiguing operation, which is taking
place while the inspection figure is exposed, a broad distribution of
reduced excitation occurs and the question now arises as to whether
this changes our interpretation of the moving line case.
We can put the matter to a similar test. We know that if a series
PERCEPTION AND REST OF COGNITIVE FACULTIES 363
of lines moves sufficiently quickly across the retina, or rotates
quickly enough as, for example, the blades of a fan, then the lines
or blades are not separately seen, but an impression of continuity
is created. This could be interpreted as the failure to achieve any
separate distributions at all, and confirmation that summation is
taking place.
But if the lines are moved slowly enough they can be seen
individually, which shows, on the theory, that summation is not
taking place. So far, so good, but we must now try to account for
the after-effect. The lines stop, and an impression of movement in
the opposite direction occurs. Fatiguing must certainly occur in
the retina, since the movement after-effects only occur after a
period of inspection, and prior to stopping the movement to derive
the effect. If, then, our supposition about the broad spread of
fatiguing is correct, we should expect that when the lines are
stationary after the inspection period, they set up an excitation
that interacts with the fatiguing excitation and creates, at the least,
a shift in the opposite direction. This shift in the opposite direction
will be maintained in the same way as the figural after-effect, and
thus create an apparent movement of much the same kind as
Osgood suggests for ordinary apparent movement.
It must be mentioned here that there is a difficulty over such
effects as the Plateau spiral, which creates movement after-effects
in roughly radial directions away from the centre of the spiral. If,
as Osgood and Heyer assume, the excitation distribution depends
on eye movements, one is faced with the somewhat perplexing
thought that the eye must move in all directions at once. The
answer to this can take one of two obvious forms: either eye
movements are unnecessary, and a spread of excitation with peak-
ing does not depend upon eye movement, or the spiral effect is
derived by sampling the visual environment and generalizing
from this sample. This last explanation might be worked into
something plausible, but it seems much more likely that eye
movements, although they may contribute to the effect, are in
practice unnecessary to it, and that the movement after-effect
needs only the interacting spreads of excitation. The theory
proposed requires that the discrimination between two adjacent
lines is greatly reduced again as fatigue sets in during the inspec-
tion period, and this seems very likely to be true.
364 THE BRAIN AS A COMPUTER
One problem that now arises is an effect that occurs when a
wheel with, say, four spokes is rotated fairly rapidly. The effect is
that the number of spokes is greatly increased phenomenally.
The explanation of this problem probably lies in the fact that in
such circumstances there is no way of identifying the individual
spokes, which are forming contours at a rate below the level of
summation, and at a rate that makes it impossible for the eye to
do any sort of count. The effect should be reduced with fatiguing
of the eye after lengthy fixation of the centre of the rotating wheel.
The method, on the theory here proposed, is to start with a slow
rate at which each spoke is visible, and increase the speed through
the successive stages of multiplying (and perhaps finally decreasing
again) and then integrating. A set of experiments is being carried
out at the time of writing to discover some more of the facts
(George and Stewart, to be published).
No more will be said here about these models of the visual
system. It is hoped that when further experiments have been
carried out it will be possible to give a more integrated account of
the perceptual activities. The model in hardware mentioned in the
previous chapter will be used to try to build up every aspect of
perceptual theory: contrast, movement (apparent and real) and
so on; but of course there will be some difficulties in showing that
the method used in the hardware model will give the same result as
that used in the human eye. It will be noticed, again, that our
technique has marked behaviouristic implications.
Other perceptual models
. We have so far discussed only general models based on classi-
fication, and some specific analysing mechanisms such as that of
Osgood and Heyer. There are, of course, many more of both of
these types of model that we shall meet and have to examine, and
here we must at least make mention of the Perceptron (Rosenblatt,
1958, 1959), the Pandemonium (Selfridge, 1959), and some of the
models that have been constructed to deal with problems such as
speech perception (Fry and Denes, 1959; Ladefoged, 1959).
These are all efforts, mostly similar to those we have analysed, to
meet the problem of modelling perceptual systems, and therefore
of the greatest interest from the cybernetic viewpoint.
PERCEPTION AND REST OF COGNITIVE FACULTIES 365
The rest of cognition
We have said quite a lot about cognitive problems, with rather
particular attention to perception and learning, but so far we have
scarcely considered the problem of thinking as such, and the nature
of cognitive terms such as 'thinking', 'problem solving', and so on.
Cybernetics apart, the last few years have seen a great deal of
progress in the process of trying to construct models of cognitive
processes, and it might be said that cybernetics has merely lent
further emphasis to this particular development.
Most people have tended to accept the Reichenbach dictum
that the context of discovery and the context of justification are
quite different from each other. We have taken this to imply a
very pronounced difference between the manner in which humans
actually think by taking big jumps, making guesses, etc. and
the manner in which they subsequently justify their intuitions.
We should notice that while learning theorists have themselves
paid scant attention to thinking, most experiments on thinking
have been built up around human subjects. But from the behaviour-
istic point of view, thinking is something that we infer from
performance, in the same way as we infer learning from per-
formance, and we should perhaps ask about the differences
between learning and thinking and even, for that matter, problem
solving, which often seems to merit a separate chapter in books on
psychology. Again from the behaviouristic point of view, we shall
want to say that thinking must apply not only to what we are
conscious of doing, it must also include processes of which we are
unaware. This means that a solution to a problem, whether arrived
at during waking or sleeping, could be said to be the result of
thinking; and since we would also want to say that learning, almost
always if not always involves solving a problem, it can be
seen that all these apparently different questions could be col-
lapsed into one.
The Reichenbach distinction, namely (as already mentioned)
that the context of discovery is wholly distinct from the context of
justification, is only obviously true when we refer to thinking as a
process of which we are consciously aware, and we cannot say that
actual internal changes which proceed towards a solution are
anything like so haphazard as the scraps of information we have
about our own thinking processes. Bartiett (1958) has pointed out
366 THE BRAIN AS A COMPUTER
that, in the series of experiments he conducted on human beings,
there were fairly systematic changes going on, usually moving to-
wards a solution. Of course the problem may not be solved, but
we should not want to say on that account that thinking had not
taken place. Just as solutions to situations may not be learned, so
thinking, or some internal changes, will go on whether or not they
lead to learning, or solve particular problems. This is perhaps the
nucleus of a distinction between the various terms.
There have been many studies of thinking (Humphrey, 1951;
Bartlett, 1958; Bruner, Goodnow and Austin, 1956) and they have
all dwelt on the human being, and on the layout of input informa-
tion and its importance for the results of problem solving; this, of
course, was well known to be a source of Gestalt theory (Kohler,
1925).
It is a question as to whether we should think of thinking as
being unified or not, and it is a semantic question, typical of the
kind we feel cybernetics can help us to solve. In the first place, as
with perception and learning, it was impossible to establish exactly
where thinking started and where it finished; indeed, it has seemed
to be a matter of convention. Certainly it is clear that there are
many different facets to the internal organization of any system
that solves problems, since there are different sorts of problems to
solve. Some demand a relationship between inputs alone, others
between inputs and outputs ; some occur in a closed situation, and
are mathematical or deductive in part of their form, others require
what Bartlett calls 'adventurous thinking' and are more obviously
inductive in form, although the differences in the examples he
gives are more in terms of the type of problem than in the differ-
ences of suggested solutions. The way information has to be put
together to form a solution is at least different on the surface in
various problem situations, though the differences may be more
apparent than real.
Bartlett's definition of thinking is, 'the extension of evidence in
accord with that evidence, so as to fill up gaps in the evidence; and
this is done by moving through a succession of interconnected steps,
which may be stated at the time or left until later to be stated*.
This seems curious at first sight, and Bartlett himself recognizes
that it may be a special case; in fact it is a statement which brings
out fairly clearly the inductive nature of thinking. His suggestion
PERCEPTION AND REST OF COGNITIVE FACULTIES 367
that thinking is a high-level form of skilled behaviour is most
acceptable from the cybernetic viewpoint.
Humphrey (1951) defines thinking, as 'what occurs in experience
when an organism, human or animal, meets, recognizes, and solves
a problem'. He also points out that the term 'reasoning* may be
preferred, and he further admits that there is no hard and fast
distinction between learning and thinking. All this is in agreement
with our argument.
Bruner et al (1956) impinge upon another aspect of thinking
when they talk of categorizing activity and its relation to the mak-
ing of inferences and to the general field of cognition. Concept
formation, or 'concept attainment' as they call it, is discussed at
some length, and they are also interested in 'selective strategy',
which is concerned with the order in which hypotheses (or beliefs)
are tested.
George (1960a) has suggested a simple model for an inference
making system in terms of logical nets. It is based precisely on the
discussion of finite automata, and therefore involves classification
of temporal sequences of events, and the association of such events
(or event names) whereby new consequences may be derived by
'conceptual' activity alone.
At this stage the subject of language obviously needs some
further discussion. Language is certainly used by human beings
in their problem solving activities, but whether it should be said
that all thinking either depended directly on language, or was
carried out entirely in language, it would be more difficult to decide.
Judging from our computer work in Chapter VI, it looks as if the
natural and easy way to solve problems is by making, and applying,
generalizations derived from some previous circumstances. The
learning, of course, goes deeper than this, because the use of signs
and symbols has itself to be learned, and after that, further learning
may take place within the language so learned. It is conceivable
that organisms could think in other than symbols, since the word
'thinking' could be used simply for a type of awareness and associa-
tion, accompanied perhaps by images, without the occurrence of
language ; but whether this is so is quite a different problem.
We should perhaps mention that attempts to understand con-
sciousness from a behaviouristic point of view and therefore
from a cybernetic point of view are not likely to provide more
368 THE BRAIN AS A COMPUTER
than a rough, heuristic idea of what constitutes consciousness,
because this throws us right into the problem called by philo-
sophers 'Other Minds'. We cannot know what it is to be another
person, and still less what it is to be a machine. Naturally we
experience great difficulty in imagining a machine having con-
sciousness in the human sense, and perhaps the only kind of
constructed system that could be thought to have the same sort
of consciousness as ourselves is one that is constructed from the
same chemical colloidal materials as is the human being. This has
really little to do with cybernetics as such, but it is perhaps worth
saying here if only to remind us of our behaviouristic commitment.
By the same token, thinking can really only be meaningful in the
cybernetic situation when considered as the method by which the
automaton proceeds to try and solve problems, learn about the
environment, or perhaps freely associate with respect to some
stimulus. This point is of some importance. A human being will
often say, 'Let me think' ; and if he thinks aloud he may say some-
thing like, 'I had it on Tuesday ... Tuesday I was in London ...
then I came back on the train ... I had it on the train, so I must have
lost it when I got back ... Now what did I do? ... I went to the
garage . . . ' This sort of operation, which seems very common in
human beings, appears to be a restimulation of the memory store.
It might be described as a chain of stimuli and responses that are
elicited by the organism, although they are to some extent tied to
the environment. Work on sensory deprivation (Bexton, Heron
and Scott, 1954, and others) has shown fairly clearly that this sort
of organized self-stimulation cannot be carried on indefinitely
when the subject is deprived of sensory stimulation. In any case,
it could be said to be an act of memorizing rather than of thinking,
which only helps to remind us of the semantic confusion that is
liable to cloud the whole subject.
In the case of a finite automaton, we could easily arrange for it to
run through its store, taking item after item in some definite order
according to its method of storage, and then draw logical inferences
as they are needed to some specific end, i.e. to solve some specific
problem, for example ( to discover the place where I lost my
fountain pen'. We should expect to find the memory store organ-
ized on the basis of recency, frequency and value, at the very least,
and thus some information would be available and some not.
PERCEPTION AND REST OF COGNITIVE FACULTIES 369
It is tempting to say that a finite automaton which could perform
deduction and induction (by induction we shall mean: able to make
generalizations of an empirical kind on the basis of probabilities)
can easily assess the credibility of statements as a function of their
objective probabilities, coupled with the weighting that certainly
seems to occur because of the emotional and motivational systems.
Indeed, these systems do seem to have the effect of weighting
events in terms of desires and prejudices and so on, which could be
characteristics of the counting and other mechanisms that vary
with different individual systems, no doubt as a result of their
experience, and of whatever built-in characteristics they have.
Here we see the relevance of the decision procedures of the theory
of games ; games will be learned by different people, perhaps often
through accidental factors, and certainly as a result of environ-
mental considerations.
The task of constructing a programme on a computer which will
show the variety demanded in mimicking a human being is cer-
tainly a colossal one, and the sheer magnitude of the system might
well be considered somewhat daunting. In the meantime, a
manner of approach has been adopted which involves showing
particular functions, building greatly extended memory storage
systems, and making use of autocoding devices, especially of the
compiler kind (Minsky, 1959; Backus, 1959).
In the language developed in Chapter V as a preliminary to
applying programme techniques and building finite automata, it
would be suitable to describe thinking simply as the utilization of
beliefs in any situation whatever. Especially would this apply to
the manipulation of existing beliefs to make deductions and induc-
tionswhich means to form new beliefs and the processes
involving regurgitation of beliefs when suitably stimulated. This
is all part of the activity of what we have called the C-system.
We have postulated that this must itself depend on the motivational
system, or M-system; but this is really a statement that is analytic
rather than one capable of being tested.
It is not for a moment felt that this brief section on thinking does
justice in any way to the vast ramifications of human thought;
what it might do is to shed some light on the relatively unified
nature that thinking takes.
Another cognitive word in frequent use is 'imagination'. The
370 THE BRAIN AS A COMPUTER
basis of this might be sought in the recombination of previously
existing items in the storage system. It is well known that it is
impossible to give any knowledge by way of explanation to another
person by any means other than by appeals to concepts already
familiar to that other person, which suggests that thinking is very
much tied to previous experience. Whether the imagination takes
the form of referring to events that have happened but have not
actually been witnessed, or whether to events that have never
happened, the function of the automaton will be the same. It must
selectively recreate an event name of some length which is taken to
represent the event itself.
This statement is, again, quite inadequate to account for all the
ramifications that occur under the names of 'imagination', 'creative
thinking', etc., indeed it makes no such attempt, but it says enough
perhaps to show how such problems may be quite easily fitted into
the scheme of the finite automaton.
The fact of being able to stimulate the sensory storage systems
directly, i.e. other than by actual external stimulation, offers an
obvious approach to the problem of imagery, since by this means
some shadowy picture of the original scene is given to the auto-
maton. The idea is, of course, obvious enough, and it is mentioned
only for the sake of some attempt at completeness.
It seems to the writer that the big problem that cybernetics has
to solve in the future is that of language. It ought to be possible
to teach an automaton a complex language this can quite easily
be done for a computer with a simple language and the auto-
maton could then be shown, under a variety of different condi-
tions, to recreate the development of, say, the English language, in
a manner to which we have already drawn attention. This is a
huge undertaking, but it is one in which it should be possible to
show that it would be natural to separate events in the environ-
ment (nouns) and their properties (adjectives) and the computer's
own outputs (verbs).
Eventually a linguistic system could be reconstructed which
would be extremely helpful in confirming the correctness or
otherwise of our conceptual systems, since quite a lot is known of
the quantitative side of linguistics (Osgood, 1953), and this must
certainly link up with the other cognitive knowledge we have, as
well as with our philosophical knowledge.
PERCEPTION AND REST OF COGNITIVE FACULTIES 371
One of the principal features that we have to acknowledge is that
the names we have come to give to cognition operations by no
means lie in a one-one correspondence with different structures or
mechanisms. As a result, one may construct a model and then
interpret the model from different points of view with respect to
our cognitive terms.
'Perceptual learning* (Drever, 1960) is a term increasingly used
in the literature of cognition, and this, like 'discrimination learn-
ing', really lays emphasis on the fact that some learning is much
more immediately tied to perceptual activities than other learning.
This should not in any way make us think of such perceptual
learning as a new process; rather it is a familiar process which is to
some extent distinctive, because it tends to one end of a continuum
of learning (and perceptual activities), for we knew from the start
that learning and perception were not wholly separable.
Summary
This chapter has directly continued the discussion of perception
started in the previous chapter, although it has concentrated
attention mainly upon the Osgood and Heyer model for the visual
system. It seems likely that this sort of model, with modifications
to be expected as it becomes more frequently tested under new
conditions, would be appropriate for the visual system, and that it
should be directly attached to a classification system which may be
expected to operate in stages, eventually integrating sensory in-
formation with information from the other sensory sources.
This summary of perception is followed by a very brief descrip-
tion of some of the other principal features of cognition. Language
is necessarily mentioned, as are the obvious cognitive terms such as
'thinking', 'problem-solving', 'imagination', and so on.
It is suggested that, with the integration of perception with
learning, the main cognitive problems are solved; but as far as
human behavour is concerned it is language that has failed to
receive, so far, sufficient attention from experimental psychologists.
It might even be claimed in a general way that we now under-
stand the type of physiological processes that are necessary to
cognition; but even if this were true and it might be thought to
be just plausible the amount of detail that we still have to work
out is tremendous.
CHAPTER XII
SUMMARY
IN this chapter we shall attempt to summarize briefly all that has
been considered and discussed in the book as a whole.
Cybernetics is the science of control and communication, and
cybernetics can be used as a method to analyse the facts of human
behaviour; but it is only one such method of analysis, and it must
take its place alongside animal work, ethological and comparative,
as well as experimental work on humans, and physiological studies
of animals and humans.
Cybernetics represents the application of an old idea, the idea
that human beings and animals are essentially very complicated
machines. It asserts that they are deterministic systems which
could be constructed (or reconstructed) in the laboratory, but
whether or not this is actually true is not of the first importance,
since the statement is only making explicit what is implicit in the
behaviouristic approach to psychology and the mechanistic
approach to biology in general. To take this assertion beyond the
level of the trivial would necessitate an examination of what is
meant by 'behaviouristic' and 'mechanistic*.
Cybernetics as a science of behaviour emerges mainly from three
considerations :
(1) The development of servosystems and computers that are
far more like human beings than any machines made previously.
(2) The need for developing a degree of precision in the models
and theories used in any science, particularly the biological sciences
of which an essential part is experimental psychology.
(3) This may be regarded as a corollary of (2), in that it lays
emphasis on the need for mathematical descriptions. It may be
confidently argued that any science develops quickly if it can be
made mathematical, and we should therefore try to introduce
mathematics into biology.
372
SUMMARY 373
The usefulness of computers and servosystems is very great
indeed, particularly because it allows us to build models with
them, and like them, by other methods such as paper and pencil
methods.
Computers, as we have seen, can be programmed to learn and
also to perceive, and it seems reasonable to say that they can also
be programmed to think, since thinking and learning are not, in
the last analysis, of great difference.
The problem, as seen from the point of view of computer pro-
gramming, was how to organize the storage system and how to
programme for the process of generalization which is so essential
to learning in computers, as of course it is in human beings. This
is by no means easy to do with a computer, for the simple reason
that most contemporary computers have small storage systems. It
is difficult for the computer to learn the first processes when start-
ing from no information at all, but the subsequent stages become
progressively easier because the computer is applying established
generalizations from one situation to another, rather than working
in terms of the one situation alone.
The computer programming technique allows us to check
theories of learning and their effectiveness, as well as offering a
means of studying new learning techniques, and appreciation of
this brings to life the sort of methodological experiment called the
'mathematico-deductive theory of rote learning', which was under-
taken by Hull and his associates (1940). This might well turn out
to be a prototype of many such experiments in the future, since a
computer can be programmed to handle with great celerity a
situation which for the human being would involve an intolerably
lengthy and tiresome process, and one which might possibly
result in a value by no means commensurate with the effort made
to attain it.
Computer programming is likely to be followed up systematic-
ally in the future, and for this method to become a standard part of
psychology, it is essential that a computer language should be
developed like FORTRAN, the special compiler language con-
structed by IBM for automatic programming, for example
which will allow us to state our programme in simple everyday
terms, and let the computer itself put it into computer form and
test its efficacy.
374 THE BRAIN AS A COMPUTER
Such work as has been done on computer programming and
learning might be taken to suggest that existing theories of learn-
ing, such as those of Guthrie, Hull, Tolman, Olds and others, do
not differ as much from each other as was once supposed, and that
in many cases differences between them are more at the level of
interpretation than in the precise process depicted. But there are
also some actual differences, and these suggest that different
theories have emphasized some and neglected other important
features in the learning process. This indicates the need for some
measure of integration of existing theories of learning, and indeed
much the same argument is true for perception and the other
features of cognition; but this book has not been primarily con-
cerned with carrying out that integration, mainly because the
author has attempted to do just this in another book which will
be appearing shortly.
The vital part played by language in human learning is a matter
that has not received very detailed attention by psychologists, and
this is perhaps strange in view of the amount of work that has been
done by philosophers and logicians in this domain. We have at any
rate tried to indicate the trend in linguistic matters, especially in
the context of computer programming, where its importance is
revealed fairly clearly.
Learning, thinking, perceiving and so on, are obviously in-
fluenced by language. Language may be learned, words perceived,
and linguistic information stored, just like any other associative
process of the kind we have discussed; but the important feature of
language is that, once it has been learned sufficiently, concepts and
generalizations if indeed they are different can be conveyed
linguistically rather than through direct experience.
This suggests that an analysis of language should be possible in
behaviouristic terms, with the aid of programming and other
cybernetic techniques, to show how language has evolved and how
big a part it has played in human learning. Quite obviously, with-
out language the accumulation of human learning would have been
an impossibility, and it seems likely that the high-speed change of
strategies high-speed learning of which humans are capable,
is due primarily to language.
This is not to say that generalizations and other concept-forming
principles would be impossible without language, but it seems
SUMMARY 375
certain that they are more effective with language, for and
what is more important a species which has symbolic skill
will inevitably use it, and it thus plays a vital part in human
behaviour.
In the computer itself it is important to distinguish the binary
code language of the internal representation of events, from the
development of a language which may also be in binary code in
the computer wherein one computer word signifies another,
or a collection of other, computer words.
There are various other ways by which we could go about
constructing precise models, and of course finite automata are the
ones favoured in this book. Information theoretic models are also of
great interest, and have been emphasized by Broadbent. The great
advantage of either conceptual system lies in its precision and
relative ease of analysis, so that logical mistakes and vagueness can
be easily detected.
No attempt has been made in this book to follow up work on
information theoretic models, but they can quite obviously be
conveniently fitted together with automata theory. The work of
Hick (1952), Grossman (1953, 1955) and Broadbent (1958) should
be consulted for developments along these lines.
The models so far referred to are all pre-wired in a sense, and
certainly this is true of computers and logical nets, but it is
important to realize that they are not fixed in their behaviour on
that account, since the programming and the input tape create
variation in behaviour of much the same kind as we might expect
from human beings.
Hardware models of finite automata are also generally pre-
wired, and we may expect that models will also be made in abund-
ance in the future which will have the properties of growth, not
only because we want to study development in the human being as
well as the developed human, but also because the growth process
must itself partly determine the nature of the grown product, a
product which is indeed never quite fixed. Although growth
models of the kind suggested by Pask, Beer, Chapman and others,
will certainly be carefully examined in the near future, as will the
chemical forms of finite automata, for the present the logical net or
tape type of finite automaton is perfectly adequate for the analysis
of existing models and theories, and can in fact be shown to be
376 THE BRAIN AS A COMPUTER
capable of representing the same set of events as could a growth
system.
There is little doubt, either, that these same methods will soon
be extensively employed in the field of applied psychology.
Already much work has been done in social and in abnormal
psychology to prepare the way for it, and no doubt the same is true
for all the relevant fields.
Apart from their practical utility, there is a deeper principle
involved in this sort of model making activity; it is that the mere
collection of empirical data does not make a science. Empirical
data, taken from observation of the world, are most certainly the
vital food on which the whole edifice of science is built, but are not
built by collection and restatement alone; they must be interpreted
and integrated into a form, usually linguistic, from which certain
logical consequences can be derived. This means that methods by
which scientific theories are constructed are of the first importance,
and this is increasingly the case as our precision in theory construc-
tion advances.
It has sometimes been said that theorizing in psychology is
premature, but in fact there are very few cases in which this
applies. After all it is not a matter of either theorizing or experi-
menting, for both go together.
Comprehension of this last fact has been slow, largely because
so much of the early theorizing seemed to be no more than empty
speculation; and indeed some theorizing has gone on in a manner
that is too remote from the facts. Many of us feel that philosophers
might help themselves to solve at least some of their own problems
if they would add empirical evidence derived from experiment to
their own armchair speculations. As for the remainder of philo-
sophers' problems, they are unlikely to be of scientific interest in
any case. The great benefit philosophers have to offer to scientists
is their sophisticated analysis of language and logic, for this is
something that the scientist needs and will increasingly need with
the progress of the behavioural sciences.
It is often denied that scientists make verbal mistakes of the kind
philosophers of science tend to attribute to them, but there is
more than an element of truth in the allegation. Certainly it is true
that a part of a science may be fairly clear-cut, and its problems not
primarily verbal; but for other parts it is also true that a verbal
SUMMARY 377
tangle may ensue, and the more the scientist is persuaded that he
doesn't get into verbal tangles, the more likely he is not to recognize
them. The words 'reinforcement', 'learning', 'motivation', 'per-
ception' are words that are hardly clear-cut in their meaning, and a
further complication is the fundamental fact that a description at
the everyday level may use terms whose significance disappears at
other levels of analysis.
This last point is clearly illustrated if we can imagine the differ-
ence in the descriptions of the performance of a car by, on the one
hand, a casual observer, and on the other hand by the same
observer after he has driven the car himself. A description by an
expert mechanic would be different again, for he would have
developed a different vocabulary. For example, while the casual
observer might attribute separate causes to different manifesta-
tions such as skidding, bad cornering and erratic steering, the
expert's description. would be in terms fundamental to all three : the
car's centre of gravity, length of wheel base, condition of tyres, etc.,
and the driver's lack of skill. Any number of other examples will
readily come to mind to show that at a given level of description
variables may be seen to be related, and at other levels they may
seem unrelated.
It is on this account that the writer believes that any model-
theory for behaviour must be at many levels, and that these levels
must be closely integrated with each other. Hence, of course, the
need for neurophysiological and, ultimately, biochemical descrip-
tions of behaviour.
As to the use of particular methods in science, it must be re-
cognized that there are various ways of making progress. The
method suggested by Broadbent, which involved local theorizing,
keeping close to experimental facts, is one, and one that is essential;
but to follow this alone would involve a narrowness of outlook
which would make for lack of integration with neighbouring
scientific disciplines.
The hypothetico-deductive method has been much maligned of
late, and mostly for the wrong reasons. It is true that the method
as such is not well defined, and the name covers lots of different
forms of theory construction; Hull's use of the method with his
quantification is sometimes uneconomical and unwieldly, but a
great deal can be said on behalf of using hypothetico-deductive
378 THE BRAIN AS A COMPUTER
methods, since they have the property of effective testability
which we look for in a cybernetic system. Indeed, axiomatic
systems are closely connected with cybernetic systems, and we
should therefore encourage their use.
This is not meant in the sense of excluding the use of the ad hoc
explanation, but rather to draw attention to the fact that, in general,
we need to fit these ad hoc explanations together into a complete
model if we are to have an effective science.
Turning now to the actual problems of cognition, it must be said
again that these problems have not been explicitly dealt with in detail.
Hull, Tolman and Guthrie as individual learning theorists have
become somewhat submerged in the general discussion of pro-
blems, and no doubt this placing of the emphasis on the problem
rather than on the person and his theory represents healthy
progress in the subject. There are, of course, many new theorists
emerging in the field: Olds, Glanzer, Deutsch, Uttley, Broadbent
and others have written extensively, and most illuminatingly, on
the current problems of learning theory.
Nevertheless, our present emphasis is on method. Recent years
have seen the development of mathematical models for learning
theory, and those of Estes, Bush and Hosteller, Gulliksen and
London, are among the first to come to mind. The methods are
either the application of the differential calculus or the use of
statistical analysis, which is of course essentially stochastic in its
nature.
These mathematical models bear some relation to the condi-
tional probability theory of learning suggested by Uttley; indeed
his system is capable of being restated in stochastic form.
Conditioning of the classical and instrumental kind is naturally
a subject to demand explanation, and the major problem is still the
matter of reinforcement. Can learning take place without reinforce-
ment? The answer is that without some selective process it would
be difficult to see why learning should not be totally indiscriminate.
Now discrimination can take place through a selective filter, but
what is it that makes the filter selective? Whatever it is could, of
course, represent the reinforcer.
But apart from the selective factor that may occur at the
perceptual end, the field of latent learning suggests that learning
may take place without reinforcement, and we are now faced with
SUMMARY 379
untestable statements to the effect that either learning always
depends on reinforcement, or it doesn't. Either statement is
untestable while we judge the presence of reinforcement by the
fact of learning having taken place.
The alternative is to show in each case what the reinforcer is,
and this quite obviously will not generally be possible.
Uttley's model, which has been a major influence on the
writer's own views, suggests the basic nature of classification,
conditional probability and reinforcement. But it should be noted
that reinforcement might not be adequately represented by drive
reduction, since we know from a number of experiments that sham
feeding will often reduce food searching activity, and that rein-
forcement is not merely need-reduction in the crude sense.
Contiguity may itself supply learning, just as concepts may
supply needs. Such a development of the idea of needs from
physiological states, such as hunger and thirst, becoming asso-
ciated with concepts which allow a person simply to think of
something and, as a result, to want it, could easily occur in a finite
automaton, and can be shown to occur in an appropriately
programmed computer.
The problem is perhaps ultimately a neurophysiological one, or
one that will be settled only by neurophysiological experiment. In
the meantime, we can at least say that a reinforcement principle
seems essential, and this principal should be generalized beyond
its form in Hull's writings to deal with the more sophisticated
types of reinforcement met in conceptual activity.
A great deal has been said recently about perceptual learning
and discrimination learning, and this serves to remind us of the
healthy fact that learning and perception are being increasingly
seen as a unified process, and that learning perceptually is not
something different from ordinary learning. The emphasis is now
on the fact that some learning is more immediately tied to percep-
tion than, other learning.
We may now summarize the cybernetic models described in this
book.
(1) Models of the visual system. These include especially the
models of Culbertson, Pitts and McCulloch, Selfridge, Rapoport,
Osgood and Heyer, Uttley, Deutsch and George.
380 THE BRAIN AS A COMPUTER
(2) General classification systems that may apply to any or all
of the special senses; these include especially the models of
Uttley, Chapman, George and Pask.
(3) The central process of conditional probability, counting and
association. In the simpler associative cases this especially includes
the hardware models of Shannon, Grey Walter, Deutsch, and in
more complex form, the conditional probability computers of
Uttley and the models of Stewart.
(4) Broadbent's auditory theories must also be mentioned here.
(5) Memory stores, including delay line and magnetic core
storage, one form of which has been described by Oldfield.
(6) Motivational systems, especially in Uttley's models, in
logical net form, and as exemplified by Ashby's Homeostat.
The list could be greatly extended to include in particular the
learning theorists such as Hull and Tolman, neurophysiologists
such as Pribram, and neurophysiological theorists such as Hebb
and Milner. We would also remind the reader of the many other
models, both in hardware and paper-and-pencil, due to Turing,
Church, Bridgman, and many others, that have a direct bearing
on our problem.
Information theorists have undertaken to model many of the
same systems from slightly different points of view. Usually the
emphasis is more operationally inclined, and is more directly
concerned with performance.
It seems fairly clear that, from the models we have, we can
supply sensory and motor systems, a central control with tem-
porary storage, probability counters, and a permanent storage
system, in a variety of different ways. Many of the models would
certainly be workable, and could be made in more than one fabric.
However, we still have a very long way to go before we can fit all
the empirical facts together, especially at the molecular level, to
supply anything like the working model we need. We are well
aware, also, that all this says little or nothing about modelling the
social situation.
The trouble is that we have reached a point where many of these
problems can be understood in a general way, and yet the very
size of the model-making undertaking is so large as to defy con-
ceptual clarity.
SUMMARY 381
At the moment there are two strikingly pressing problems in
cybernetics, the first one being the need for a notation that allows
an easy, detailed description of a vast iterated system. Obvious
places to look for help are in algebra, set theory, statistics and
logic, and the best that can be done involves all these means; but
to develop a suitably integrated language or notation in which we
could construct conceptual or paper and pencil models will be a
major task indeed. Of course an answer may lie in computer
programming, and especially in auto-codes, but those particular
auto-codes called generating routines which are so vital to learning
are not as yet developed.
The second big problem for cybernetics is to find an inexpensive
unit, or set of units, so that very large scale special purpose com-
puters may be constructed. This problem is partly answered by
general purpose digital computers and partly by transistors, and
in the future it is likely to be greatly helped by new storage
techniques, and by the micro-module method of computer
construction.
There are, of course, many other problems to be solved before
we have effective theories which will allow us to predict the
behaviour of individuals and groups of people, but from the
cybernetician's point of view the two mentioned above are the
most urgent.
We shall now outline very briefly what we consider to be the
most likely principles applying in the construction of the human
organism. This could have been the subject of the whole book, and
it has been to some extent interwoven with a discussion that has
been more concerned with the development of conceptual models
and the methodological implications of these models. In the main
the model will be concerned with only one sensory input, vision,
and the reactions that are involved with this, though of course the
system could be extended to include all the other senses. The main
points are:
(1) In the first place we have to decide between different models
of the visual system. The Osgood Heyer model still seems the most
promising in describing the actual transmission of patterns to the
visual cortex. The method by which colour vision may be fitted
into this particular model is not yet entirely clear, but it should not
382 THE BRAIN AS A COMPUTER
prove a major problem simply to associate colour properties with
the various configurations transmitted from retina to cortex.
Conceptually, there are many possible methods by which this
might be done, but the question has not been discussed in this
book.
(2) Information in the visual cortex is assumed to be classified,
and may proceed by stages where each sensory modality starts its
partial classification independently. Ultimately the information
from the various special senses is integrated.
(3) It seems likely that information from all the senses could be
described in terms of a filter, and the partial classification process
is itself a temporary storage system it certainly could be such
that information is processed in terms of its urgency, the urgency
factor operating at some level of classificatory recognition.
(4) The process of visual recognition depends upon classifica-
tion, either with or without eye movements. Eye movements are
certainly normally involved, but whether it is possible to learn to
perceive without eye movements remains an open question.
(5) Learning is dependent upon the principle of selective
association. The storage system at the earlier levels is assumed to
store spatial and temporal associations, and these associations are
kept in the first storage while conditional probabilities about their
associations are being established. The most frequent, the most
recent and the most valuable are the ones for which the condi-
tional probabilities are first sought, and in terms of which, at some
critical value, they are transferred to some other store as having
been learned.
(6) The second store, for information actually learned, is
primarily a verbal storage system where what is remembered is a
linguistic form of description in particular or general terms.
Words, and languages, are learned like all other associations, and
transferred into the second storage in the same way. This means
that the logical operations that can be enacted on information in
the secondary storage are, in fact, a set of operations on words.
(7) Thinking is in no essential way different from learning
although the emphasis is here on language and consists in the
formation^ of linguistic hypotheses from the conditional proba-
bilities in storage^at*are*tEemselves derived logically from storage,
or directly transferred from the first storage system.
SUMMARY 383
(8) Memory is ordered storage of information and, when needed,
its reconstruction is effected by stimulation, either through an
internal association process or through an external sensory process.
(9) Recall involves the internal partial firing of centres that are
normally sensorially elicited.
(10) Motivation is presumed to operate in a reinforcing manner
on the associations dealt with at all levels of the system, where
secondary motivation occurs to transfer positive or negative
values to associations that did not originally have those positive
or negative values. This allows the thinking operation to produce
a need since, when an association with a value particularly a
strong value occurs, it may itself change the direction of
behaviour towards satisfying a new need.
(11) From the last comment it is clear that needs are to be
thought of as being organic, representing states of hunger, thirst,
etc., and also conceptual in that 'thinking about something' may
lead to a need. The satisfaction of a need may be either organic or
conceptual, and here curiosity will be regarded as a basic, although
rather general, drive.
(12) Emotions are thought to be closely associated with states
of need, so that with satisfaction of need pleasant feelings occur,
and conversely, with the frustration of needs, unpleasant feelings
occur. The built-in principle of the organism that must survive is
that the pleasant feelings should be maximized and the unpleasant
minimized. Here, the words pleasant and unpleasant are being
stretched somewhat beyond their everyday meanings, since they
must also include activities that are not inherently pleasure
giving or otherwise, but whose operations may be vitally important
for survival.
(13) The apparatus for 11 and 12 is built in, as is the basic
principle of association. From these beginnings the principle of
generalization (concept formation) is acquired by experience.
(14) Learning may sometimes be closely integrated in a sequence
with innate components, and it may be centred around primarily
perceptual material, in which case we call it perceptual learning.
When we learn in terms of relations rather than properties, we call
it discrimination learning; and when we learn in terms of concept
formation we simply call it learning, or conceptual learning. When
it involves the use of logic and language we call it thinking.
384 THE BRAIN AS A COMPUTER
(15) Thinking', when used behaviouristically, means just what
we said in (14) although, as far as one can tell, when the word is
used in the everyday sense it may mean only those logical and
linguistic operations of which we are conscious.
(16) Thinking may ramify in curious ways which represent the
operations of extrapolation (induction) and the drawing of con-
sequences (deduction). These are by no means only linguistic
processes, for they involve the associations of the store system
where the association is simply between event-names, and not the
names for event-names. This is a rather clumsy distinction made
necessary by the fact that there is a sense in which everything
inside the nervous system is at least in coded form.
(17) Consciousness is not a property of a system that can be
examined cybernetically, and in the shadow of the problem of
'other minds' we should simply say that it probably represents a
certain neural activity whereby we are given a private glimpse of
our own cerebral activity, through images and sensations.
(18) The basic associations on which the system is founded have
a large compass of complexity, ranging from simple habits, through
commonplace 'beliefs' or 'expectancies', to highly complex pieces
of problem solving, which we might call hypothesis formation.
(19) Perception is assumed to be essentially the same as the
process of recognition, which is simply the classification of
objects, events, etc.
(20) Problem solving is assumed to be essentially the same as
the process of learning or thinking, as opposed to the subsequent
stage of 'having learned'.
(21) Receptor systems are assumed to be available so that they
may be switched into the system where they may actively change
the central state, in a homeostatic manner. They may also be
classified as a particular case, and respond only to internal elicita-
tion. The ideas of Deutsch are relevant here, and his type of
homeostatic responding system seems the most likely type of output.
This list has grown long, and we must now summarize the
more molecular level of description.
Neurologically speaking, we have already seen how much current
neurophysiological thought is running parallel to the type of closed
loop homeostatic processes we have been assuming. The work of
SUMMARY 385
Pribram, mentioned in Chapter IX, paints a picture with which
we are in essential agreement.
(1) The cortex is a storage and analysing system. It has input
systems connected directly to it, and their cortical representation
makes up the bulk of the storage system. These input representa-
tions are relatively well established in terms of localization.
(2) The cortex also has the two stages of storage system to
which we have already referred. The first stage is ramified, and
starts even in the sensory endings, such as the retina, and con-
tinues to classify throughout the visual cortex. Similarly, the
process may be supposed to operate through the rest of the sensory
cortex and the areas of cortical elaboration.
(3) The second storage system is presumably in the temporal-
parietal regions of the cortex and in the frontal regions as well.
(4) The cortex is presumed to be partially localized in that the
density of particular functional connexions tend to occur together
in particular areas. Nevertheless, there is a considerable amount of
cortical overlap, due to the different functions being represented
by neurons, or collections of neurons, with widely ramified
connexions.
(5) It is assumed that the sub-cortical areas are concerned with
the channelling and timing of information flow from the lower
and to the lower centres. The hypothalamus is representative of
the emotional centres, and is connected with the activating reti-
cular system in mediating feelings and sensations from internal
states of the organisms, the limbic system then representing sorts
of pleasure and pain centres.
(6) The cerebellum is concerned with the integration of motor
activating information.
(7) The reflex arc unit of nervous activity is a special case of a
homeostatic unit whereby there exist graded neural responses
which modify the homeostatic control associated with cortical and
subcortical centres.
(8) It is assumed that there is a feedback of information from
effectors that modify the central state.
(9) It is assumed that sets of neurons fire together circuitously
in something like the manner suggested by Milner-cell assemblies
with differential inhibition.
386 THE BRAIN AS A COMPUTER
(10) The logical net analysis, which has been used prominently
in clarifying principles expressed in this book, while not appro-
priate for a description of the details of the neurophysiological
picture as they stand, comes sufficiently near for a direct compari-
son to be made between a model couched in neurophysiological
terms, such as Milner's, and the logical net equivalent.
On finishing a book such as this, one is very conscious that fresh
information is coming in with each succeeding journal and each
new book, and for that and for other reasons, much has inevitably
been left unsaid. This book has been written in the hope that it will
encourage more people to realize that cybernetics has a serious
contribution to make to our understanding of behaviour, and that
most readers will find the arguments sufficiently clear and cogent
to convince them that there is a perfectly good sense in which we
should want to say that the 'brain is a computer'.
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AUTHOR INDEX
ADAMS D. K., 180
ALBINO, R. C., 261
ARNOT, E., 274
ASHBY, W. R., 108, no, 118, 303,
380
BABBAGE, C., 17
BACKUS, J., 369
BARD, P., 268
BARLOW, H. B., 256, 320, 350
BARTLETT, F. C., 143, 365, 366
BEACH, F. A., 246
BEER, S., 110, 152, 248, 375
BEKHTEREV, V. M., 184
BERITOFF, S., 293
BERLYNE, D. E., 192
BEURLE, R. L., 257, 302
BEXTON, W. H., et. aL, 368
BIGELOW, J., 1 8
BISHOP, G. H. and CLARE, M. H.,
307
BLODGETT, H. C., 205, 215
BLUM, J. S., CHOW, K. L., and
BLUM, R. A., 275
BORING, E. G., 317$ 331, 332
BOWDEN, B. V., 158
BRAITHWAITE, R. B., 9, 49, 55, 76,
90, 120
BRIDGMAN, P. W., 50, 380
BROADBENT, D. E., 7, 1 19, 150, 192,
230^, 257, 375
BRODMANN, K., 258
BROGDEN, W. J., 193
BROUWER, L. E. J., 16
BROWN, G., 278
BRUNER, J. S., GOODNOW, J. J. and
AUSTIN, G. A., 366, 367
BRUNSWICK, E., 208
BUCY, P. C., 272
BULLOCK, T t . H., 236
BURNS, B. D., 261
BURSTEN, B. and DELGADO, J. M.
R., 300
BUSH, R. R., 1 8
BUSH, R. R. and MOSTELLER, F., 34,
78, 87, 88, 117, 161, 230
CAJAL, R. Y, 258
CAMPBELL, A. W., 272
CAMPBELL, R. J. and HARLOW, H.
F., 276
CANNON, W. B., 181
CANTRIL, H., AMES, A., HASTORF,
A. H. and ITTELSON, W. H., 329
CARNAP, R., 40, 45, 8iff, 152
CATE, J. TEN, 291
CHAPMAN, B. L. M., n^ff, 152^,
250, 311, 320, 348, 375, 380
CHILD, C. M., 332
CHOW, K. L., BLUM, J. S. and
BLUM, R. A., 276
CHOW, K. L., 279
CHURCH, A., 3, 15, 62, 70, 74, 380
CLARK, G. and LASHLEY, K. S., 273
COBURN, H. E., 312
COGHILL, G. E., 181
COLLIER, R. M., 341
CRASHAY-WILLIAMS, R., 46
CREED, R. S., DENNY-BROWN, D.,
ECCLES, J. C., LlDDELL, E. G. T.
and SHERRINGTON, C. S., 252
GROSSMAN, E. R. F. W., 375
CULBERTSON, J. T., 96, 138, 143,
3i 319, 335, 338ff
CULLER, E. and METTLER, F. A.
291
406
AUTHOR INDEX
407
DARROW, C. W., 260
DAVIS, D. M., 172
DELAFRESNAYE, J. R, 266
de LEEUW, K., MOORE, E. F.,
SHANNON, C. E. and SHAPIRO, N.,
104
DEUTSCH, J. A., 119, 150, 316, 334,
335#, 357#, 358, 379, 380, 384
DEWEY, J., 331
DEWEY, J. and BENTLEY, A., 329
DODWELL, P. C., 358
DREVER, J., 371
DUSSER de BARENNE, J. G. and
McCuLLOCH, W. S., 259, 291
DUSSER de BARENNE, J. G., CAROL,
H. W. and MCCULLOCH, W. S.,
259
ECCLES, J. C., 245, 246, 249, 252,
253, 262, 296, 297
ELWORTHY,?. H. and SAUNDERS, L.,
247
ERLANGER, J. and GASSER, H. S.,
252
ESTES, W. K., 78, 185, 230, 378
FEIGL, H., 51
FITCH, F. B. and BARRY, G., 200
FRANKENHAUSER, B., 259
FREGE, G., 16
FRY, G. A. and BARTLEY, S. H., 360
FRY, D. B. and DENES, P., 364
FULTON, J. F., 252, 263, 267, 271,
73, 274
FULTON, J. F., LIVINGSTON, R. B.
and DAVIS, G. D., 274
GALAMBOS, R., 307
GALE, D. and STEWART, F. M., 155
GASSER, H. S., 252
GELLHORN, E. and JOHNSON, D. A.,
260
GEORGE, F. H., 46, 47, 50, 56, 77,
79, 117, 127, 132, 145, 147, 174,
312, 320, 322, 327, 342, 358, 360,
367, 379, 380
GEORGE, F. H. and HANDLON, J. H.,
154
GEORGE, F. H. and STEWART, D. J.,
364
GIBSON, J. J., 318
GODEL, K, 3, 15, 74, 96
GOLDMAN, S., 35
GOLDSTEIN, K., 282, 285
GOODE, H. H. and MACHOL, R. E.,
155
GRAHAM, C. H., 333
GRANIT, R., 307, 349, 353
GULLICKSEN, H., 378
GUTHRIE, E. R., 119, 182, 184, 187
GUTHRIE, E. R. and HORTON, G.
P., 180
HALL, K. R. L., EARLE, A. E.
and CROOKES, T. G., 315
HANEY, G. W., 2156*
HARLOW, H. F., MEYER, D. and
SETTLAGE, P. H., 275
HARTLEY, R. V. L., 38
HAYEK, S. A., 112, 319
HEAD, H., 285, 337
HEBB, D. O., 248, 266, 271, 274,
293, 297, 299, 303, 308, 313, 314,
332, 335$ 340, 35i, 359, 380
HEMPEL, C. G. and OPPENHEIM, P.,
81, 151
HENRY, C. E. and SCOVILLE, W.
B., 262
HERNANDEZ-PEON, R., SHERRER,
H. and JOUVET, M., 342
HEYTING, A., 16, 66
HICK, W. E., 375
HILBERT, D., 16
HlLGARD, E. R., 182, 183, 184
HILGARD, E. R. and MARQUIS, D.
G., 182, I93ff 233, 294
HILL, D., 261
HINES, M., 272
HODGKIN, A. L., 245
HOLT, E. B., 293
HOLWAY, A. H. and BORING, E. G.,
3i8
HOUSEHOLDER, A. S. and LANDAHL,
H. D., 312
HULL, C. L., 10, 83, 119, i73ff, 178,
182, 196, 207, 214, 218, 379, 380
HUMPHREY, G., 179, 180, 366, 367
HUMPHREYS, L. G., 207
408
THE BRAIN AS A COMPUTER
ITTELSON, W. H. and CANTRILL, H.,
329
JACKSON, J. H., 278, 280, 385
JACOBSEN, H., 350
JACOBSON, C. F., 275, 276
JACOBSON, C. F. and ELDER, J. H.,
275
JACOBSON, C. F. and HASLERND,
G. M., 275
JACOBSON, C. F., WOLFE, J. B.
and JACKSON, T. A., 274, 275
JAMES, P. H. R., 227
JAMES, W., 179
JASPER, H. H., 264, 265, 266, 270
JENKINS, W. O. and STANLEY, J. C.,
208, 20QfF, 213
KAPLAN, A. and SCHOTT, 84
KAPPERS, C. U. A., HUBER, G. C.
and CROSBY, E. C., 293
KELLER, F. S., 212
KENDLER, H. H., 2isff
KENNARD, M. A., SPENCER, S.
and FOUNTAIN, G., 275
KENNEDY, A., 262
KILPATRICK, F. P., 328
KLEENE, S. C., 90, 94, 96, 97, 117,
311
KLUVER, H., 274
K6HLER, W., 180, 314, 366
KOHLER, W. and WALLACH, H., 3 15
KONORSKI, J., 291, 292:8:, 313
K5RNER, S., 8, 9, 84
KRAGNAGORSKY, N. I., 290
KJRECHEVSKI, I., 139, 2O5, 206
KULPE, O., 179
LADEFOGED, P., 364
LANDAHL, H. D., 348
LASHLEY, K. S., 266, 276, 280, 281,
282, 283, 284, 298
LAWRENCE, M., 329
LE GROS CLARK, W. E., 258, 267,
268
LEWIS, C. I., 67
LEWIS, C. I. and LANGFORD, C.
H., 67
Li, C. L., CULLER, C. and JASPER,
LIDDELL, E. G. T. and PHILLIPS,
C. G., 295
LILLIE, R. S., 241
LILLY, J. C., 295
LlNDSLEY, D. B., 266
LONDON, I. D., 378
LORENTE DE N6, 2$ I, 252, 291
LORENZ, K., 297
MACKAY, D. M., 20, 309
MACCORQUODALE, K. and MEEHL,
P, E., 204, 210
MACFARLANE, D. A., 205
McCuLLOCH, W. S., 235, 263
McCuLLOCH, W. S. and PITTS, W.,
43, 90, 97, H7, 120, 298, 338
MCDOUGALL, W., 179, 180, 183
MAGOUN, H. W., 265
MALTZMAN, L, 2i5ff
MARSAN, C. A. and STOLL, J., 279
MARSHALL, W. H. and TALBOT,
S. A., 315, 352
MASSERMAN, J. H., 268
MEEHL, P. E., 189, 198
MEEHL, P. E. and MACCORQUO-
DALE, K., 200, 204
METTLER, F. A., 274
MEYER, D. R., 279, 280
MILLER, G. A., GALLANTER, E. H.
and PRIBRAM, K. H., 307
MILLER, N, E, and DOLLARD, J. C.,
213
MILLER, N. E. and KESSEN, M. L.,
192
MILNER, B., 279, 380, 386
MILNER, B. and PENFOLD, W., 280
MILNER, P. M., 116, 304ff, 313
MINSKY, M. L., 170, 298, 369
MOORE, G. E., 52
MORRELL, F. and JASPER, H. H.,
265
MORRIS, C. W., 50
MORRUZZI, G. and MAGOUN, H.
W., 265
MOWRER, O. H. and JONES, H. M.,
213
MULLER, C. G. JR. and SCHOEN-
AUTHOR INDEX
409
OETTINGER, A. .,157,158, 163,218
OLDFIELD, R. C., 138, 380
OLDS, J. A., 308
OLDS, J. A. and MILNER, P., 265,
300
OSGOOD, C. E., 222, 362, 370
OSGOOD, C. E. and HEYER, A. W.,
186, 315, 316, 352, 379, 381
PAP, A., 50, 82
PASCAL, B., 17
PASCH, A., 46
PASK, A. G., 115, 152, 237, 248, 375,
380
PAVLOV, I. P., 181, 184, 187, 188,
195, 208, 288, 289, 291, 292,
3i3
PEANO, G., 16
PENFIELD, W., 278, 280
PENFIELD, W., and RASMUSSEN, T.,
278, 279, 282, 299
PlERCEY, M. F., 228ff
PITTS, W. and McCuLLOCH, W. S.,
264, 322
POSTMAN, L., 189, 198
POLYAK, S. I., 337
PRIBRAM, K. H., 151, 270, 287, 307,
380, 385
PRICE, H. H., 8, 131, 323
PRINGLE, J. W. S., 297
QUINE, W. V. O., 47, So
RABIN, M. O., 155
RABIN, M. O., and SCOTT, D., 104
RAMSEY, F. P., 77
RAPOPORT, A., 5, 256ff, 320, 335,
336, 338
RASHEVSKY, A., 312
REICHENBACH, H., 66, 365
RIESEN, A., 341
RIGGS, L. A., RATCLIFFE, F.,
CORNSWEET, J. C. and CORN-
SWEET, T. N., 357
RIOPELLE, A. J., ALPER, R. G.,
STRONG, P. N. and ADES, H. W.,
279
ROSENBLATT, F., 364
ROSSER, J. B. and TURQUETTE, A.
R., 66
RUCH, T. C. and SHENKIN, H. A.,
274
RUSSELL, G., 218, 233
RYLE, G., 8
SAUNDERS, L., 247
SCOVILLE, W. B. and MILNER, B.,
269, 280
SELFRIDGE, O. G., 322, 335, 338,
364, 379
SELLARS, W., 50
SETTLAGE, P., ZABLE, M. and
HARLOW, H. F., 275
SEWARD, P. J., 119, 185, 198, 199,
200
SHANES, A. M., 246
SHANNON, C. E., 18, no, 116, 1586,
380
SHANNON, C. E. and WEAVER, W., 34
SHARPLESS, S. and JASPER, H. H.,
192, 342
SHEFFIELD, F. D., 214
SHEFFIELD, F. D. and ROBY, T. B.,
183
SHEFFIELD, F. D. and TENMER, H.
W., 214
SHEFFIELD, F. D., ROBY, T. B. and
CAMPBELL, B. A., 185
SHEFFIELD, F. D., WOLFF, J. J.
and BACKER, R., 185
SHEPHERDSON, J. C., 104
SHERRINGTON, C. S., 250, 252ff,
278, 288
SHIMBEL, A., 298
SHOLL, D. A., 250, 257, 258, 271,
277, 302, 312
SKINNER, B. F., 190, 208
SMITH, K. R., 316
SOLOMONOFF, R. J., 9
SPENCE, K. W., 214
SPENCE, K. W. and LIPPITT, R., 216
SPERRY, R. W., 342
SPERRY, R. W., STAMM, J. S. and
MINER, N., 300
STANLEY, W. C. and JANES, J., 271,
274
STARZL, T. E. and MAGOUN, H. W.,
267
410
THE BRAIN AS A COMPUTER
STEWART, D. J., 114, 144, 150,
262, 303, 349
STOUT, G. F., 179
SUTHERLAND, N. S., 256, 321, 340,
34i
TAYLOR, W. K., 248, 341
THISTLETHWAITE, D. L., 215, 217,
218
THORNDIKE, E. L., 180, 189
THORPE, W. H., 183, 297
THOULESS, R. H., 317
THRALL, R. M., COOMBS, C. H. and
DAVIS, R. L., 154
TlNBERGEN, N., l8l, 2Q7
TlNKELPAUGH, O. L., 205
TOLMAN, E. C., 119, 139, 174,
178, 200, 204, 207, 208, 214, 380
TOLMAN, E. C. and HONZIK, C. H.,
205
TOWER, D. B., 246
TROTTER, J. R., 213
TURING, A. M., 3, 6, 15, 69, 70, 74,
104, 380
UTTLEY, A. M., 112, 118, 119, 131,
174, 23off, 312, 319, 32, 322,
379, 380
VOGT, O., 272
VON NEUMANN, J., 18, 21, 63, 97,
100, 103, 118, 153, 311
VON NEUMANN and MORGENSTERN,
i54, 155
VON SENDEM, M., 341
WALKER, A. E., 272
WALTER, W. G., 105, io7ff, 118,
380
WARD, A. A., 274
WARD, J., 179
WERTHEIMER, M., 332
WERNER, H., 360
WHITEHEAD, A. N. and RUSSELL, B.,
16
WIENER, N., 13, 18, 38
WILMER, E. N., 349
WITTGENSTEIN, L., 8, 48, 49
WOHLGEMUTH, A., 360
WOLPE, J., 198
WOODGER, J. H., 9, 67, 84, 86
WOODWORTH, R. S., 318, 332
WUNDT, W., 179
YERKES, R. M., 180
ZANGWILL, O. L., 361
SUBJECT INDEX
Alpha Rhythm (waves), 262, 354
Amygdaloid Nuclei, 241, 270
Animal Experiments,
after frontal ablation, 274-279
in latent learning, 215, 216, 217,
> 274
in mazes, 194, 205, 212
Animal Learning,
behaviourism, 180, 181, 208, 209
discrimination, 194, 205, 206,
276, 277
insight, 205
Aphasia, 285
Autocoding, 138, 165, 369
Automata,
finite, 4, 5,43, 90,94, "7
infinite, 4, 6
Autonomic Nervous System, 239,
263, 269
Axiomatic systems, 68
Basal Ganglia, 241, 269
Behaviourism, 32, 80, 332, 365
Beliefs, 126, 139, 187
Binary Notation, 22, 23
Blind Spot, 344
Brain, 258, 264, 270
Brain Lesions, 299
Cathexis, 202
Caudate Nuclei, 241
Cerebellum, 264
Cerebral Cortex, 236, 250, 258,
265, 266, 269, 290
cerebral cortex structure, 270
cortical stimulation, 278
temporal and parietal lobes, 278
Cerebrum, 258
Changing Goals, 172
Classification, 26, 112, 130, 132,
152,300,319,320,325,327,347
Cognition, 134, 356, 365
Colour Vision, 343, 348, 349, 354
Communication Theory, 36, 37
Completeness, 16, 20, 21
Computers,
digital 1 6
arialogue 30
Conditional Probability, 112, 136,
320
Conditioned Reflexes, 125
Conditioned Response, 125, 181
Conditioned Stimulus, 125
Confirmation, 161
Consciousness, 310, 367, 368
Constancy, 317, 330
Contiguity, 167, 185, 186, 379
Contour Formation, 340, 345, 353,
360, 361
Control, 134, 135, 136, 236, 351
Corpus Striatum
(See Basal Ganglia)
Cybernetics definition, 2, 44
Decision Procedure, 3, 15, 70
Diencephalon, 237, 266, 267
Drive, 173, .196, 197, 198, 308
Effect, 1 88
Effective Procedure,
(see Decision Procedure)
Electrical Stimulation, 260
Electroencephalography, 260, 266
Emotion, 135, 142, 306
Empirical Logic, 84
Entrophy, 35
Ergodic Process, 34
Error Control, 41
412
THE BRAIN AS A COMPUTER
Ethology, 297
Excitation, 123
Expectancy, 190, 201, 205
Experimental Psychology, 76
Extinction, 125, 202, 209, 214,
230, 232
Feedback, 18, 150, 255, 307, 346
Figural After-effect, 315, 316, 352,
357, 359> 360, 362
Final Common Path, 252
Formalization, 45
Form Perception, 334
Frontal Lobes, 271
Games Theory, 153, 155
Generalization, 57, 289, 298
Geniculate Bodies, 241, 267
Gestalt Theory, 137, 314, 332, 226
Growth Nets, 116, 152, 311, 348,
375
Hartley Law, 38
Homeostatic Process, 261, 303, 307,
310
Hypothalamus, 237, 241, 262, 267
Imagination, 369
Induction, 166, 289
Information Theory, 32, 255
Inhibition, 123, 124, 288, 289, 291
central inhibition, 252, 254
central inhibitory state (c.i.s.),
251
retroactive inhibition, 220
Input Systems, 24
Insight, 164, 172
Intervening Variables, 204
Ionic Hypothesis, 245, 246
Rappers' Growth, 294
Language, 34, 35, 40, 52, 55, 59,
77, 166, 351, 367, 370
for the computer, 170, 368, 369
Lashley's Theory, 298
Learning,
association, 108
conditioning, 141
field theory, 149, 150, 173, 176,
Hull's theory, 196
insight, 164, 712, 181
latent, 183, 205, 207, 215
neurophysiological interpreta-
tion, 256, 299, 300
perceptual, 371
place, 205
sets, 225, 227
Tolman's theory, 200
trial and error, 181
Limbic System (or cortex), 308,
309
Linear Programming, 24, 25, 26
Logic,
Boolean Algebra, 22, 59, 60
many-valued logic, 66
mathematical logic, 59
probabilistic logic, 97
prepositional calculus, 58, 62
Logical Networks, 43, 58, 119, 256
Machines (see Models)
Mammillary bodies, 237, 267
Markov Process or Chain, 34, 134,
174, 326
Matrices, 91, 92, 93, 116, 157, 219,
220, 227, 321, 232
Memory, 142, 177, 278, 280, 283
Mesencephalon (medulla), 237, 264
Meta-language, 47
Metencephalon, 237, 263
Methodology, 45, 232, 258
Models, 31, 57, 69, 288, 302, 311,
338, 340, 342, 348, 357
Ashby's model, 108
George's models, 145
Grey Walter's models, 105
Shannon's model, i 10
Stewart's models, 144
summary, 279, 380
Turing machine, 6, 70, 104
Uttley's models, 112
Motivation, 133, 135, 139, 150, 154,
160, 167, 185, 196, 306, 318
secondary, z 14
Movement,
after-effects, 362, 363
apparent and real, 315, 316
Multiole Line Trick. 07, loo
SUBJECT INDEX
413
Multiplexing, 21, 100, 153
Myelencephalon, 237, 263
Nervous System, 235, 237, 239,
248
chemistry, 241, 243, 245
Neural Nets, 90
Neurons, 236, 248
Occlusion, 294, 295
Optic Nerve, 315, 349, 350
Output Systems, 24
Perception, 136, 138, 314, 356
Phenomenalism, 51
Plasticity, 293, 294
Plateau Spiral, 315
Postulational Method, 83
Pragmatics, 46, 50
Probability, 33, 101, 112, 152, 221,
222, 325
Problem Solving, 365
Programming, 30, i57fF, 369
Psycho-Physics, 333
Purpose (purposive behaviour), no,
204
Randomness, 153, 344
Realism, 5 1
Recruitment, 349
Recursive Functions, 73, 96, 104,
172
Reduction Sentence Methods, 81
Reflex, 250, 251
Reinforcement, 125, 167, 173, 182,
184, 193, 198
heterogeneous, 193
homogeneous, 193
partial, 207, 209, 210, 212, 215
primary, 185, 192, 196
secondary, 185, 192, 196, 213,
214
Respondent Behaviour, 210
Response System, 150
Restoring Organs, 311
Reticular System, 264, 265
Retina, 315, 336, 337, 359
Scanning, 345, 346, 35?
Self Organizing Systems, r 14
Servosystems, 41, 307, 308
Set, 138, 143, 177, 324, 334, 347,
359
ShefTer Stroke, 97
Spinal Cord, 236, 237
Statistics, 33, 88, 257
Stimulus Generalizations, 222
Stochastic Processes, 34, 38, 87
Storage Systems, 131, 132, 142,
161, 174, 224, 300, 350
Summation, 249, 251, 255, 256,
257, 303, 337
Synapse, 248, 249
Thalamus, 237, 241, 267
Theorem, definition, 63
Theory Construction, 53, 55
Thinking, 31, 32, 143, 365, 3^6,
367
Transfer of Training, 222
Truth Tables, 64
Turing Machines, 6, 70, 104
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