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DESIGN FOR A BRAIN
AN INTRODUCTION TO
CYBERNETICS
by
Copyright © 1956, 1999
by The Estate of W. Ross Ashby
Non- profit reproduction and distribution of this text for
educational and research reasons is permitted
providing this copyright statement is included
Referencing this text:
W. Ross Ashby, An Introduction to Cybernetics,
Chapman & Hall, London, 1956. Internet (1999):
http://pcp.vub.ac.be/books/IntroCyb.pdf
W. ROSS ASHBY
M.A., M.D.(Cantab.), D.P.M.
Director of Research
Barnwood House, Gloucester
Prepared for the Principia
Cybernetica Web
With kind permission of the Estate trustees
SECOND IMPRESSION
Jill Ashby
Sally Bannister
Ruth Pettit
Many thanks to
Mick Ashby
Concept
Francis Heylighen
Realisation
Alexander Riegler
with additional help from
Didier Durlinger
An Vranckx
Véronique Wilquet
LONDON
CHAPMAN & HALL LTD
37 ESSEX STREET WC2
1957
First published 1956
Second impression 1957
PR E FAC E
Many workers in the biological sciences—physiologists,
psychologists, sociologists—are interested in cybernetics and
would like to apply its methods and techniques to their own spe-
ciality. Many have, however, been prevented from taking up the
subject by an impression that its use must be preceded by a long
study of electronics and advanced pure mathematics; for they
have formed the impression that cybernetics and these subjects
are inseparable.
The author is convinced, however, that this impression is false.
The basic ideas of cybernetics can be treated without reference to
electronics, and they are fundamentally simple; so although
advanced techniques may be necessary for advanced applications,
a great deal can be done, especially in the biological sciences, by
the use of quite simple techniques, provided they are used with a
clear and deep understanding of the principles involved. It is the
author’s belief that if the subject is founded in the common-place
and well understood, and is then built up carefully, step by step,
there is no reason why the worker with only elementary mathe-
matical knowledge should not achieve a complete understanding
of its basic principles. With such an understanding he will then be
able to see exactly what further techniques he will have to learn if
he is to proceed further; and, what is particularly useful, he will be
able to see what techniques he can safely ignore as being irrele-
vant to his purpose.
The book is intended to provide such an introduction. It starts
from common-place and well-understood concepts, and proceeds,
step by step, to show how these concepts can be made exact, and
how they can be developed until they lead into such subjects as
feedback, stability, regulation, ultrastability, information, coding,
noise, and other cybernetic topics. Throughout the book no
knowledge of mathematics is required beyond elementary alge-
bra; in particular, the arguments nowhere depend on the calculus
(the few references to it can be ignored without harm, for they are
intended only to show how the calculus joins on to the subjects
discussed, if it should be used). The illustrations and examples are
mostly taken from the biological, rather than the physical, sci-
ences. Its overlap with
Design for a Brain is
small, so that the two
books are almost independent. They are, however, intimately
related, and are best treated as complementary; each will help to
illuminate the other.
v
Catalogue No.
567/4
MADE AND PRINTED IN GREAT BRITAIN BY
WILLIAM CLOWES AND SONS, LIMITED, LONDON AND BECCLES
A N I N T R O D UC T I O N T O C Y B E R NE T I C S
PRE FAC E
It is divided into three parts.
Part I deals with the principles of Mechanism, treating such
matters as its representation by a transformation, what is meant by
“stability”, what is meant by “feedback”, the various forms of
independence that can exist within a mechanism, and how mech-
anisms can be coupled. It introduces the principles that must be
followed when the system is so large and complex (e.g. brain or
society) that it can be treated only statistically. It introduces also
the case when the system is such that not all of it is accessible to
direct observation—the so-called Black Box theory.
Part II uses the methods developed in Part I to study what is
meant by “information”, and how it is coded when it passes
through a mechanism. It applies these methods to various prob-
lems in biology and tries to show something of the wealth of pos-
sible applications. It leads into Shannon’s theory; so after reading
this Part the reader will be able to proceed without difficulty to the
study of Shannon’s own work.
Part III deals with mechanism and information as they are used
in biological systems for regulation and control, both in the inborn
systems studied in physiology and in the acquired systems studied
in psychology. It shows how hierarchies of such regulators and
controllers can be built, and how an amplification of regulation is
thereby made possible. It gives a new and altogether simpler
account of the principle of ultrastability. It lays the foundation for
a general theory of complex regulating systems, developing fur-
ther the ideas of
Design for a Brain.
Thus, on the one hand it pro-
vides an explanation of the outstanding powers of regulation
possessed by the brain, and on the other hand it provides the prin-
ciples by which a designer may build machines of like power.
Though the book is intended to be an easy introduction, it is not
intended to be merely a chat about cybernetics—it is written for
those who want to work themselves into it, for those who want to
achieve an actual working mastery of the subject. It therefore con-
tains abundant easy exercises, carefully graded, with hints and
explanatory answers, so that the reader, as he progresses, can test his
grasp of what he has read, and can exercise his new intellectual mus-
cles. A few exercises that need a special technique have been marked
thus: *Ex. Their omission will not affect the reader’s progress.
For convenience of reference, the matter has been divided into
sections; all references are to the section, and as these numbers are
shown at the top of every page, finding a section is as simple and
direct as finding a page. The section is shown thus: S.9/14—indi-
cating the fourteenth section in Chapter 9. Figures, Tables, and
vi
Exercises have been numbered within their own sections; thus
Fig. 9/14/2 is the second figure in S.9/14. A simple reference, e.g.
Ex. 4, is used for reference within the same section. Whenever a
word is formally defined it is printed in
bold-faced
type.
I would like to express my indebtedness to Michael B. Sporn,
who checked all the Answers. I would also like to take this oppor-
tunity to express my deep gratitude to the Governors of Barnwood
House and to Dr. G. W. T. H. Fleming for the generous support that
made these researches possible. Though the book covers many top-
ics, these are but means; the end has been throughout to make clear
what principles must be followed when one attempts to restore nor-
mal function to a sick organism that is, as a human patient, of fear-
ful complexity. It is my faith that the new understanding may lead
to new and effective treatments, for the need is great.
Barnwood House
Gloucester
W. R
OSS
A
SHBY
vii
CO N TEN TS
CONTENTS
Page
Preface
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Chapter
1: W
HAT
I
S
N
EW
. . . . . . . . . . . . . . . . . . 1
The peculiarities of cybernetics . . . . . . . . . . 1
The uses of cybernetics . . . . . . . . . . . . . 4
PART ONE: MECHANISM
2: C
HANGE
. . . . . . . . . . . . . . . . . . . . 9
Transformation . . . . . . . . . . . . . . . . 10
Repeated change . . . . . . . . . . . . . . . 16
3: T
HE
D
ETERMINATE
M
ACHINE
. . . . . . . . . . . 24
Vectors . . . . . . . . . . . . . . . . . . . 30
4: T
HE
M
ACHINE
W
ITH
I
NPUT
. .
Coupling systems . . . . .
Feedback . . . . . . . .
Independence within a whole
The very large system . . .
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42
48
53
55
61
8: T
RANSMISSION OF
V
ARIETY
. . . . .
Inversion . . . . . . . . . . .
Transmission from system to system.
Transmission through a channel . .
9: I
NCESSANT
T
RANSMISSION
The Markov chain . .
Entropy. . . . . . .
Noise . . . . . . .
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140
145
151
154
161
165
174
186
PART THREE: REGULATION AND CONTROL
10: R
EGULATION
I
N
B
IOLOGICAL
S
YSTEMS
. . . . . . 195
Survival. . . . . . . . . . . . . . . . . . . 197
11: R
EQUISITE
V
ARIETY
The law. . . . .
Control . . . . .
Some variations .
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202
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251
255
259
265
265
270
271
12: T
HE
E
RROR
-C
ONTROLLED
R
EGULATOR
.
The Markovian machine . . . . . .
Markovian regulation . . . . . . .
Determinate regulation. . . . . . .
The power amplifier. . . . . . . .
Games and strategies . . . . . . .
13: R
EGULATING
T
HE
V
ERY
L
ARGE
S
YSTEM
Repetitive disturbance . . . . . . .
Designing the regulator . . . . . .
Quantity of selection . . . . . . .
Selection and machinery . . . . . .
14: A
MPLIFYING REGULATION
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What is an amplifier? . .
Amplification in the brain
Amplifying intelligence .
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5: S
TABILITY
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Disturbance . . . . . . . . . . . . . . . . . 77
Equilibrium in part and whole . . . . . . . . . . 82
6: T
HE
B
LACK
B
OX
. . . . . . . . .
Isomorphic machines . . . . .
Homomorphic machines . . . .
The very large Box . . . . . .
The incompletely observable Box
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86
94
102
109
113
R
EFERENCES
. . . . . . . . . . . . . . . . . . . 273
A
NSWERS
T
O
E
XERCISES
. . . . . . . . . . . . . . 274
I
NDEX
. . . . . . . . . . . . . . . . . . . . . 289
PART TWO: VARIETY
7: Q
UANTITY
O
F
V
ARIETY
. .
Constraint . . . . . .
Importance of constraint
Variety in machines.. .
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121
127
130
134
ix
Chapter
1
WHAT IS NE W
1/1
. Cybernetics was defined by Wiener as “the science of control
and communication, in the animal and the machine”—in a word,
as the art of
steermanship,
and it is to this aspect that the book will
be addressed. Co-ordination, regulation and control will be its
themes, for these are of the greatest biological and practical inter-
est.
We must, therefore, make a study of mechanism; but some
introduction is advisable, for cybernetics treats the subject from a
new, and therefore unusual, angle. Without introduction, Chapter
2 might well seem to be seriously at fault. The new point of view
should be clearly understood, for any unconscious vacillation
between the old and the new is apt to lead to confusion.
1/2.
The peculiarities of cybernetics.
Many a book has borne the
title “Theory of Machines”, but it usually contains information
about
mechanical
things, about levers and cogs. Cybernetics, too,
is a “theory of machines”, but it treats, not things but
ways of
behaving.
It does not ask “what
is
this thing?” but “
what does it
do?”
Thus it is very interested in such a statement as “this variable
is undergoing a simple harmonic oscillation”, and is much less
concerned with whether the variable is the position of a point on
a wheel, or a potential in an electric circuit. It is thus essentially
functional and behaviouristic.
Cybernetics started by being closely associated in many ways
with physics, but it depends in no essential way on the laws of
physics or on the properties of matter. Cybernetics deals with all
forms of behaviour in so far as they are regular, or determinate, or
reproducible. The materiality is irrelevant, and so is the holding or
not of the ordinary laws of physics. (The example given in S.4/15
will make this statement clear.)
The truths of cybernetics are not
conditional on their being derived from some other branch of sci-
ence.
Cybernetics has its own foundations. It is partly the aim of
this book to display them clearly.
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