An Introduction to Cybernetics (Ashby)

8/14/2019 An Introduction to Cybernetics (Ashby)

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By the same author

DESIGN FOR A BRAIN

Copyright 1956, 1999by The Estate of W. Ross Ashby

Non- profit reproduction and distribution of this text foreducational 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

Prepared for the PrincipiaCybernetica Web

With kind permission of the Estate trustees

Jill AshbySally Bannister

Ruth Pettit

Many thanks to

Mick Ashby

Concept

Francis Heylighen

AN INTRO

CYBER

W. RO

M.A., M.D

Directo

Barnwood H

SECOND


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Francis Heylighen


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Chapter

WHAT

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. Cybernetics was defined band communication, in the anas the art ofsteermanship, and

be addressed. Co-ordination,themes, for these are of the greest.

We must, therefore, makeintroduction is advisable, for cnew, and therefore unusual, an2 might well seem to be serioushould be clearly understoodbetween the old and the new i

1/2.

The peculiarities of cybetitle Theory of Machines, babout mechanical things, abouis a theory of machines, bbehaving. It does not ask wh

do? Thus it is very interestedis undergoing a simple harmconcerned with whether the va wheel, or a potential in an efunctional and behaviouristic.

Cybernetics started by bein


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AN INTRODUCTION TO CYBERNETICS

the study, and control, of systems that are intrinsically extremelycomplex. It will do this by first marking out what is achievable(for probably many of the investigations of the past attempted theimpossible), and then providing generalised strategies, of demon-

strable value, that can be used uniformly in a variety of specialcases. In this way it offers the hope of providing the essentialmethods by which to attack the illspsychological, social, eco-nomicwhich at present are defeating us by their intrinsic com-plexity. Part III of this book does not pretend to offer suchmethods perfected, but it attempts to offer a foundation on whichsuch methods can be constructed, and a start in the right direction.

PAR

MEC

The properties commare, in last analysis, n


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Chapter

CH

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The most fundamental coference, either that two thing

one thing has changed with timbe described now, for the subrange abundantly. All the chanaturally included, for whenmachines move some change fSo our first task will be to devonly making it more precise ba form that experience has shdevelopments are to be made.

Often a change occurs con

steps, as when the earth movskin darkens under exposure. infinitesimal, however, raisesdifficulties, so we shall avoid twe shall assume in all cases thin time and that any differencethe change occurs by a measuaccount changes by at least a pseem artificial in a world in wgreat advantages in an Introd

Wh th diff


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system is not wholly different from the systems considered in theearlier chapters, and to show that the construction of a really ade-quate theory of systems in general is more a question of time andlabour than of any profound or peculiar difficulty.

The subject of the very large system is taken up again in S.6/14.


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Chapter

STAB

5/1. The word stability is apof machines, but is not alwaysto it as . . . stability, that muchbilised definition. Since the practical importance, we shall

distinguishing the various typeTodays terminology is unsa

attempt to establish a better. Ractual facts to which the varioutend to think of the facts ratherused are concerned, I shall try usages, and to be consistent wbe carefully defined, and the d

5/2.Invariant. Through all the

invariant: that although the schanges, there is some aspectment can be made that, in spiunchangingly. Thus, if we takand tilt it by 5 degrees and letposition follow. A statement sone moment but it is false at thment its tilt does not exceed truth is invariant for the systempoint and released, like the cu


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output) of the one machine into those of the other can convert theone representation to the other.

Thus, in the example given, apply the one-one transformation P

toNs table, applying it to the borders as well as to the body. Theresult is

This is essentially the same asM. Thus, c and in the border give

d in both. The isomorphism thus corresponds to the definition.(The isomorphism can be seen more clearly if first the rows areinterchanged, to

and then the columns interchanged, to

P: g h j k

c a b d

c a b d

d b a c d a c c

c a b d

d a c c d b a c

a b c d

Fig. 6/9/2

THE B

The transformation P:

is a shorthand way of describipairs off states in S andR thus

(Compare Uof S.4/9.) Applyresult is

which is algebraically identica

Ex. 1: What one-one transformation morphic?

(Hint: Try to identify some charrium.)

Ex. 2: How many one-one transformasystems to be isomorphic?

*Ex. 3: Write the canonical equationthat they are isomorphic. (Hint: Htem is to be a machine with inpu

Ex. 4: Find a re-labelling of variableB to be isomorphic.

P:

in S, (2,3,, ,, (1,0,, ,, (4,5,, ,, (3,0

i.e. ,, ,, (u,v

yx

Y: a b c d ec c d d b

A: a b cb c a

A: x' = x2 + y y' = x2 y


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PAR

VA

Now the soldier realisedwas. If he struck it once, chest of copper money, if who had the silver; and iappeared the dog who ha


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QUANTIT

Chapter

QUANTITY

7/1. In Part I we considered tusually with the assumption thabout which we would make sence to what it is doing here a

however, we shall have to extfundamental questions in reguonly when we are able to consdo, when might is given som

Throughout Part II, thereforset of possibilities. The study wmation and communication, asages through mechanism. Thunderstanding of regulation amost elementary or basic cons

7/2. A second reason for conscience is little interested in sogle experiment, conducted ongeneralisations, statements thexperiment; conducted in a vaof occasions. Galileos discowould have been a little interpendulum on that afternoon. Ito the fact that it is true over a


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Ex. 1: (See Ex. 2/14/11.) If A"' is at the point (0,0) andB"'at (0,1), reconstructthe position of A.

Ex. 2: A transducer has two parameters: (which can take the values a or A) and (which can take the values b or B). Its statesW, X, Y, Zare trans-formed according to:

Two messages, one a series ofvalues and the other a series of values,are transmitted simultaneously, commencing together. If the recipient isinterested only in the message, can he always re-construct it, regardlessof what is sent by ? (Hint: S.8/6.)

Ex. 3: Join rods by hinge-pins, as shown in Fig. 8/17/1:

(The pinned and hinged joints have been separated to show the construc-tion.) P is a pivot, fixed to a base, on which the rod R can rotate; similarlyfor Q and S. The rod M passes over P without connexion; similarly for N andQ. A tubular constraint C ensures that all movements, for small arcs, shall beto right or left (as represented in the Figure) only.

W X Y Z

(a,b) W Y Y Y (a,B) X X W W (A,b) Z W X X (A,B) Y Z Z Z

Fig 8/17/1


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Chapter

INCESSANT T

9/1. The present chapter will cand will study variety and its rather with the special case ofor an indefinitely long time. Tor the telephone cable, that g

sages, unlike the transmissiowere studied for only a few stIncessant transmission has

and this chapter will, in fact, bMathematical Theory of Comon how it is related to the othe

What is given in this chapintended to supplement Shandescription that is complete regarded as the primary sour

assumethat the reader has it a

9/2. The non-determinate trango on for an indefinitely long and therefore not like the catransmission of variety stoppeminate system of finite size cnitely long (S.4/5). We muscomprehensive form of mach


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PART

REGULATION

The fourldation of all phy

of permanence.

REGULATION IN


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Chapter

REGULATION SYS

10/1. The two previous Parts hprocesses within the system) communication between systehad to be studied first, as they

them, and in Part III we shallcybernetics regulation and cThis first chapter reviews th

shows briefly why it is of fundregulation is essentially relatechapter (11) studies this relatquantitative lawthat the qachieved is bounded by the qtransmitted in a certain channequestion of how the abstract

embodiedwhat sort of machThis chapter introduces a newwhich extends the possibilitieing chapters consider the achiethe difficulties increase, partictem becomes very large.

At first, in Part III, we will provided, either by being inbmanufacturer, or by some otmade the regulator, of how th


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as an interaction between several regulations. Thus a signalmanmay have to handle several trains coming to his section simulta-neously. To handle any one by itself would be straightforward,but here the problem is the control of them as a complex wholepattern.

This case is in fact still covered by the basic formulation. Fornothing in that formulation prevents the quantities or states or ele-ments in D, R, T, or Efrom being made of parts, and the partsinterrelated. The fact that D isa single letter in no way impliesthat what it represents must be internally simple or unitary.

The signalmans disturbance D is the particular set of trainsarriving in some particular pattern over space and time. Otherarrangements would provide other values for D, which must, ofcourse, be a vector. The outcomesEwill be various complex pat-terns of trains moving in relation to one another and moving away

from his section. The acceptable set will certainly include a com-ponent no collision and will probably include others as well. HisresponsesR will include a variety of patterns of movements of sig-nals and points. Tis what is giventhe basic matters of geography,mechanics, signalling techniques, etc., that lead determinately fromthe situation that has arisen and his reaction pattern to outcome.

It will be seen therefore that the basic formulation is capable, inprinciple, of including cases of any degree of internal complexity.


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Chapter

THE ERRORREGU

12/1. In the previous chapter and showed that certain relatiois to be achieved. There we asand then studied what was necthough useful, hardly corresp

practice. Let us change to a neIn practice, the question of r

The essential variables Eare states in which they must bsurvive (or the industrial planmust be given before all else.Btaken or even discussed, we what is wanted. Any particgiventhe cat must keep itseA servo-mechanism has its ai

one must keep an incubating roerating room cold. Throughouconsiderations have already dewhat are the acceptable statessolely with the problem of howturbances and difficulties.

The disturbancesD threateacts through some dynamic sydiagram of immediate effects


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that R2 may be of capacity greater thanR1, so that an amplificationThi ibili i di d i h h h


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occurs. This possibility is studied in the next chapter, where weshall see that, apart from being necessarily wasteful, the methodof regulation by stages opens up some remarkable possibilities.


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Chapter

AMPLIFYING

14/1. What is an amplifier? Athat, if given a little of sometamplifier, if given a little soulot of sound. A power-ampliS.12/21, if given a little powerof power (from H). And a mthat, if given a little money, w

Such devices work by havinwhat is to be emitted, and thento the flow from the reservoir.magnifying the input, as doemore commonly it works power-amplifier has some sodantly (the compressed air asource that provides most of contributing little or nothing work performed by the cranenothing directly towards liftinhis work is expended in movin

It will be seen that in the pow1) the whole processthat offorce atLgoes in two stagesseparation into two stages thable, for otherwise, i.e. in oneenergy would make any simplimpossible Stage 1 consists o


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INDEX


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289

INDEX

(The number refers to the page. A bold-faced number indicates a definition.)

ABSOLUTESYSTEM, 41, 89Absorbing state, 229

Aerofoil, 94Air-conditioner, 200Altitude, 222Amino-acid, 111, 197Ammonia, 110

Amphioxus, 3Amplifier, of power, 238 of regulation, 265 of intelligence, 271Andersen, H., 119Aphasia, 86Argon, 64Arrow, 130Ashby, W. Ross, 273Association, 133Asterisk, viAtom, 261Auspices, 259

Autocatalysis, 71, 196Automatic pilot, 199, 200Avalanche, 71Averages, 91

BACTERIA, 29, 30, 125, 183Balancing, 156Basin, 23 as selector, 260Battle of Life, 241Behaviour, line of, 25, change of, 43Behaviourism, IBellman, R., 73, 273Beverage, 123Bicycle, 199Binary digit, 126Bit, 126

Black Box, 86, 255Blood count, 190Blood group, 125Bomb-sight, 86

Boom and slump, 109Borrowed knowledge, 90

Bourbaki, N., 97, 113, 158, 273Boyles law, 45Braille, 185Breeding, 70Brewing, 112Bridge, 258Brownian movement, 78, 186Buses, aggregation, 81Button and string, 22, 100

CANNON, W. B., 195, 273Canonical representation, 29, 36 , deduction of, 90Capacity, 179Car, 215, 257 skidding, 203Carbon dioxide, 81, 237Card, identifying, 125 cutting, 141Cash register, 15Casting, 26Cat, 122, 197Causalgia, 82Chain, Markov, 165Chair, 131Chameleon, 130Change of state, 9 of input, 43Channel, 130, 154 capacity, 179Chaos, 131Chasing, 145Chess, 12, 241Clock, 25Closure, 11, 28, 76, 108Cloud, 30

Coding, 140, 243, alphabetic, 11in brain, 140Coenetic variable, 212

AN IN TRO D UCTION TO CY BERNETICS

Coffee, 123, 137Coin, 156, 232Cold, 238Commander, 211Communication, 123

Degrees of freedom, 129Delay, 156Delayer, 148Derivative, 116Design, 251

INDEX

136, 177Environment, 271Epistemology, 87Equality of vectors, 31Equations, differential, 35

Ghosts, 60Goal, 81, 219, 230Goldman, S., 110, 273Golfer, 231Grand Disturbance, 249


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290

Communication, 123Complex system, 4Component, 31Composition, 21Compound, 216, 217Computer, 96, 116Conditioned reflex, 133Cone, 73

Confidence, 163Confluence, 134Conjuring, 114, 125, 137Connexion, 65, deducing, 92Conservation of energy, 131, 265Constant, 215Constraint, 100, 127, 173, 247Continuity, 9, 28 as constraint, 133Control, 193, 213 -flow chart, 57 by error, 219 panel, 88Convergence, 134Cooling, 26, 137Correction, 211Corruption, 186

Cough, 247Counterfeit coin, 156Coupling, 48, random, 63 and equilibrium, 82 Markovian machines, 227Crane, 240Cricket, 15Criterion, 257Cube, 73Culture medium, 29, 30Cutting pack, 141Cybernetics defined, 1Cycle, 75

DARLINGTON, C. D., 193Death, 197Decay of variety, 136

De-coding, 141Definition, viiDegeneracy, 46Degree of confidence, 163

Design, 251Design for a Brain, v, 41, 52, 79, 84116, 143, 196, 262, 273Determinacy, search for, 91 in Bridge, 259Determinate machine, 24, 225Diagonal, 16Diagram of immediate effects, 57

, deduction of, 92Diagram of ultimate effects, 57Dichotomy, 261Dictator, 213Die, 169Difference, 9Differential equation, 35, 96 , stability theory, 113Discrete change, 9, 28Discrimination, 103Displacement, 77Dissociation, 169Distinction, 103Distortion, 188Disturbance, 77, 198repetitive, 247Divergence, 134Dominance, 53

Door, 86Duel, 201Duration of selection, 260

EARTH, CONSTRAINTSON, 131, age of, 196, reducibility on, 262Economic system, 37Effect, immediate, 56, ultimate, 57Effector, 220Elastic, 112Electro-mechanical analogy, 96Element, 122, 191Elimination, 18Embody, 29Emergent property, 110Energy, 3, 131, 240, 265

English, 170Entropy (of communication theory),174, 207Entropy (of thermodynamics), 112

291

Equations, differential, 35, unsolvable, 37Equilibrium, 74, stable, 77, unstable, 78, neutral, 78 and coupling, 82 in Markov chain, 167, 229

, absent, 258Equivocation, 189Error, 190, 219Essential variables, 197Ethyl acetate, 71Even and odd, 104Everyman, 122Evolution, 196Exercises, viExperience, law of, 137Experimentation, 89Exponential growth, 70 series, 173Expression, 30Eyes, 130

FACTOR, 5Feedback, 51, 53, 237

and stability, 80 and variety, 157Felis, 122Fencer, 201Fermentation, 125, 183Fibonacci, 19Fisher, Sir Ronald, 5, 245, 259 and F. Yates, 234, 273Fluxion, 74Fly-paper, 167, 229Flying Saucer, 87Form, 31Fourier analysis, 47Frequency, 47, 163

GALE WARNING, 140Galileo, 121Game, 202, 240Gas law, 45, 62Gene-pattern, 62, 198, 270General, 211Geometry, 2

Grand Disturbance, 249 Response, 249Granit, R., 82, 273Graph, 94, kinematic, 22 as constraint, 130Guest, 204Gunpowder, 70

HALF-TRUTH, 104Haunted house, 60Heart, 252History of system, 115, 170Hitler, A., 213Homeostasis, 81, 196Homeostat, 83, 233, 260, 271

Homo, 198, 252Homomorphism, 103Hot or cold ?, 235House lights, 125Humours, 191Hunt and stick, 230Hunter, 200Hunting, 236Hydrogen chloride, 110 1odide, 122

IDENTITY, 15Immediate effect, 56diagram, 57Inaccessible,92Incense, 60Incessant transmission, 161Incomplete observation, 113Incubator, 236Independence in behaviour, 58 in variety, 128Infinitesimal, 9Information, 123, 245 theory, 3, gain of, 178Initial state as noise, 217Input, 44, 87 and design, 254Insect, 165

Insolubility, 69Instinct, 26Instrumentation, 143Insulator, 93


Integration, 37, 173Intelligence, 82, 271Interference, 158Invariant, 73, 121, 130, 215Inverse, 142

as regulator, 251 as selector, 259MacKay, D. M., 252, 273Magnetic tape, 116Maiden over, 15

INDEX

Normal co-ordinates, 101Notation, 13, 20, 33

OBJECT, 131Observation incomplete 113

Posture, 30Power amplifier, 238Power of transformation, 16, 170

Predator 241


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292

,Inversion, 145Inverter, 147Iionization, 122I.Q., 272Isomorphism, 92, 97Iterated systems, 262

JOINING, 48 and equilibrium, 82Jump, 9, 28

KEY, 142Kinematic graph, 22

LACTOSE, 125Laplace transform, 145Large system: see VeryLashley, K. S., 62, 273Lattice, 107Laughter, 60Law of Nature, 130 of Experience, 137 of Requisite Variety, 206Learning, 92, 133, 271

Lethal, 197Lewin, K., 113,273Lights, house, 125, traffic, 127Limit, 197 of regulation, 211Line, transformation of, 20 of behaviour, 25Linear system, 36LocalisatiOn, 68, 112Locomotive, 80Logarithm to new base, 126

Lumbricus, 252

MACHINE, THEORYOF, 1, determinate, 24 with input, 44 seeing itself, 55

, test for, 90 as constraint, 132 set of states, 135, Markovian, 225

,Main diagonal, 16Manipulation, 92Maneuvre, 211Many-one, 15Map, 94Markov chain, 91, 166Markovian machine, 225

Massless spring, 2Materiality, 60Mathematical physics, 2, 27, 96Matrix, 15 transition probabilities, 163, pay-off, 241Matter, laws of, 60Maze, 86, 114, 134, 228Meaning, 143Mechanism, 24Mega-pick, 261Memory, 115, 170Message, 123Mine, 92Mode, 101Model, 96, 105Momentum, 40Monitoring, 180

Morgenstern, 0., 241, 273Motor channel, 220Mouse, 197Multiplication, 104, mental, 180Myelin, 221

NATURAL SELECTION, 196Nature, law of, 130Neighbourhood, 77Negative feedback, 80Network, 66, 93, 160, 252Neumann, J. von, 62, 241, 273Neurons, 252, number of, 62, circuit of, 82, 137Neutral equilibrium, 78Nitrogen, 64

Noise, 186, 216, correction of, 211Noises, ghostly, 60Non-determinate, 161

293

Observation, incomplete, 113Odd and even, 104Omen, 259One-one, 14Operand, 10Operator, 10 of clock, 25Organ-playing, 60Oscillation, 168Oscillator, 36Outcome, 203Output, 46, 88Ovum, 3Oxygen, 222Oyster, 69

PANTAGRUEL, 129Parameter,43Parry, 201, 241Part, 100, 112 and equilibrium, 82Part-function, 66Pattern, 30, 94Pavlov, I. p., 133, 273Pay-off matrix, 241

Pendulum, 34, 39, 121, feedback within, 54Permanence, 193Persistence, 108, 193Personality Test, 125Petrol, 81pH, 237Phase space, 37Photograph, 94Physiological limits, 197Physiology, 193, 259Pilot, 211, automatic, 199, 200Playfair, 141Pneumatic amplifier, 238Pneumonia, 26Poincar, H., 113Point, representative, 22Pool, 165Population, 29, 30, 167Position, 31Positive feedback, 81

Predator, 241Prediction, 132Pre-fabrication, 268Pressure, 45Prey, 241Prices, 34Prisoner, 123, 124Probability, 122 as variable, 40, constant, 162Problem-solving, 272Product, 21Programming, 252Properties, breeding, 70Protocol, 88, constraint in, 132Protoplasm, 68Provider, 201Psychology, topological, 113Puzzle, 272

RADIO DESIGNING, 253Rana, 252Random, 63, 259 numbers, 234

searching, 236, 258Rayleigh, Lord, 64Receptor, 220Red corpuscles, 222Reducibility, 60 and selection, 261Redundancy, 130, 182References, 273Reflex, 247Regenerative circuit, 82, 137Region, stable, 76, 229Regulation, 193, limit of, 211, automatic, 251, amplifying, 265Reinforcement, 133Re-labelling, 97Relay, 84, 93Repetition, 89, 121, 247Replicates, 136Representation, canonical, 29Representative point, 22Requisite Variety, law of, 206, 245


Reservoir, 238Residues, 35Resistances, 256Respiratory centre, 81Retina, 188

Square of transformation, 17Stability, 23, 73, 113 under displacement, 77 and survival, 197 in Markovian machine, 228

INDEX

Thermal agitation, 78, 186Thermodynamics, 136Thermostat, 135, 198, 200Thing, 131Thirst, 224

Uniselector, 84Unsolvable equations, 37Unstable, 78

VARIABLE 31 100


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Reverberation, 137Riguet, J., 158, 273Rods, 160Rubber, 112

SAMPLING, REPEATED, 172School, 139Science, 107, 121, 131Scout, 155Searching, 236, 258Secrecy system, 141, 243, 273See-saw, 82Selection, 235, 236natural, 196, quantity of, 255by machine, 259Self-locking, 69, 234Self-observation, 55Self~reproduction, 111, 196Semaphore, 125Sensory channel, 220Sequence, 155, 172Series, exponential, 173Set, 122 and machine, 135

Shannon, C. E., vi, 93, 123, 161,207, 243, 245, 260, 273Shell, 198Shivering, 238Shuffling, 259Signal, 183, 221Silver chloride, 68Simple proportions, 131Simplification, 103Singing, 60Single-valued, 14 system, 39Siphon, 238Size of system, 61 of inverter, 151Skid, 203Skull, 201Smoke, 183

Sommerhoff, G., 211, 273S hi i i 92

Stable region, 76, 229Stages of regulation, 263 of amplification, 265Stamp, 256Standard, 246Star cluster, 113State, 25

stationary, 30 of equilibrium, 74, 229, inaccessible, 92, initial, as noise, 217, absorbing, 229Stationary, 30Statistical mechanics, 62Statistics, 245, determinacy in, 91Steady state, 30, 169Steering, 203, 211, 215Steermanship, 1Step-function, 242Stepping switch, 84Stickleback, 26Stochastic, 162Stock breeder, 62Strategy, 205, 240

Sub-system, 48Sugar, 111Supernova, 248Supplementation, 65, 162 of selection, 258Survival, 77, 197Switch, as input, 43, 253System, 40, complex, 4, economic, 37, absolute, 41, definition of, 106, 227, very large: see Very

TABETIC, 220Tachometer, 146Tap, 234Tea-taster, 135

Telegraph, 161, 211T l h 161

Threat, 221Threshold, 66Till, 15Tinbergen, N., 26, 273Tinder Box, 119Topology, 85, 113Tortoise, 198

Trace, 115Traffic lights, 127Train, 80Trajectory, 25, 94 of Markovian machine, 229Transducer, 44, 143Transform, 10, multiple, 161Transformation, 10, single-valued, 14, one-one, 14, many-one, 15, identical, 15, geometric, 20, embodiment, 29, random, 65, 126, 135, inverse, 142Transient, 48

Transition, 10, observing, 146, probability, 163Transmission, 140, incessant, 161Trial and error, 230Triunique, 45Tustin, A., 37, 237, 273Twenty Questions, 126Tyrant, 213Tyre, 122

ULTIMATE EFFECT, 57Ultrastability, 83, 233, 242

VARIABLE, 31, 100 in system, 40, missing, 114, essential, 197Variety, 119, 125, 126, requisite, 206 in vectors, 249Vector, 31 equality, 31 constraint, 128, sequence as, 172, variety in, 249Velocity, 74Very large system, 61, 85, 109 , regulating the, 244Veto, 83, regulation by, 233, 260Vitamins, 40Vocabulary, 4Vocal cords, 180Volume, 45

WAGES, 34Warder, 123Water-amplifier, 266

Water-bath, 135, 198, 249Way of behaving, 43Weather, 31Weaver, W., 273Weighing coins, 156Whole, 112 and equilibrium, 82Wholeness, degree of, 68Wiener, N., 1, 123, 177, 273Work amplifier, 240

ZERO VARIETY, 126, 137 entropy, message of, 211

Documents

An Introduction to Cybernetics (Ashby)