CYBERNETICS or Control and Communication in the Animal and the Machine Second Edit

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Y ERNETI S

or ontrol nd ommuni tion

in the nim l n the m hine

NOR ERT W N RPRO SSOR OF M THEM TICS

TH I SS CHUSETTS INSTITUT O F T E CH N O LO G Y

second edition

THE M T PR SS

ambridge Massachusetts



and variable stars, a star is a definite object, eminently suitable forcounting and cataloguing; and if a human urchmU terung o f t he

stars-as we call these catalogues-stops short for stars less intensethan a certain magnitude, there is nothing too repugnant to us theidea of a divine urchmusterunggoing much further.

On the other hand, if you were to ask the meteorologist to giveyou a similar urchmusterungof the clouds, he might laugh in your

face, or he might pat ient ly explain that in all the language ofmeteorology there is no such thing as a cloud, defined as an objectwith a quasi-permanent identity; and that if there were, he neitherpossesses the facilities to count them, nor is he in fact interested incounting them. topologically inclined meteorologist mightperhaps define a cloud as a connected region of space in which thedensity of the par t o f the water content in the solid or liquid stateexceeds a certain amount, but this definition would not be o f theslightest value to anyone, and would at most represent an extremelytransitory state. What really concerns the meteorologist is somesuch statistical statement as, Boston: January 17, 1950: Sky 38

overcast: Cirrocumulus.There is of course a branch of astronomy which deals with what

may be called cosmic meteorology: the study ofgalaxies and nebulaeand star clusters and their .s tat .ist ics, as pursued for example byChandrasekhar, but this is a very young branch of astronomy,

younger than meteorology itself, and is something outside thetradition of classical astronomy. This tradition, apart from i ts

purely classificatory, urcltmusterung aspects, was originally concerned rather with the solar system than with the world of the fixed

stars. is the astronomy of the solar system which is that chieflyassociated with the names of Copernicus, Kepler, Galileo, and Newton, and which was the wet nurse of modern physics.

I t is indeed an idea))y simple science. Even before the existence

of any adequate dynamical theory , even as far back as the Baby

lonians, it was realized that eclipses occurred in regular predictablecycles, extending backward and forward over time. It was realizedthat time itself could better be measured by the motion of the starsin theircourses than in any othe rway. The pattern for all events in

the solar system was the revolution of a wheel or a series of wheels,whether in the form of the Ptolemaic theory of epicycles or theCopernican theory of orbits, and in such theory the future aftera fashion repeats the past. The music of the spheresis a palindrome,and the book of astronomy reads the same backward as forward.

There is no difference save of initial positions and directions between

Ne\\rtonian and Bergsonian Time

There is a l ittle hymn or song familiar to every German child.

It goes:

Weisst du, wioviel Stemlein stehen n dem blauen Himmelszelt?Weisst duo wieviel Wolken gohenWeithin fiber aile Welt?Gott, der erro ha t sic gczihlet asa ihm auch nicht eines fehlet n der gnnzell, grossen Zahl.

W.Hoy

In English this says: Knowestthou how many stars stand in theblue tent of heaven? Knowcst thou how many clouds pass far overthe whole world? The Lord God hath counted them, that not one of

the whole great number be lacking.This little song is nn interesting theme for the philosopher and the

historian of science, in t ha t i t puts side by side two sciences whichhave the one similar ity of dealing with the heavens above us, bu twhich in almost every o ther respect offer an extreme contrast.

Astronomy is the oldest of the sciences, while meteorology is amongthe youngest to begin to deserve the name. The more familiarastronomical phenomena can be predicted for many centuries, whilea precise prediction of tomorrow s weather is generally not easy andin many places very crude indeed.To go back to the poem, the answer to the first question is that,

within limits, we do know how many s tars there are. In the first

place, apart from minor uncertainties concerning some of the double30

NEWTONIAN AND BEROSONIAN TIl\fE 31



the motion of an orrery turned forward and one run in reverse.Finally when all this was reduced by Newton to a formal set of

postulates and a closed mechanics the fundamental laws of thismechanics were unaltered by the transformation ofthe time variablet into its negative.

Thus if we were to take a motion picture of the planets speeded

up to show a perceptible picture of activity and were t o run the filmbackward it would stiU be a possible picture of planets conformingto the Newtonian mechanics. On the other hand if we were to take

a motion picture photograph of the turbulence of the clouds in athunderhead and reverse it it would look altogether wrong. Weshould see downdrafts where we expect updrafts turbulence growingcoarser in texture lightning precedinginstead of following the changesof cloud which usually precede it and so on indefinitely.

What is the difference between the astronomical and the meteor-ological situation which brings about all these d i f f e r e n ~ s and inparticular the difference between the apparent reversibility of

astronomical time and the apparent irreversibility of meteorological

time? In the first place the meteorological system is one involvinga vast number of approximately equal particles some of them veryclosely coupled to one another while the astronomical system of the

solar universe contains only a relatively small number of particlesgreatly diverse in size and coupled with one another in a sufficiently

loose way that the second order coupling effects do not change the

general aspect of the picture we observe and the very high ordercoupling effects are completely negligible. The planets move underconditions more favorable t o the isolation of a certain limited set of

forces than those of any physical experiment we can set up in the

Ia.boratory. Compared with the distances between them the planets

and even the sun are very nearly points. Compared with the elasticand plasticdeformations they suffer the planets are eithervery nearlyrigid bodies or where they are not their·internal forces are at any

rate of a relatively slight significance where the relative motion of

their centers is concerned. The space in which they move is almostperfectly free from impeding matter; and in their mutual attraction

their masses may be considered to lie very nearly at their centers and

to be constant . The depar ture of the law of gravity from the

inverse square law is most minute. The positions velocities and

masses of the bodies of the solar system are extremely well known at

any time and the computation of their future and pas t positionswhile not easy in detail is easy and precise in principle. On the

other hand in meteorology the number of particles concerned is so

enormous that an accurate record of their initial positions and

velocities is utterly impossible; and i f this record were actually madeand their future positions and velocities computed we should havenothing but an impenetrable mass of figures which would need

radical reinterpretation before it could be ofany service t o us. Theterms cloud temperature turbulence etc. are al l terms

referring not to one single physical situation but to a distribution ofpossible situations of which only one actual case is realized. aU

the readings of aU the meteorological stations on earth were simul-taneously taken they would not give a billionth part o f the data

necessary to characterize the actual state of the atmosphere from a

Newtonian point of view. They would only give cer ta in constantsconsistent with an infinity of different atmospheres and at mosttogether with certain pr or assumptions capable of giving as a

probability distribution a measure over t he s et o f possible atmos-pheres. Using the Newtonian laws o r any o ther system of causallaws whatever. all that we can predict at any future time is aprobability distribution of the constants of the system and even

this predictability fades ou t with the increase of time.Now even in a Newtonian system in which time is perfectly

reversible questions of probability and prediction lead to answersasymmetrical as between past and future because the questions towhich they are answers are asymmetrical. I set up a physicalexperiment I bring the system I am considering from the past intothe presen t in such a wa y that I fix certain quantities and have areasonable right to assume that certain other quantities have knownstatisticaldistributions. I thenobserve thestatistical distribution of

results after a given time. This is not a process which I can reverse.in order to do so it would be necessary to pick out a fair distribution

of systems which without intervention on our par t would eml upwithin certain statistical limits and find out what the antecedent

condit ions were a given time ago. However for a system starting

from an unknown position to end up in any tightly defined statisticalrange is so rare an occurrence that we may regard it as a miracleand we cannot base our experimental technique on awaiting and

counting miracles. In short we are directed in time and our

relation to the future is different from our relation to the past. Allour questions are conditioned by this asymmetry and aU our answersto these questions are equally conditioned by it.

A very interesting astronomical question concerning the direction of time comes up in connection with t he time of astrophysics

in which we are observing remote heavenly bodies in a single

32 CYBERNETICS NEWTONIAN AND BERGSONIAN TIME 33



obsen ation and in which the re seems to be no unidirectionalness

in the nature ofour experiment. Why then does the unidirectional

thermodynamics which is based on experimental terrestrial observa-

tions stand us in such good stead in astrophysics? The answer is

interesting and not too obvious. Our observations of the stars are

through the agency of light of rays or particles emerging from the

observed object and perceived by us. We can perceive incoming

light bu t can no t perceive outgoing light or at least the perception

of outgoing light is not achieved by an experiment as simple and

direct as that of incoming light. In th e perception of incoming

light we end up with the eye or a photographic plate. We condition

these for the reception of images by put ting them in a s ta te o f

insulation for some time past: we dark condition the eye to avoid

after images and we wrap our plates in black paper t o p revent

halation. t is clear that only such an eye and only such plates are

any usc to us: if we were given to pre images we might as well be

blind; and if we had to pu t our pla tes in black paper after we use

them and develop them before using phot ography would be a very

difficult ar t indeed. This being the case we can see those starsradiating to us and to the whole world; while if there are any stars

whose evolution is in th e reverse direction they will attract radiation

from the whole heavens and even this attraction from us will not be

perceptible in any way in view of the fact that we already know our

own past bu t notour future. Thus the part of the universe which we

sec must have i ts past-future relations as far as the emission of

radiation is concemed concordant with our own. The very fact

that we see a star means that its thermodynamics is like our own.

Indeed it is a very interesting intellectual experiment to make the

fantasy of an intelligent being whose time should run the other way

to our own. To such a being all communicat ion with us would beimpossible . Any signal he might send would reach us with a logica l

stream of consequents from his point of view anteccdente from

ours. These antecedents would already be in our experience and

would have served to us as the natural explanation of his signal

without presupposing an intelligent being to have sent it. he

drew us a square we should see the remains of his figure as i ts pre-

cursors and i t would seem to be the curious crystallization-always

perfectly explainable-of these remains. It s meaning would seem to

be as fortuitous as the faces we read into mountains and cliffs. The

drawing of the square would appear to us as a catastrophe-sudden

indeed bu t explainable by natural laws-by which that square

would cease to exist . Our counterpart would have exactly similar

ideas concerning us. IVithin ny world with which can communi-

cate t direction o time is ttniJonn

To retum to the contrast between Newtonian astronomy and

meteorology: most sciences lie in an intermediate position bu t most

are rather nearer to meteorology t han t o astronomy. Even astron

omy as we have seen contains a cosmic meteorology. t cont.ains

as well that extremely interesting field studied by SirGeorge Danvin,

and known as the theory of tidal evolut ion. We have said that we

can treat the relative movements of the sun and the planets as the

movements of rigid bodies bu t this is no t quite the case. The earth,

for example is nearly surrounded by oceans. The water nearer thc

moon than the center of the earth is more strongly a tt racted to the

moon than the solid part of the earth, and the water on the other side

is less s trongly a tt ra ct ed . Th is relatively slight effect pulls the

water into two hills onc under the moon and one opposite to the

moon. In a perfectly liquid sphere these hills could follow the moon

around the earth with no great dispersal of energy and consequently

would remain almost precisely under the moon and opposite t o t he

moon. They would consequently have a pul l on the moon whichwould not greatly influence the angular position of the moon in the

heavens. However the t idal wave they produce on the earth gets

tangled up and delayed on coasts and in shal low seas such as the

Bering Sea and the Irish Sea. consequently lags behind the

position of the moon and the forces producing th is a re largely

turbulent, dissipative forces of a character much like the forces met

in meteorology and need a statist ical treatment. Indeed ocean-

ography may be called the meteorology of the hydrosphere rather

than of the atmosphere.

These frictional forces drag the moon back in its course about the

ear th and accelerate the rotation of the earth forward. They tend

to bring the lengths of the month and o f the day ever closer to one

ano ther . Indeed the day of the moon is the month, and the moon

always presents nearly the same face to th e earth . It has been

suggested that this is the result of an ancient tidal evolution when

th e moon conta ined some l iquid or gas or plastic material which

could give under the earth s attraction, and in sogiving could dissipate

large amounts of energy. This phenomenon of tidal evolution is no t

confined to the ear th and t he moon bu t may be observed to some

degree throughout all gravitating systems. In ages past it has

seriously modified the face of the solar system though in anything

like h is to ri c times thi s modification is s li gh t compared with the

.. rigid-body motion of the planets of the solar system.

34 OYBERNETICS NEWTONIAN AND BEROSONIAN TIME



Thus even gravitational astronomy involves frictional processes

that run down. There is not a single science which co nf or ms

precisely to the s tr ic t Newtonian pattern. The biological sciences

certainly have their full share of one-way phenomena. Birth is not

the exact reverse of death nor is anabolism-the building up of

tissues-the exact reverse of catabolism-their breaking down. The

division of cells does not follow a pattern symmetrical in time nor

does the union of the germ cells to form th e f er ti li zed o vu m. T heindividual is an arrow pointed through time in one way and the race

is equally directed from the past into the future.The record of paleontology indicates a definite long-time trend

interrupted and complicated though it might be from th e simple to

the complex. By t he m id dl e of the l ast century this t rend had

become apparent to all scientists with an honestly open mind and it

is n o a cc id en t that the problem of discovering its mechanisms wascarried ahead through the same great s tep by t wo m en w or ki ng at

about the same time: Charles Darwin and Alfred Wallace. This stepwas the realization that a mere fortuitous variation of the individuals

of a species m ig ht b e c ar ve d i nt o the form of a more or less onedirectional or few-directional progress for each line by the varyingdegrees of viability of the several variations either from the pointof

view of the individual or of the race. A mutant dog without legs

will certainly starve while a long thin lizard that has developed the

mechanism of crawling on its ribs may have a better chance forsurvival i f i t has clean lines and is freed from the impeding projec

tions of limbs. n aquatic animal whether fish lizard or mammalwill swim better with a fusiform shape powerful body muscles and

a p oste rio r a pp en da ge which will c at ch th e water; and if it isd ep en de nt fo r i ta fo od on the pursuit of swift prey its chances of

survival may depend on it s assuming this form.

Darwinian evolution is thus a mechanism by wh ich a m or e or lessfortuitous variability is combined into a rather definite pattern.

Darwin s principle still holds today though we have a much better

knowledge of t he m ec ha ni sm o n wh ic h it depends. T he work of

Mendel h as given us a f ar more precise and discontinuous view of

heredity than that held by Darwin while the notion of mutation

from the time of de Vries on has completely altered our conceptionof the statistical basis of mutation. We have studied the fineanatomy ofthe chromosome and have localized the gene on it. The

list of m od er n g en et ic is ts is long and distinguished. Several of

these such as Haldane have made the statistical study of Mendelian

ism an effective tool for the study of evolution.

We have already spoken of the tidal evolution of Sir George

Darwin Charles Darwin s son. Neither the connection ofthe idea of

the son with that of the f at he r n o r the choice of the name evolu

tion is fortuitous. In t id al ev olu tio n a s well a s in the origin of

species we have a mechanism by means of wh ich a f or tu it ou s

variability that of the random motions of t he waves in a tid al se a

a nd of the molecules ofthe water is converted by a dynamical process

in to a pattern of development which reads in one direction. The

theory of tidal evolution is quite definitely an astronomical applica

tion of the elder Darwin.The third of the dynasty of Darwins Sir Charles is one o f the

a ut ho ri ti es o n m od er n quantum mechanics. This fact may befortuitous but it nevertheless represents an even further invasion of

Newtonian ideas by ideas of statistics. The succession of namesMaxwell-Boltzmann-Gibbs represents a progressive reduction of

thermodynamics to statistical mechanics: that is a reduction of the

phenomena concerning heat and temperature to phenomena in

which a Newtonian mechanics is applied to a s it ua ti on i n which we

deal no t with a single dynamical system bu t with a statistical distribution of dynamical systems; and in which our conclusions concernnot all suchsystems bu t an ovenvhelming majority of them. About

the year 1900 it became apparent that there was something seriously

wrong with thermodynamics particularly where it concerned

r ad ia tio n. T he ether showed much less power to absorb radiationsof high frequency-as shown by the law of Planck-than any existing

mechanization of radiation theory had allowed. Planck gave a

quasi-atomic theory of radiation-the quantum theory-which

accounted satisfactorily enough for these phenomena but which

was at o dd s w it h the whole remainder of physics; and Niels Bohr

followed this up with a similarly o theory of the atom. Thus

Newton and Planck-Bohr formed respectively the thesis andantithesis of a Heg elian a nt in om y. T he sy nth esi s is the statisticaltheory discovered by Heisenberg in 1925 in which the statisticalNewtonian dynamics of Gibbs is replaced by a statistical theory very

similar to that of Newton and Gibbs for large-scale phenomena but

in which the complete collection of data for the present and t he past

is not sufficient to predict th e future more than statistically. It is

thus not t oo m uc h to say that not only the Newtonian astronomy

but even the Newtonian physics has become a picture of the averageresults of a statistical situation and hence an account of an evolution

ary process.

This transition from a Newtonian reversible time to a Gibbsian

36 CYBERNETICS

h

NEWTONIAN AND BERGSONIAN TIl\IE 7



irre rersible time has.had ita philosophical echoes. Bergson empha- sized the difference between the reversible time of physics in whichn othing new h ap pens and the irreversible time of evolution and

biol ogy i n which t he re i s a lw ay s s om et hi ng new. r fh e r ea li za ti on

that the Newtonian physics was not the p rop er frame for b io lo gy

was perhaps the central point in the old controversy between vitalisma nd m ec ha ni sm ; a lt ho ug h t hi s was c om pl ic at ed by the desire to

conserve in some form or other at least the shadows of the soul and

of God against the inroads of materialism. In the end as we have

seen the vi ta li st p rov ed t oo m uch. Instead of buil ding a wallbetween the claims of life and those of physics the wall h as bee n

e re ct ed t o s ur ro un d so wide a eom pa ss that both matter an d lifefind themselves inside it . It is t ru e that the mat te r o f the newer

physics is n ot the mat te r of Newton b ut it is something q u ite as

remot.e from the anthropomorphizing desires of the vitalists. The

chance of the quantum theoretician is no t the ethical freedom of the

Augustinian and Ty ch e is as relentless a mistress as Ananke.

The thought of e ve ry a ge is r ef te cte d i n its technique. The civil

engineers of ancient days were land surveyors astronomers andnavigators; those of the seventeenth and early eighteenth centurieswere clockmakers and grinders of lenses. As in a nc ie nt t im es th e

craftsmen mad e their too ls in the image of the heavens. A watch is

nothing hut a pocket orrery moving by necessity as do the celestial

spheres; and if friction and the dissipation of e ne rgy p la y a role i n

it they are effects to be overcome so that the resulting motion of

the h and s m ay be as periodic a nd r egu la r as possible. The chief

technical result of this engineering after the model of Huyghens and

Newt.on was the age of navigation in which for the first time it was

possible to compute longitudes with a respectable precision and to

convert the commerce of the great o cean s from a thing of chance and

adventure to a regular understood business. t is the engineeringof the mercantilists.

To the merchant succeeded the manufacturer and to the chronom

eter the steam engine. From the Newcomen engine almost to the

present time the central field of engineering has been the study of

prime movers. Heat h as been c on ve rt ed into u sable energy of

r ot at io n a nd t ra ns la ti on and the physics of Newton ha s been

supplemented by that of Rumford Camot and J ou le . T he rm o

dynamics makes its appearance a science in which time is eminently

irreversible; and although the earlier stages of this science seem to

represent a region of thought almost without contact with the New

tonian dynamics the theory of the conservation of energy a nd the

later statistical explanation of the Camot principle or second law of

thermodynamics or principle of the degradation of energy that

p rincip le which mak es the maximum efficiency obtainable by as te am engine d ep en d on the working temperatures of the boilerand t he condenser all these h av e fused thermo dy namics a nd the

Newtonian dynamics into th e statistical and the nOll-statisticalaspects of the same science.

the seventeenth and early eighteenth centuries a·re the age of

clocks and the latereighteenth and thenineteenthcenturiesconstitute

the age of steam engines the p resen t time is the age of communica

tion and c on tr ol . T he re is i n e le ct ri ca l e ng in ee ri ng a split whieh is

known in Germany as the split between the technique of strongcurrents and the technique of weak currents and which we k no w as

the distinction between power and communication engineering. It

is tlu s split which separates the age jt:·t past from that in wluch we

a re now li vi ng. A ct ua ll y c om mu ni ca ti on e ng in ee ri ng c an d ea lwith currents ofany size whatever and with the movement of engine o

powerful enough to swing massive gun turrets; what distinguishes it

from power engineering is that i ts m ai n i nt er es t i s not economy ofenergy but the accurate reproduction of a signal. T hi s signal may

be the tap of a k ey to be reproduced as the tap ofa telegraph receiver

at the other end; or it may he a sound transmitted and received

through the apparatus of a telephone; or it may be the turn of a

ship s wheel received as the angular position o f the rudder. Thus

communication engineering began with Gauss Wheatstone and the

first telegraphers. t received its first reasonably scientific treat-

ment at the hands of Lord Kelvin after the failure of the first

tran satlan tic cab le in the middle of the last century; and from the

eighties on it was p erh ap s Heaviside who d id the m os t t o br ing it

into a modern shape. The discovery of r ad ar a nd i ts use in the

Secon d World War to gether with the exigencies o f the control of

anti·aircraft fire have brought to the field a large number of weU-trained mathematicians and physicists. The wonders of the auto-

matic computing machine belong t o th e same realm of ideas which

w as c er ta in ly n ev er so a ct iv el y p ur su ed i n the past as it is at the

present day.

At every stage of t.echnique since Daedalus or Hero of Alexandriathe ability of the artificer to p ro du ce a working simulacru m of a

liv in g o rganism h as alway s intrigu ed p eo ple. This d esire to produce

and to s t u ~ automata h as alway s b een exp ressed in t.erms o f the

living technique of t he age. In the days of magic we have the

bizarre and sinister concept of the Golem that figure of clay into

38 CYBERNETICS NEWTONIAN AND BEROSONIAN TIl\IE J



which the Rabbi of Prague breathed life with the blasphemy of

the Ineffable Name of God. In the time of Newton, the automaton

becomes the clockwork music box, with the little effigies pirouettingstiffly on top. In the nineteenth century , the automaton is a

glorified heat engine, burning some combustible fuel instead of the

glycogen of the human muscles. F inal ly, the p resent automaton

opens doors by means of photocells, or points guns to the place atwhich a radar beam picks up an airplane, or computes the solution

of a differential equation.Neither the Greek nor the magical automaton lies along the main

lines of the direction of development of the modern machine, nor do

they seem to have had much of an influence on serious philosophicthought. I t is far d ifferent with the clockwork automaton. This

idea h as played a ve ry genuine and important role in the early

history of modern philosophy, although we are rather prone to ignore

it.To begin with, Descartes considers the lower animals as automata.

This is done to avoid questioning the orthodox Christian attitude that

animals have no souls to be saved or damned. Just how these living

automata function is something that Descartes, so far as I know,

never discnsses. However, the important allied question of the

mode of coupling of the human soul, both in sensation a nd in will,

with it s material environment is one which Descartes does discuss,

although in a very unsatisfactory manner. He places this couplingin the one median part ofthe brain known to him, the pineal gland.As to the nature of his coupling whether or not it represents a

direct action of mind on matter and of matter on mind he is nonetoo clear. He probably does regard it as a direct action in both

ways, bu t he attributes the validity of human experience in its action

011 the out.side world to the goodness and honesty of God.The role attributed to God in this matter is unstable. Either God

is ent irely passive, in which case it is hard to see how Descartes

explanation really explains anything, o r H e is an active participant,in which case it is hard to see how the guarantee given by His

honesty can be anything bu t an active participation in th e a ct of

sensation . Thus the causal chain of material phenomena isparalleled

by a causal chain starting with theact of God, by which He produces

in us the experiences corresponding to a given material s ituation .Once this is assumed, it is entirely natural to a tt ribu te the corre

spondence between our will and the effe t s it seems to produce in

the external world to a similar divine intel Vention. This is the path

followed by the Occasionalists, Geulincx and Malebranche. In

Spinoza, who is i n man y ways the continuator of this school, the

doctrine of Occasionalism assumes the more reasonable form of

asserting that the correspondence between mind and matter is that

of two self-contained attributes of God; but Spinoza is not dynam

ically minded, and gives l it tle or no attention to the mechanism of

this correspondence.

This isth e

situation from which Leibniz starts,bu t

Leibniz is asdynamically minded as Spinoza is geometrically minded. First, he

replaces the pair of cor-responding elements, mind and matter by a

continuum of corresponding elements: the monads. While these are

conceived after the pattem ofthe soul, they include many instances

which do not rise to the degree of self-consciousness of full souls, and

which form part ofthat world which Descarteswould have attributed

to matter. Each of them l ives in it s own closed universe, with a

perfect causal chain from the creation or from minus infinity in time

to the indefinitely remote future; bu t closed though they are. they

correspond one t o the other through the pre-established harmony of

God. Lcibniz compares t hem to clocks which have so been wound

up as to keep time together from the creat ion for all e te rn ity.Unlike humanly made clocks, they do no t drift into asynchronism;

but t hi s is due to the miraculously perfect workmanship of the

Creator.Thus Leibniz considers a world of automata which, as is natural in

a disciple of Huyghens, he constructs after the model of clockwork.

Though the monads reflect one another, the reflection does not consist

in a transfer of the causal chain from one to anot he r. They are

actually as self-contained as, or rather more self-contained than. the

passively dancing figures on top of a music box. They have no real

influence on the outside world, nor are they effectively influenced by

it. As he says, they have no windows. The apparent organizationof the world we see is something between a figment and a miracle.

The monad is a Newtonian solar system writ small.In th e nineteenth century, the automata which are human ly

constnlcted and those other natural automata, the animals and

plants of the materialist , are s tudied from a very different aspect.

The conservation and the degradation of energy are the nlling

principles of the day. The l iving organism is above all a heat engine,

burning glucose or glycogen or s ta rch, fa ts, and proteins into

carbon dioxide, water, and urea. It is the metabolic balance which

is the center of attention; and if the low working temperatures of

animal muscle attract attention as opposed to the high working

temperatures of a heat engine of similar efficiency, this fact is pushed

40 CYBERNETICS

NEWTONIAN AND BERGSONIAN TUlE 41



into a corner and glibly explained by a contrast between the chemicalenergy of the living organism and the thermal energy of the heat

engine. All the fundamental notions are those associated withenergy and the chief of these is tha t o f potential. The engineering

of the body is a branch of power engineering. Even today thisis the

predominating point of view of the more classically minded con-servative physiologists; and the whole trend o f thought o f suchbiophysicists 118 Rll8hevsky and his school bears witness to its

continued potency.

Today we are coming to realize that t he body is very far from aconservative system and that its component parts work in an

environment where the available power is much less limited than

we have taken it to be. The electronic tube has shown us that a

system with an outside source of energy almost all of which iswRsted may be a very effective agency for performing desiredoperations especially if it is worked at a low energy level. We are

beginning to see that such important elements as the neurons the

atoms ofthe nervous complex of our body do their work under much

the same condit ions as vacuum tubes with their relat ively smallpower supplied from outside by the circulation and that the book-kee}Jing which is most essential to describe their function is not one

of energy. In short the newer study of automata whether in th e

metal or in the flesh is a branch of communication engineering and

its cardinal notions are those of message amount of disturbance or

..noise a term taken over from the telephone engineer quantity

of information coding technique and so on.

In such a theory we deal with automata effectively coupled to theexternal world not merely by their energy How their metabolism

bu t also by a How of impressions of incoming messages an d o f th e

actions of outgoing messages. The organs by which impressions arereceived are th e equivalents of the human and animal sense organs.They comprise photoelectric cells an d o the r receptors for light;radar systems receiving their own short Hertzian waves; hydrogen-ion potential recorders which may be said to taste; thermometers;pressure gauges of various sorts; microphones; and so on. The

effectors may be electrical motors or solenoids or heating coils or

other instruments of very diverse sor ts . Between the receptor or

sense organ and the effector stands an intermediate set of elementswhose function is to recombine the incoming impressions into suchform as to produce a desired type of response the effectors. The

information fed into this cen tral control sys tem will very often

contain information concerning the functioning of the effectors

themselves. These correspond among other things to the kinestheticorgans and other proprioceptors of the human system for we toohave organs which record the position of a joint or the rate of con-traction of a muscle etc. Moreover the information received by

the automaton need not be used at once bu t may be delayed or

stored so as to become available at some future time. This is the

analogue of memory. Finally as long as the automaton is rurnungits very rules of operation are susceptible to some change on the bll8isof the data which have passed through its receptors in the past and

this is not unlike the process of learning.

The machines of which we are now speaking are not the dream of

the sensationalist nor the hope of some future time. They alreadyexist as thermostats automatic gyrocompass ship steering systemsself propelled missiles especially such 118 seek their target anti-

aircraft fire control systems automatically controlled oil crackingstills ultra rapid computing macltines and th e like. They had

begun to be used long before the war indeed the very old steam-

engine governor belongs among them but the great mechanization

ofthe Second World War brought them into their own and the needof handling the extremely dangerous energyof the atom will probablybring them to a still higher point of development. Scarcely a month

passes but a new book appears on these so called control mechanismsor servomechanisms and the presen t age is 118 truly the age of

servomechanisms as the nineteenth century was the age of the steamengine or the eighteenth century the age of the clock.

To sum up: the many automata of the present age are coupled toth e outside world both for the reception of impressions and for thoperformance of actions. They contain sense organs effectors and

th e equivalent of a nervous system to integrate th e transfer of

information from the one to the other . They lend themselves verywell to description in physiological terms. I t is scarcely a miracle

that they can besubsumed under one theory with the mechalUsms of

physiology.

The relation of these mechanisms to time demands careful study.

is clear of course that the relation input output is a consecutive

one in time and involves definite past future order. What is

perhaps not so clear is that the theory of the sensitive automata is astatistical one. We are scarcely ever interested in the performanceof a communication engineering machine for IL sirlgle input . Tofunction adequately it must give a satisfactory performance for a

whole class of inputs and this means a statistically satisfactory

performance for the class ofinput which it is statistically expected to

4 CYBERNETICS NEWTONIAN AND BEROSONIAN TIME 43



CYBERNETICS

receive. Thus its theory belongs totheGibbsiansta tistical mechanicsrather than to the classical Newtonian mechanics. We shall study

this in much more detail in the chapter devo ted to the theory of

communication.Thus the modern automaton exists in the same sor t ofBergsonian

time as the living organism; and hence there is no reason in Bergson sconsiderations why the essential mode of functioning of the living

organism should no t be the same as that of the automaton of thistype. Vitalism has won to the extent that even mechanisms

correspond to the time-structure of vitalism; bu t as we have said,

this victory is a complete defeat, for from every point of view which

has the slightest relation to morality or religion, the new mechanics

is fully as mechanistic as the old. Whether we should call the newpoint of view mater ia li st ic is large ly a quest ion of words: the

ascendancy of matter characterizes a phase of nineteenth-centuryphysics far more than the present age, and materialism has cometo be bu t little more than a loose synonym for mechanism. In

fact, the whole mechanist-vitalist controversy has been relegated to

the limbo of badly posed questions.

•

b

Groups and Statistical Mechanics

At about the beginning of the present century, two scientists, onc

in the United States and one in France, were working along lines

which would have seemed to each of them entirely unrelated, i f

either had had the remotest idea of the existence .of the other. In

New Haven, Willard Gibbs wasdeveloping his new point of view in

statistical mechanics. In PariS, Henri Lebesgue was rivalling the

fame of his master Emile Borel by the discovery of a revised and

more powerful theory of integration for use in the study of trigono

metric series. The two discoverers were alike in this, that each wasa man ofthe study rather than ofthe laboratory, bu t from this point

on, their whole attitudes to science were diametrically opposite.

Gibbs , mathematician though he was, always regarded mathe

matics as ancillary to physics. Lebesguewas an analyst ofthe purest

type, an able exponent of the extremely exacting modern standardsof mathematical rigor, and a \\Titer whose works, as fa r as I know, do

no t contain one single example of a problem or a method originating

directly from physics. Nevertheless, the work of these two men

forms a single whole in which the questions asked by Gibbs find their

answers, not in his own work bu t in the work of Lebesgue.

The keyidea of Gibbs is this: in Newton s dynamics, in its original

form, we are concerned with an individual system, with given initial

velocities and momenta, undergoing changes according to a certainsystem of forces under the Newtonian laws which l ink force and

acceleration. In the vast majority of practical cases, however, we

are far from knowing all the initial velocities and momenta. I f we

assume a certain ini tial d is tr ibut ion of the incompletely known 5



X

nLearning

and Self Reproducing Machines

Two of the phenomena which we consider to be characteristic of

living systems are the power to learn and the power to reproducethemselves. These properties different as they appear are inti-mately related to one another . An animal that learns is one which iscapable of being transformed by its past environment into a different

being and is therefore adjus table to i ts environment within its

individual lifetime. An animal that multiplies is able to createotheranimals in its own likeness at least approximately although not socompletely in its own likeness that they cannot vary in the course of

time. tillS variation is itselfinheritable we have the raw materialon willch natural selection can work. the hereditary invariability

concerns manners of behavior tlien among the varied patterns of

behavior which are propagated some will be found advantageous to

the continuing existence o f the race and will establish themselveswhile others which are detrimental to this continuing existence \ ll

be eliminated. The result is a certain sor t of racial or phylogeneticlearning as contrasted with the ontogeneticlearningof the individual.Both ontogenetic and phylogenetic learning are modes by which the

animal can adjust itself to its environment.Both ontogenetic and phylogenetic learning and certainly the

latter extend themselves no t only to animals but to plants andindeed to all organisms which in any sense may be considered to beliving. However the degree to which these two forms of learningare found to be important in different sorts of living beings varies

widely. n man and to a lesser extent in the other mammals160



Huxley J J Ewlulion: The odern ynlltuia Harper Bros. New Yark 1943.

I von Neumann J. and O. Morgenstern Theory Ga nes a ld Economic Behavior

Princeton University Press. Princeton. N.J. 1944.

7N L E ARNI NG AND SELF-REPRODUCING MACHINES

ginning. When this is feasible it is manifestly th e bes t way of

playing th e game. However in manygames like chess an d checkersour knowledge is not sufficient to permit a complete strategy of thissort a nd t he n we can only approximate to it. The von Neumanntype of approximate theory tends to lead a player to ac t with th e

utmost caution assuming that his opponent is th e perfectly wise

sort of a master.

This attitude however is not always justified. n war which is asort of game this will in general lead t o a n indecisive action which willoften be no t much better than a defeat. Le t me give two historicalexamples. When Napoleon fought th e Austrians in Italy it wasp a rt o f his effectiveness that he knew th e Austrian mode of militaryt ho ug ht t o be hidebound and traditional so that he was q ui tejustified in aasuming that they were incapable of taking advantage of

th e new decision compelling methods of war which ha d been devel-oped by th e soldiers of the French Revolution. When Nelsonfoughtth e combined fleets of continental Europe he ha d th e advantage of

fighting with a naval machine which had kept th e seas for years an d

which ha d developed methods of thought of which as he was wellaware his enemies were inca.pable. he ha d no t made th e fullestpossible use of this advantage instead of acting as cautiously as hewould have h ad t o ac t under th e supposition tha.t he was facing an

enemy of equal naval experience he might have won in th e long ru n

bu t could no t have won so quickly an d decisively as to establish th e

tight naval blockade which was th e ultimate downfall of Napoleon.Thus in both cases th e guiding factor was th e known record of th e

commanderan d of hisopponents as exhibitedstatisticallyin th e past

of their actions rather than an a tt emp t t o play th e perfect gameagainst th e perfect opponent. Any direct use of th e von Neumannmethod of game theory in these cases would have proved futile.

In a similar way books on chess theory are no t written from th evon Neumann point of view. They are compendia of principlesdrawn from th e practical experience of chess players playing againstother chess players of high quality an d wide knowledge; an d they

establish certain values or weightings to be given to th e loss of eachpiece to mobility to command to development an d to other factorswhich m ay v ar y with th e stage of th e game.

t is no t very difficult to make machines which w ll play chess of asort. The mere obedience t o t he la ws ofthe game so that only legalmoves are made is easily within th e power of quite simple computing

machines. Indeed it is not hard to a dapt an ordinary digita.lmachine to these purposes.

.

·r

CYBERNETICS70

ontogenetic learning an d individual adaptability are raised to th e

highest point. Indeed it may be said that a large part o f t h e phylo-

genetic learning of man has been devoted to establishing th e pos-sibility of good ontogenetic learning.

t has been pointed ou t by Jul ian Huxley in his fundamentalpa.per on th e mind of birds that birds have a small capacity forontogeneticlearning. Somethingsimilaris true in th e case of insects

an d in both instances it may be aasociated with th e terrific demandsmade on the individual by Bight a nd t he consequential pre emption

of th e capabilities of th e nervous system which might otherwise beapplied to ontogenetic learning. Complicated as th e behaviorpatterns of birds a re -i n flying in courtship in th e care of th e youngan d in nes t building-they are carried ou t correctly th e very firsttime without th e need o f a ny large amount of instruction from th e

mother. t is altogether appropriate to devote a chapter of this book to

these two related subjects. Can man made machines learn an d canthey reproduce themselves? We shall tr y to show in this chapter

that in fact they can learn an d can reproduce themselves an dwe

shall give an account of th e technique needed for both these activities.The simpler of these two processes is that of learning an d it is

there that th e technical development has gone furthest. I shall talkhere particularly of th e learning of game playing machines which

enables them to improve th e strategy and tactics of their performanceby experience.

There is an established theory of th e playing of games-the vonNeumann theory.2 I t concerns policy which is best considered by

working from the end of th e game rather than from th e beginning.

In th e last move o f t he game a player strives to make a winningmove if possible an d if not then at least a drawing move. His

opponent at the previous stage strives to make a move which willprevent th e other player from making a winning or a drawing move.

he can himself make a winning move at that stage he will do soan d this will not be th e next to the last bu t the laststage of th e game.Th e other player at th e move before this will t ry t o a c t insuch a waythat th e very best resources of his opponent will no t prevent himfrom ending with a winning move and so on backward.

There are games such as ticktacktoe where th e entire strategyis known an d it is possible to start this policy from th e very be



172 CYBERNETICS

O N L E AR N IN G A N D S E L F- R E PR O D UC I N G M AC H IN ES 173

Now comes th e question of policy within th e rules of th e game.

Every evaluation of pieces, command, mobility, and so forth, is

intrinsically capable of being reduced to numerical terms; an d whenthis is done, th e maxims of a chess book ma y be used for th e de

termination of th e best moves of each stage. Such machines have

been made; an d they will playa very fair amateur chess, although at

present not a game of maater caliber.

Imagine yourself in th e position of playing chess against such amachine. To make th e situation fair, le t us suppose yo u are playingcorrespondence chess without th e knowledge that it is such a machineyou are playing and without th e prejudices that this knowledge ma y

excite. Natural ly, asalways is th e case vith chess, yo u will come to

a judgment of your opponent s chess personality. You willfind that

when th e same situation comes up twice on th e chessboard, your

opponent s reaction will be th e sameeach time, an d you will find that

he ha s a very rigid personality. an y trick of yours will work, then

it will always work u nd er t h e same conditions. t is thus no t toohard for an expert to ge t a line on h is machine opponent an d to

defeat him every time.However, there ar e machines that cannot be defeated so trivially.

Le t us suppose that every few games th e machine takes time off an d

uses its facilities for another purpose . Thi s time, it does no t play

against an opponent, bu t examines all th e previous games which it

has recorded on ita memory to determine what weighting o f t he

different evaluations of the worth of pieces, command, mobility, an d

th e l ike, will conduce most to winning. n this way, it learns no t

only from it s own failures bu t its opponent s successes. It nowreplaces its earlier valuations by th e new ones and goes on playing as

a new and better machine. Such a machine would no longer have as

rigid a personality, an d th e tricks which were once successful against

it will ult imately fail. More t h an t h at it ma y absorb in th e courseof time something o f t he policy of it s opponents.

All this is very difficult to do in chess, an d a8 a matter of fact th e

full development of this technique, so aa to give rise to a machine

that can play master chess, has no t been accomplished. Checkers

offers an easier problem. Th e homogeneity o f t he values o f t he

pieces greatly reduces th e number of combinations to be considered.

Moreover, partly as a consequence of this homogeneity, th e checker

game is much less divided into distinct stages than th e chess game.Even in checkers, th e main problem of t he e nd game is no longer to

take pieces bu t to establish contact with th e enemy so that one is in

a posit ion to take l)ieces. Similarly, th e valuation of moves in th e

.t

chess game must be made independent ly for th e different stages.No t only is th e en d game different from th e middle game in th e considerations which are paramount bu t th e openings are much more

devoted to getting th e pieces into a posit ion of free mobil ity fora t ta ck a n d defense than is th e middle game. Th e result is that wecannot be even approximately content with a uniform evaluation of

th e various weighting factors for th e game a s a whole, bu t must

divide th e learning process into a number of separate s tages. Onlythen can we hope to construct a learning machine which can play

master chess.Th e idea of a first-order programming, which ma y be linear in

certain cases, combined with a second-order programming, whichuses a much more extensivesegmentofthe paat for th e determination

of th e policy to be carried ou t in th e first-order programming, has

been mentioned earlier in this book in connection w it h t he problemof prediction. Th e predictor uses th e immediate p as t o f th e flightof th e airplane as a tool fm th e prediction of th e future by means of

a l inea r opera tion; bu t th e determination of th e correct linear

operation is a statistical problem in which tho long p as t o f t h e flightan d th e p as t o f many similar Rights are used to give th e basis o f t he

statistics.Th e statistical studies necessary to use a long past for a determina

tion of th e policy to be adopted in view of t h e s h or t past are highly

non-linear. As a m at te r o f faot, in th e use of th e Wiener-Hopf

equation for prediction,l th e determination of th e coefficients of tWsequation is carried ou t in a non-linearmanner. In general, a learningmachine operates by non-linear feedback. Th e ohecker-playingmachine described by Samuel z an d Watanabo 3 can learn to defeat

th e ma n that programmed it in a fairly consistent way on th e basis

of from 10 to 20 operating hours of programming.Watanabe s philosopWcal ideas on the use of programming

machinesarevery exciting. On th e one hand, he is treating a method

of proving an elementary geometrical theorem which shall conform

n an optimal way according to certain criteria of elegance an d

simplicity, as a learning gamo to be played no t against an individual

opponent bu t against what we ma y call Colonel Bogey. A similar

I Wiener, N • EztrapoloJion, InlerpoloJion, and SrMOlhi fI oj Stationary Time Seriu

with Engineering Applicalion8. The Technolog) Preas of ~ U T and John Wiloy

Sons, New York 1949,

a Samuel,A. L., ..Some Studies in MachineLearning. Using tho Gameof Checkers,

IB Y Journal oj ut rchand Detoelopment, 3 210-229 (1959).

S Watanabe S ..Information Theoretical AnaJ) Sis of ~ I u l t i v a r i a w Correlation,

IB M Journal oj Rt4tJJrch and Devw,prnn t, 4. 66-82 (1960).



game which Watanabe is studying is played in logical induction,when we \\ ish build up a theory which is opt imal in a similarquasi-aesthetic way, on the basis of an evaluation of economy,directness, and the like, by the determination of the evaluation of afinite number of parameters which are lef t free. This, it is t rue, isonly a limited logical induction, bu t it is well worth studying.

Many forms of the activity of struggle, which we do no t ordinarilyconsider as games, have a great deal of light thrown on t hem by the

theory of game-playing machines. One interesting example is the

fight between a mongoose and a snake. As Kipling points out in..Rikki-Tikki-Tavi, the mongoose is no t immune to the poison of

the cobra, although it is to some extent protected by i ts coat of stiffhairs which makes it difficult for the snake to bite home. As

}{ipling states, the fight is a dance with death, a struggle of muscular

skil l and agil ity. There is no reason to suppose that the individualmotions ofthe mongoose are faster or more accurate than those of the

cobra. Yet the mongoose almost invariably kills the cobra and comesou t of the contest unscathed. How is it able to do this?

I am here giving an account which appears valid me, fromhaving seen such a fight, as well as motion pictures of other suchfights. I do not gua ran tee the correctness of my observations asinterpretations. The mongoose begins with a feint, which provokes

the snake to strike. The mongoose dodges and makes another suchfeint, so that we have a rhythmical pattern ofactivity on the part of

the two animals. However, th is dance is not static bu t developsprogressively. As it goes on, the feints of the mongoose come earlierand earlier in phase with respect to the darts of the cobra, untilfinally the mongoose attacks when the cobra is extended and not ina position to moye rapidly. This t ime the mongoose s attack is no t

a feint bu t a dMdly accurate bite through the cobra s brain.In other words, the snake s pattern of action is confined to singledarts, each one for itself, while the pattern of the mongooso s actioninvolves an appreciable, i f not very long, segment of the whole past

of the fight. To this extent the mongoose acts like a learning ma

chine, and the real deadliness of its attack is dependent on a muchmore highly organized nervous system.

As a Walt Disney movie of several years ago showed, somethingvery similar happens when one of our western birds, the road runner, ~ t k s a rat tlesnake. While the b ird fights with beak and claws,and a mongoose it h its teeth, the pattern ofactivity is very similar.A bullfight is a very fine example of the same thing. For it must be

remembered that the bullfight is not a sport bu t a dance with death,

174 OYBERNETICS

.

i--·

.,

ON LEARNING AND SELF REPRODUCING l\IACHINES 175

to exhibit the beauty and the interla-eed coordinating actions of the

bull and the man. Fai rness to the bull has no part in i t, and we canleave ou t from our point of view the preliminary goading andweakening of the bull, which have the purpose of bringing the contest to alevel where the interaction of the patterns of the two participants ismost highly developed. The skilled bullfighter has a large repertoryof possible actions, such as the flaunting ofthe cape, various dodges

and pirouettes, and the like, which are intended to bring the bullinto a position in which it has completed its rush and is extended at

the precise moment that the bullfighter is ready to plunge the

ut qu into the bull s heart.What I have said concerning the fight between the mongoose and

the cobra, o r the toreador and the bull, will also apply to physicalcontests between man and man. Consider a duel with the smallsword. It consists of a sequence of feints, parries, and thrusts, withthe intention on the part of each participant to bring his opponent ssword ou t of line to such an extent that he can thrust home withoutlaying himself open to a double encouuter . Again, in a champion

ship game of tennis, it is not enough to serve or return the ballperfectly as far as each individual stroke is considered; the strategyis rather to force the opponent into a series of returns which pu t himprogressively in a worse position until there is noway in which he can

return the ball safely.These physical contests and the sort of games which we have

supposed the game-playing machine to play both have the sameelement of learning in terms of experience of the opponent s habits aswell as one s own. What is t rue of games of physical encounter isalso true of contestsin which the intellectual element is stronger, suchas war and the games which simulate war, by which our staffofficerswin the elements of their military experience. This is t rue for

classical war both on land and at sea, and isequally true with the newand as yet unt ried war wi th atomic weapons. Some degree of

mechanization, parallel to the mechanization of checkers by learningmachines, is possible in all these.

There is nothing more dangerous to contemplate than World War

III. It is worth considering whether part of the danger may not be

intrinsic in the unguarded use of learning machines. Again and

aga in I have heard the statement that learning machines cannotsubject us t o any new dangers, because we can turn them off whenwe feel like it. But can we? To turn a machine off effectively, wemust be in possession of information as to whether the danger pointhas come. The mere fact that we have made the machine does no t



180 CYBERNETICS

ensemble of the possible inputs by taking their product and averagingit over the time. The repertory of operations needed for all theseprocesses involves nothing more than the addition of potentials the .multiplication of potentials and the operationof averagingover time.Devices e xi st for all t hes e. As a matter of fact the elementarydevices needed in Professor Gabor s methodology are the s am e a sthose neededin mine. One of hisstudents has inventeda particularlyeffective and inexpensive multiplying device depending on the piezo

electric effect on a crystal of the attraction of two magnetic coils.What this amounts to is that w c an i mi ta te a ny u nk no wn n on

linear transducer by a s um of linear terms each of fixed characteristics and with an adjustable coefficient. This coefficient can bedetermined as the average product o f the outpu ts o f the unknowntransducer and a particular known transducer when the same shoteffect generator is connected to the input of both. What is moreinstead of computing this result on the scale of an instrument and

then transferring it by hand to the appropriate transducer thus

producing a piecemeal simulation of the a pp ar at us t he re is no

particular problem in automatically effecting the transfer of thecoefficients to the pieces of feedback apparatus. What w havesucceeded in doing is to m ak e a white box which c an p ot en ti al lyassume the characteristics of any non-linear transducer whatever

and t he n t o draw it into the similitude of a given black-box transducer by subjecting the two to the same random input and cOlmectingthe outputs of the structures in the proper manner 8 as t o arr iveat the suitable combination without any intervention on our part

I as k if this is philosophically very differentfrom what isdone whena gene a ct s as a template to form other molecules of the same genefrom an indeterminate mixture of amino and nucleic acids or when avirus guides into its own form other molecules of the same virus out

ofthe tissues and juices of its host. I do not in the least claim that

the details of these processes are the same bu t I do claim that they

are philosophically very similar phenomena.

x

Brain Waves

and Self-Organizing Systems

In the previous chapter I discussed the problems of learning and

self-propagation as they apply both to machines and at least byanalogy to li vi ng s ys te ms . H er e I s ha ll r ep ea t c er ta in c om me nt sI made in the P re fa ce a nd whi ch I i nt en d to pu t to immediate use.As I have pointed out these two phenomena are closely related to

each other for the first is the basis for the adaptation of the individualto its environment by means of experience which is what w may call

ontogenetic learning while the second as it furnishes the materialon which variation and natural selection may operate is the basis ofphylogenetic learning. s I have already mentioned the mammalsi n p ar ti cu la r m an do a l ar ge par t o f their adjustment t o t he ir environment by ontogenetic learning whereas the birds with theirhighly varied patterns of behavior which are not learned in the lifo

of the individual have devoted themselves much more to phylogenetic learning. e have seen the importance of non-linear feedbacks in the originatIon of b ot h processes. T he p re se nt c ha pt er is d ev ot ed to the

study ofa specific self-organizing system in which non-linear phenom

ena playa large part What I here describe is what I believe to behappening in the self-organization of electroencephalograms or brainwaves.

Before w can discuss this matter intelligently I must say something of what brain waves are and how t he ir s tr uc tu re m ay be s ub jected to precise mathematical treatment It h as been k no wn for

many years that activity of the nervous system is accompanied by181

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