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https://github.com/ianchanning/turing-test-paper

A faithful LaTeX recreation of Alan Turing's 'Computing Machinery and Intelligence' (Mind, 1950).
https://github.com/ianchanning/turing-test-paper

1949 alan-turing computer-science history papers turing-test

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A faithful LaTeX recreation of Alan Turing's 'Computing Machinery and Intelligence' (Mind, 1950).

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A faithful LaTeX recreation of Alan Turing's 'Computing Machinery and Intelligence' (Mind, 1950).



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# MIND



#### A QUARTERLY REVIEW



##### OF



#### PSYCHOLOGY AND PHILOSOPHY



---



### I.—COMPUTING MACHINERY AND INTELLIGENCE



**BY A. M. TURING**



##### 1. _The Imitation Game._



I **PROPOSE** to consider the question, 'Can machines think?'

This should begin with definitions of the meaning of the terms 'machine'

and 'think'. The definitions might be framed so as to reflect so far as

possible the normal use of the words, but this attitude is dangerous. If

the meaning of the words 'machine' and 'think' are to be found by

examining how they are commonly used it is difficult to escape the

conclusion that the meaning and the answer to the question, 'Can

machines think?' is to be sought in a statistical survey such as a

Gallup poll. But this is absurd. Instead of attempting such a definition

I shall replace the question by another, which is closely related to it

and is expressed in relatively unambiguous words.



The new form of the problem can be described in terms of a game which we

call the 'imitation game'. It is played with three people, a man (A), a

woman (B), and an interrogator (C) who may be of either sex. The

interrogator stays in a room apart from the other two. The object of the

game for the interrogator is to determine which of the other two is the

man and which is the woman. He knows them by labels X and Y, and at the

end of the game he says either 'X is A and Y is B' or 'X is B and Y is

A'. The interrogator is allowed to put questions to A and B thus:



**C**: Will X please tell me the length of his or her hair ?



Now suppose X is actually A, then A must answer. It is A's



object in the game to try and cause C to make the wrong identification.

His answer might therefore be "My hair is shingled, and the longest

strands are about nine inches long."



In order that tones of voice may not help the interrogator the answers

should be written, or better still, typewritten. The ideal arrangement

is to have a teleprinter communicating between the two rooms.

Alternatively the question and answers can be repeated by an

intermediary. The object of the game for the third player (B) is to help

the interrogator. The best strategy for her is probably to give truthful

answers. She can add such things as "I am the woman, don't listen to

him!" to her answers, but it will avail nothing as the man can make

similar remarks.



We now ask the question, 'What will happen when a machine takes the part

of A in this game?' Will the interrogator decide wrongly as often when

the game is played like this as he does when the game is played between

a man and a woman? These questions replace our original, 'Can machines

think?'



##### 2. _Critique of the New Problem._



As well as asking, 'What is the answer to this new form of the

question,' one may ask, 'Is this new question a worthy one to

investigate?' This latter question we investigate without further ado,

thereby cutting short an infinite regress.



The new problem has the advantage of drawing a fairly sharp line between

the physical and the intellectual capacities of a man. No engineer or

chemist claims to be able to produce a material which is

indistinguishable from the human skin. It is possible that at some time

this might be done, but even supposing this invention available we

should feel there was little point in trying to make a 'thinking

machine' more human by dressing it up in such artificial flesh. The form

in which we have set the problem reflects this fact in the condition

which prevents the interrogator from seeing or touching the other

competitors, or hearing their voices. Some other advantages of the

proposed criterion may be shown up by specimen questions and answers.

Thus:



**Q**: Please write me a sonnet on the subject of the Forth Bridge.



**A**: Count me out on this one. I never could write poetry.



**Q**: Add 34957 to 70764



**A**: (Pause about 30 seconds and then give as answer) 105621.



**Q**: Do you play chess ?



**A**: Yes.



**Q**: I have K at my K1, and no other pieces. You have only K at K6 and R

at R1. It is your move. What do you play ?



**A**: (After a pause of 15 seconds) R-R8 mate.



The question and answer method seems to be suitable for introducing

almost any one of the fields of human endeavour that we wish to include.

We do not wish to penalise the machine for its inability to shine in

beauty competitions, nor to penalise a man for losing in a race against

an aeroplane. The conditions of our game make these disabilities

irrelevant. The 'witnesses' can brag, if they consider it advisable, as

much as they please about their charms, strength or heroism, but the

interrogator cannot demand practical demonstrations.



The game may perhaps be criticised on the ground that the odds are

weighted too heavily against the machine. If the man were to try and

pretend to be the machine he would clearly make a very poor showing. He

would be given away at once by slowness and inaccuracy in arithmetic.

May not machines carry out some-thing which ought to be described as

thinking but which is very different from what a man does? This

objection is a very strong one, but at least we can say that if,

nevertheless, a machine can be constructed to play the imitation game

satisfactorily, we need not be troubled by this objection.



It might be urged that when playing the 'imitation game' the best

strategy for the machine may possibly be something other than imitation

of the behaviour of a man. This may be, but I think it is unlikely that

there is any great effect of this kind. In any case there is no

intention to investigate here the theory of the game, and it will be

assumed that the best strategy is to try to provide answers that would

naturally be given by a man.



##### 3. _The Machines concerned in the Game._



The question which we put in §1 will not be quite definite until we have

specified what we mean by the word 'machine'. It is natural that we

should wish to permit every kind of engineering technique to be used in

our machines. We also wish to allow the possibility than an engineer or

team of engineers may construct a machine which works, but whose manner

of operation cannot be satisfactorily described by its constructors

because they have applied a method which is largely experimental.

Finally, we wish to exclude from the machines men born in the usual

manner. It is difficult to frame the definitions so as to satisfy these

three conditions. One might for instance insist that the team of

engineers should be all of one sex, but this would not really be

satisfactory, for it is probably possible to rear a complete individual

from a single cell of the skin (say) of a man. To do so would be a feat

of biological technique deserving of the very highest praise, but we

would not be inclined to regard it as a case of 'constructing a thinking

machine'. This prompts us to abandon the requirement that every kind of

technique should be permitted. We are the more ready to do so in view of

the fact that the present interest in 'thinking machines' has been

aroused by a particular kind of machine, usually called an 'electronic

computer' or 'digital computer'. Following this suggestion we only

permit digital computers to take part in our game.



This restriction appears at first sight to be a very drastic one. I

shall attempt to show that it is not so in reality. To do this

necessitates a short account of the nature and properties of these

computers.



It may also be said that this identification of machines with digital

computers, like our criterion for 'thinking', will only be

unsatisfactory if (contrary to my belief), it turns out that digital

computers are unable to give a good showing in the game.



There are already a number of digital computers in working order, and it

may be asked, 'Why not try the experiment straight away? It would be

easy to satisfy the conditions of the game. A number of interrogators

could be used, and statistics compiled to show how often the right

identification was given.' The short answer is that we are not asking

whether all digital computers would do well in the game nor whether the

computers at present available would do well, but whether there are

imaginable computers which would do well. But this is only the short

answer. We shall see this question in a different light later.



##### 4. _Digital Computers._



The idea behind digital computers may be explained by saying that these

machines are intended to carry out any operations which could be done by

a human computer. The human computer is supposed to be following fixed

rules; he has no authority to deviate from them in any detail. We may

suppose that these rules are supplied in a book, which is altered

whenever he is put on to a new job. He has also an unlimited supply of

paper on which he does his calculations. He may also do his

multiplications and additions on a 'desk machine', but this is not

important. If we use the above explanation as a definition we shall be

in danger of circularity of argument. We avoid this by giving an outline

of the means by which the desired effect is achieved. A digital computer

can usually be regarded as consisting of three parts:



1.  Store.



2.  Executive unit.



3.  Control.



The store is a store of information, and corresponds to the human

computer's paper, whether this is the paper on which he does his

calculations or that on which his book of rules is printed. In so far as

the human computer does calculations in his head a part of the store

will correspond to his memory. The executive unit is the part which

carries out the various individual operations involved in a calculation.

What these individual operations are will vary from machine to machine.

Usually fairly lengthy operations can be done such as 'Multiply

3540675445 by 7076345687' but in some machines only very simple ones

such as 'Write down 0' are possible. We have mentioned that the 'book of

rules' supplied to the computer is replaced in the machine by a part of

the store. It is then called the 'table of instructions'. It is the duty

of the control to see that these instructions are obeyed correctly and

in the right order. The control is so constructed that this necessarily

happens. The information in the store is usually broken up into packets

of moderately small size. In one machine, for instance, a packet might

consist of ten decimal digits. Numbers are assigned to the parts of the

store in which the various packets of information are stored, in some

systematic manner. A typical instruction might say- "Add the number

stored in position 6809 to that in 4302 and put the result back into the

latter storage position."



Needless to say it would not occur in the machine expressed in English.

It would more likely be coded in a form such as 6809430217. Here 17 says

which of various possible operations is to be performed on the two

numbers. In this case the operation is that described above, viz. "Add

the number\...." It will be noticed that the instruction takes up 10

digits and so forms one packet of information, very conveniently. The

control will normally take the instructions to be obeyed in the order of

the positions in which they are stored, but occasionally an instruction

such as



"Now obey the instruction stored in position 5606, and continue from

there."



may be encountered, or again "If position 4505 contains 0 obey next the

instruction stored in 6707, otherwise continue straight on."



Instructions of these latter types are very important because they make

it possible for a sequence of operations to be repeated over and over

again until some condition is fulfilled, but in doing so to obey, not

fresh instructions on each repetition, but the same ones over and over

again. To take a domestic analogy. Suppose Mother wants Tommy to call at

the cobbler's every morning on his way to school to see if her shoes are

done, she can ask him afresh every morning. Alternatively she can stick

up a notice once and for all in the hall which he will see when he

leaves for school and which tells him to call for the shoes, and also to

destroy the notice when he comes back if he has the shoes with him.



The reader must accept it as a fact that digital computers can be

constructed, and indeed have been constructed, according to the

principles we have described, and that they can in fact mimic the

actions of a human computer very closely.



The book of rules which we have described our human computer as using is

of course a convenient fiction. Actual human computers really remember

what they have got to do. If one wants to make a machine mimic the

behaviour of the human computer in some complex operation one has to ask

him how it is done, and then translate the answer into the form of an

instruction table. Constructing instruction tables is usually described

as 'programming'. To 'programme a machine to carry out the operation A'

means to put the appropriate instruction table into the machine so that

it will do A.



An interesting variant on the idea of a digital computer is a 'digital

computer with a random element'. These have instructions involving the

throwing of a die or some equivalent electronic process; one such

instruction might for instance be, "Throw the die and put the resulting

number into store 1000".' Sometimes such a machine is described as

having free will (though I would not use this phrase myself). It is not

normally possible to determine from observing a machine whether it has a

random element, for a similar effect can be produced by such devices as

making the choices depend on the digits of the decimal for $\pi$.



Most actual digital computers have only a finite store. There is no

theoretical difficulty in the idea of a computer with an unlimited

store. Of course only a finite part can have been used at any one time.

Likewise only a finite amount can have been constructed, but we can

imagine more and more being added as required. Such computers have

special theoretical interest and will be called infinitive capacity

computers.



The idea of a digital computer is an old one. Charles Babbage, Lucasian

Professor of Mathematics at Cambridge from 1828 to 1839, planned such a

machine, called the Analytical Engine, but it was never completed.

Although Babbage had all the essential ideas, his machine was not at

that time such a very attractive prospect. The speed which would have

been available would be definitely faster than a human computer but

something like 100 times slower than the Manchester machine, itself one

of the slower of the modern machines. The storage was to be purely

mechanical, using wheels and cards.



The fact that Babbage's Analytical Engine was to be entirely mechanical

will help us to rid ourselves of a superstition. Importance is often

attached to the fact that modern digital computers are electrical, and

that the nervous system also is electrical. Since Babbage's machine was

not electrical, and since all digital computers are in a sense

equivalent, we see that this use of electricity cannot be of theoretical

importance. Of course electricity usually comes in where fast signalling

is concerned, so that it is not surprising that we find it in both these

connections. In the nervous system chemical phenomena are at least as

important as electrical. In certain computers the storage system is

mainly acoustic. The feature of using electricity is thus seen to be

only a very superficial similarity. If we wish to find such similarities

we should look rather for mathematical analogies of function.



##### 5. _Universality of Digital Computers._



The digital computers considered in the last section may be classified

amongst the 'discrete state machines'. These are the machines which move

by sudden jumps or clicks from one quite definite state to another.

These states are sufficiently different for the possibility of confusion

between them to be ignored. Strictly speaking there are no such

machines. Everything really moves continuously. But there are many kinds

of machine which can profitably be thought of as being discrete state

machines. For instance in considering the switches for a lighting system

it is a convenient fiction that each switch must be definitely on or

definitely off. There must be intermediate positions, but for most

purposes we can forget about them. As an example of a discrete state

machine we might consider a wheel which clicks round through 120 once a

second, but may be stopped by a lever which can be operated from

outside; in addition a lamp is to light in one of the positions of the

wheel. This machine could be described abstractly as follows. The

internal state of the machine (which is described by the position of the

wheel) may be $q_1$, $q_2$ or $q_3$. There is an input signal $i_0$, or

$i_1$ (position of lever). The internal state at any moment is

determined by the last state and input signal according to the table



|           |       |       |       |                |

| --------- | ----- | ----- | ----- | -------------- |

|           |       |       |       | **Last State** |

|           |       | $q_1$ | $q_2$ | $q_3$          |

| **Input** | $i_0$ | $q_2$ | $q_3$ | $q_1$          |

|           | $i_1$ | $q_1$ | $q_2$ | $q_3$          |



The output signals, the only externally visible indication of the

internal state (the light) are described by the table



|            |       |       |       |

| ---------- | ----- | ----- | ----- |

| **State**  | $q_1$ | $q_2$ | $q_3$ |

| **Output** | $o_0$ | $o_0$ | $o_1$ |



This example is typical of discrete state machines. They can be

described by such tables provided they have only a finite number of

possible states.



It will seem that given the initial state of the machine and the input

signals it is always possible to predict all future states. This is

reminiscent of Laplace's view that from the complete state of the

universe at one moment of time, as described by the positions and

velocities of all particles, it should be possible to predict all future

states. The prediction which we are considering is, however, rather

nearer to practicability than that considered by Laplace. The system of

the 'universe as a whole'' is such that quite small errors in the

initial conditions can have an overwhelming effect at a later time. The

displacement of a single electron by a billionth of a centimetre at one

moment might make the difference between a man being killed by an

avalanche a year later, or escaping. It is an essential property of the

mechanical systems which we have called 'discrete state machines'' that

this phenomenon does not occur. Even when we consider the actual

physical machines instead of the idealised machines, reasonably accurate

knowledge of the state at one moment yields reasonably accurate

knowledge any number of steps later.



As we have mentioned, digital computers fall within the class of

discrete state machines. But the number of states of which such a

machine is capable is usually enormously large. For instance, the number

for the machine now working at Manchester is about $2^{165,000}$,

i.e. about $10^{50,000}$. Compare this with our example of the clicking

wheel described above, which had three states. It is not difficult to

see why the number of states should be so immense. The computer includes

a store corresponding to the paper used by a human computer. It must be

possible to write into the store any one of the combinations of symbols

which might have been written on the paper. For simplicity suppose that

only digits from 0 to 9 are used as symbols. Variations in handwriting

are ignored. Suppose the computer is allowed 100 sheets of paper each

containing 50 lines each with room for 30 digits. Then the number of

states is $10^{100 \times 50 \times 30}$, i.e. $10^{150,000}$. This is

about the number of states of three Manchester machines put together.

The logarithm to the base two of the number of states is usually called

the 'storage capacity' of the machine. Thus the Manchester machine has a

storage capacity of about 165,000 and the wheel machine of our example

about 1.6. If two machines are put together their capacities must be

added to obtain the capacity of the resultant machine. This leads to the

possibility of statements such as "The Manchester machine contains 64

magnetic tracks each with a capacity of 2560, eight electronic tubes

with a capacity of 1280. Miscellaneous storage amounts to about 300

making a total of 174,380."



Given the table corresponding to a discrete state machine it is possible

to predict what it will do. There is no reason why this calculation

should not be carried out by means of a digital computer. Provided it

could be carried out sufficiently quickly the digital computer could

mimic the behaviour of any discrete state machine. The imitation game

could then be played with the machine in question (as B) and the

mimicking digital computer (as A) and the interrogator would be unable

to distinguish them. Of course the digital computer must have an

adequate storage capacity as well as working sufficiently fast.

Moreover, it must be programmed afresh for each new machine which it is

desired to mimic.



This special property of digital computers, that they can mimic any

discrete state machine, is described by saying that they are universal

machines. The existence of machines with this property has the important

consequence that, considerations of speed apart, it is unnecessary to

design various new machines to do various computing processes. They can

all be done with one digital computer, suitably programmed for each

case. It will be seen that as a consequence of this all digital

computers are in a sense equivalent.



We may now consider again the point raised at the end of §3. It was

suggested tentatively that the question, 'Can machines think?' should be

replaced by 'Are there imaginable digital computers which would do well

in the imitation game?' If we wish we can make this superficially more

general and ask 'Are there discrete state machines which would do well?'

But in view of the universality property we see that either of these

questions is equivalent to this, 'Let us fix our attention on one

particular digital computer C. Is it true that by modifying this

computer to have an adequate storage, suitably increasing its speed of

action, and providing it with an appropriate programme, C can be made to

play satisfactorily the part of A in the imitation game, the part of B

being taken by a man?'



##### 6. _Contrary Views on the Main Question._



We may now consider the ground to have been cleared and we are ready to

proceed to the debate on our question, 'Can machines think?' and the

variant of it quoted at the end of the last section. We cannot

altogether abandon the original form of the problem, for opinions will

differ as to the appropriateness of the substitution and we must at

least listen to what has to be said in this connexion.



It will simplify matters for the reader if I explain first my own

beliefs in the matter. Consider first the more accurate form of the

question. I believe that in about fifty years' time it will be possible

to programme computers, with a storage capacity of about $10^9$, to make

them play the imitation game so well that an average interrogator will

not have more than 70 per cent. chance of making the right

identification after five minutes of questioning. The original question,

'Can machines think?' I believe to be too meaningless to deserve

discussion. Nevertheless I believe that at the end of the century the

use of words and general educated opinion will have altered so much that

one will be able to speak of machines thinking without expecting to be

contradicted. I believe further that no useful purpose is served by

concealing these beliefs. The popular view that scientists proceed

inexorably from well-established fact to well-established fact, never

being influenced by any unproved conjecture, is quite mistaken. Provided

it is made clear which are proved facts and which are conjectures, no

harm can result. Conjectures are of great importance since they suggest

useful lines of research.



I now proceed to consider opinions opposed to my own.



\(1\) _The Theological Objection._ Thinking is a function of man's

immortal soul.[^1] God has given an immortal soul to every man and

woman, but not to any other animal or to machines. Hence no animal or

machine can think.



I am unable to accept any part of this, but will attempt to reply in

theological terms. I should find the argument more convincing if animals

were classed with men, for there is a greater difference, to my mind,

between the typical animate and the inanimate than there is between man

and the other animals. The arbitrary character of the orthodox view

becomes clearer if we consider how it might appear to a member of some

other religious community. How do Christians regard the Moslem view that

women have no souls? But let us leave this point aside and return to the

main argument. It appears to me that the argument quoted above implies a

serious restriction of the omnipotence of the Almighty. It is admitted

that there are certain things that He cannot do such as making one equal

to two, but should we not believe that He has freedom to confer a soul

on an elephant if He sees fit? We might expect that He would only

exercise this power in conjunction with a mutation which provided the

elephant with an appropriately improved brain to minister to the needs

of this soul. An argument of exactly similar form may be made for the

case of machines. It may seem different because it is more difficult to

"swallow". But this really only means that we think it would be less

likely that He would consider the circumstances suitable for conferring

a soul. The circumstances in question are discussed in the rest of this

paper. In attempting to construct such machines we should not be

irreverently usurping His power of creating souls, any more than we are

in the procreation of children: rather we are, in either case,

instruments of His will providing mansions for the souls that He

creates.



However, this is mere speculation. I am not very impressed with

theological arguments whatever they may be used to support. Such

arguments have often been found unsatisfactory in the past. In the time

of Galileo it was argued that the texts, "And the sun stood still... and

hasted not to go down about a whole day" (Joshua x. 13) and "He laid the

foundations of the earth, that it should not move at any time" (Psalm

cv. 5) were an adequate refutation of the Copernican theory. With our

present knowledge such an argument appears futile. When that knowledge

was not available it made a quite different impression.



\(2\) _The 'Heads in the Sand' Objection._ "The consequences of machines

thinking would be too dreadful. Let us hope and believe that they cannot

do so."



This argument is seldom expressed quite so openly as in the form above.

But it affects most of us who think about it at all. We like to believe

that Man is in some subtle way superior to the rest of creation. It is

best if he can be shown to be necessarily superior, for then there is no

danger of him losing his commanding position. The popularity of the

theological argument is clearly connected with this feeling. It is

likely to be quite strong in intellectual people, since they value the

power of thinking more highly than others, and are more inclined to base

their belief in the superiority of Man on this power.



I do not think that this argument is sufficiently substantial to require

refutation. Consolation would be more appropriate: perhaps this should

be sought in the transmigration of souls.



\(3\) _The Mathematical Objection._ There are a number of results of

mathematical logic which can be used to show that there are limitations

to the powers of discrete-state machines. The best known of these

results is known as _Gödel_'s theorem,[^2] and shows that in any

sufficiently powerful logical system statements can be formulated which

can neither be proved nor disproved within the system, unless possibly

the system itself is inconsistent. There are other, in some respects

similar, results due to _Church_, _Kleene_, _Rosser_, and _Turing_. The

latter result is the most convenient to consider, since it refers

directly to machines, whereas the others can only be used in a

comparatively indirect argument: for instance if _Gödel_'s theorem is to

be used we need in addition to have some means of describing logical

systems in terms of machines, and machines in terms of logical systems.

The result in question refers to a type of machine which is essentially

a digital computer with an infinite capacity. It states that there are

certain things that such a machine cannot do. If it is rigged up to give

answers to questions as in the imitation game, there will be some

questions to which it will either give a wrong answer, or fail to give

an answer at all however much time is allowed for a reply. There may, of

course, be many such questions, and questions which cannot be answered

by one machine may be satisfactorily answered by another. We are of

course supposing for the present that the questions are of the kind to

which an answer 'Yes' or 'No' is appropriate, rather than questions such

as 'What do you think of Picasso?' The questions that we know the

machines must fail on are of this type, "Consider the machine specified

as follows.... Will this machine ever answer 'Yes' to any question?" The

dots are to be replaced by a description of some machine in a standard

form, which could be something like that used in §5. When the machine

described bears a certain comparatively simple relation to the machine

which is under interrogation, it can be shown that the answer is either

wrong or not forthcoming. This is the mathematical result: it is argued

that it proves a disability of machines to which the human intellect is

not subject.



The short answer to this argument is that although it is established

that there are limitations to the powers of any particular machine, it

has only been stated, without any sort of proof, that no such

limitations apply to the human intellect. But I do not think this view

can be dismissed quite so lightly. Whenever one of these machines is

asked the appropriate critical question, and gives a definite answer, we

know that this answer must be wrong, and this gives us a certain feeling

of superiority. Is this feeling illusory? It is no doubt quite genuine,

but I do not think too much importance should be attached to it. We too

often give wrong answers to questions ourselves to be justified in being

very pleased at such evidence of fallibility on the part of the

machines. Further, our superiority can only be felt on such an occasion

in relation to the one machine over which we have scored our petty

triumph. There would be no question of triumphing simultaneously over

all machines. In short, then, there might be men cleverer than any given

machine, but then again there might be other machines cleverer again,

and so on.



Those who hold to the mathematical argument would, I think, mostly be

willing to accept the imitation game as a basis for discussion. Those

who believe in the two previous objections would probably not be

interested in any criteria.



\(4\) _The Argument from Consciousness._ This argument is very well

expressed in Professor _Jefferson_'s Lister Oration for 1949, from which

I quote. "Not until a machine can write a sonnet or compose a concerto

because of thoughts and emotions felt, and not by the chance fall of

symbols, could we agree that machine equals brainthat is, not only write

it but know that it had written it. No mechanism could feel (and not

merely artificially signal, an easy contrivance) pleasure at its

successes, grief when its valves fuse, be warmed by flattery, be made

miserable by its mistakes, be charmed by sex, be angry or depressed when

it cannot get what it wants."



This argument appears to be a denial of the validity of our test.

According to the most extreme form of this view the only way by which

one could be sure that machine thinks is to be the machine and to feel

oneself thinking. One could then describe these feelings to the world,

but of course no one would be justified in taking any notice. Likewise

according to this view the only way to know that a man thinks is to be

that particular man. It is in fact the solipsist point of view. It may

be the most logical view to hold but it makes communication of ideas

difficult. A is liable to believe 'A thinks but B does not' whilst B

believes 'B thinks but A does not'. Instead of arguing continually over

this point it is usual to have the polite convention that everyone

thinks.



I am sure that Professor _Jefferson_ does not wish to adopt the extreme

and solipsist point of view. Probably he would be quite willing to

accept the imitation game as a test. The game (with the player B

omitted) is frequently used in practice under the name of _viva voce_ to

discover whether some one really understands something or has 'learnt it

parrot fashion'. Let us listen in to a part of such a _viva voce_:



Interrogator: In the first line of your sonnet which reads 'Shall I

compare thee to a summer's day', would not 'a spring day' do as well or

better?



**Witness**: It wouldn't scan.



**Interrogator**: How about 'a winter's day' That would scan all right.



**Witness**: Yes, but nobody wants to be compared to a winter's day.



**Interrogator**: Would you say Mr. Pickwick reminded you of Christmas?



**Witness**: In a way.



**Interrogator**: Yet Christmas is a winter's day, and I do not think Mr.

Pickwick would mind the comparison.



**Witness**: I don't think you're serious. By a winter's day one means a

typical winter's day, rather than a special one like Christmas.



And so on. What would Professor _Jefferson_ say if the sonnet-writing

machine was able to answer like this in the _viva voce_? I do not know

whether he would regard the machine as 'merely artificially signalling'

these answers, but if the answers were as satisfactory and sustained as

in the above passage I do not think he would describe it as 'an easy

contrivance'. This phrase is, I think, intended to cover such devices as

the inclusion in the machine of a record of someone reading a sonnet,

with appropriate switching to turn it on from time to time.



In short then, I think that most of those who support the argument from

consciousness could be persuaded to abandon it rather than be forced

into the solipsist position. They will then probably be willing to

accept our test.



I do not wish to give the impression that I think there is no mystery

about consciousness. There is, for instance, something of a paradox

connected with any attempt to localise it. But I do not think these

mysteries necessarily need to be solved before we can answer the

question with which we are concerned in this paper.



\(5\) _Arguments from Various Disabilities._ These arguments take the

form, "I grant you that you can make machines do all the things you have

mentioned but you will never be able to make one to do X". Numerous

features X are suggested in this connexion. I offer a selection:



> Be kind, resourceful, beautiful, friendly (p. 448), have initiative,

> have a sense of humour, tell right from wrong, make mistakes (p. 448),

> fall in love, enjoy strawberries and cream (p. 448), make some one

> fall in love with it, learn from experience (pp. 456 f.), use words

> properly, be the subject of its own thought (p. 449), have as much

> diversity of behaviour as a man, do something really new (p. 450).

> (Some of these disabilities are given special consideration as

> indicated by the page numbers.)



No support is usually offered for these statements. I believe they are

mostly founded on the principle of scientific induction. A man has seen

thousands of machines in his lifetime. From what he sees of them he

draws a number of general conclusions. They are ugly, each is designed

for a very limited purpose, when required for a minutely different

purpose they are useless, the variety of behaviour of any one of them is

very small, etc., etc. Naturally he concludes that these are necessary

properties of machines in general. Many of these limitations are

associated with the very small storage capacity of most machines. (I am

assuming that the idea of storage capacity is extended in some way to

cover machines other than discrete-state machines. The exact definition

does not matter as no mathematical accuracy is claimed in the present

discussion.) A few years ago, when very little had been heard of digital

computers, it was possible to elicit much incredulity concerning them,

if one mentioned their properties without describing their construction.

That was presumably due to a similar application of the principle of

scientific induction. These applications of the principle are of course

largely unconscious. When a burnt child fears the fire and shows that he

fears it by avoiding it, I should say that he was applying scientific

induction. (I could of course also describe his behaviour in many other

ways.) The works and customs of mankind do not seem to be very suitable

material to which to apply scientific induction. A very large part of

space-time must be investigated, if reliable results are to be obtained.

Otherwise we may (as most English Children do) decide that everybody

speaks English, and that it is silly to learn French.



There are, however, special remarks to be made about many of the

disabilities that have been mentioned. The inability to enjoy

strawberries and cream may have struck the reader as frivolous. Possibly

a machine might be made to enjoy this delicious dish, but any attempt to

make one do so would be idiotic. What is important about this disability

is that it contributes to some of the other disabilities, e.g. to the

difficulty of the same kind of friendliness occurring between man and

machine as between white man and white man, or between black man and

black man.



The claim that "machines cannot make mistakes" seems a curious one. One

is tempted to retort, "Are they any the worse for that?" But let us

adopt a more sympathetic attitude, and try to see what is really meant.

I think this criticism can be explained in terms of the imitation game.

It is claimed that the interrogator could distinguish the machine from

the man simply by setting them a number of problems in arithmetic. The

machine would be unmasked because of its deadly accuracy. The reply to

this is simple. The machine (programmed for playing the game) would not

attempt to give the right answers to the arithmetic problems. It would

deliberately introduce mistakes in a manner calculated to confuse the

interrogator. A mechanical fault would probably show itself through an

unsuitable decision as to what sort of a mistake to make in the

arithmetic. Even this interpretation of the criticism is not

sufficiently sympathetic. But we cannot afford the space to go into it

much further. It seems to me that this criticism depends on a confusion

between two kinds of mistake. We may call them 'errors of functioning'

and 'errors of conclusion'. Errors of functioning are due to some

mechanical or electrical fault which causes the machine to behave

otherwise than it was designed to do. In philosophical discussions one

likes to ignore the possibility of such errors; one is therefore

discussing 'abstract machines'. These abstract machines are mathematical

fictions rather than physical objects. By definition they are incapable

of errors of functioning. In this sense we can truly say that 'machines

can never make mistakes'. Errors of con-clusion can only arise when some

meaning is attached to the output signals from the machine. The machine

might, for instance, type out mathematical equations, or sentences in

English. When a false proposition is typed we say that the machine has

committed an error of conclusion. There is clearly no reason at all for

saying that a machine cannot make this kind of mistake. It might do

nothing but type out repeatedly '0=1'. To take a less perverse example,

it might have some method for drawing conclusions by scientific

induction. We must expect such a method to lead occasionally to

erroneous results.



The claim that a machine cannot be the subject of its own thought can of

course only be answered if it can be shown that the machine has some

thought with some subject matter. Nevertheless, 'the subject matter of a

machine's operations' does seem to mean something, at least to the

people who deal with it. If, for instance, the machine was trying to

find a solution of the equation $x^2 - 40x - 11 = 0$ one would be

tempted to de-scribe this equation as part of the machine's subject

matter at that moment. In this sort of sense a machine undoubtedly can

be its own subject matter. It may be used to help in making up its own

programmes, or to predict the effect of alterations in its own

structure. By observing the results of its own behaviour it can modify

its own programmes so as to achieve some purpose more effectively. These

are possibilities of the near future, rather than Utopian dreams.



The criticism that a machine cannot have much diversity of behaviour is

just a way of saying that it cannot have much storage capacity. Until

fairly recently a storage capacity of even a thousand digits was very

rare.



The criticisms that we are considering here are often disguised forms of

the argument from consciousness. Usually if one maintains that a machine

can do one of these things, and describes the kind of method that the

machine could use, one will not make much of an impression. It is

thought that the method (whatever it may be, for it must be mechanical)

is really rather base. Compare the parenthesis in _Jefferson_'s

statement quoted on p. 21.



\(6\) _Lady Lovelace's Objection._ Our most detailed information of

_Babbage_'s Analytical Engine comes from a memoir by Lady _Lovelace_

(1842). In it she states, "The Analytical Engine has no pretensions to

originate anything. It can do whatever we know how to order it to

perform" (_her italics_). This statement is quoted by _Hartree_ (p. 70)

who adds: "This does not imply that it may not be possible to construct

electronic equipment which will 'think for itself', or in which, in

biological terms, one could set up a conditioned reflex, which would

serve as a basis for 'learning'." Whether this is possible in principle

or not is a stimulating and exciting question, suggested by some of

these recent developments. But it did not seem that the machines

constructed or projected at the time had this property.



I am in thorough agreement with _Hartree_ over this. It will be noticed

that he does not assert that the machines in question had not got the

property, but rather that the evidence available to Lady _Lovelace_ did

not encourage her to believe that they had it. It is quite possible that

the machines in question had in a sense got this property. For suppose

that some discrete-state machine has the property. The Analytical Engine

was a universal digital computer, so that, if its storage capacity and

speed were adequate, it could by suitable programming be made to mimic

the machine in question. Probably this argument did not occur to the

Countess or to _Babbage_. In any case there was no obligation on them to

claim all that could be claimed.



This whole question will be considered again under the heading of

learning machines.



A variant of Lady _Lovelace_'s objection states that a machine can

'never do anything really new'. This may be parried for a moment with

the saw, 'There is nothing new under the sun'. Who can be certain that

'original work' that he has done was not simply the growth of the seed

planted in him by teaching, or the effect of following well-known

general principles. A better variant of the objection says that a

machine can never 'take us by surprise'. This statement is a more direct

challenge and can be met directly. Machines take me by surprise with

great frequency. This is largely because I do not do sufficient

calculation to decide what to expect them to do, or rather because,

although I do a calculation, I do it in a hurried, slipshod fashion,

taking risks. Perhaps I say to myself, 'I suppose the voltage here ought

to be the same as there: anyway let's assume it is'.



Naturally I am often wrong, and the result is a surprise for me for by

the time the experiment is done these assumptions have been forgotten.

These admissions lay me open to lectures on the subject of my vicious

ways, but do not throw any doubt on my credibility when I testify to the

surprises I experience.



I do not expect this reply to silence my critic. He will probably say

that such surprises are due to some creative mental act on my part, and

reflect no credit on the machine. This leads us back to the argument

from consciousness, and far from the idea of surprise. It is a line of

argument we must consider closed, but it is perhaps worth remarking that

the appreciation of some-thing as surprising requires as much of a

'creative mental act' whether the surprising event originates from a

man, a book, a machine or anything else.



The view that machines cannot give rise to surprises is due, I believe,

to a fallacy to which philosophers and mathematicians are particularly

subject. This is the assumption that as soon as a fact is presented to a

mind all consequences of that fact spring into the mind simultaneously

with it. It is a very useful assumption under many circumstances, but

one too easily forgets that it is false. A natural consequence of doing

so is that one then assumes that there is no virtue in the mere working

out of consequences from data and general principles.



\(7\) _Argument from Continuity in the Nervous System._ The nervous

system is certainly not a 'discrete-state machine'. A small error in the

information about the size of a nervous impulse impinging on a neuron,

may make a large difference to the size of the outgoing impulse. It may

be argued that, this being so, one cannot expect to be able to mimic the

behaviour of the nervous system with a 'discrete-state system'.



It is true that a 'discrete-state machine' must be different from a

'continuous machine'. But if we adhere to the conditions of the

imitation game, the interrogator will not be able to take any advantage

of this difference. The situation can be made clearer if we consider

some other simpler 'continuous machine'. A 'differential analyser' will

do very well. (A 'differential analyser' is a certain kind of machine

not of the 'discrete-state type' used for some kinds of calculation.)

Some of these provide their answers in a typed form, and so are suitable

for taking part in the game. It would not be possible for a digital

computer to predict exactly what answers the differential analyser would

give to a problem, but it would be quite capable of giving the right

sort of answer. For instance, if asked to give the value of $\pi$

(actually about 3.1416) it would be reasonable to choose at random

between the values 3.12, 3.13, 3.14, 3.15, 3.16 with the probabilities

of 0.05, 0.15, 0.55, 0.19, 0.06 (say). Under these circumstances it

would be very difficult for the interrogator to distinguish the

differential analyser from the digital computer.



\(8\) _The Argument from Informality of Behaviour._ It is not possible

to produce a set of rules purporting to describe what a man should do in

every conceivable set of circumstances. One might for instance have a

rule that one is to stop when one sees a red traffic light, and to go if

one sees a green one, but what if by some fault both appear together?

One may perhaps decide that it is safest to stop. But some further

difficulty may well arise from this decision later. To attempt to

provide rules of conduct to cover every eventuality, even those arising

from traffic lights, appears to be impossible. With all this I agree.



From this it is argued that we cannot be machines. I shall try to

reproduce the argument, but I fear I shall hardly do it justice. It

seems to run something like this. 'If each man had a definite set of

'rules of conduct' by which he regulated his life he would be no better

than a machine. But there are no such rules, so men cannot be machines.'

The undistributed middle is glaring. I do not think the argument is ever

put quite like this, but I believe this is the argument used

nevertheless. There may however be a certain confusion between 'rules of

conduct' and 'laws of behaviour' to cloud the issue. By 'rules of

conduct' I mean precepts such as 'Stop if you see red lights', on which

one can act, and of which one can be conscious. By 'laws of behaviour' I

mean laws of nature as applied to a man's body such as 'if you pinch him

he will squeak'. If we substitute 'laws of behaviour which regulate his

life' for 'laws of conduct by which he regulates his life' in the

argument quoted the undistributed middle is no longer insuperable. For

we believe that it is not only true that being regulated by laws of

behaviour implies being some sort of machine (though not necessarily a

discrete-state machine), but that conversely being such a machine

implies being regulated by such laws. However, we cannot so easily

convince ourselves of the absence of complete laws of behaviour as of

complete rules of conduct. The only way we know of for finding such laws

is scientific observation, and we certainly know of no circumstances

under which we could say, 'We have searched enough. There are no such

laws.'



We can demonstrate more forcibly that any such statement would be

unjustified. For suppose we could be sure of finding such laws if they

existed. Then given a discrete-state machine it should certainly be

possible to discover by observation sufficient about it to predict its

future behaviour, and this within a reasonable time, say a thousand

years. But this does not seem to be the case. I have set up on the

Manchester computer a small programme using only 1,000 units of storage,

whereby the machine supplied with one sixteen-figure number replies with

another within two seconds. I would defy anyone to learn from these

replies sufficient about the programme to be able to predict any replies

to untried values.



\(9\) _The Argument from Extra-Sensory Perception._ I assume that the

reader is familiar with the idea of extra-sensory perception, and the

meaning of the four items of it, viz., telepathy, clairvoyance,

precognition and psycho-kinesis. These disturbing phenomena seem to deny

all our usual scientific ideas. How we should like to discredit them!

Unfortunately the statistical evidence, at least for telepathy, is

overwhelming. It is very difficult to rearrange one's ideas so as to fit

these new facts in. Once one has accepted them it does not seem a very

big step to believe in ghosts and bogies. The idea that our bodies move

simply according to the known laws of physics, together with some others

not yet discovered but somewhat similar, would be one of the first to

go.



This argument is to my mind quite a strong one. One can say in reply

that many scientific theories seem to remain workable in practice, in

spite of clashing with E.S.P.; that in fact one can get along very

nicely if one forgets about it. This is rather cold comfort, and one

fears that thinking is just the kind of phenomenon where E.S.P. may be

especially relevant.



A more specific argument based on E.S.P. might run as follows: "Let us

play the imitation game, using as witnesses a man who is good as a

telepathic receiver, and a digital computer. The interrogator can ask

such questions as 'What suit does the card in my right hand belong to?'

The man by telepathy or clairvoyance gives the right answer 130 times

out of 400 cards. The machine can only guess at random, and perhaps gets

104 right, so the interrogator makes the right identification." There is

an interesting possibility which opens here. Suppose the digital

computer contains a random number generator. Then it will be natural to

use this to decide what answer to give. But then the random number

generator will be subject to the psycho-kinetic powers of the

interrogator. Perhaps this psycho-kinesis might cause the machine to

guess right more often than would be expected on a probability

calculation, so that the interrogator might still be unable to make the

right identification. On the other hand, he might be able to guess right

without any questioning, by clairvoyance. With E.S.P. anything may

happen.



If telepathy is admitted it will be necessary to tighten our test up.

The situation could be regarded as analogous to that which would occur

if the interrogator were talking to himself and one of the competitors

was listening with his ear to the wall. To put the competitors into a

'telepathy-proof room' would satisfy all requirements.



##### 7. _Learning Machines._



The reader will have anticipated that I have no very convincing

arguments of a positive nature to support my views. If I had I should

not have taken such pains to point out the fallacies in contrary views.

Such evidence as I have I shall now give.



Let us return for a moment to Lady Lovelace's objection, which stated

that the machine can only do what we tell it to do. One could say that a

man can 'inject' an idea into the machine, and that it will respond to a

certain extent and then drop into quiescence, like a piano string struck

by a hammer. Another simile would be an atomic pile of less than

critical size: an injected idea is to correspond to a neutron entering

the pile from without. Each such neutron will cause a certain

disturbance which eventually dies away. If, however, the size of the

pile is sufficiently increased, the disturbance caused by such an

incoming neutron will very likely go on and on increasing until the

whole pile is destroyed. Is there a corresponding phenomenon for minds,

and is there one for machines? There does seem to be one for the human

mind. The majority of them seem to be 'sub-critical', i.e. to correspond

in this analogy to piles of sub-critical size. An idea presented to such

a mind will on average give rise to less than one idea in reply. A

smallish proportion are super-critical. An idea presented to such a mind

may give rise to a whole 'theory' consisting of secondary, tertiary and

more remote ideas. Animals minds seem to be very definitely

'sub-critical'. Adhering to this analogy we ask, 'Can a machine be made

to be super-critical?'



The 'skin of an onion' analogy is also helpful. In considering the

functions of the mind or the brain we find certain operations which we

can explain in purely mechanical terms. This we say does not correspond

to the real mind: it is a sort of skin which we must strip off if we are

to find the real mind. But then in what remains we find a further skin

to be stripped off, and so on. Proceeding in this way do we ever come to

the 'real' mind, or do we eventually come to the skin which has nothing

in it ? In the latter case the whole mind is mechanical. (It would not

be a discrete-state machine however. We have discussed this.)



These last two paragraphs do not claim to be convincing arguments. They

should rather be described as 'recitations tending to produce belief'.



The only really satisfactory support that can be given for the view

expressed at the beginning of §6, will be that provided by waiting for

the end of the century and then doing the experiment described. But what

can we say in the meantime ? What steps should be taken now if the

experiment is to be successful?



As I have explained, the problem is mainly one of programming. Advances

in engineering will have to be made too, but it seems unlikely that

these will not be adequate for the requirements. Estimates of the

storage capacity of the brain vary from $10^{10}$ to $10^{15}$ binary

digits. I incline to the lower values and believe that only a very small

fraction is used for the higher types of thinking. Most of it is

probably used for the retention of visual impressions. I should be

surprised if more than $10^9$ was required for satisfactory playing of

the imitation game, at any rate against a blind man. (_Note_—The capacity

of the _Encyclopaedia Britannica_, 11th edition, is $2 \times 10^9$) A

storage capacity of $10^9$ would be a very practicable possibility even

by present techniques. It is probably not necessary to increase the

speed of operations of the machines at all. Parts of modern machines

which can be regarded as analogs of nerve cells work about a thousand

times faster than the latter. This should provide a 'margin of safety'

which could cover losses of speed arising in many ways. Our problem then

is to find out how to programme these machines to play the game. At my

present rate of working I produce about a thousand digits of programme a

day, so that about sixty workers, working steadily through the fifty

years might accomplish the job, if nothing went into the waste-paper

basket. Some more expeditious method seems desirable.



In the process of trying to imitate an adult human mind we are bound to

think a good deal about the process which has brought it to the state

that it is in. We may notice three components.



1.  The initial state of the mind, say at birth,



2.  The education to which it has been subjected,



3.  Other experience, not to be described as education, to which it has

    been subjected.



Instead of trying to produce a programme to simulate the adult mind, why

not rather try to produce one which simulates the child's? If this were

then subjected to an appropriate course of education one would obtain

the adult brain. Presumably the child brain is something like a

note-book as one buys it from the stationers. Rather little mechanism,

and lots of blank sheets. (Mechanism and writing are from our point of

view almost synonymous.) Our hope is that there is so little mechanism

in the child brain that something like it can be easily programmed. The

amount of work in the education we can assume, as a first approximation,

to be much the same as for the human child.



We have thus divided our problem into two parts. The child-programme and

the education process. These two remain very closely connected. We

cannot expect to find a good child-machine at the first attempt. One

must experiment with teaching one such machine and see how well it

learns. One can then try another and see if it is better or worse. There

is an obvious connection between this process and evolution, by the

identifications



$$

\begin{aligned}

\text{Structure of the child machine} &= \text{Hereditary material} \\

\text{Changes of the child machine} &= \text{Mutations} \\

\text{Natural selection} &= \text{Judgment of the experimenter}

\end{aligned}

$$



One may hope, however, that this process will be more expeditious than

evolution. The survival of the fittest is a slow method for measuring

advantages. The experimenter, by the exercise of intelligence, should be

able to speed it up. Equally important is the fact that he is not

restricted to random mutations. If he can trace a cause for some

weakness he can probably think of the kind of mutation which will

improve it.



It will not be possible to apply exactly the same teaching process to

the machine as to a normal child. It will not, for instance, be provided

with legs, so that it could not be asked to go out and fill the coal

scuttle. Possibly it might not have eyes. But however well these

deficiencies might be overcome by clever engineering, one could not send

the creature to school without the other children making excessive fun

of it. It must be given some tuition. We need not be too concerned about

the legs, eyes, etc. The example of Miss _Helen Keller_ shows that

education can take place provided that communication in both directions

between teacher and pupil can take place by some means or other.



We normally associate punishments and rewards with the teaching process.

Some simple child machines can be constructed or programmed on this sort

of principle. The machine has to be so constructed that events which

shortly preceded the occurrence of a punishment signal are unlikely to

be repeated, whereas a reward signal increased the probability of

repetition of the events which led up to it. These definitions do not

presuppose any feelings on the part of the machine, I have done some

experiments with one such child machine, and succeeded in teaching it a

few things, but the teaching method was too unorthodox for the

experiment to be considered really successful.



The use of punishments and rewards can at best be a part of the teaching

process. Roughly speaking, if the teacher has no other means of

communicating to the pupil, the amount of information which can reach

him does not exceed the total number of rewards and punishments applied.

By the time a child has learnt to repeat 'Casabianca' he would probably

feel very sore indeed, if the text could only be discovered by a 'Twenty

Questions' technique, every 'NO' taking the form of a blow. It is

necessary therefore to have some other 'unemotional' channels of

communication. If these are available it is possible to teach a machine

by punishments and rewards to obey orders given in some language, e.g.,

a symbolic language. These orders are to be transmitted through the

'unemotional' channels. The use of this language will diminish greatly

the number of punishments and rewards required.



Opinions may vary as to the complexity which is suitable in the child

machine. One might try to make it as simple as possible consistently

with the general principles. Alternatively one might have a complete

system of logical inference 'built in'.[^3] In the latter case the store

would be largely occupied with definitions and propositions. The

propositions would have various kinds of status, e.g., well-established

facts, conjectures, mathematically proved theorems, statements given by

an authority, expressions having the logical form of proposition but not

belief-value. Certain propositions may be described as 'imperatives.'

The machine should be so constructed that as soon as an imperative is

classed as 'well established' the appropriate action automatically takes

place. To illustrate this, suppose the teacher says to the machine, 'Do

your homework now.' This may cause "Teacher says 'Do your homework now'

" to be included amongst the well-established facts. Another such fact

might be, "Everything that teacher says is true." Combining these may

eventually lead to the imperative, 'Do your homework now,' being

included amongst the well-established facts, and this, by the

construction of the machine, will mean that the homework actually gets

started, but the effect is very satisfactory. The processes of inference

used by the machine need not be such as would satisfy the most exacting

logicians. There might for instance be no hierarchy of types. But this

need not mean that type fallacies will occur, any more than we are bound

to fall over unfenced cliffs. Suitable imperatives (expressed within the

systems, not forming part of the rules of the system) such as 'Do not

use a class unless it is a subclass of one which has been mentioned by

teacher' can have a similar effect to 'Do not go too near the edge'.



The imperatives that can be obeyed by a machine that has no limbs are

bound to be of a rather intellectual character, as in the example (doing

homework) given above. Important amongst such imperatives will be ones

which regulate the order in which the rules of the logical system

concerned are to be applied, For at each stage when one is using a

logical system, there is a very large number of alternative steps, any

of which one is permitted to apply, so far as obedience to the rules of

the logical system is concerned. These choices make the difference

between a brilliant and a footling reasoner, not the difference between

a sound and a fallacious one. Propositions leading to imperatives of

this kind might be "When Socrates is mentioned, use the syllogism in

Barbara" or "If one method has been proved to be quicker than another,

do not use the slower method." Some of these may be 'given by

authority', but others may be produced by the machine itself, e.g. by

scientific induction.



The idea of a learning machine may appear paradoxical to some readers.

How can the rules of operation of the machine change? They should

describe completely how the machine will react whatever its history

might be, whatever changes it might undergo. The rules are thus quite

time-invariant. This is quite true. The explanation of the paradox is

that the rules which get changed in the learning process are of a rather

less pretentious kind, claiming only an ephemeral validity. The reader

may draw a parallel with the Constitution of the United States.



An important feature of a learning machine is that its teacher will

often be very largely ignorant of quite what is going on inside,

although he may still be able to some extent to predict his pupil's

behaviour. This should apply most strongly to the later education of a

machine arising from a child machine of well-tried design (or

programme). This is in clear contrast with normal procedure when using a

machine to do computations one's object is then to have a clear mental

picture of the state of the machine at each moment in the computation.

This object can only be achieved with a struggle. The view that 'the

machine can only do what we know how to order it to do',[^4] appears

strange in face of this. Most of the programmes which we can put into

the machine will result in its doing something that we cannot make sense

(if at all, or which we regard as completely random behaviour.

Intelligent behaviour presumably consists in a departure from the

completely disciplined behaviour involved in computation, but a rather

slight one, which does not give rise to random behaviour, or to

pointless repetitive loops. Another important result of preparing our

machine for its part in the imitation game by a process of teaching and

learning is that 'human fallibility' is likely to be omitted in a rather

natural way, i.e., without special 'coaching'. (The reader should

reconcile this with the point of view on pp. 24, 25.) Processes that are

learnt do not produce a hundred per cent certainty of result; if they

did they could not be unlearnt.



It is probably wise to include a random element in a learning machine. A

random element is rather useful when we are searching for a solution of

some problem. Suppose for instance we wanted to find a number between 50

and 200 which was equal to the square of the sum of its digits, we might

start at 51 then try 52 and go on until we got a number that worked.

Alternatively we might choose numbers at random until we got a good one.

This method has the advantage that it is unnecessary to keep track of

the values that have been tried, but the disadvantage that one may try

the same one twice, but this is not very important if there are several

solutions. The systematic method has the disadvantage that there may be

an enormous block without any solutions in the region which has to be

investigated first, Now the learning process may be regarded as a search

for a form of behaviour which will satisfy the teacher (or some other

criterion). Since there is probably a very large number of satisfactory

solutions the random method seems to be better than the systematic. It

should be noticed that it is used in the analogous process of evolution.

But there the systematic method is not possible. How could one keep

track of the different genetical combinations that had been tried, so as

to avoid trying them again?



We may hope that machines will eventually compete with men in all purely

intellectual fields. But which are the best ones to start with? Even

this is a difficult decision. Many people think that a very abstract

activity, like the playing of chess, would be best. It can also be

maintained that it is best to provide the machine with the best sense

organs that money can buy, and then teach it to understand and speak

English. This process could follow the normal teaching of a child.

Things would be pointed out and named, etc. Again I do not know what the

right answer is, but I think both approaches should be tried.



We can only see a short distance ahead, but we can see plenty there that

needs to be done.



**BIBLIOGRAPHY**



Samuel Butler, _Erewhon_, London, 1865. Chapters 23, 24, 25, _The Book

of the Machines_.



Alonzo Church, "An Unsolvable Problem of Elementary Number Theory",



_American J. of Math._, 58 (1936), 345-363.



K. Gödel, "Über formal unentscheidbare Sätze der Principia Mathematica



und verwandter Systeme, I", _Monatshefte für Math. und Phys._,



(1931), 173-189.



D. R. Hartree, _Calculating Instruments and Machines_, New York, 1949.



S. C. Kleene, "General Recursive Functions of Natural Numbers",



_American J. of Math._, 57 (1935), 153-173 and 219-244.



G. Jefferson, "The Mind of Mechanical Man". Lister Oration for 1949.



_British Medical Journal_, vol. i (1949), 1105-1121.



Countess of Lovelace, 'Translator's notes to an article on Babbage's



_Analytical Engine_, _Scientific Memoirs_ (ed. by R. Taylor), vol. 3



(1842), 691-731.



Bertrand Russell, _History of Western Philosophy_, London, 1940.



A. M. Turing, "On Computable Numbers, with an Application to the



Entscheidungsproblem", _Proc. London Math. Soc._ (2), 42 (1937),



230-265.



_Victoria University of Manchester._



[^1]:

    Possibly this view is heretical. St. Thomas Aquinas (_Summa

    Theologica_, quoted by Bertrand Russell, p. 480) states that God

    cannot make a man to have no soul. But this may not be a real

    restriction on His powers, but only a result of the fact that men's

    souls are immortal, and therefore indestructible.



[^2]: Author's names in italics refer to the Bibliography.



[^3]:

    Or rather 'programmed in' for our child-machine will be programmed

    in a digital computer. But the logical system will not have to be

    learnt.



[^4]:

    Compare Lady Lovelace's statement (p.450), which does not contain

    the word 'only'.