La máquina de Turing es un modelo computacional creado
por Alan Turing con el cual él afirmaba que se podía realizar cualquier
cómputo.
Diagrama artístico de una máquina de Turing.La máquina de Turing, como modelo
matemático, consta de un cabezal lector/escritor y una cinta infinita en
la que el cabezal lee el contenido, borra el contenido anterior y escribe
un nuevo valor. Las operaciones que se pueden realizar en esta máquina se
limitan a: avanzar el cabezal lector/escritor para la derecha; avanzar el
cabezal lector/escritor para la izquierda.
El cómputo es determinado a partir de una tabla de estados de la forma:
(estado,valor) (\nuevo estado, \nuevo valor, dirección)
Esta tabla toma como parámetros el estado actual de la máquina y el carácter
leído de la cinta, dando la dirección para mover el cabezal, el nuevo estado
de la máquina y el valor a ser escrito en la cinta.
Con este aparato extremadamente sencillo es posible realizar cualquier cómputo
que un computador digital sea capaz de realizar.
Mediante este modelo teórico y el análisis de complejidad de algoritmos,
fue posible la categorización de problemas computacionales de acuerdo a
su comportamiento, apareciendo así, el conjunto de problemas denominados
P y NP, cuyas soluciones en tiempo polinómico son encontradas según el determinismo
y no determinismo respectivamente de la máquina de Turing. Si lo desea descargue
aqui el texto en txt
Texto original de Turing - Computing Machinery And Inteligence
De hecho, se puede probar matemáticamente que para cualquier programa de
computadora es posible crear una máquina de Turing equivalente. Esta prueba
resulta de la Tesis de Church-Turing, formulada por Alan Turing y Alonzo
Church, de forma independiente a mediados del siglo XX.
Google y Turing
If Google is a religion, what is its God? It would have
to be The Algorithm. Faith in the possibility of an omniscient and omnipotent
algorithm appears to be what Messrs Page and Brin have in common. It's “in
their DNA,” says Michael Moritz, a venture capitalist
famous for investing early in both Yahoo! and Google. Whereas Yahoo! was
started by two Stanford students who turned a hobby into a business, Google
was started by two Stanford students who turned an intellectual obsession
into a quest, says Mr Moritz. And what is that quest? Merely upstaging Microsoft
would be almost banal. “We're not trying to build a better operating system,”
says Mr Schmidt (although that will not kill the rumour). Part of the plan
is certainly “organising the world's information”. But some people think
they detect an even more grandiose design. Google is already working on
a massive and global computing grid. Eventually, says Mr Saffo, “they're
trying to build the machine that will pass the Turing test”—in other words,
an artificial intelligence that can pass as a human in written conversations.
Wisely or not, Google wants to be a new sort of deus ex machina.
Jan 12th 2006 From The Economist print editiondsd
¿Por que se ponia nervioso Leon en Blade Runner?
Turing propuso que la pregunta “¿puede pensar una máquina?” era demasiado
filosófica para tener valor y, para hacerlo más concreto, propuso “un juego de
imitación”. En la prueba de Turing intervienen dos personas y un computadora.
Una persona, el interrogador, se sienta en una sala y teclea preguntas en la
terminal de una computadora. Cuando aparecen las respuestas en la terminal, el
interrogador intenta determinar si fueron hechas por otra persona o por una
computadora. Si actúa de manera inteligente, según Turing es inteligente.
Turing, señaló que una máquina podría fracasar y aún ser inteligente. Aun así
creía que las máquinas podrían superar la prueba a fin del siglo:
"El principal objetivo del texto consiste en Cuestionar hipótesis acerca de si
“Las maquinas pueden pensar”. El propósito de este objetivo que formula el
autor, es intentar demostrar bajo ejercicios teóricos si las maquinas, uno de
los inventos del ser humano, pueden llegar a comportarse como tal adoptando
inclusive, sus propiedades deductivas racionales.
La tesis principal que
se deriva del objetivo, radica en una concepción alrededor de la capacidad de
imitar la conducta humana que puede llegar a tener una maquina artificial. Se deduce esta tesis, de acuerdo a las estipulaciones que
realiza Turing en el texto, en el cual se supone la inteligencia alrededor de un
organismo artificial, el cual es programado con una serie de datos y premisas
que lo orientan en su forma de proceder a una serie estímulos
técnicos.
Estos “estímulos técnicos” hacen referencia a las
argumentaciones estructurales que realiza Turing, en el texto para demostrar sus
tesis y sus suposiciones teóricas. La principal sustentación del texto sobre la
capacidad inteligente de una maquina, se realiza a través de un juego de
imitación, en el cual A.M. Turing, intenta establecer roles entre humanos y
maquinas a partir de una serie de preguntas que produzcan el patrón de la causa
y el efecto.
En este juego de imitación, un interrogador envía una serie
de preguntas (o estímulos) a dos miembros A y B, los cuales deben responder de
acuerdo con sus capacidades cognoscitivas y su memoria de datos que almacena
información. Entre los miembros indagados, se encuentra una máquina, la cual en
un momento determinado, puede comenzar a ejecutar el papel de coordinar los
cuestionamientos y así llegaría alcanzar una capacidad deductiva similar a la
que posee un ser humano, ya que sus preguntas (y respuestas, cuando es
interrogado) pueden contener el mismo nivel racional que un ser humano de
inteligencia media. Al respecto: “la maquina tiene que luchar contra una fuerza
demasiado superior. Si el hombre tratara de fingir que él es la maquina,
evidentemente haría un mal papel. Seria descubierto por su lentitud
aritmética”!"
Llegado este momento resulta inevitable mencionar el test de Turing. Se trata
de una prueba ideada para juzgar el grado de inteligencia de una máquina y que
fue creada por Alan Turing, considerado el padre de la AI, en los años
cincuenta. Consiste en situar a un juez en una habitación y a un humano y a la
máquina a juzgar en otra. El juez debe descubrir quién es el humano y quién la
máquina atendiendo a las respuestas escritas que le faciliten. A la máquina le
está permitido mentir. Recuerda bastante, aunque tiene poco que ver, al test
Voigt-Kampff empleado en Blade Runner para identificar a los
replicantes.
Hasta la fecha, ni computadoras ni robots han logrado pasar el test de Turing
con el suficiente éxito como para ser confundidas de manera definitiva con
humanos.
El británico predijo que en el año 2000, una máquina con 119 Mb
de memoria podría engañar al 30% de sus jueces humanos luego de una conversación
de cinco minutos. Esto no ha sucedido aún, ni siquiera con máquinas muchas veces
más potentes.
Los programas que sí han engañado a sus interlocutores (por
ejemplo el llamado "ELIZA") lo han hecho partiendo de una mentira: no decirle al
juez que posiblemente quien hablaba con él era una máquina. El Test de Turing
parte de la base de que el interrogador está intentando activamente diferenciar
a su interlocutor humano del mecánico, lo que invalida los estudios antedichos.
Si a la persona se le dice que del otro lado puede haber una máquina, ningún
programa puede engañarla.
Existe un test llamado "Juego de la Imitación", que se
desarrolla de la siguiente manera: se colocan en una habitación un hombre y una
mujer, frente a sendas terminales de computación con, por ejemplo, algún sistema
de comunicación del tipo del IRC (Turing, por supuesto, les daba teletipos en
1950). En otra habitación aislada se encontraba el sujeto del estudio: el
interrogador. El objetivo del juego era que el interrogador se diera cuenta de
cuál era el hombre y cuál la mujer, haciéndoles cualquier pregunta que se le
antojara -en lenguaje normal- a través del teletipo (o IRC). Los participantes,
a su vez, se comportan de manera diferente con él: mientras que el hombre trata
de convencerlo de que él es la mujer, ella intentará ayudar al interrogador a
llegar a la verdad. Las preguntas podían versar sobre absolutamente cualquier
tema. Es interesante observar los resultados: el interrogador muchas veces se
equivoca, lo que significa que el hombre y la mujer logran su objetivo de
engañarlo.
Lo que Turing propone en su trabajo de hace 56 años es
reemplazar a una de las dos personas (el hombre) por una computadora. ¿Se
equivocarían los sujetos tanto como cuando jugaban con dos seres humanos?
Lamentablemente, la ambigüedad de los papeles de Turing no nos permite saber si
su idea era que la mujer dijese la verdad sobre su condición ("Soy mujer") o si,
además, intentaría engañar al sufrido sujeto. Mas informacion en Marcelo Dos Santos
Pensador Google
El texto original de Turing
A. M. Turing (1950) Computing Machinery and Intelligence. Mind 49: 433-460.
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 front 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 something 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:
(i) Store.
(ii) Executive unit.
(iii) 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 bead 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)e 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 replaced 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 .
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 I 00 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 took 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 ]ever 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 q1, q2 or q3. There is an input signal i0. or i1 (position of ]ever).
The internal state at any moment is determined by the last state and input
signal according to the table
(TABLE DELETED)
The output signals, the only externally visible indication of the internal
state (the light) are described by the table
State q1 q2 q3
output o0 o0 o1
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 100x50x30
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 behavior
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 'ill 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 109, 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 improved 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. 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 sort[. 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 Godel's theorem ( 1931 ) 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 (1936), Kleene (1935), Rosser, and
Turing (1937). 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 Godel'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 If 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 he 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 brain-that 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, have initiative, have a sense
of humour, tell right from wrong, make mistakes, fall in love, enjoy strawberries
and cream, make some one fall in love with it, learn from experience, use
words properly, be the subject of its own thought, have as much diversity
of behaviour as a man, do something really new.
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, f 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 conclusion
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 "O = I." 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 x2 - 40x - 11 = 0 one would be tempted to describe 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 tile
method (whatever it may be, for it must be mechanical) is really rather
base. Compare the parentheses in Jefferson's statement quoted on page 22.
(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
( 1949) 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 he 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
h 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 something
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 sonic 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 (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 Extrasensory Perception
I assume that the reader is familiar with the idea of extrasensory perception,
and the meaning of the four items of it, viz., telepathy, clairvoyance,
precognition and psychokinesis. 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 ESP; 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 ESP may be especially relevant.
A more specific argument based on ESP 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 psychokinetic powers
of the interrogator. Perhaps this psychokinesis 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 ESP 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, tire 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 "subcritical," i.e., to correspond
in this analogy to piles of subcritical size. An idea presented to such
a mind will on average give rise to less than one idea in reply. A smallish
proportion are supercritical. An idea presented to such a mind that may
give rise to a whole "theory" consisting of secondary, tertiary and more
remote ideas. Animals minds seem to be very definitely subcritical. Adhering
to this analogy we ask, "Can a machine be made to be supercritical?"
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 1010 to 1015 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 109 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 X 109) A storage
capacity of 107, 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 progratiirne a day, so that about sixty workers, working
steadily through the fifty years might accomplish the job, if nothing went
into the wastepaper 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.
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