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.
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
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.
(a)
The
initial state of the mind, say at birth,
(b)
The
education to which it has been subjected,
(c)
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 notebook as one buys it from the
stationer's. 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
Structure of the child machine =
hereditary material
Changes of the child machine =
mutation,
Natural selection = judgment of
the experimenter
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 he 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."' 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 behavior. 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,"' 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 pages 23 and 24.)
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.
One glaring omission from the standard
model is gravity; where does that fit in? According to Albert Einstein’s view
of gravity, apples fall to the ground and the Earth orbits the sun because
space-time is an active and malleable fabric. Massive bodies like the sun bend
space-time. A planet that orbits a star is actually following a straight path
through a curved space-time. This means we have to replace the Euclidean
geometry we learned at school with the curved geometry developed by the
19th-century mathematician Bernhard Riemann.
The quarks and leptons that make up matter
seem very different to the particles that carry nature’s forces. So it came as
a great surprise in the 1970s when theorists showed that it is possible to
construct equations which stay the same when you swap the two around.
In superstring theory, the fundamental
building blocks of matter are not point-like particles. Instead they are one-dimensional
strings that live in a universe with 10 space-time dimensions. Just like violin
strings, they can vibrate in various modes, each one representing a different
elementary particle. Certain string vibrations can even describe gravitons, the
hypothetical carriers of the gravitational force.
M, he says, stands for magic, mystery or
membrane according to taste.
