the unknown guest(陌生客)-第36节
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which； in this instance； spans the gulf between the animal and man is
much more the expression of thought than thought itself。 We may go
further and grant that certain elementary calculations； such as little
additions； little subtractions of one or two figures； are； after all；
conceivable； and I； for my part； am inclined to believe that the horse really
executes them。 But where we get out of our depth； where we enter into the
realm of pure enchantment is when it becomes a matter of mathematical
operations on a large scale； notably of the finding of roots。 We know； for
instance； that the extraction of the fourth root of a number of six figures
calls for eighteen multiplications； ten subtractions and three divisions and
that the horse does thirty…one sums in five or six seconds； that is to say；
during the brief； careless glance which he gives at the black…board on
which the problem is inscribed； as though the answer came to him
intuitively and instantaneously。
Still； if we admit the theory of intelligence； we must also admit that the
horse knows what he is doing； since it is not until after learning what a
squared number or a square root means that he appears to understand or
that； at any rate； he gradually works out correctly the ever more
complicated calculations required of him。 It is not possible to give here the
details of this instruction； which was astonishingly rapid。 The reader will
find them on pages 117 et seq。 of Krall's book； Denkende Tiere。 Krall
begins by explaining to Mohammed that 2 squared is equal to 2 X 2 = 4；
that 2 cubed is equal to 2 X 2 X 2 = 6； that 2 is the square root of 4； and so
on。 In short； the explanations and demonstrations are absolutely similar to
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THE UNKNOWN GUEST
those which one would give to an extremely intelligent child； with this
difference； that the horse is much more attentive than the child and that；
thanks to his extraordinary memory； he never forgets what he appears to
have understood。 Let us add； to complete the magical and incredible
character of the phenomenon that； according to Krall's own statement； the
horse was not taught beyond the point of extracting the square root of the
number 144 and that he spontaneously invented the manner of extracting
all the others。
27
Must we once more repeat； in connection with these startling
performances； that those who speak of audible or visible signals； of
telegraphy and wireless telegraphy； of expedients； trickery or deceit； are
speaking of what they do not know and of what they have not seen？ There
is but one reply to be made to any one who honestly refuses to believe：
〃Go to Elberfeld…the problem is sufficiently important； sufficiently
big with consequences to make the journey worth whileand； behind
closed doors； alone with the horse； in the absolute solitude and silence of
the stable； set Mohammed to extract half…a dozen roots which； like that
which I have mentioned； require thirty…one operations。 You must yourself
be ignorant of the solutions； so as to do away with any transmission of
unconscious thought。 If he then gives you； one after the other； five or six
correct solutions； as he did to me and many others； you will not go away
with the conviction that the animal is able by its intelligence to extract
those roots； because that conviction would upset too thoroughly the
greater part of the certainties on which your life is based； but you will； at
any rate； be persuaded that you have been for a few minutes in the
presence of one of the greatest and strangest riddles that can disturb the
mind of man； and it is always a good and salutary thing to come into
contact with emotions of this order。〃
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Truth to say； the theory of intelligence in the animal would be so
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THE UNKNOWN GUEST
extraordinary as to be almost untenable。 If we are determined； at whatever
cost； to pin our faith to it； we are bound to call in the aid of other ideas； to
appeal； for instance； to the extremely mysterious and essentially
uncomprehended and incomprehensible nature of numbers。 It is almost
certain that the science of mathematics lies outside the intelligence。 It
forms a mechanical and abstract whole； more spiritual than material and
more material than spiritual； visible only through its shadow and yet
constituting the most immovable of the realities that govern the universe。
From first to last it declares itself a very strange force and； as it were； the
sovereign of another element than that which nourishes our brain。 Secret；
indifferent； imperious and implacable； it subjugates and oppresses us from
a great height or a great depth； in any case； from very far； without telling
us why。 One might say that figures place those who handle them in a
special condition。 They draw the cabalistic circle around their victim。
Henceforth； he is no longer his own master； he renounces his liberty； he is
literally 〃possessed〃 by the powers which he invokes。 He is dragged he
knows not whither； into a formless； boundless immensity； subject to laws
that have nothing human about them； in which each of those lively and
tyrannical little signs which move and dance in their thousands under the
pen represents nameless； but eternal； invincible and inevitable verities。 We
think that we are directing them and they enslave us。 We become weary
and breathless following them into their uninhabitable spaces。 When we
touch them； we let loose a force which we are no longer able to control。
They do with us what they will and always end by hurling us； blinded and
benumbed； into blank infinity or upon a wall of ice against which every
effort of our mind and will is shattered。
It is possible； therefore； in the last resort； to explain the Elberfeld
mystery by the no less obscure mystery that surrounds numbers。 This
really only means moving to another spot in the gloom； but it is often just
by that moving to another spot that we end by discovering the little gleam
of light which shows us a thoroughfare。 In any case； and to return to more
precise ideas； more than one instance has been cited to prove that the gift
of handling great groups of figures is almost independent of the
intelligence proper。 One of the most curious is that of an Italian shepherd
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boy； Vito Mangiamele； who was brought before the Paris Academy of
Science in 1837 and who； at the age of ten； though devoid of the most
rudimentary education； was able in half a minute to extract the cubic root
of a number of seven figures。 Another； more striking still； also mentioned
by Dr。 Clarapede in his paper on the learned horses； is that of a man blind
from birth； an inmate of the lunatic…asylum； at Armentieres。 This blind
man； whose name is Fleury； a degenerate and nearly an idiot； can calculate
in one minute and fifteen seconds the number of seconds in thirty…nine
years； three months and twelve days； not forgetting the leap…years。 They
explain to him what a square root is； without telling him the conventional
method of finding it； and soon he extracts almost as rapidly as Inaudi
himself； without a blunder； the square roots of numbers of four figures；
giving the remainder。 On the other hand； we know that a mathematical
genius like Henri Pomcare confessed himself incapable of adding up a
column of figures without a mistake。
29
》From the maybe enchanted atmosphere that surrounds numbers we
shall pas
