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 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.
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