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e do not follow the luminous trail that summons us to an unknown world； we go on turning in our dismal circle； like contented sleep…walkers； while Isis' sistrum rattles without respite to rouse the faithful。
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I repeat； the great miracle of Elberfeld is that of having been able to prolong and reproduce at will those isolated 〃psychic flashes。〃 The horses； in comparison with the other animals； are here in the state of a man whose subliminal consciousness had gained the upper hand。 That man would lead a higher existence； in an almost immaterial atmosphere； of which the phenomena of metaphysics； sparks falling from a region which we shall perhaps one day reach； sometimes give us an uncertain and fleeting glimpse。 Our intelligence； which is really lethargy and which keeps us imprisoned in a little hollow of space and time； would there be replaced by intuition； or rather by a sort of imminent knowledge which would forthwith make us sharers in all that is known to a universe which perhaps knows all things。 Unfortunately； we have not； or at least； unlike the horses； we are not acquainted with a superior being who interests himself in us and helps us to throw off our torpor。 We have to become our own god； to rise above ourselves and to keep ourselves raised by our unaided strength。 It is almost certain that the horse would never have come out of his nebulous sphere without man's assistance； but it is not forbidden to hope that man； with no other help than his own courage and high purpose； may yet succeed in breaking through the sleep that cramps him and blinds him。
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To come back then to our horses and to the main point； which is the isolated 〃psychic flash；〃 it is admitted that they know the values of figures； that they can distinguish and identify smells； colours； forms； objects and even graphic reproductions of those objects。 They also understand a large number of words； including some of which they were； never taught the meaning； but which they picked up as they went along by hearing them spoken around them。 They have learnt； with the assistance of an exceedingly complicated alphabet； to reproduce the words； thanks to which they manage to convey impressions； sensations； wishes； associations of ideas； observations and even spontaneous reflections。 It has been held that all this implies real acts of intelligence。 It is； in fact； often very difficult to decide exactly how far it is intelligence and how far memory； instinct； imitative genius； obedience or mechanical impulse； the effects of training； or happy coincidences。
There are cases； however； which admit of little or no hesitation。 I give a few。
One day Krall and his collaborator； Dr。 Scholler； thought that they would try and teach Mohammed to express himself in speech。 The horse； a docile and eager pupil； made touching and fruitless efforts to reproduce human sounds。 Suddenly； he stopped and； in his strange phonetic spelling； declared； by striking his foot on the spring…board：
〃Ig hb kein gud Sdim。 I have not a good voice。〃
Observing that he did not open his mouth； they strove to make him understand； by the example of a dog； with pictures； and so on； that； in order to speak； it is necessary to separate the jaws。 They next asked him：
〃What must you do to speak？〃
He replied； by striking with his foot：
〃Open mouth。〃
〃Why don't you open yours？〃
〃Weil kan nigd： because I can't。〃
A few days after； Zarif was asked how he talks to Mohammed。
〃Mit Munt： with mouth。〃
〃Why don't you tell me that with your mouth？〃
〃Weil ig kein Stim hbe： because I have no voice。〃 Does not this answer； as Krall remarks； allow us to suppose that he has other means than speech of conversing with his stable…companion？
In the course of another lesson； Mohammed was shown the portrait of a young girl whom he did not know。
〃What's that？〃 asked his master。
〃Metgen： a girl？〃
On the black…board：
〃Why is it a girl？〃
〃Weil lang Hr hd： because she has long hair。〃
〃And what has she not？〃
〃Moustache。〃
They next produced the likeness of man with no moustache。
〃What's this？〃
〃Why is it a man？〃
〃Weil kurz Hr hd： because he has short hair。〃
I could multiply these examples indefinitely by drawing on the voluminous Elberfeld minutes； which； I may say in passing； have the convincing force of photographic records。 All this； it must be agreed； is unexpected and disconcerting； had never been foreseen or suspected and may be regarded as one of the strangest prodigies； one of the most stupefying revelations that have taken place since man has dwelt in this world of riddles； Nevertheless； by reflecting； by comparing； by investigating； by regarding certain forgotten or neglected landmarks and starting…points； by taking into consideration the thousand imperceptible gradations between the greatest and the least； the highest and the lowest； it is still possible to explain； admit and understand。 We can； if it comes to that； imagine that； in his secret self； in his tragic silence； our dog also makes similar remarks and reflections。 Once again； the miraculous bridge 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 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 sq