Chapter IV: The Elberfeld Horses (2)

Let us see how those who have interested themselves in these extraordinary manifestations have attempted to explain them.

As we go along, we will just shear through the feeble undergrowth of childish theories. I shall not, therefore, linger over the suggestions of cheating, of manifest signs addressed to the eye or ear, of electrical installations that are supposed to control the answers, nor other idle tales of an excessively clumsy character. To realize their inexcusable inanity we have but to spend a few minutes in the honest Elberfeld stable.

At the beginning of this essay, I mentioned the attack made by Herr Pfungst. Herr Pfungst, the reader will remember, claims to prove that all the horse's replies are determined by imperceptible and probably unconscious movement on the part of the person putting the questions. This interpretation, which falls to the ground, like all the others, in the face of the actual facts, would not deserve serious discussion, were it not that the Berlin psychologist's report created an immense sensation some years ago and has succeeded in intimidating the greater part of the official German scientific world to this day. It is true that the report in question is a monument of useless pedantry, but we are none the less bound to admit that, such as it was, it annihilated poor Von Oaten, who, being no controversialist and not knowing how to proclaim the truth which was struggling for utterance, died in gloom and solitude.

To make an end of this cumbrous and puerile theory, is it necessary to emphasize again that experiments in which the animal does not see the questioner are as regularly successful as the others? Krall, if you ask him, will stand behind the horse, will speak from the end of the room, will leave the stable altogether; and the results are just the same. They are the same again when the tests are made in the dark or when the animal's head is covered with a close-fitting hood. They do not vary either in the case of Berto, who is stone-blind, or when any other person whatever sets the problem in Krall's absence. Will it be maintained that this outsider or that stranger is acquainted beforehand with the imperceptible signs that are to dictate the solution which he himself often does not know?

But what is the use of prolonging this fight against a cloud of smoke? None of it can bear examination; and it calls for a genuine effort of the will to set one's self seriously to refute such pitiful objections.

18

On the ground thus cleared and at the portal of this unlooked-for riddle, which comes to disturb our peace in a region which we thought to be finally explored and conquered, there are only two ways, if not of explaining, at least of contemplating the phenomenon: to admit purely and simply the almost human intelligence of the horse, or to have recourse to an as yet very vague and indefinite theory which, for lack of a better designation, we will call the mediumistic or subliminal theory and of which we will strive presently--and no doubt vainly--to dispel the grosser darkness. But, whatever interpretation we adopt, we are bound to recognize that it plunges us into a mystery which is equally profound and equally astonishing on either side, one directly related to the greatest mysteries that overwhelm us; and it is open to us to accept it with resignation or rejoicing, according as we prefer to live in a world wherein everything is within the reach of our intelligence or a world wherein everything is incomprehensible.

As for Krall, he does not doubt for an instant that his horses solve for themselves, without any assistance, without any outside influence, simply by their own mental powers, the most arduous problems set them. He is persuaded that they understand what is said to them and what they say, in short, that their brain and their will perform exactly the same functions as a human brain and will. It is certain that the facts seem to prove him right and that his opinion carries way great weight, for, after all, he knows his horses better than any one does; he has beheld the birth or rather the awakening of that dormant intelligence, even as a mother beholds the birth or the awakening of intelligence in her child; he has perceived its first gropings, known its first resistance and its first triumphs; he has watched it taking shape, breaking away and gradually rising to the point at which it stands to-day; in a word, he is the father and the principal and sole perpetual witness of the miracle.

19

Yes, but the miracle comes as such a surprise that, the moment we set foot in it, a sort of instinctive aberration seizes us, refusing to accept the evidence and compelling us to search in every direction to see if there is not another outlet. Even in the presence of those astounding horses and while they are working before our eyes, we do not yet sincerely believe that which fills and subdues our gaze. We accept the facts, because there is no means of escaping them; but we accept them only provisionally and with all reserve, putting off till later the comfortable explanation which will give us back our familiar, shallow certainties. But the explanation does not come; there is none in the homely and not very lofty regions wherein we hoped to find one; there is neither fault nor flaw in the mighty evidence; and nothing delivers us from the mystery.

It must be confessed that this mystery, springing from a point where we least expected to come upon the unknown, bears enough within itself to scatter all our convictions. Remember that, since man appeared upon this earth, he has lived among creatures which, from immemorial experience, he thought that he knew as perfectly as he knows an object fashioned by his hands. Out of these creatures he chose the most docile and, as he called them, the most intelligent, attaching in this case to the word intelligence a sense so narrow as to be almost ridiculous. He observed them, scrutinized them, tried them, analyzed them and dissected them in every imaginable way; and whole lives were devoted to nothing but the study of their habits, their faculties, their nervous system, their pathology, their psychology, their instincts. All this led to certainties which, among those supported by our unexplained little existence on an inexplicable planet, would seem to be the least doubtful, the least subject to revision. There is no disputing, for instance, that the horse is gifted with an extraordinary memory, that he possesses the sense of direction, that he understands a few signs and even a few words and that he obeys them. It is equally undeniable that the anthropoid apes are capable of imitating a great number of our actions and of our attitudes: but it is also manifest that their bewildered and feverish imagination perceives neither their object nor their scope. As for the dog, the one of all these privileged animals who lives closest to us, who for thousands and thousands of years has eaten at our table and worked with us and been our friend, it is manifest that, now and then, we catch a rather uncanny gleam in his deep, watchful eyes. It is certain that he sometimes wanders in a curious fashion along the mysterious border that separates our own intelligence from that which we grant to the other creatures inhabiting this earth with us. But it is no less certain that he has never definitely passed it. We know exactly how far he can go; and we have invariably found that our efforts, our patience, our encouragement, our passionate appeals, have hitherto failed to draw him out of the somewhat narrow, darkly enchanted circle wherein nature seems to have imprisoned him once and for all.

20

There remains, it is true, the insect-world, in which marvellous things happen. It includes architects, geometricians, mechanicians, engineers, weavers, physicists, chemists and surgeons who have forestalled most of our human inventions. I need not here remind the reader of the wasps' and bees' genius for building, the social and economic organization of the hive and the ant-hill, the spider's snares, the eumenes' nest and hanging egg, the odynerus' cell with its neat stacks of game, the sacred beetle's filthy but ingenius ball, the leafcutter's faultless disks, the brick-laying of the mason-bee, the three dagger-thrusts which the aphex administers to the three nerve-centres of the cricket, the lancet of the cerceris, who paralyses her victims without killing them and preserves them for an indefinite period as fresh meat, nor a thousand other features which it would be impossible to enumerate without recapitulating the whole of Henri Fabre's work and completely altering the proportions of the present essay. But here such silence and such darkness reign that we have nothing to hope for. There exists, so to speak, no bench-mark, no means of communication between the world of insects and our own; and we are perhaps less far from grasping and fathoming what takes place in Saturn or Jupiter than what is enacted in the ant-hill or the hive. We know absolutely nothing of the quality, the number, the extent or even the nature of their senses. Many of the great laws on which our life is based do not exist for them: those, for instance, which govern fluids are completely reversed. They seem to inhabit our planet, but in reality move in an entirely different world. Understanding nothing of their intelligence pierced with disconcerting gaps, in which the blindest stupidity suddenly comes and destroys the ablest and most inspired schemes, we have given the name of instinct to that which we could not apprehend, postponing our interpretation of a word that touches upon life's most insoluble riddles. There is, therefore, from the point of view of the intellectual faculties, nothing to be gathered from those extraordinary creatures who are not, like the other animals, our "lesser brothers," but strangers, aliens from we know not where, survivors or percursors of another world.

21

We were at this stage, slumbering peacefully in our long-established convictions, when a man entered upon the scene and suddenly showed us that we were wrong and that, for long centuries, we had over looked a truth which was scarcely even covered with a very thin veil. And the strangest thing is that this astonishing discovery, is in no wise the natural consequence of a new invention, of processes or methods hitherto unknown. It owes nothing to the latest acquirements of our knowledge. It springs from the humblest idea which the most primitive man might have conceived in the first days of the earth's existence. It is simply a matter of having a little more patience, confidence and respect for all that which shares our lot in a world whereof we know none of the purposes. It is simply a matter of having a little less pride and of looking a little more fraternally upon existences that are much more fraternal than we believed. There is no secret about the almost puerile ingenuousness of Von Osten's methods and Krall's. They start with the principle that the horse is an ignorant but intelligent child; and they treat him as such. They speak, explain, demonstrate, argue and mete out rewards or punishments like a schoolmaster addressing little boys of five or six. They begin by placing a few skittle-pins in front of their strange pupil. They count them and make him count them by alternately lifting and lowering the horse's hoof. He thus obtains his first notion of numbers. They next add one or two more skittles and say, for instance:

"Three skittles and two skittles are five skittles."

In this way, they explain and teach addition; next, by the reverse process, subtraction, which is followed by multiplication, division and all the rest.

At the beginning, the lessons are extremely laborious and demand an untiring and loving patience, which is the whole secret of the miracle. But; as soon as the first barrier of darkness is passed, the progress becomes bewilderingly rapid.

All this is incontestable; and the facts are there, before which we must need bow. But what upsets all our convictions or, more correctly, all the prejudices which thousands of years have made as invincible as axioms, what we do not succeed in understanding is that the horse at once understands what we want of him; it is that first step, the first tremor of an unexpected intelligence, which suddenly reveals itself as human. At what precise second did the light appear and was the veil rent under? It is impossible to say; but it is certain that, at a given moment, without any visible sign to reveal the prodigious inner transformation, the horse acts and replies as though he suddenly understood the speech of man. What is it that sets the miracle working? We know that, after a time, the horse associates certain words with certain objects that interest him or with three or four events whose infinite repetition forms the humble tissue of his daily life. This is only a sort of mechanical memory which has nothing in common with the most elementary intelligence. But behold, one fine day, without any perceptible transition, he seems to know the meaning of a host of words which possess no interest for him; which represent to him no picture, no memory; which he has never had occasion to connect with any sensation, agreeable or disagreeable. He handles figures, which even to man are nothing but obscure and abstract ideas. He solves problems that cannot possibly be made objective or concrete. He reproduces letters which, from his point of view, correspond with nothing actual. He fixes his attention and makes observations on things or circumstances which in no way affect him, which remain and always will remain alien and indifferent to him. In a word, he steps out of the narrow ring in which he was made to turn by hunger and fear--which have been described as the two great moving powers of all that is not human--to enter the immense circle in which sensations go on being shed till ideas come into view.

22

Is it possible to believe that the horses really do what they appear to do? Is there no precedent for the marvel? Is there no transition between the Elberfeld stallions and the horses which we have known until this day? It is not easy to answer these questions, for it is only since yesterday that the intellectual powers of our defenseless brothers have been subjected to strictly scientific experiments. We have, it is true more than one collection of anecdotes in which the intelligence of animals is lauded to the skies; but we cannot rely upon these ill-authenticated stories. To find genuine and incontestable instances we must have recourse to the works, rare as yet, of scientific men who have made a special study of the subject. M. Hachet-Souplet, for example, the director of the Institut de Psychologie Zoologique, mentions the case of a dog who learnt to acquire an abstract idea of weight. You put in front of him eight rounded and polished stones, all of exactly the same size and shape, but of different weights. You tell him to fetch the heaviest or the lightest; he judges their weight by lifting them and, without mistake, picks out the one required.

The same writer also tells the story of a parrot to whom he had taught the word "cupboard" by showing him a little box that could be hung up on the wall at different heights and in which his daily allowance of food was always ostentatiously put away;

"I next taught him the names of a number of objects," says M. Hachet-Souplet, "by holding them out to him. Among them was a ladder; and I prevailed upon the bird to say, 'Climb,' each time that he saw me mount the steps. One morning, when the parrot's cage was brought into the laboratory, the cupboard was hanging near the ceiling, while the little ladder was stowed away in a corner among other objects familiar to the bird. Now the parrot, every day, when I opened the cupboard, used to scream, 'Cupboard! Cupboard! Cupboard!' with all his might. My problem was, therefore, this: seeing that the cupboard was out of my reach and that, therefore, I could not take his food out of it; knowing, on the other hand, that I was able to raise myself above the level of the floor by climbing the ladder; and having the words 'climb' and 'ladder' at his disposal: would he employ them to suggest to me the idea of using them in order to reach the cupboard? Greatly excited, the parrot flapped his wings, bit the bars of his cage, and screamed:

"'Cupboard! Cupboard! Cupboard!'"

"And I got no more out of him that day. The next day, the bird, having received nothing but millet, for which he did not much care, instead of the hemp-seed contained in the cupboard, was in paroxysms of anger; and, after he had made numberless attempts to force open his bars, his attention was at last caught by the ladder and he said:

"'Ladder, climb, cupboard!'"

We have here, as the author remarks, a marvellous intellectual effort. There is an evident association of ideas; cause is linked with effect; and examples such as this lesson appreciably the distance separating our learned horses from their less celebrated brethren. We must admit, however, that this intellectual effort, if we observe, animals a little carefully, is much less uncommon than we think. It surprises us in this case because a special and, when all is said, purely mechanical arrangement of the parrot's organ gives him a human voice. At every moment, I find in my own dog associations of ideas no less evident and often more complex. For instance, if he is thirsty, he seeks my eyes and next looks at the tap in the dressing-room, thus showing that he very plainly connects the notions of thirst, running water and human intervention. When I dress to go out, he evidently watches all my movements. While I am lacing my boots, he conscientiously licks my hands, in order that my divinity may be good to him and especially to congratulate me on my capital idea of going out for a constitutional. It is a sort of general and as yet vague approval. Boots promise an excursion out of doors, that is to say, space, fragrant roads, long grass full of surprises, corners scented with offal, friendly or tragic encounters and the pursuit of wholly illusory, game. But the fair vision is still in anxious suspense. He does not yet know if he is going with me. His fate is now being decided; and his eyes, melting with anguish, devour my mind. If I buckle on my leather gaiters, it means the sudden and utter extinction, of all that constitutes the joy of life. They leave not a ray of hope. They herald the hateful, lonely motorcycle, which he cannot keep up with; and he stretches himself sadly in a dark corner, where he goes back to the gloomy dreams of an unoccupied, forsaken dog. But, when I slip my arms into the sleeves of my heavy great-coat, one would think that they were opening the gates of the most dazzling paradise. For this implies the car, the obvious, indubitable motor-car, in other words, the radiant summit of the most superlative delight. And delirious barks, inordinate bounds, riotous, embarrassing demonstrations of affection greet a happiness which, for all that, is but an immaterial idea, built up of artless memories and ingenuous hopes.

23

I mention these matters only because they are quite ordinary and because there is nobody who has not made a thousand similar observations. As a rule, we do not notice that these humble manifestations represent sentiments, associations of ideas, inferences, deductions, an absolute and altogether human mental effort. They lack only speech; but speech is merely a mechanical accident which reveals the operations of thought more clearly to us. We are amazed that Mohammed or Zarif should recognize the picture of a horse, a donkey, a hat, or a man on horseback, or that they should spontaneously report to their master the little events that happen in the stable; but it is certain that our own dog is incessantly performing a similar work and that his eyes, if we could read them, would tell us a great deal more. The primary miracle of Elberfeld is that the stallions should have been given the means of expressing what they think and feel. It is momentous; but, when closely looked into, it is not incomprehensible. Between the talking horses and my silent dog there is an enormous distance, but not an abyss. I am saying this not to detract from the nature or extent of the prodigy, but to call attention to the fact that the theory of animal intelligence is more justifiable and less fanciful than one is at first inclined to think.

24

But the second and greater miracle is that man should have been able to rouse the horse from his immemorial sleep, to fix and direct his attention and to interest him in matters that are more foreign and indifferent to him than the variations of temperature in Sirius or Aldebaran are to us. It really seems, when we consider our preconceived ideas, that there is not in the animal an organic and insurmountable inability to do what man's brain does, a total and irremediable absence of intellectual faculties, but rather a profound lethargy and torpor of those faculties. It lives in a sort of undisturbed stolidity, of nebulous slumber. As Dr. Ochorowicz very justly remarks, "its waking state is very near akin to the state of a man walking in his sleep." Having no notion of space or time, it spends its life, one may say, in a perpetual dream. It does what is strictly necessary to keep itself alive; and all the rest passes over it and does not penetrate at all into its hermetically closed imaginings. Exceptional circumstances--some extraordinary need, wish, passion or shock--are required to produce what M. Hachet-Souplet calls "the psychic flash" which suddenly thaws and galvanizes its brain, placing it for a minute in the waking state in which the human brain works normally. Nor is this surprising. It does not need that awakening in order to exist; and we know that nature never makes great superfluous efforts.. "The intellect," as Professor Clarapede well says, "appears only as a makeshift, an instrument which betrays that the organism is not adapted to its environment, a mode of expression which reveals a state of impotence."

It is probable that our brain at first suffered from the same lethargy, a condition, for that matter, from which many men have not yet emerged; and it is even more probable that, compared with other modes of existence, with other psychic phenomena, on another plane and in another sphere, the dense sleep in which we move is similar to that in which the lower animals have their being. It also is traversed, with increasing frequency, by psychic flashes of a different order and a different scope. Seeing, on the one side, the intellectual movement that seems to be spreading among our lesser brothers and, on the other, the ever more constantly repeated manifestations of our subconsciousness, we might even ask ourselves if we have not here, on two different planes, a tension, a parallel pressure, a new desire, a new attempt of the mysterious spiritual force which animates the universe and which seems to be incessantly seeking fresh outlets and fresh conducting rods. Be this as it may, when the flash has passed, we behave very much as the animals do: we promptly lapse into the indifferent sleep which suffices also for our miserable ways. We ask no more of it, we 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.

25

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.

26

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 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 while--and, 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."

28

Truth to say, the theory of intelligence in the animal would be so 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 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.

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>From the maybe enchanted atmosphere that surrounds numbers we shall pass more easily to the even more magic mists of the final theory, the only one remaining to us for the moment: the mediumistic or subliminal theory. This, we must remember, is not the telepathic theory proper which decisive experiments have made us reject. Let us have the courage to venture upon it. When one can no longer interpret a phenomenon by the known, we must needs try to do so by the unknown. We, therefore, now enter a new province of a great unexplored kingdom, in which we shall find ourselves without a guide.

Mediumistic phenomena, manifestations of the secondary or the subliminal consciousness, between man and man, are, as we have more than once had occasion to assure ourselves, capricious, undisciplined, evasive and uncertain, but more frequent than one thought and, to one who examines, them seriously and honestly, often undeniable. Have similar manifestations been discovered between man and the animals? The study of these manifestations, which is very difficult even in the case of man, becomes still more so when we question witnesses doomed to silence. There are, however, some animals which are looked upon as "psychic," which, in other words, seem indisputably to be sensitive to certain subliminal influences. One usually classes the cat, the dog and the horse in this somewhat ill-defined category. To these superstitious animals one might perhaps add certain birds, more or less birds of omen, and even a few insects, notably the bees. Other animals, such as, for instance, the elephant and the monkey, appear to be proof against mystery. Be this as it may, M. Ernest Bozzano, in an excellent article on Les Perceptions psychiques des animaux,[1] collected in 1905 sixty-nine cases of telepathy, presentiments and hallucinations of sight or hearing in which the principal actors are cats, dogs and horses. There are, even among them, ghosts or phantoms of dogs which, after their death, return to haunt the homes in which they were happy. Most of these cases are taken from the Proceedings of the S. P. R., that is to say, they have nearly all been very strictly investigated. It is impossible, short of filling these pages with often striking and touching but rather cumbersome anecdotes, to enumerate them here, however briefly. It will be sufficient to note that sometimes the dog begins to howl at the exact moment when his master loses his life, for instance, on a battlefield, hundreds of miles from the place where the dog is. More commonly, the cat, the dog and the horse plainly manifest that they perceive, often before men do, telepathic apparitions, phantasms of the living or the dead. Horses in particular seem very sensitive to places that pass as haunted or uncanny. On the whole, the result of these observations is that we can hardly dispute that these animals communicate as much as we do and perhaps in the same fashion with the mystery that lies around us. There are moments at which, like man, they see the invisible and perceive events, influences and emotions that are beyond the range of their normal senses. It is, therefore, permissible to believe that their nervous system or some remote or secret part of their being contains the same psychic elements connecting them with an unknown that inspires them with as much terror as it does ourselves. And, let us say in passing, this terror is rather strange; for, after all, what have they to fear from a phantom or an apparition, they who, we are convinced have no after-life and who ought, therefore, to remain perfectly indifferent to the manifestations, of a world in which they will never set foot?

[1] Annales des sciences psychiques, August, 1905, pp 422-469.

I shall perhaps be told that it is not certain that these apparitions are objective, that they correspond with an external reality, but that it is exceedingly possible that they spring solely from the man's or the animal's brain. This is not the moment to discuss this very obscure point, which raises the whole question of the supernatural and all the problems of the hereafter. The only important thing to observe is that at one time it is man who transmits his terror, his perception or his idea of the invisible to the animal and at another the animal which transmits its sensations to man. We have here, therefore, intercommunications which spring from a deeper common source than any that we know and which, to issue from it or go back to it, pass through other channels than those of our customary senses. Now all this belongs to that unexplained sensibility, to that secret treasure, to that as yet undetermined psychic power which, for lack of a better term, we call subconsciousness or subliminal consciousness. Moreover, it is not surprising that in the animals, these subliminal faculties not only exist, but are perhaps keener and more active than in ourselves, because it is our conscious and abnormally individualized life that atrophies them by relegating them to a state of idleness wherein they have fewer and fewer opportunities of being exercised, whereas in our brothers who are less detached from the universe, consciousness--if we can give that name to a very uncertain and confused notion of the ego--is reduced to a few elementary actions. They are much less separated than ourselves from the whole of the circumambient life and they still possess a number of those more general and indeterminate senses whereof we have been deprived by the gradual encroachment of a narrow and intolerant special faculty, our intelligence. Among these senses which up to the present we have described as instincts, for want--and it is becoming a pressing want--of a more suitable and definite word, need I mention the sense of direction, migration, foreknowledge of the weather, of earthquakes and avalanches and many others which we doubtless do not even suspect? Does all this not belong to a subconsciousness which differs from ours only in being so much richer?

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I am fully aware that this explanation by means of the subliminal consciousness will not explain very much and will at most invoke the aid of the unknown to illuminate the incomprehensible. But to explain a phenomenon, a Dr. J. de Modzelwski very truly says, "is to put forward a theory which is more familiar and more easily comprehensible to us than the phenomenon at issue." This is really what we are constantly and almost exclusively doing in physics, chemistry, biology and in every branch of science without exception. To explain a phenomenon is not necessarily to make it as clear and lucid as that two and two are four; and, even so, the fact that two and two are four is not, when we go to the bottom of things, as clear and lucid as it seems. What in this case, as in most others, we wrongfully call explaining is simply confronting the unexpected mystery which these horses offer us with a few phenomena which are themselves unknown, but which have been perceived longer and more frequently. And this same mystery, thus explained, will serve one day to explain others. It is in this way that science goes to work. We must not blame it: it does what it can; and it does not appear that there are other ways.

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If we assent to this explanation by means of the subliminal consciousness, which is a sort of mysterious participation in all that happens in this world and the others, many obstacles disappear and we enter into a new region in which we draw strangely nearer to the animals and really become their brothers by closer links, perhaps the only essential links in life. They take part from that moment in the great human problems, in the extraordinary actions of our unknown guest; and, if, since we have been observing the indwelling force more attentively, nothing any longer surprises us of that which it realizes in us, no more should anything surprise us of that which it realizes in them. We are on the same plane with them, in some as yet undetermined element, when it is no longer the intelligence that reigns alone, but another spiritual power, which pays no heed to the brain, which passes by other roads and which might rather be the psychic substance of the universe itself, no longer set in grooves, isolated and specialized by man, but diffused, multiform and perhaps, if we could trace it, equal in everything that exists.

There is, henceforth, no reason why the horses should not participate in most of the mediumistic, phenomena which we find existing between man and man; and their mystery ceases to be distinct from those of human metaphysics. If their subliminal is akin to ours, we can begin by extending to its utmost limits the telepathic theory, which has, so to speak, no limits, for, in the matter of telepathy, as Myers has said, all that we are permitted to declare is that "life has the power of manifesting itself to life." We may ask ourselves, therefore, if the problem which I set to the horse, without knowing the terms of it, is not communicated to my subliminal, which is ignorant of it, by that of the horse, who has read it. It is practically certain that this is possible between human subliminals. Is it I who see the solution and transmit it to the horse, who only repeats it to me? But, suppose that it is a problem which I myself am incapable of solving? Whence does the solution come, then? I do not know if the experiment has been attempted, under the same conditions, with a human medium. For that matter, if it succeeded, it would be very much the same as the no less subliminal phenomenon of the arithmetical prodigies, or lightning calculators, with which, in this rather superhuman atmosphere, we are almost forced to compare the riddle of the mathematical horses. Of all the interpretations, it is the one which, for the moment, appears to me the least eccentric and the most natural.

We have seen that the gift of handling colossal figures is almost foreign to the intelligence proper; one can, even declare that, in certain cases, it is evidently and completely independent of such intelligence. In these cases, the gift is manifested prior to any education and from the earliest years of childhood. If we refer to the list of arithmetical prodigies given by Dr. Scripure,[1] we see that the faculty made its appearance in Ampere at the age of three, in Colburn at six, in Gauss at three, in Mangiamele at ten, in Safford at six, in Whateley at three, and so on. Generally, it lasts for only a few years, becoming rapidly enfeebled with age and usually vanishing suddenly at the moment when its possessor begins to go to school.

[1] American Journal of Psychology, 1 April 1891.

When you ask those children and even most of the lightning calculators who have come to man's estate how they go to work to solve the huge and complicated problems set them, they reply that they know nothing about it. Bidder, for instance, declares that it is impossible for him to say how he can instinctively tell the logarithm of a number consisting of seven or eight figures. It is the same with Safford, who, at the age of ten, used to do in his head, without ever making a mistake, multiplication-sums the result of which ran into thirty-six figures. The solution presents itself authoritatively and spontaneously; it is a vision, an impression, an inspiration, an intuition coming one knows not whence, suddenly and indubitably. As a role, they do not even try to calculate. Contrary to the general belief, they have no peculiar methods; or, if method there be, it is more a practical way of subdividing the intuition. One would think that the solution springs suddenly from the very enunciation of the problem, in the same way as a veridical hallucination. It appears to rise, infallible and ready-done, from a sort of eternal and cosmic reservoir wherein the answers to every question lie dormant. It must, therefore, be admitted that we have here a phenomenon that occurs above or below the brain, by the side of the consciousness and the mind, outside all the intellectual methods and habits; and it is precisely for phenomena of this kind that Myers invented the word "subliminal."[1]

[1] I have no need to recall the derivation of the term subliminal: beneath (sub) the threshold (limen) of consciousness. Let us add, as M. de Vesme very rightly remarks, that the subliminal is not exactly what classical psychology calls the subconsciousness, which latter records only notions that are normally perceived and possesses only normal faculties, that is to say, faculties recognized to-day by orthodox science.

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Does not all this bring us a little nearer to our calculating horses? From the moment that it is demonstrated that the solution of a mathematical problem no longer depends exclusively on the brain, but on another faculty, another spiritual power whose presence under various forms has been ascertained beyond a doubt in certain animals, it ceases to be wholly rash or extravagant to suggest that perhaps, in the horse, the same phenomenon is reproduced and developed in the same unknown, wherein moreover the mysteries of numbers and those of subconsciousness mingle in a like darkness. I am well aware that an explanation laden to such an extent with mysteries explains but very little more than silence does; nevertheless, it is at least a silence traversed by restless murmurs, and sedulous whispers that are better than the gloomy and hopeless ignorance to which we would have perforce to resign ourselves if we did not, in spite of all, to perform the great duty of man, which is to discover a spark in the darkness.