I will first sum up as briefly as possible, for who so may still be ignorant of them, the facts which it is necessary to know if one would fully understand the marvelous story of the Elberfeld horses. For a detailed account, I can refer him to Herr Karl Krall's remarkable work, Denkende Tiere (Leipsig, 1912), which is the first and principal source of information amid a bibliography that is already assuming considerable dimensions.

Some twenty years ago there lived in Berlin an old misanthrope named Wilhelm von Osten. He was a man with a small private income, a little eccentric in his ways and obsessed by one idea, the intelligence of animals. He began by undertaking the education of a horse that gave him no very definite results. But, in 1900, he became the owner of a Russian stallion who, under the name of Hans, to which was soon added the Homeric and well-earned prefix of Kluge, or Clever, was destined to upset all our notions of animal psychology and to raise questions that rank among the most unexpected and the most absorbing problems which man has yet encountered.

Thanks to Von Osten, whose patience, contrary to what one might think, was in no wise angelic but resembled rather a frenzied obstinacy, the horse made rapid and extraordinary progress. This progress is very aptly described by Professor E. Clarapede, of the university of Geneva, who says, in his excellent monograph on the Elberfeld horses:

"After making him familiar with various common ideas, such as right, left, top, bottom and so on, his master began to teach him arithmetic by the intuitive method. Hans was brought to a table on which were placed first one, then two, then several small skittles. Von Osten, kneeling beside Hans, uttered the corresponding numbers, at the same time making him strike as many blows with his hoof as there were skittles on the table. Before long, the skittles were replaced by figures written on a blackboard. The results were astonishing. The horse was capable not only of counting (that is to say, of striking as many blows as he was asked), but also of himself making real calculations, of solving little problems....

"But Hans could do more than mere sums: he knew how to read; he was a musician, distinguishing between harmonious and dissonant chords. He also had an extraordinary memory: he could tell the date of each day of the current week. In short, he got through all the tasks which an intelligent schoolboy of fourteen is able to perform."

The rumour of these curious experiments soon spread; and visitors flocked to the little stable-yard in which Von Osten kept his singular pupil at work. The newspapers took the matter up; and a fierce controversy broke forth between those who believed in the genuineness of the phenomenon and those who saw no more in it than a barefaced fraud. A scientific committee was appointed in 1904, consisting of professors of psychology and physiology, of the director of a zoological garden, of a circus manager and of veterinary surgeons and cavalry-officers. The committee discovered nothing suspicious, but ventured upon no explanation. A second committee was then appointed, numbering among its members Herr Oskar Pfungst, of the Berlin psychological laboratory. Herr Pfungst, after a long series of experiments, drew up a voluminous and crushing report, in which he maintained that the horse was gifted with no intelligence, that it did not recognize either letters or figures, that it really knew neither how to calculate nor how to count, but merely obeyed the imperceptible, infinitesimal and unconscious signs which escaped from its master.

Public opinion veered round suddenly and completely. People felt a sort of half-cowardly relief at beholding the prompt collapse of a miracle which was threatening to throw confusion into the self satisfied little fold of established truths. Poor Von Osten protested in vain: no one listened to him; the verdict was given. He never recovered from this official blow; he became the laughing-stock of all those whom he had at first astounded; and he died, lonely and embittered, on the 29th of June, 1909, at the age of seventy-one.

But he left a disciple whose faith had not been shaken by the general defection. A well-to-do Elberfeld manufacturer, Herr Krall, had taken a great interest in Von Osten's labours and, during the latter years of the old man's life, had eagerly followed and even on occasion directed the education of the wonderful stallion. Von Osten left Kluge Hans to him by will; on his own side, Krall had bought two Arab stallions, Mohamed and Zarif whose prowess soon surpassed that of the pioneer. The whole question was reopened, events took a vigorous and decisive turn and, instead of a weary, eccentric old man, discouraged almost to sullenness and with no weapons for the struggle, the critics of the miracle found themselves faced by a new adversary, young and high-spirited, endowed with remarkable scientific instinct, quick-witted, scholarly and well able to defend himself.

His educational methods also differ materially from Von Osten's. It was a strange thing, but deep down in the rather queer, cross-grained soul of the old enthusiast there had grown up gradually a sort of hatred for his four-legged pupil. He felt the stallion's proud and nervous will resisting his with an obstinacy which he qualified as diabolical. They stood up to each other like two enemies: and the lessons almost assumed the form of a tragic and secret struggle in which the animal's soul rebelled against man's domination.

Krall, on the other hand, adores his pupils; and this atmosphere of affection has in a manner of speaking humanized them. There are no longer those sudden movements of wild panic which reveal the ancestral dread of man in the quietest and best-trained horse. He talks to them long and tenderly, as a father might talk to his children; and we have the strange feeling that they listen to all that he says and understand it. If they appear not to grasp an explanation or a demonstration, he will begin it all over again, analyze it, paraphrase it ten times in succession, with the patience of a mother. And so their progress has been incomparably swifter and more astounding than that of old Hans. Within a fortnight of the first lesson Mohamed did simple little addition and subtraction sums quite correctly. He had learnt to distinguish the tens from the units, striking the latter with his right foot and the former with his left. He knew the meaning of the symbols plus and minus. Four days later, he was beginning multiplication and division. In four months' time, he knew how to extract square and cubic roots; and, soon after, he learnt to spell and read by means of the conventional alphabet devised by Krall.

This alphabet, at the first glance, seems rather complicated. For that matter, it is only a makeshift; but how could one find anything better? The unfortunate horse, who is almost voiceless, has only one way in which to express himself: a clumsy hoof, which was not created to put thought into words. It became necessary, therefore, to contrive, as in table-turning, a special alphabet, in which each letter is designated by a certain number of blows struck by the right foot and the left. Here is the copy handed to visitors at Elberfeld to enable them to follow the horse's operations:

To mark the letter E, for instance, the stallion will strike one blow with his left foot and one with his right; for the letter L, two blows with his left foot and three with his right; and so on. The horses have this alphabet so deeply imprinted in their memory that, practically speaking, they never make a mistake; and they strike their hoofs so quickly, one after the other, that at first one has some difficulty in following them.

Mohamed and Zarif — for Zarif's progress was almost equal to that of his fellow-pupil, though he seems a little less gifted from the standpoint of higher mathematics-Mohamed and Zarif in this way reproduce the words spoken in their presence, spell the names of their visitors, reply to questions put to them and sometimes make little observations, little personal and spontaneous reflections to which we shall return presently. They have created for their own use an inconceivably fantastic and phonetic system of spelling which they stubbornly refuse to relinquish and which often makes their writing rather difficult to read. Deeming most of the vowels useless, they keep almost exclusively to the consonants; thus Zucker, for instance, becomes Z K R; Pferd, P F R T, or F R T, and so on.

I will not set forth in detail the many different proofs of intelligence lavished by the singular inhabitants of this strange stable. They are not only first-class calculators, for whom the most repellent fractions and roots possess hardly any secrets: they distinguish sounds, colours, and scents, read the time on the face of a watch, recognize certain geometrical figures, likenesses and photographs.

Following on these more and more conclusive experiments and especially after the publication of Krall's great work, Denkende Tiere, a model of precision and arrangement, men's minds were faced with clear and definite problem which, this time, could not be challenged. Scientific committees followed one another at Elberfeld; and their reports became legion. Learned men of every country — including Dr. Edinger, the eminent Frankfort neurologist; Professors Dr. H. Kraemer and H. E. Ziegler, of Stuttgart; Dr. Paul Saresin, of Bale; Professor Ostwald, of Berlin; Professor A. Beredka, of the Pasteur Institute; Dr. E. Clarapede, of the university of Geneva; Professor Schoeller and Professor Gehrke, the natural philosopher, of Berlin; Professor Goldstein, of Darmstadt; Professor von Buttel-Reepen, of Oldenburg; Professor William Mackenzie, of Genoa; Professor R. Assagioli, of Florence; Dr. Hartkopf, of Cologne; Dr. Freudenberg, of Brussels; Dr. Ferrari, of Bologna, etc., etc., for the list is lengthening daily — came to study on the spot the inexplicable phenomenon which Dr. Clarapede proclaims to be "the most sensational event that has ever happened in the psychological world."

With the exception of two or three sceptics or convinced misoneists and of those who made too short a stay at Elberfeld, all were unanimous in recognizing that the facts were as stated and that the experiments were conducted with absolute fairness. Disagreement begins only when it becomes a matter of commenting on them, interpreting them and explaining them.

To complete this short preamble, it is right to add that, for some time past, the case of the Elberfeld horses no longer stands quite alone. There exists at Mannheim a dog of a rather doubtful breed who performs almost the same feats as his equine rivals. He is less advanced than they in arithmetic, but does little additions, subtractions and multiplications of one or two figures correctly. He reads and writes by tapping with his paw, in accordance with an alphabet which, it appears, he has thought out for himself; and his spelling also is simplified and phoneticized to the utmost. He distinguishes the colour in a bunch of flowers, counts the money in a purse and separates the marks from the pfennigs. He knows how to seek and find words to define the object or the picture placed before him. You show him, for instance, a bouquet in a vase and ask him what it is.

"A glass with little flowers," he replies.

And his answers are often curiously spontaneous and original. In the course of a reading-exercise in which the word Herbst, autumn, chanced to attract attention, Professor William Mackenzie asked him if he could explain what autumn was.

"It is the time when there are apples," Rolf replied.

On the same occasion, the same professor, without knowing what it represented, held out to him a card marked with red and blue squares:

"What's this?"

"Blue, red, lots of cubes," replied the dog.

Sometimes his repartees are not lacking in humour.

"Is there anything you would like me to do for you?" a lady of his acquaintance asked, one day.

And Master Rolf gravely answered:

"Wedelen," which means, "Wag your tail!"

Rolf, whose fame is comparatively young, has not yet, like his illustrious rivals of the Rhine Province, been the object of minute enquiries and copious and innumerable reports. But the incidents which I have just mentioned and which are vouched for by such men as Professor Mackenzie and M. Duchatel, the learned and clear-sighted vice-president of the Societe Universelle d'Etudes Psychiques,¹ who went to Mannheim for the express purpose of studying them, appear to be no more controvertible than the Elbenfeld occurrences, of which they are a sort of replica or echo. It is not unusual to find these coincidences amongst abnormal phenomena. They spring up simultaneously in different quarters of the globe, correspond with one another and multiply as though in obedience to a word of command. It is probable therefore that we shall see still more manifestations of the same class. One might almost say that a new spirit is passing over the world and, after awakening in man forces whereof he was not aware, is now reaching other creatures who with us inhabit this mysterious earth, on which they live, suffer and die, as we do, without knowing why.

I have not been to Mannheim, but I made my pilgrimage to Elberfeld and stayed long enough in the town to carry away with me the conviction shared by all those who have undertaken the journey.

A few months ago, Herr Krall, whom I had promised the year before that I would come and see his wonderful horses, was kind enough to repeat his invitation in a more pressing fashion, adding that his stable would perhaps be broken up after the 15th of September and that, in any case, be would be obliged, by his doctor's orders, to interrupt for an indefinite period a course of training which he found exceedingly fatiguing.

I at once left for Elberfeld, which, as everybody knows, is an important manufacturing-town in Rhenish Prussia and is, in fact, more quaint, pleasing and picturesque than one might expect. I had long since read everything that had been published on the question; and I was wholly persuaded of the genuineness of the incidents. Indeed it would be difficult to have any doubts after the repeated and unremitting supervision and verification to which the experiments are subjected, a supervision which is of the most rigorous type, often hostile and almost ill-mannered. As for their interpretation, I was convinced that telepathy, that is to say, the transmission of thought from one subconsciousness to another, remained, however strange it might be in this new region, the only acceptable theory; and this in spite of certain circumstances that seemed plainly to exclude it. In default of telepathy proper, I inclined toward the mediumistic or subliminal theory, which was very ably outlined by M. de Vesmes in a remarkable lecture delivered, on the 22nd of December, 1912, before the Société Universelle d'Études Psychiques. It is true that telepathy, especially when carried to its extreme limits, appeals above all to the subliminal forces, so that the two theories overlap at more than one point and it is often difficult to make out where the first ends and the second begins. But this discussion will be more appropriate a little later.

I found Herr Krall in his goldsmith's shop, a sort of palace of Golconda, streaming and glittering with the most precious pearls and stones on earth. Herr Krall, it is well to remember, in order to dispel any suspicion of pecuniary interest, is a rich manufacturer whose family for three generations, from father to son, have conducted one of the most important jewelry businesses in Germany. His researches, so far from bringing him the least profit, cost him a great deal of money, take up all his leisure and some part of the time which he would otherwise devote to his business and, as usually happens, procure him from his fellow citizens and from not a few scientific men more annoyance, unfair criticism and sarcasm than consideration or gratitude. His work is preeminently the disinterested and thankless task of the apostle and pioneer.

For the rest, Herr Kraft, though his faith is active, zealous and infectious, has nothing in common with the visionaries or illuminati. He is a man of about fifty, vigorous, alert and enthusiastic, but at the same time well-balanced; accessible to every idea and even to every dream, yet practical and methodical, with a ballast of the most invincible common-sense. He inspires from the outset that fine confidence, frank and unrestrained, which instantly disperses the instinctive doubt, the strange uneasiness and the veiled suspicion that generally separate two people who meet for the first time; and one welcomes in him, from the very depths of one's being, the honest man, the staunch friend whom one can trust and whom one is sorry not to have known earlier in life.

We go together through the streets and along the bustling quays of Elberfeld to the stable, situated at a few hundred steps from the shop. The horses are taking the air outside the doors of their boxes, in the yard shaded by a lime-tree. There are four of them: Mohamed, the most intelligent, the most gifted of them all, the great mathematician of the party; his double, Zarif, a little less advanced, less tractable, craftier, but at the same time more fanciful, more spontaneous and capable of occasional disconcerting sallies; next, Hänschen, a little Shetland pony, hardly bigger than a Newfoundland dog, the street-urchin of the band, always quivering with excitement, roguish, flighty, uncertain and passionate, but ready in a moment to work you out the most difficult addition and multiplication sums with a furious scrape of the hoof; and lastly the latest arrival, the plump and placid Berto, an imposing black stallion, quite blind and lacking the sense of smell. He has been only a few months at school and is still, so to speak, in the preparatory class, but already does — a little more clumsily, but more good humouredly and conscientiously — small addition and subtraction sums quite as well as many a child of the same age.

In a corner, Kama, a young elephant two or three years old, about the size of an outrageously "blown" donkey, rolls his mischievous and almost knavish eye, under the shelter of his wide ears, each resembling a great rhubarb-leaf, and with his stealthy, insinuating trunk carefully picks up whatever he considers fit to eat, that is to say, pretty well everything that lies about on the stones. Great things were hoped of him, but hitherto he has disappointed all expectations: he is the dunce of the establishment. Perhaps he is too young still: his little elephant-soul no doubt resembles that of a sucking-babe which, in the place of its feet and hands, plays with the stupendous nose that must first explore and question the universe. It is impossible to grip his attention; and, when they set out before him his alphabet of movable letters, instead of naming those which are pointed out to him he applies himself to pulling them off their stems, in order to swallow them surreptitiously. He has disheartened his kind master, who, pending the coming of the reason and wisdom promised by the proboscidian legends, leaves him in a contented state of ignorance made more blissful by an almost insatiable appetite.

But I ask to see the great pioneer, Kluge Hans, Clever Hans. He is still alive. He is old: he must be sixteen or seventeen; but his old age, alas, is not exempt from the baneful troubles from which men themselves suffer in their decline! Hans has turned out badly, it appears, and is never mentioned save in ambiguous terms. An imprudent or vindictive groom, I forget which, having introduced a mare into the yard, Hans the Pure, who till then had led an austere and monkish existence, vowed to celibacy, science and the chaste delights of figures, Hans the Irreproachable incontinently lost his head and cut himself open on the hanging-rail of his stall. They had to force back his intestines and sew up his belly. He is now rusticating miserably in a meadow outside the town. So true it is that a life cannot be judged except at its close and that we are sure of nothing until we are dead.

Before the sitting begins, while the master is making his morning inspection, I go up to Muhamed, speak to him and pat him, looking straight into his eyes meanwhile in order to catch a sign of his genius. The handsome creature, well-bred and in hard condition, is as calm and trusting as a dog; he shows himself excessively gracious and friendly and tries to give me some huge licks and mighty kisses which I do my best to avoid because they are a little unexpected and over-demonstrative. The expression of his limpid antelope-eyes is deep, serious and remote, but it differs in no wise from that of his brothers who, for thousands of years, have seen nothing but brutality and ingratitude in man. If we were able to read anything there, it would not be that insufficient and vain little effort which we call thought, but rather an indefinable, vast anxiety, a tear-dimmed regret for the boundless, stream-crossed plains where his sires sported at will before they knew man's yoke. In any case, to see him thus fastened by a halter to the stable-door, beating off the flies and absently pawing the cobbles, Muhamed is nothing more than a well-trained horse who seems to be waiting for his saddle or harness and who hide, his new secret as profoundly as all the others which nature has buried in him.

But they are summoning me to take my place in the stable where the lessons are given. It is a small room, empty and bare, with peat-moss litter bedding and white-washed walls. The horse is separated from the people present by breast-high wooden partitions. Opposite the four-legged scholar is a black-board, nailed to the wall; and on one side a corn-bin which forms a seat for the spectators. Muhamed is led in. Krall, who is a little nervous, makes no secret of his uneasiness. His horses are fickle animals, uncertain, capricious and extremely sensitive. A trifle disturbs them, confuses them, puts them off. At such times, threats, prayers and even the irresistible charm of carrots and good rye-bread are useless. They obstinately refuse to do any work and they answer at random. Everything depends on a whim, the state of the weather, the morning meal or the impression which the visitor makes upon them. Still, Krall seems to know, by certain imperceptible signs, that this is not going to be a bad day. Muhamed quivered with excitement, snorts loudly through his nostrils, utters a series of indistinct little whinnyings: excellent symptoms, it appears. I take my seat on the corn-bin. The master, standing beside the black-board, chalk in hand, introduces me to Muhamed in due form, as to a human being:

"Muhamed, attention! This is your uncle" — pointing to me — "who has come all the way to honour you with a visit. Mind you don't disappoint him. His name is Maeterlinck." Krall pronounced the first syllable German-fashion: Mah. "You understand: Maeterlinck. Now show him that you know your letters and that you can spell a name correctly, like a clever boy. Go ahead, we're listening." Muhamed gives a short neigh and, on the small, movable board at his feet, strikes first with his right hoof and then with his left the number of blows which correspond with the letter M in the conventional alphabet used by the horses. Then, one after the other, without stopping or hesitating, he marks the letters A D R L I N S H, representing the unexpected aspect which my humble name assumes in the equine mind and phonetics. His attention is called to the fact that there is a mistake. He readily agrees and replaces the S H by a G and then the G by a K. They insist that he must put a T instead of the D; but Muhamed, content with his work, shakes his head to say no and refuses to make any further corrections.

I assure you that the first shock is rather disturbing, however much one expected it. I am quite aware that, when one describes these things, one is taken for a dupe too readily dazzled by the doubtless childish illusion of an ingeniously-contrived scene. But what contrivances, what illusions have we here? Do they lie in the spoken word? Why, to admit that the horse understands and translates his master's words is just to accept the most extraordinary part of the phenomenon! Is it a case of surreptitious touches or conventional signs? However simple-minded one may be, one would nevertheless notice them more easily than a horse, even a horse of genius. Krall never lays a hand on the animal; he moves all round the little table, which contains no appliances of any sort; for the most part, he stands behind the horse which is unable to see him, or comes and sits beside his guest on the innocuous corn-bin, busying himself, while lecturing his pupil, in writing up the minutes of the lesson. He also welcomes with the most serene readiness any restrictions or tests which you propose. I assure you that the thing itself is much simple, and clearer than the suspicions of the arm-chair critics and that the most distrustful mind world not entertain the faintest idea of fraud in the frank, wholesome atmosphere of the old stable.

"But," some one might have said, "Krall, who knew that you were coming to Elberfeld, had of course thoroughly rehearsed his little exercise in spelling, which apparently is only an exercise in memory."

For conscience' sake, though I did not look upon the objection as serious, I submitted it to Krall, who at once said: "Try it for yourself. Dictate to the horse any German word of two or three syllables, emphasizing it strongly. I'll go out of the stable and leave you alone with him."

Behold Muhamed and me by ourselves. I confess that I am a little frightened. I have many a time felt less uncomfortable in the presence of the great ones or the kings of the earth. Whom am I dealing with exactly? However, I summon my courage and speak aloud the first word that occurs to me, the name of the hotel at which I am staying: Weidenhof. At first, Muhamed, who seems a little puzzled by his master's absence, appears not to hear me and does not even deign to notice that I am there. But I repeat eagerly, in varying tones of voice, by turns insinuating, threatening, beseeching and commanding:

"Weidenhof! Weidenhof! Weidenhof!"

At last, my mysterious companion suddenly makes up his mind to lend me his ears and straightway blithely raps out the following letters, which I write down on the black-board as they come:

It is a magnificent specimen of equine spelling! Triumphant and bewildered, I call in friend Krall, who, accustomed as he is to the prodigy, thinks it quite natural, but knits his brows:

"What's this, Muhamed? You've made a mistake again. It's an F you want at the end of the word, not a Z. Just correct it at once, please."

And the docile Muhamed, recognizing his blunder, gives the three blows with his right hoof, followed by the four blows with his left, which represent the most unexceptionable F that one could ask for.

Observe, by the way, the logic of his phonetic writing: contrary to his habit, he strikes the mute E after the W, because it is indispensable; but, finding it included in the D, he considers it superfluous and suppresses it with a high hand.

You rub your eyes, question yourself, ask yourself in the presence of what humanized phenomenon, of what unknown force, of what new creature you stand. Was all this what they hid in their eyes, those silent brothers of ours? You blush at arm's long injustice. You look around you for some sort of trace, obvious or subtle, of the mystery. You feel yourself attacked in your innermost citadel, where you held yourself most certain and most impregnable. You have felt a breath from the abyss upon your face. You would not be more astonished if you suddenly heard the voice of the dead. But the most astonishing thing is that you are not astonished for long. We all, unknown to ourselves, live in the expectation of the extraordinary; and, when it comes, it moves us much less than did the expectation. It is as though a sort of higher instinct, which knows everything and is not ignorant of the miracles that hang over our heads, were reassuring us in advance and helping us to make an easy entrance into the regions of the supernatural. There is nothing to which we grow accustomed more readily than to the marvellous; and it is only afterwards, upon reflection, that our intelligence, which knows hardly anything, appreciates the magnitude of certain phenomena.

But Muhamed gives unmistakable signs of impatience to show that he has had enough of spelling. Thereupon, as a diversion and a reward, his kind master suggests the extraction of a few square and cubic roots. Muhamed appears delighted: these are his favourite problems: for he takes less interest than formerly in the most difficult multiplications and divisions. He doubtless thinks them beneath him.

Krall therefore writes on the blackboard various numbers of which I did not take note. Moreover, as nobody now contests the fact that the horse works them with ease, it would hardly be interesting to reproduce here several rather grim problems of which numerous variants will be found in the accounts and reports of experiments signed by Drs. Mackenzie and Hartkopff, by Overbeck, Clarapede and many others. What strikes one particularly is the facility, the quickness, I was almost saying the joyous carelessness with which the strange mathematician gives the answers. The last figure is hardly chalked upon the board before the right hoof is striking off the units, followed immediately by the left hoof marking the tens. There is not a sign of attention or reflection; one is not even aware of the exact moment at which the horse looks at the problem: and the answer seems to spring automatically from an invisible intelligence. Mistakes are rare or frequent according as it happens to be a good or bad day with the horse; but, when he is told of them, he nearly always corrects them. Not unseldom, the number is reversed: 47, for instance, becomes 74; but he puts it right without demur when asked.

I am manifestly dumbfounded; but perhaps these problems are prepared beforehand? If they were, it would be very extraordinary, but yet less surprising than their actual solution. Krall does not read this suspicion in my eyes, because they do not show it; nevertheless, to remove the least shade of it, he asks me to write a number of my own on the black-board for the horse to find the root.

I must here confess the humiliating ignorance that is the disgrace of my life. I have not the faintest idea of the mysteries concealed within these recondite and complicated operations. I did my humanities like everybody else; but, after crossing the useful and familiar frontiers of multiplication and division I found it impossible to advance any farther into the desolate regions, bristling with figures, where the square and cubic roots hold sway, together with all sorts of other monstrous powers, without shapes or faces, which inspired me with invincible terror. All the persecutions of my excellent instructors wore themselves out against a dead wall of stolidity. Successively disheartened, they left me to my dismal ignorance, prophesying a most dreary future for me, haunted with bitter regrets. I must say that, until now, I had scarcely experienced the effects of these gloomy predictions; but the hour has come for me to expiate the sins of my youth. Nevertheless, I put a good face upon it: and, taking at random the first figures that suggest themselves to my mind, I boldly write on the black-board an enormous and most daring number. Muhamed remains motionless. Krall speaks to him sharply, telling him to hurry up. Muhamed lifts his right hoof, but does not let it fall. Krall loses patience, lavishes prayers, promises and threats; the hoof remains poised, as though to bear witness to good intentions that cannot be carried out. Then my host turns round, looks at the problem and asks me:

"Does it give an exact root?"

Exact? What does he mean? Are there roots which. . .? But I dare not go on: my shameful ignorance suddenly flashes before my eyes. Krall smiles indulgently and, without making any attempt to supplement an education which is too much in arrears to allow of the slightest hope, laboriously works out the problem and declares that the horse was right in refusing to give an impossible solution.

Muhamed receives our thanks in the form of a lordly portion of carrots; and a pupil is introduced whose attainments do not tower so high above mine: Hanschen, the little pony, quick and lively as a big rat. Like me, he has never gone beyond elementary arithmetic: and so we shall understand each other better and meet on equal terms.

Krall asks me for two numbers to multiply. I give him 63 X 7. He does the sum and writes the product on the board, followed by the sign of division: 441 / 7. Instantly Hanschen, with a celerity difficult to follow, gives three blows, or rather three violent scrapes with his right hoof and six with his left, which makes 63, for we must not forget that in German they say not sixty-three, but three-and-sixty. We congratulate him; and, to evince his satisfaction, he nimbly reverses the number by marking 36 and then puts it right again by scraping 63. He is evidently enjoying himself and juggling with the figures. And additions, subtractions, multiplications and divisions follow one after the other, with figures supplied by myself, so as to remove any idea of collusion. Hanschen seldom blunders; and, when he does, we receive a very clear impression that his mistake is voluntary: he is like a mischievous schoolboy playing a practical joke upon his master. The solutions fall thick as hail upon the little spring-board; the correct answer is released by the question as though you were pressing the button of an electric push. The pony's flippancy is as surprising as his skill. But in this unruly flippancy, in this hastiness which seems inattentive there is nevertheless a fixed and permanent idea. Hanschen paws the ground, kicks, prances, tosses his head, looks as if he cannot keep still, but never leaves his spring-board. Is he interested in the problems, does he enjoy them? It is impossible to say; but he certainly has the appearance of one accomplishing a duty or a piece of work which we do not discuss, which is important, necessary and inevitable.

But the lesson suddenly ends with a joke carried rather too far by the pupil, who catches his good master by the seat of his trousers, into which he plants disrespectful teeth. He is severely reprimanded, deprived of his carrots and sent back in disgrace to his private apartments.

Next comes Bette, who is like a big, sleek Norman horse. He makes the calm, dignified, peaceful entrance of a blind giant. His large, dark, brilliant eyes are quite dead, deprived of any reflex power. He feels about with his hoof for the board on which he is to rap his answers. He has not yet gone beyond the rudiments of mathematics; and the early part of his education was particularly difficult. They managed to make him understand the value and meaning of the numbers and of the addition- and multiplication-signs by means of little taps on his sides. Krall speaks to him as a father might speak to the youngest of his sons. He explains to him fondly the easy sums which I suggest his doing: two plus three, eight minus four, four times three; he says:

"Mind! It's not plus three or minus three this time, but four multiplied by three!"

Berto hardly ever makes a mistake. When he does not understand the question, he waits for it to be written with the finger on his side; and the careful way in which he works it out like some backward and afflicted child is an infinitely pathetic sight. He is much more zealous and conscientious than his fellow-pupils; and we feel that, in the darkness wherein he dwells, this work is, next to his meals, the only spark of light and interest in his existence. He will certainly never rival Muhamed, for instance, who is the arithmetical prodigy, the Inaudi, of horses; but he is a valuable and living proof that the theory of unconscious and imperceptible signs, the only one which the German theorists have hitherto seriously considered, is now clearly untenable.

I have not yet spoken of Zarif. He is not in the best of tempers; and besides, in arithmetic, he is only a less learned and more capricious Muhamed. He answers most of the questions at random, stubbornly raising his foot and declining to lower it, so as clearly to mark his disapproval; but he solves the last problem correctly when he is promised a panful of carrots and no more lessons for that morning. The groom enters to lead him away and makes some movement or other at which the horse starts, rears and shies.

"That's his bad conscience," says Krall, gravely.

And the expression assumes a singular meaning and importance in this hybrid atmosphere, steeped in an indefinable something from another world.

But it is half-past one, the sacred German dinner-hour. The horses are taken back to their racks and the men separate, wishing one another the inevitable Mahlzeit.

As he walks with me along the quays of the black and muddy
Wupper, Krall says:

"It is a pity that you did not see Zarif in one of his better moods. He is sometimes more startling than Muhamed and has given me two or three surprises that seem incredible. One morning, for instance, I came to the stable and was preparing to give him his lesson in arithmetic. He was no sooner in front of the spring-board than he began to stamp with his foot. I left him alone and was astounded to hear a whole sentence, an absolutely human sentence, come letter by letter from his hoof: 'Albert has beaten Hanschen,' was what he said to me that day. Another time, I wrote down from his dictation, 'Hanschen has bitten Kama.' Like a child seeing its father after an absence, he felt the need to inform me of the little doings of the stable; he provided me with the artless chronicle of a humble and uneventful life."

Krall, for that matter, living in the midst of his miracle, seems to think this quite natural and almost inevitable. I, who have been immersed in it for only a few hours, accept it almost as calmly as he does. I believe without hesitation what he tells me; and, in the presence of this phenomenon which, for the first time in man's existence, gives us a sentence that has not sprung from a human brain, I ask myself whither we are tending, where we stand and what lies ahead of us.. . .

After dinner, the experiments begin again, for my host is untiring. First of all, pointing to me, he asks Muhamed if he remembers what his uncle's name is. The horse raps out an H. Krall is astonished and utters fatherly reprimands:

"Come, take care! You know it's not an H."

The horse raps out an E. Krall becomes a little impatient: he threatens, he implores, he promises in turn, carrots and the direst punishments, such as sending for Albert, the groom, who, on special occasions, recalls idle and inattentive pupils to a sense of duty and decorum, for Krall himself never chastises his horses, lest he should lose their friendship or their confidence. So he continues his reproaches:

"Come now, are you going to be more careful and not rap out your letters anyhow?"

Muhamed obstinately goes his own way and strikes an R. Then
Krall's open face lights up:

"He's right," he says. "You understand: H E R, standing for Herr. He wanted to give you the title to which every man wearing a top hat or a bowler has the right. He does it only very rarely and I had forgotten all about it. He probably heard me call you Herr Maeterlinck and wanted to get it perfectly. This special politeness and this excess of zeal augur a particularly good lesson. You've done very well, Mohamed, my child; you've done very well and I beg your pardon. Now kiss me and go on."

But Mohamed, after giving his master a hearty kiss, still seems to be hesitating. Then Krall, to put him on the right track observes that the first letter of my name is the same as the first letter of his own. Mohamed strikes a K, evidently thinking of his master's name. At last, Krall draws a big M on the black-board, whereupon the horse, like one suddenly remembering a word which he could not think of, raps out, one after the other and without stopping, the letters M A Z R L K, which, stripped of useless vowels, represent the curious corruption which my name has undergone, since the morning, in a brain that is not a human brain. He is told that this is not correct. He seems to agree, gropes about a little and writes, M A R Z L E G K. Krall repeats my name and asks which is the first letter to be altered. The stallion marks an R.

"Good, but what letter will you put instead?"

Mohamed strikes an N.

"No, do be careful!"

He strikes a T.

"Very good, but in what place will the T come?"

"In the third," replies the horse; and the corrections continue until my patronomic comes out of its strange adventure almost unscathed.

And the spelling, the questioning, the sums, the problems are resumed and follow upon one another, as wonderful, as bewildering as before, but already a little dimmed by familiarity, like any other prolonged miracle. It is important, besides, to notice that the instances which I have given are not to be classed among the most remarkable feats of our magic horses. Today's is a good ordinary lesson, a respectable lesson, not illumined by flashes of genius. But in the presence of other witnesses the horses performed more startling exploits which broke down even more decisively the barrier, which is undoubtedly an imaginary one, between animal and human nature. One day, for instance, Zarif; the scamp of the party, suddenly stopped in the middle of his lesson. They asked him the reason.

"Because I am tired."

Another time, he answered:

"Pain in my leg."

They recognize and identify pictures shown to them, distinguish colours and scents. I have made a point of stating only what I saw with my own eyes and heard with my own ears; and I declare that I have done so with the same scrupulous accuracy as though I were reporting a criminal trial in which a man's life depended on my evidence.

But I was practically convinced of the truth of the incidents before going to Elberfeld; and it was not to check them that I made the journey. I was anxious to make certain if the telepathic theory, which was the only one that I considered admissible, would withstand the tests which I intended to apply to it. I opened my mind on the subject to Krall, who at first did not quite grasp what I was asking. Like most men who have not made a special study of the questions, he imagined that telepathy meant above all a deliberate and conscious transmission of thought; and he assured me that he never made any effort to transmit his and that, for the most part, the horses gave a reply which was the exact opposite of what he was expecting. I did not doubt this for a moment; in fact, direct and deliberate transmission of thought is, even among men, a very rare, difficult and uncertain, phenomenon, whereas involuntary, unpremeditated and unsuspected communications between one subconsciousness and another can no longer be denied except by those who of set purpose ignore studies and experiments that are within the reach of any one who will take the trouble to engage in them. I was persuaded therefore that the horses acted exactly like the "tipping-tables" which simply translate the subliminal ideas of one or another of those present by the aid of conventional little taps. When all is said, it is much less surprising to see a horse than a table lift its foot and much more natural that the living substance of an animal rather than the inert matter of a thing should be sensitive and susceptible to the mysterious influence of a medium. I knew quite well that experiments had been made in order to eliminate this theory. People, for instance, prepared a certain number of questions and put them in sealed envelopes. Then, on entering the presence of the horse, they would take one of the envelopes at random, open it and write down the problem on the black-board; and Mohamed or Zarif would answer with the same facility and the same readiness as though the solution had been known to all the onlookers. But was it really unknown to their subconsciousness? Who could say for certain? Tests of this kind require extraordinary precautions and a special dexterity; for the action of the subconsciousness is so subtle, takes such unexpected turns, delves in the museum of so many forgotten treasures and operates at such distances that one is never sure of escaping it. Were those precautions taken? I was not convinced that they were; and, without pretending to decide the question, I said to myself that my blissful ignorance of mathematics might perhaps be of service in shedding light upon some part of it.

For this ignorance, however deplorable from other points of view, gave me a rare advantage in this case. It was in fact extremely unlikely that my subliminal consciousness, which had never known what a cubic root was or the root of any other power, could help the horse. I therefore took from a table a list containing several problems, all different and all equally unpleasant looking, covered up the solutions, asked Krall to leave the stable and, when alone with Zarif, copied out one of them on the black-board. In order not to overload these pages with details which would only be a repetition of one another, I will at once say that none of the antitelepathic tests succeeded that day. It was the end of the lesson and late in the afternoon; the horses were tired and irritable; and, whether Krall was there or not, whether the problem was elementary or difficult, they gave only absurd replies, wilfully "putting their foot in it," as one might say with very good reason. But, next morning, on resuming their task, when I proceeded as described above, Mohamed and Zarif, doubtless in a better temper and already more accustomed to their new examiner, gave in rapid succession correct answers to nearly every problem set them. I am bound in fairness to say that there was no appreciable difference between these results and those which are obtained in the presence of Krall or other onlookers who, consciously or unconsciously, are already aware of the answer required.

I next thought of another and much simpler test, but one which, by virtue of its very simplicity, could not be exposed to any elaborate and farfetched suspicions. I saw on one of the shelves in the stable a panel of cards, about the size of an octavo volume, each bearing an arabic numeral on one of its sides. I once more asked my good friend Krall, whose courtesy is inexhaustible, to leave me alone with his pupil. I then shuffled the cards and put three of them in a row on the spring-board in front of the horse, without looking at them myself. There was therefore, at that moment, not a human soul on earth who knew the figures spread at the feet of my companion, this creature so full of mystery that already I no longer dare call him an animal. Without hesitation and unasked, he rapped out correctly the number formed by the cards. The experiment succeeded, as often as I cared to try it, with Hanschen, Mohamed and Zarif alike. Mohamed did even more: as each figure was of a different colour, I asked him to tell me the colour — of which I myself was absolutely ignorant — of the first letter on the right. With the aid of the conventional alphabet, he replied that it was blue, which proved to be the case. Of course, I ought to have multiplied these experiments and made them more exhaustive and complicated by combining, with the aid of the cards and under the same conditions, exercises in multiplication, division and the extracting of roots. I had not the time; but, a few days after I left, the subject was resumed and completed by Dr. H. Hamel. I will sum up his report of the experiments: the doctor, alone in the stable with the home (Krall was away, travelling), puts down on the black-board the sign + and then places before and after this sign, without looking at either of them, a card marked with a figure which he does not know. He next asks Mohamed to add up the two numbers. Mohamed at first gives a few heedless taps with his hoof. He is called to order and requested to be serious and to attend. He then gives fifteen distinct taps. The doctor next replaces the sign + by X and, again without looking at them, places two cards on the blackboard and asks the horse not to add up the two figures this time, but to multiply them. Mohamed taps out, "27," which is right, for the black-board says, "9 X 3." The same success follows with other multiplication sums: 9 X 2, 8 X 6. Then the doctor takes from an envelope a problem of which he does not know the solution: fourth root of 7890481. Mohamed replies, "53." The doctor looks at the back of the paper: once more, the answer is perfectly correct.

Does this mean that every risk of telepathy is done away with? It would perhaps be rash to make a categorical assertion. The power and extent of telepathy are as yet, we cannot too often repeat, indefinite, indiscernible, untraceable and unlimited. We have but quite lately discovered it, we know only that its existence can no longer be denied; but, as for all the rest, we are at much the same stage as that whereat Galvani was when he gave life to the muscles of his dead frogs with two little plates of metal which roused the jeers of the scientists of his time, but contained the germ of all the wonders, of electricity.

Nevertheless, as regards telepathy in the sense in which we understand and know it to-day, my mind is made up. I am persuaded that it is not in this direction that we must seek for an explanation of the phenomenon; or, if we are determined to find it there, the explanation becomes complicated with so many subsidiary mysteries that it is better to accept the prodigy as it stands, in its original obscurity and simplicity. When, for instance, I was copying out one of the grisly problems which I have mentioned, it is quite certain that my conscious intelligence could make neither head nor tail of it. I did not so much as know what it meant or whether the exponent 3 · 4 · 5 called for a multiplication, a division or some other mathematical operation which I did not even try to imagine; and, rack my memory as I may, I cannot remember any moment in my life when I knew more about it than I do now. We should therefore have to admit that MY subliminal self is a born mathematician, quick, infallible and endowed with boundless learning. It is possible and I feel a certain pride at the thought. But the theory simply shifts the miracle by making it pass from the horse's soul to mine; and the miracle becomes no clearer by the transfer, which, for that matter, does not sound probable. I need hardly add that, a fortiori, Dr. Hamel's experiments and many others which I have not here the space to describe finally dispose of the theory.

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.

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.

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.

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 ingenious 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 precursors of another world.

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.

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.

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 Mohamed 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.

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.

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.

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 Mohamed 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 Mohamed.

"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, Mohamed 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?"

"Man."

"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 Mohamed 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.

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 Mohamed 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."

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.

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,² 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?

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?

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.

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,³ 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.

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."⁴

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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.

It goes without saying that objections are raised from every side. Among men, arithmetical prodigies are looked upon as monsters, as a sort of extremely rare teratological phenomenon. We can count, at most, half-a-dozen in a century, whereas, among horses, the faculty would appear to be almost general, or at least quite common. In fact, out of six or seven stallions whom Krall tried to initiate into the secrets of mathematics, he found only two that appeared to him too poorly gifted for him to waste time on their education. These were, I believe, two thoroughbreds that were presented to him by the Grand-duke of Mecklenburg and sent back by Krall to their sumptuous stables. In the four or five others, taken at random as circumstances supplied them, he met with aptitudes unequal, it is true, but easily developed and giving the impression that they exist normally, latent and inactive, at the bottom of every equine soul. From the mathematical point of view, is the horse's subliminal consciousness then superior to man's? Why not? His whole subliminal being is probably superior to one, of greater range, younger, fresher, more alive and less heavy, since it is not incessantly attacked, coerced and humiliated by the intelligence which gnaws at it, stifles it, cloaks it and relegates it to a dark corner which neither light nor air can penetrate. His subliminal consciousness is always present, always alert; ours is never there, is asleep at the bottom of a deserted well and needs exceptional operations, results and events before it can be drawn from its slumber and its unremembered deeps. All this seems very extraordinary; but, in any case, we are here in the midst of the extraordinary; and this outlet is perhaps the least hazardous. It is not a question, we must remember, of a cerebral operation, an intellectual performance, but of a gift of divination closely allied to other gifts of the same nature and the same origin which are not the peculiar attribute of man. No observation, no experiment enables us, up to the present, to establish a difference between the subliminal of human beings and that of animals. On the contrary, the as yet restricted number of actual cases reveals constant and striking analogies between the two. In most of those arithmetical operations, be it noted, the subliminal of the horse behaves exactly like that of the medium in a rate of trance. The horse readily reverses the figures of the solution; he replies, "37," for instance, instead of "73," which is a mediumistic phenomenon so well-known and so frequent that it has been styled "mirror-writing." He makes mistakes fairly often in the most elementary additions, and subtractions and much less frequently in the extraction of the most complicated roots, which again, in similar cases, such as "xenoglossy" and psychometry, is one of the eccentricities of human mediumism and is explained by the same cause, namely, the inopportune intervention of the ever fallible intelligence, which, by meddling in the matter, alters the certainties of a subliminal which, when left to itself, never makes a mistake. It is, in fact, quite probable that the horse, being really able to do the small sums, no longer relies solely on his intuition and, from that moment, gropes and flounders about. The solution hovers between the intelligence and the subliminal and, passing from the one, which is not quite sure of it, to the other, which is not urgently appealed to, comes out of the conflict as best it may. The case is the same with the psychometric or spiritualistic medium who seeks to profit by what he knows in the ordinary way, so as to complete the visions or revelations of his subconscious sensibility. He, too, in this instance, is nearly always guilty of flagrant and inexplicable blunders.

Many other similarities will be found to exist, notably the way in which the lessons vary. Nothing is more uncertain and capricious than manifestations of human mediumism. Whether it be a question of automatic writing, psychometry, materializations or anything else, we meet with series of sittings that yield none but absurd results. Then, suddenly, for reasons as yet obscure — the state of the weather, the presence of this or that witness, or I know not what — the most undeniable and bewildering manifestations occur one after the other. The case is precisely the same with the horses: their queer fancies, their unaccountable and disconcerting freaks drive poor Krall to despair. He never opens the door of that uncertain stable, on important days, without a sinking at the heart. Let the beard or the frown of some learned professor fail to please the horses: they will, forthwith, take an unholy delight in giving the most irrelevant answer to the most elementary question, for hours and even days on end.

Other common features are the strongly-marked personality of the mediumistic "raps" and the communications known as "deferred telepathic communications," that is to say, those in which the answer is obtained at the end of a sitting to a question put at the beginning and forgotten by all those present. What at first sight seems one of the strongest objections urged against the mediumism of the horse even tends to confirm it. If the reply comes from the horse's subconsciousness, it has been asked, how is it that it should be necessary first to teach him the elements of language, mathematics and so forth, and that Berto, for instance, is incapable of solving the same problems as Mohamed? This objection has been very ably refuted by M. de Vesme, who writes:

"To produce automatic writing, a medium must have learnt to write; before Victorien Sardou or Mlle Helene Schmidt could produce their mediumistic drawings and paintings, they had to possess an elementary knowledge of drawing and painting; Tartini would never have composed The Devil's Sonata in a dream, if he had not known music; and so forth. Unconscious cerebration, however wonderful, can only take effect upon elements already acquired in some way or another. The subconscious cerebration of a man blind from birth will not make him see colours."

Here, then, in this comparison which might easily be extended, are several fairly well- defined features of resemblance. We receive a vivid impression of the same habits, the same contradictions, and the same eccentricities; and we once more recognize the strange and majestic shadow of our unknown guest.

One great objection remains, based upon the very nature of the phenomenon, upon the really inseparable distance that separates the whole life of the horse from the abstract and impenetrable life of numbers. How can his subliminal consciousness interest itself for a moment in signs that represent nothing to him, have no relation to his organism and will never touch his existence? But in the first place, it is just the same with the child or the illiterate calculator. He is not interested either in the figures which he lets loose. He is completely ignorant of the consequences of the problems which he solves. He juggles with digits which have hardly any more meaning to him than to the horse. He is incapable of accounting for what he does; and his subconsciousness also acts in a sort of indifferent and remote dream. It is true that, in his case, we can appeal to heredity and to memory; but is this difference enough to settle the difficulty and definitely to separate the two phenomena? To appeal to heredity is still to appeal to the subliminal; and it is not at all certain that the latter is limited by the interest of the organism sheltering it. It appears, on the contrary, in many circumstances, to spread and extend far beyond that organism in which it is domiciled, one would say, accidentally and provisionally. It likes to show, apparently, that it is in relation with all that exists. It declares itself, as often as possible, universal and impersonal. It has but a very indifferent care, as we have seen in the matter of apparitions and premonitions, for the happiness and even the safety of its host and protector. It prophesies to its companion of a lifetime events which he cannot avoid or which do not concern him. It makes him see beforehand, for instance, all the circumstances of the death of a stranger whom he will only hear of after the event, when this event is irrevocable. It brings a crowd of barren presentiments and conjures up veridical hallucinations that are wholly alien and idle. With psychometric, typtological or materializing mediums, it practises art for art's sake, mocks at space and time, passes through personalities, sees through solid bodies, brings into communication thoughts and motions worlds apart, reads souls and lives by the light of a flower, a rag of a scrap of paper; and all this for nothing, to amuse itself, to astonish us, because it adores the superfluous, the incoherent, the unexpected, the improbable, the bewildering, or rather, perhaps, because it is a huge, rough, undisciplined force still struggling in the darkness and coming to the surface only by wild fits and starts, because it is an enormous expansion of a spirit striving to collect itself, to achieve consciousness, to make itself of service and to obtain a hearing. In any case, for the time being, it appeals just what we have described, and would be unlike itself if it behaved any otherwise in the case that puzzles us.

Lastly, to close this chapter, let us remark that it is nearly certain that the solution given by calculating children and horses is not of a mathematical nature at all. They do not in any way consider the problem or the sum to be worked. They simply find the answer straight away to a riddle, the guessing of which is made easy by the actual nature of figures which keep their secrets badly. To any one in the requisite state of mind, it becomes a question of a sort of elementary charade, which hides its answer only from those who speak another language. It is evident that every problem, however complex it may appear, carries within its very enunciation its one, invariable solution, scarce veiled by the indiscreet signs that contain or cover it. It is there, under the numbers that have no other object than to give it life, coming, stirring and ceaselessly proclaiming itself a necessity. It is not surprising therefore that eyes sharper than ours and ears open to other vibrations should see and hear it without knowing what it represents, what it implies or from what prodigious mass of figures and operations it merges. The problem itself speaks; and the horse but repeats the sign which he hears whispered in the mysterious life of numbers or deep down in, the abyss where the eternal verities hold sway. He understands none of it, he has no need to understand, he is but the unconscious medium who lends his voice or his limbs to the mind that inspires him. There is here but a bare and simple answer, bearing no precise significance, seized in an alien existence. There is here but a mechanical revelation, so to speak, a sort of special reflex which we can only record and which, for the rest, is as inexplicable as any other phenomenon of consciousness or instinct. After all, when we think of it, it is just as, astonishing that we should not perceive the solution as it is that we should discover it. However, I grant that all this is but a venturesome interpretation to be taken for what it is worth, an experimental or interim theory with which we must needs content ourselves since all the others have hitherto been controverted by the facts.

Let us now briefly sum up what the Elberfeld experiments have yielded us. Having put aside telepathy in the narrow sense — which perhaps enters into more than one phenomenon but is not indispensable to it, for we see these same phenomena repeated when telepathy is practically impossible — we cannot help observing that, if we deny the existence or the influence of the subliminal, it is all the more difficult to contest the existence and the intervention of the intelligence, at any rate up to the extracting of roots, after which there is a steep precipice which ends in darkness. But, even if we stop at the roots, the sudden discovery of an intellectual force so similar to our own, where we were accustomed to see but an irremediable impotency, is no doubt one of the most unexpected revelations that we have received since the invisible and the unknown began to press upon us with a persistence and an impatience which they had not displayed heretofore. It is not easy to foresee as yet the consequences and the promises of this new aspect which the great riddle of the intelligence is suddenly adopting. But I believe that we shall soon have to revise some of the essential ideas which are the foundations of our life and that some rather strange horizons are appearing out of the mists in the history of psychology, of morality, of human destiny and of many other things.

So much for the intelligence. On the other hand, what we deny to the intelligence we are constrained to grant to the subliminal; and the revelation is even more disconcerting. We should then have to admit that them is in the horse — and hence most probably in everything that lives on this earth — a psychic power similar to that which is hidden beneath the veil of our reason and which, as we learn to know it, astonishes, surpasses and dominates our reason more and more. This psychic power, in which no doubt we shall one day be forced to recognize the genius of the universe itself, appears, as we have often observed, to be all-wise, all-seeing and all-powerful. It has, when it is pleased to communicate with us or when we are allowed to penetrate into it, an answer for every question, and perhaps a remedy for every ill. We will not enumerate its virtues again. It will be enough for us to recall with what ease it mocks at space, time and all the obstacles that beset our poor human knowledge and understanding. We believed it, like all that seems to us superior and marvellous, the intangible, inalienable and incommunicable attribute of man, with even better reason than his intelligence. And now an accident, strangely belated, it is true, tells us that, at one precise point, the strangest and least foreseen of all, the horse and the dog draw more easily and perhaps more directly than ourselves upon its mighty reservoirs. By the most inexplicable of anomalies, though one that is fairly consistent with the fantastic character of the subliminal, they appear to have access to it only at the spot that is most remote from their habits and most unknown to their propensities, for there is nothing in the world about which animals trouble less than figures. But is this not, perhaps because we do not see what goes on elsewhere? It so happens that the infinite mystery of numbers can sometimes be expressed by a very few simple movements which are natural to most animals; but there is nothing to tell us that, if we could teach the horse and the dog to attach to these same movements the expression of other mysteries, they would not draw upon them with equal facility. It has been successfully attempted to give them a more or less clear idea of the value of a few figures and perhaps of the course and nature of certain elementary operations; and this appears to have been enough to open up to them the most secret regions of mathematics in which every question is answered beforehand. It is not wholly illusive to suppose that, if we could impart to them, for instance, a similar notion of the future, together with a manner of conveying to us what they see there, they might also have access to strange visions of another class, which are jealously kept from us by the too-watchful guardians of our intelligence. There is an opportunity here for experiments which will doubtless prove exceedingly arduous, for the future is not so easily seen and above all not so easily interpreted and expressed as a number. It is possible, moreover, that, when we know how to set about it, we shall obtain most of the human mediumistic phenomena; rapping, the moving of objects, materialization even and Heaven knows what other surprises held in store for us by that astounding subliminal to whose fancy there appears to be no bounds. In any case, if we accept the divining of numbers, as we are almost forced to do, it is almost certain that the divining of other matters must follow. An unexpected breach is made in the wall behind which lie heaped the great secrets that seem to us, as our knowledge and our civilization increase, to become stronger and more inaccessible. True, it is a narrow breach; but it is the first that has been opened in that part of the hitherto uncrannied wall which is not turned towards mankind. What will issue through it? No one can foretell what we may hope.

What astonishes us most is that this revelation has been so long delayed. How are we to explain that man has lived to this day with his domestic animals never suspecting that they harboured mediumistic or subliminal faculties as extraordinary as those which he vaguely felt himself to possess. One would have in this connection to study the mysterious practices of ancient India and of Egypt; the numerous and persistent legends of animals talking, guiding their masters and foretelling the future; and, nearer to ourselves, in history proper, all that science of augury and soothsaying which derived its omens from the flight of birds, the inspection of entrails, the appetite or attitude of the sacred or prophetic animals, among which horses were often numbered. We here find one of those innumerous instances of a lost or anticipated power which make us suspect that mankind has forestalled or forgotten all that we believe ourselves to be discovering. Remember that there is almost always some distorted, misapprehended or dimly — seen truth at the bottom of the most eccentric and wildest creeds, superstitions and legends. All this new science of metaphysics or of the investigation of our subconsciousness and of unknown powers, which has scarcely begun to unveil its first mysteries, thus finds landmarks and defaced but recognizable traces in the old religions, the most inexplicable traditions and the most ancient history. Besides, the probability of a thing does not depend upon undeniably established precedents. While it is almost certain that there is nothing new under the sun or in the eternity preceding the suns, it is quite possible that the same forces do not always act with the same energy. As I observed, nearly twenty years ago, in The Treasure of the Humble, at a time when I hardly knew at all what I know so imperfectly to-day:

"A spiritual" — I should have said, a psychic — "epoch is perhaps upon us, an epoch to which a certain number of analogies are found in history. For there are periods recorded when the soul, in obedience to unknown laws, seemed to rise to the very surface of humanity, whence it gave clearest evidence of its existence and of its power…. It would seem, at moments such as these, as though humanity,"  — and, I would add to-day, all that lives with it on this earth — "were on the point of struggling from beneath the crushing burden of matter that weighs it down."

One might in fact believe that a shudder which we have not yet experienced is passing over everything that breathes; that a new activity, a new restlessness is permeating the spiritual atmosphere which surrounds our globe; and that the very animals have felt its thrill. One might say that, by the side of the niggardly private spring which would only supply our intelligence, other streams are spreading and rising to the same level in every form of existence. A sort of word of command is being passed from rank to rank; and the same phenomena are bursting forth in every quarter of the globe in order to attract our attention, as though the obstinately dumb genius that lay hidden in the pregnant silence of the universe, from that of the stones, the flowers and the insects to the mighty silence of the stars, were at last trying to tell us some secret whereby it would be better known to us or to itself. It is possible that this is but an illusion. Perhaps we are simply more attentive and better informed than of old. We learn at the very instant what happens in every part of our earth and we have acquired the habit of more minutely observing and examining the things that happen. But the illusion would in this case have all the force, all the value and all the meaning of the reality and would enjoin the same hopes and the same obligation.

¹ See the interesting lecture by M. Edmond Duchatel, published in the Annales des Sciences Psychiques, October 1913.

² Annales des Sciences Psychiques, August, 1905, pp 422-469.

³ American Journal of Psychology, 1 April 1891.

⁴ 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.