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.