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

There is, henceforth, no reason why the horses should not participate in most of the mediumistic, phenomena which we find existing between man and man; and their mystery ceases to be distinct from those of human metaphysics. If their subliminal is akin to ours, we can begin by extending to its utmost limits the telepathic theory, which has, so to speak, no limits, for, in the matter of telepathy, as Myers has said, all that we are permitted to declare is that "life has the power of manifesting itself to life." We may ask ourselves, therefore, if the problem which I set to the horse, without knowing the terms of it, is not communicated to my subliminal, which is ignorant of it, by that of the horse, who has read it. It is practically certain that this is possible between human subliminals. Is it I who see the solution and transmit it to the horse, who only repeats it to me?

But, suppose that it is a problem which I myself am incapable of solving? Whence does the solution come, then? I do not know if the experiment has been attempted, under the same conditions, with a human medium. For that matter, if it succeeded, it would be very much the same as the no less subliminal phenomenon of the arithmetical prodigies, or lightning calculators, with which, in this rather superhuman atmosphere, we are almost forced to compare the riddle of the mathematical horses. Of all the interpretations, it is the one which, for the moment, appears to me the least eccentric and the most natural.

We have seen that the gift of handling colossal figures is almost foreign to the intelligence proper; one can, even declare that, in certain cases, it is evidently and completely independent of such intelligence. In these cases, the gift is manifested prior to any education and from the earliest years of childhood. If we refer to the list of arithmetical prodigies given by Dr.

Scripure,[1] we see that the faculty made its appearance in Ampere at the age of three, in Colburn at six, in Gauss at three, in Mangiamele at ten, in Safford at six, in Whateley at three, and so on. Generally, it lasts for only a few years, becoming rapidly enfeebled with age and usually vanishing suddenly at the moment when its possessor begins to go to school.

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

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

[1] I have no need to recall the derivation of the term subliminal: beneath (sub) the threshold (limen) of consciousness.

Let us add, as M. de Vesme very rightly remarks, that the subliminal is not exactly what classical psychology calls the subconsciousness, which latter records only notions that are normally perceived and possesses only normal faculties, that is to say, faculties recognized to-day by orthodox science.