It seems to me clear that the mathematical faculty—assuming always, let it be understood, that it may give rise to more or less conscious phenomena in the biological subject—may be amongst the most natural of imaginable causes, and that even the smallest amount of consciousness may help this existing capacity in the animal to express itself. That we are concerned with an expression by raps or not, does not seem to me as important as a proper estimation of the importance of the central fact constituted by this mathematical capacity.

From this central fact, proved over and over again without any possible doubt to be true of the "thinking" animals, there have been developed two distinct groups of consequences: (1) the prodigious mathematical performances occurring as by magic among the Elberfeld horses at a certain point of their "education": (2) the apparent manifestations of thought through the typtology or rapping out of words, culminating in the "philosophic" achievements of Rolf and Lola.

For the reasons just mentioned the first group of consequences seems to me to admit largely of biological (i.e. biopsychical) explanation; however, anything which eventually does not fit into the biological explanation may be made to enter without any effort into the second method of explanation which, in view of the facts, it seems to me that we must adopt for the second of the two groups of consequences above referred to.

That mathematics can be "lived" rather than "known"—or, if any one prefers the term, "realized"—by an organism which is without any psychical accompaniment whatever of the human type, is a fact which I find credible. But when Rolf speaks to me of the origin of the soul, or makes up poetry; when Lola complains to me of honour lost, etc., the thing is not credible to me in any way except by paying attention to nothing except the feeling, which is so difficult to avoid, that what is here speaking to me, versifying and complaining, is a psychical "quid," absolutely human and only human; a "quid" which therefore is (after all) not the animal's, although manifested in some way through it. The difficulty naturally consists in deciding precisely how this happens. But it does not seem to me altogether impossible to arrive at a proper hypothesis.

I have already said that we must discard, because of its inability to explain a great part of the facts, the most easy and simple hypothesis—that of some mechanical signal (e.g. by means of a supposed pressure of the hand under the cardboard, or by the hand itself which is held out to the animal, in the case of the dogs which have so far been experimented with). Here we also have to remember the proposition laid down by Miss Kindermann herself that "She did not wish to let herself be carried away by sentiment," and that she would seek all possible proofs which were good logically. Having excluded the hypothesis of deceit, it is a further proof of the sheer impotency of the theory of signals, when regard is had to the available amount of the material observed and recorded in the authoress, if we ask how is it possible to imagine that she (knowing very well, as she says, the suspicion resting on the method) in a year or more of work with Lola should not herself have perceived that she herself had been producing by mechanical means the rapped answers of her pupil?

In my opinion the answer is that the authoress was not only not aware of, but could not in the least have been aware of, the action that may have passed from herself to the dog so as to bring about the rapping of the answers; and that on the other hand it is not a question at all of thinking of a simple mechanical operation of the kind mentioned above, because in the presumed action of the authoress on the dog there is no need to have recourse to such a crude hypothesis (as surely there was no similar action of Krall's on his horses, especially when they were separated from him). I maintain, in fact, that in principle, even without any contact by hand, we may still presume that all the "wonders" obtained by Miss Kindermann are obtainable, taking, of course, into account the peculiar endowments of the animal we are dealing with. For if there be any automatism (and there is surely a good dose of it), it is certainly not a question of a mechanical automatism (of the type of Neumann's), but quite certainly of a true and proper psychic automatism; a very different thing, and without doubt much more complex.

In all probability the first condition for the occurrence of genuine phenomena similar to those attributed to "thinking" animals must be a very particular psychic relationship between the animal and his master. And such a relation, although with reluctance, I am compelled to call of the mediumistic type.

My reluctance is due in part to the very unhappy etymology of the term, derived from the famous word "medium," so unscientific both in its origin and in the meaning which some even now wish to associate with it. But even after having freed it from any "spiritistic" meaning, the term still leaves me reluctant; for I cannot hide from myself the weakness of a hypothesis which, in order to explain (only in part) one enigmatical fact (in this case, that of "thinking animals"), must have recourse to another unsolved enigma (in this case that of the "mediumistic phenomena").

However, it will already be something if the two problems are eventually merged together and so become a single problem; but it is not my object to explain any psychical facts themselves, whatever they may be, under which the phenomena of Lola and others of a similar nature may be eventually classified. It will be sufficient for me at present to group the performances of the animals, if possible, with something better known. And "mediumistic" facts, extrinsically at least, are certainly better known. I refer therefore to them as I find them described in the psychology called supernormal; because, from force of circumstances I am compelled to recognize that it is within this psychology that I must now continue the discussion.

IV. MEDIUMISTIC "RAPPORT" AND TELEPATHY