Since, after all this preliminary instruction, Hans really began to give solutions of new problems, the master believed that this was proof that he had succeeded in inculcating the inner meaning of the number concepts, and not merely an external association of memory images with certain movement responses. But he always remained within the sphere of the ideas thus developed, and adhered closely to the customary vocabulary and its usage. Every new concept, each additional word was explained anew.
It would not be legitimate to condemn the whole procedure from the very beginning on the ground of the horse's lack of knowledge of language or of its use. It was Mr. von Osten's aim to convey to the horse an understanding of the language, by means of sense-presentations, adequate to give rise to the proper sense-perceptions. Helen Keller and other blind deaf-mutes have been educated to an understanding of the language without the aid of vision and hearing. They have come to it through the sense of touch alone. Everything depends upon whether or not the predisposition for it is present. And it was quite rational that Mr. von Osten should have chosen counting and arithmetical calculation as the processes by which to make his attack upon the animal mind, for as a matter of fact, nowhere else is it so easy to bridge the gap between perception and conception and nowhere else can the sign of success or failure be perceived so readily as in the handling of numbers. It is unfortunate, however, that he did not utilize these same signs for purposes of counter-testing also, as, for instance, by inquiring for the cube root of 729. But he was prevented from doing this by his close adherence to his pedagogical principle and by his unquestioning faith in the soundness of the entire procedure.
In teaching multiplication the counting machine was used. Two of the ten balls on one of the rods were pushed far to the left, thus: 00. "How many are there?" Two taps. "Very well. That is once two." Another group of two was pushed to the left, at a short interval from the first group, thus: 00 00. "How many times two balls are there?" was asked, with a decided movement of the hand toward the two groups. Two taps. "How many, therefore, are two times two?" Four taps.