by no means implies that he was conscious of the
movements on his part, which were associated with the thought process.

Everything up to this point might be explained as the working of simple
memory association, but when we come to problems in counting and
arithmetical calculation, we are in the field of conceptual thought.
Here, again, it was necessary for Mr. von Osten to invent a suitable
means of expression for the horse, and once more this had to be borrowed
from the treasury of gesture-language. Tapping with the hoof was
naturally hit upon as one of the normal, expressive movements of the
horse. This has long been used by trainers, in preparing horses for show
purposes. The method used in training the horse to make this response is
of no import, whether it was by touching his foot with the hand, or
tapping his leg, or by any other means.

It is possible that many will declare, as being nonsensical, any attempt
to introduce number-concepts[AJ] into an animal's mind, because the
necessary motor basis is lacking. We will not, just at this point, stop
to discuss whether or not it was not possible to develop number-concepts
from purely auditory or visual representations. It is evident, however,
that Mr. von Osten believed that a motor basis of some sort was
essential. In the case of man this basis is found in the enunciation of
the number names (or in the manipulation of the fingers). Mr. von Osten
seemed to think that he was justified in assuming that, even in the case
of the horse, some form of inner articulation of the word-sounds was
possible;--at the same time, in so doing, he did not blink at the
psychological difficulty of this hypothesis. The tapping of the foot was
to be regarded merely as the expression of the process of inner
counting, but not as the motor basis of the process. For this latter
purpose tapping would be quite inadequate, for the number complexes
which arise in the summation process of counting, could not be
differentiated by mere tapping with the foot, any more than a child
could learn to count by employing only one finger. Mr. von Osten
evidently imagined the process was somewhat like this: Whenever Hans was
about to count 5, he would enunciate inwardly the numbers from 1 to 5,
and would accompany each word with a tap of the foot. Since,
furthermore, wooden pins and balls could be used--as in the case of
children--for giving visual content in learning the significance of the
number-terms,