But Hans was not to acquire merely this relatively mechanical process of counting (hardly to be called counting), but he was to acquire also some meaning content for the number terms. For this purpose everything depended upon the concept "and". Only he who can grasp its meaning will be able to understand a number. 2 is 1 _and_ 1, 3 is 2 _and_ 1. Mr. von Osten had someone hold a large cloth before the horse, where the wooden pins usually were placed. He then had the cloth taken up and he would pronounce emphatically the word "and". After this had been done a number of times, he put up two of the pins and obscured them by the cloth. The cloth was again raised and the word "and" pronounced. Then Hans, as a result of his previous instruction (so Mr. von Osten thought) would give two taps at sight of the pins. The thing was repeated with three pins, then with one, and so on, and the horse would always execute the proper number of taps.
Now, five pins were set up, the three to the right being covered by the cloth. The horse tapped twice and Mr. von Osten said "two". Then the cloth was raised, Hans gave three further taps, and Mr. von Osten said "and three" with emphasis.
In this simple manner he tried to get the horse to understand that the three belongs to the two, and that both together make five. The image of the five pins as it was known from previous experience, was to be associated with the combined groups of two and three, and conversely, it was to be reproduced when these groups were presented. Later the cloth and pins were omitted and the question was asked: "How much is two and three?". The horse tapped five times. It had learned how to add. Still this could be regarded only as a mechanical process, if the horse were able to add only those numbers which had been presented together one or more times in the manner just described. And so long as we remained within the first decade, we could get twenty-five binary combinations whose sum does not exceed 10 (counting inverted orders we would have forty-five binary permutations),--all of which might have been practised separately. But as a matter of fact, Mr. von Osten did not take this course, for as he himself says, he allowed Hans to discover a great deal for himself. "Hans had to develop the multiplication table for himself."--With larger numbers and more addends, the number of combinations becomes so great that there can be no doubt they were not practised separately.