s.

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.

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