ce
was the plaything of the Greek, the consolation of the Middle Ages, and
only for the modern has it become an instrument in such fashion as to
mark an epoch in the still dawning discovery of mind.

Man is, after all, rational only because through his nervous system he
can hold his immediate responses in check and finally react as a being
that has had experiences and profited by them. Concepts are the medium
through which these experiences are in effect preserved; they express
not merely a fact recorded but also the significance of a fact, not
merely a contact with the world but also an attitude toward the future.
It may be that the mere judgment of fact, a citation of resemblances
and differences, is the basis of scientific knowledge, but before
knowledge is worthy of the name, these facts have undergone an ideal
transformation controlled by the needs of successful prediction and
motivated by that self-conscious realization of the value of control
which has raised man above the beasts of the field.

The realm of mathematics, which we have been examining, is but one
aspect of the growth of intelligence. But in theory, at least, it is
among the most interesting, since in it are reached the highest
abstractions of science, while its empirical beginnings are not lost.
But its processes and their significance are in no way different in
essence from those of the other sciences. It marks one road of
specialization in the discovery of mind. And in these terms we may read
all history. To quote Professor Woodbridge (_Columbia University
Quarterly_, Dec., 1912, p. 10): "We may see man rising from the ground,
startled by the first dim intimation that the things and forces about
him are convertible and controllable. Curiosity excites him, but he is
subdued by an untrained imagination. The things that frighten him, he
tries to frighten in return. The things that bless him, he blesses. He
would scare the earth's shadow from the moon and sacrifice his dearest
to a propitious sky. It avails not. But the little things teach him and
discipline his imagination. He has kicked the stone that bruised him
only to be bruised again. So he converts the stone into a weapon and
begins the subjugation of the world, singing a song of triumph by the
way. Such is his history in epitome--a blunder, a conversion, a
conquest, and a song. That sequence he will repeat in greater things. He
will repeat it yet and rejoice where he now despairs, converting