So that we are shut
up to this--that the business of education is, in the first place, to
provide the young with the means and the habit of observation; and,
secondly, to supply the subject-matter of knowledge either in the shape
of science or of art, or of both combined.
Now, it is a very remarkable fact--but it is true of most things in this
world--that there is hardly anything one-sided, or of one nature; and
it is not immediately obvious what of the things that interest us may be
regarded as pure science, and what may be regarded as pure art. It may
be that there are some peculiarly constituted persons who, before they
have advanced far into the depths of geometry, find artistic beauty
about it; but, taking the generality of mankind, I think it may be
said that, when they begin to learn mathematics, their whole souls
are absorbed in tracing the connection between the premisses and the
conclusion, and that to them geometry is pure science. So I think it
may be said that mechanics and osteology are pure science. On the other
hand, melody in music is pure art. You cannot reason about it; there
is no proposition involved in it. So, again, in the pictorial art, an
arabesque, or a "harmony in grey,"[80] touches none but the aesthetic
faculty. But a great mathematician, and even many persons who are not
great mathematicians, will tell you that they derive immense pleasure
from geometrical reasonings.
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