As in traditional symmetry, the element of unity or
identity, in unequal division, is a repetition, in
quantitative terms, on one side, of what is given
on the other. In the simple line the *equal*
division gives us obviously exact objective repetition,
so that the psychophysical correlates are more easily
inferred, while the *unequal* offers apparently
no compensation. But the psychophysical contribution
of energies is not gratuitous. The function of
the increment of length on one side, which in the
centrally divided line makes the divisions equal,
is assumed in unequal division by the end point of
the short side; the uniform motor innervations in the
former become, in the latter, the additional innervation
of antagonists, which gives the equality. The
two are separated only in degree. The latter
may truly be called, however, a symmetry of a higher
order, because objectively the disposition of its
elements is not graphically obvious, and psychophysically,
the quantitative unity is attained through a greater
variety of processes. Thus, in complex works of
art, what at first appears to be an unsymmetrical
composition, is, if beautiful, only a subtle symmetry.
There is present, of course, an arithmetically unequal
division of horizontal extent, aside from the filling.
But our pleasure in this, *without* filling, has
been seen to be also a pleasure in symmetry.
We have, then, the symmetry of equally divided extents
and of unequally divided extents. They have in
common bilateral equivalence of psychophysical processes;
the nature of these differs. In both the principle
of unity is the same. The variety through which
it works is different.

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STUDIES IN ANIMAL PSYCHOLOGY.