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.