Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

INVARIANCE 197
that similar examples might be cited at great length;
and I need hardly say that, if some of those cited by
Rankine and MacMahon may have to be withdrawn in
view of recent physical refinements, the weight and
justice of their main contentions remain unimpaired.
Interest in things that abide,-interest in stable
values, transcending time and change,-is as fundamental
and regnant in art as in natural science. It is true that
the invariants which art seeks in its own way to find and
in its own way to disclose or represent are not sharply
defined; like personal identity, they are of the class of
those which a little while ago we described as unformulated or qualitative invariants; they are none the less
genuine invariants, and no defect of their definition can
disguise or dim the fact that, like natural science and like
mathematics, art,-art in its great moods and proper
character as art, —contemplates the world under the
aspect of eternity, aims at what is permanent in the
"fleeting show," devotes itself to goods that are everlasting. For the fact is manifest in many ways. A
thing of beauty is a joy forever. Who does not know, or
at all events feel, the deep and proper meaning of this
familiar mot? It is not that any phrase or picture or poem
or symphony or statue or temple will escape the doom of
temporal things; nor that the joy they may give you or
me will endure; it is that a certain quality,-the quality
in virtue of which a thing of beauty is such a thing,-is
timeless, unbegotten and, though its temporal embodiments must perish, is itself imperishable. " The purpose
of art," said John LaFarge, "is commemoration." In
cternitatum pingo, said Zeuxis, the Greek painter. One
need not be an artist to understand that, in the words of
Joshua Reynolds, " The idea of beauty in each species of