urgency of business, the spontaneity of his activities returns. The
doings of children, of the rich, and of all men on a holiday illustrate
this. Compare, for example, the speech of trade, where one says the
brief and needful thing only, with the talk of excursionists, where
verbal expression, having no end beyond itself, develops at length and
at leisure; where brevity is no virtue and abundant play takes the
place of a narrow seriousness.

But we have not yet so limited the field of expression that it becomes
equivalent to the aesthetic; for not even all of free expression is
art. The most important divergent type is science. Science also is
expression,--an embodiment in words, diagrams, mathematical symbols,
chemical formula, or other such media, of thoughts meant to portray
the objects of human experience. Scientific expressions have, of course,
a practical function; concepts are "plans of action" or servants of
plans, the most perfect and delicate that man possesses. Yet scientific
knowledge is an end in itself as well as a utility; for the mere
construction and possession of concepts and laws is itself a source
of joy; the man of science delights in making appropriate formulations
of nature's habits quite unconcerned about their possible uses.

In science, therefore, there is much free expression; but beauty not
yet. No abstract expression such as Euclid's _Elements_, Newton's
_Principia_, or Peano's _Formulaire_, no matter how rigorous and
complete, is a work of art. We admire the mathematician's formula
for its simplicity and adequacy; we take delight in its clarity and
scope, in the ease with which it enables the mind to master a thousand
more special truths, but we do not find it beautiful. Equally removed
from the sphere of the beautiful are representations or descriptions
of mere things, whether inaccurate or haphazard, as we make them in