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

NON-EUCLIDEAN GEOMETRIES 845
more than purification, more than elimination of dross;
it involves, besides, a constructive process, a process of
creation. But, though the statement is not a complete
characterization of science in general nor of any branch
thereof, yet, regarded as a partial characterization, it is
fundamentally true of every branch: of all science common experience,-common sense,-is the basic soil. And
not only do scientific specialists know that all scientific
ideas have their roots in the soil of common sense but
they know, too, that every single term in the vast jargon
of science ultimately derives its meaning, in one way or
another, from generic ideas which, though ill defined in
the common consciousness, are present there and are
constantly employed by your man-in-the-street. The
process of such derivation is a perfectly natural one;
natural processes are, for the most part, not reversible;
but this one is; there is, I mean, no scientific idea whatever, however complicated and refined, and there never
will be one, that does not admit of being analyzed and
ultimately expressed in the language appropriate to the
vulgar elements whence the idea was originally derived.
In the case of many ideas, such elemental analysis requires
great patience and skill, and their expression in common
speech can not be made perfectly clear; it will sometimes,
of necessity, be so cumbrous and prolix as to be unprofitable except as an exercise; but the thing can be done, and
the point is that, in an immense multitude of cases, it can
be done in a way to edify not only the general public,
but also the experts who render the service.
The radical explanation of the scientific ignorance of
the educated public is to be found in the fact that, with
rare exceptions, those who understand do not teach-do
not teach, I mean, save in a manner suitable for the train