etician, the
algebraist, and more generally the analyst, in whom invention obtains in
the most abstract form of discontinuous functions--symbols and their
relations--cannot imagine like the geometrician. One may well speak of
the ideal figures of geometry--the empirical origin of which is no
longer anywhere contested--but we cannot escape from representing them
as somehow in space. Does anyone think that Monge, the creator of
descriptive geometry, who by his work has aided builders, architects,
mechanics, stone cutters in their labors, could have the same type of
imagination as the mathematician who has been given up all his life to
the theory of number? Here, then, are at least two well-marked
varieties, to say nothing of mixed forms. The physicist's imagination is
necessarily more concrete; since he is incessantly obliged to refer to
the data of sense or to that totality of visual, tactile, motor,
acoustic, thermic, etc., representations that we term the "properties
of matter." Our eye, says Tyndall, cannot see sound waves contract and
dilate, but we construct them in thought--i.e., by means of visual
images. The same remarks are true of chemists. The founders of the
atomic theory certainly _saw_ atoms, and pictured them in the mind's
eye, and their arrangement in compound bodies. The complexity of the
imagination increases still more in the geologist, the botanist, the
zoologist; it approaches more and more, with its increasing details, to
the level of perception. The physician, in whom science becomes also an
art, has need of visual representations of the exterior and interior,
microscopic and macroscopic, of the various forms of diseased
conditions; auditory representations (auscultation); tactile
representations (touch, reverberation, etc.); and let us also add that
we are not speaking merely of diagnosis of diseases, which is a matter
of reproductive imagination, but of the discovery of a new pathologic
"entity," proven and made certain from the symptoms. Lastly, if we do
not hesitate to give a very broad extension to the term "scientific,"
and apply it also to invention in social matters, we shall see that the
latter is still more exacting, for one must represent to oneself not
only the elements of the past and of the present, but in addition
construct a picture of the future according to probable inductions and
deductions.

It might be objected that the foregoing enumeration proves a great
variety in the _cont