s may perhaps be best found the genesis of the
present superstitions in regard to "lucky" and "unlucky" numbers,
like the number 13, which have such persistence. (Tr.)

[102] See Part Two, chapter II.

[103] Groos, _Die Spiele der Thiere_, pp. 308-312.

[104] Mabilleau, _op. cit._, p. 132.

[105] If we leave out oriental influences and the Mysteries, which,
according to Aristotle, were not dogmatic teaching, but a show, an
assemblage of symbols, acting by evocation, or suggestion, following
the special mode of mystic imagination that we already know.

[106] Recejac, _op. cit._, pp. 139 ff.

[107] One at once calls to mind Plotinus, whose highest philosophy
is a kind of indescribable ecstacy. (Tr.)

[108] Hartmann, _op. cit._, vol. I, part 2, chapter IX.

CHAPTER IV

THE SCIENTIFIC IMAGINATION

It is quite generally recognized that imagination is indispensable in
all sciences; that without it we could only copy, repeat, imitate; that
it is a stimulus driving us onward and launching us into the unknown. If
there does exist a very widespread prejudice to the contrary--if many
hold that scientific culture throttles imagination--we must look for the
explanation of this view first, in the equivocation, pointed out several
times, that makes the essence of the creative imagination consist of
images, which are here most often replaced by abstractions or extracts
of things--whence it results that the created work does not have the
living forms of religion, of art, or even of mechanical invention; and
then, in the rational requirements regulating the development of the
creative faculty--it may not wander at will. In either case its end is
determined, and in order to exist, i.e., in order to be accepted, the
invention must become subject to preestablished rules.

This variety of imagination being, after the esthetic form, the one
that psychologists have best described, we may therefore be brief. A
complete study of the subject, however, remains yet to be made. Indeed,
we may remark that there is no "scientific imagination" in general, that
its form must vary according to the nature of the science, and that,
consequently, it really resolves itself into a certain number of genera
and even of species. Whence arises the need of monographs, each one of
which should be the work of a competent man.

No one will question that mathematicians have a way of thinking all
their own; but even this is too general. The arithm