While the evils to which science is exposed by the necessarily
unfashionable character of experimental manipulation are neither few
nor trivial, there are still evils which arise from the directly
opposite cause--from excess of intellectual cultivation; as is shown
in the exclusive love of mathematics by a great number of
philosophers. Minds which, left to themselves, might have eliminated
the most valuable results, have, dazzled by the lustre cast by fashion
upon abstract mathematical speculations, lost themselves in a mazy
labyrinth of transcendentals. The fashion of mathematics has ruined
many who might be most useful experimentalists; but who, wishing to
take a higher flight, seek to attain distinction in mathematical
analysis, and having acquired a certain celebrity for experimental
research, dissipate, in simple equations, the fame they had acquired
in a field equally productive, but not so select. Like Claude, who in
his later years said, "Buy my figures, and I will give you my
landscapes for nothing;" they fall in love with their own weakness,
and estimate their merit by the labour they have undergone, not by the
results they have deduced. M. Comte expresses himself well on this
subject. "Mathematicians, too frequently taking the means for the end,
have embarrassed Natural Philosophy with a crowd of analytical
labours, founded upon hypotheses extremely hazardous, or even upon
conceptions purely visionary; and consequently sober-minded people can
see in them really nothing more than simple mathematical exercises, of
which the abstract value is sometimes very striking, without their
influence, in the slightest degree, accelerating the natural progress
of Physics."[21]
[21] Cours de Philosophie Positive, vol. ii. p. 409.
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