Posted by: Ian Bruk | July 10, 2012


Yes, yes try to get beyond the didactic criticism to the epiphany. Remember it was written by a mathematician.

From Zen and the Art of Motorcycle Maintenance’s explanation of Poincare:

Mathematics, he said, isn’t merely a question of
applying rules, any more than science. It doesn’t
merely make the most combinations possible according
to certain fixed laws. The combinations so obtained
would be exceedingly numerous, useless and cumbersome.
The true work of the inventor consistes in choosing
among these combinations so as to eliminate the
useless ones, or rather, to avoid the trouble of
making them, and the rules that must guide the choice
are extremely fine and delicate. It’s almost
impossible  to state them precisely; they must be felt
rather than formulated.

Poincare then hypothesized that this selection is made
by what he called the “subliminal self,” an entity
that corresponds exactly with what Phaedrus called
preintellectual awareness. The subliminal self,
Poincare said, looks at a a large number of solutions
to a problem, but only the interesting ones break into
the domain of consciousness. Mathematical solutions
are selected by the subliminal self on the basis of
“mathematical beauty”, of the harmony of numbers and
forms, of geometric elegance. “This is a true esthetic
feeling which all mathematiicans know,” Poincare said,
“but of which the profane are so ignorant as often to
be tempted to smile.” But it is this harmony, this
beauty, that is at the center of it all.


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