By “the Pythagorean maxim” Melville means the forbidding of eating beans, which was believed in antiquity to have been one of the rules of the Pythagorean cult.
> Plato then asserts that we should bring our bodies into such a disposition before we go to sleep as to leave nothing which may occasion error or perturbation in our dreams. For this reason, perhaps, **Pythagoras laid it down as a rule, that his disciples should not eat beans** , because this food is very flatulent, and contrary to that tranquillity of mind which a truth-seeking spirit should possess.
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> Marcus Tullius Cicero (44 BCE). _On Divination_ 1.30. Translated by C. D. Yonge (1853).
The passage from _Moby-Dick_ is thus a fart joke: if you “violate the Pythagorean maxim” (eat beans) then you will find that “winds from astern” (farts) become prevalent.