From Herman Melville's Moby Dick.
For as in this world, head winds are far more prevalent than winds from astern (that is, if you never violate the Pythagorean maxim), so for the most part the Commodore on the quarter-deck gets his atmosphere at second hand from the sailors on the forecastle.
I understand the Pythagorean theorem (a^2 + b^2 = c^2) but I'm not sure what he means in applying it to head winds and winds from astern.
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.
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.
The "Pythagorean maxim" bit has several meanings.
First, it's a poetic way of saying that you are much more likely to encounter hardships (headwinds) than ease and comfort (winds from astern).
Second, it's referring to the fact that when sailing, it is possible to sail into a headwind (although its not as fast as having the wind at your back) but your sail has to be at a specific angle to generate lift via Bernoulli's principle, and Pythagoras is well known for his math involving angles.
Finally, it's a fart joke; Pythagoras believed you should not eat fava beans because they cause you to fart (again, winds from astern) and flatulence took away from your precious "breath of life". Additionally he's saying that when a working sailor on the front deck (forecastle) of a ship farts, it will be blown into the face of his boss on the rear deck.
In my opinion this passage suggests the author is making a double entendre, not only a joke.
First, it is clear that a headwind will go against direction which the ship wants to travel and a wind from astern will push in the direction of travel. By bringing that into metaphor with the phrase "For as in this world", Herman Melville is, foremost, suggesting that hardships are more common than advantages. As for the Pythagorean maxim, there were many maxims spoken in the Pythagorean school, so that singling out just one might not give the full meaning of what Melville was saying. This idea is also supported by the long collection of quotes about whales which Melville places at the beginning of the book.
I believe the most relevant maxim, given the context of the passage, would be koinà tà phílōn "All things in common among friends" from the communal life of the Pythagoreans.
The adherents were bound by a vow to Pythagoras and each other, for the purpose of pursuing the religious and ascetic observances, and of studying his religious and philosophical theories. The members of the sect shared all their possessions in common and were devoted to each other to the exclusion of outsiders. Ancient sources record that the Pythagoreans ate meals in common after the manner of the Spartans. One Pythagorean maxim was "koinà tà phílōn" ("All things in common among friends"). - Wikipedia
In other words, Melville is saying in one sense of the double entendre, that hardships are more common among the community (sailors), as long as you stay with the community. This idea is supported in the author's description of a sailor as a slave and in the following sentence:
For as in this world, head winds are far more prevalent than winds from astern (that is, if you never violate the Pythagorean maxim), so for the most part the Commodore on the quarter-deck gets his atmosphere at second hand from the sailors on the forecastle. He thinks he breathes it first; but not so. In much the same way do the commonalty lead their leaders in many other things, at the same time that the leaders little suspect it
The more risque meaning of a "fart joke" comes from the Pythagorean rule of not eating beans which would produce flatulence. This theory is supported by Melville's description of the location of the forecastle:
No, when I go to sea, I go as a simple sailor, right before the mast, plumb down into the forecastle, aloft there to the royal mast-head.
"plumb down into" would suggest a vertical drop which is in reality horizontal from mast to forecastle, which later helps imply a "drop" from the body's head to butt. A fart oriented as described would manifest in the same direction as an "astern" wind.
To recap, the fart joke adds to the idea that the leader does not always know what is leading him. However, without the bonds holding sailors together, there is no lead by community. The sense of lead is awkward in Melville's sense that one leads into hardship often, metaphorically represented by his commodore getting lead by the sailors and the sailors getting led by fate.
Not just metaphor. I think he may also be referring to that fact that while sailing you literally feel headwind more than tailwind. If you are sailing at a given speed you can subtract that speed from a tailwind, or add it to a headwind, and that's how much wind you will feel. I've heard this called 'apparent wind' by sailors.
