Twice before I have posted mathematical passages that I have stumbled upon in works of literature. Yesterday I finished reading Moby-Dick (great book, great ending!), so I thought I’d highlight a few mathematical passages that it contains.
Especially interesting to me is the second one in which Melville mentions the impossibility of squaring a circle. At the time Moby-Dick was written (1851), that was an open question. The impossibility of squaring the circle was proved in 1882 when Lindemann proved that is transcendental. I also think it is cool that Melville knows about the tautochrone problem (third quote).
In Chapter 74 (on the sperm whale having eyes on opposite sides of its head):
A curious and most puzzling question might be started concerning this visual matter as touching the Leviathan. But I must be content with a hint. So long as a man’s eyes are open in the light, the act of seeing is involuntary; that is, he cannot then help mechanically seeing whatever objects are before him. Nevertheless, any one’s experience will teach him, that though he can take in an undiscriminating sweep of things at one glance, it is quite impossible for him, attentively, and completely, to examine any two things—however large or however small—at one and the same instant of time; never mind if they lie side by side and touch each other. But if you now come to separate these two objects, and surround each by a circle of profound darkness; then, in order to see one of them, in such a manner as to bring your mind to bear on it, the other will be utterly excluded from your contemporary consciousness. How is it, then, with the whale? True, both his eyes, in themselves, must simultaneously act; but is his brain so much more comprehensive, combining, and subtle than man’s, that he can at the same moment of time attentively examine two distinct prospects, one on one side of him, and the other in an exactly opposite direction? If he can, then is it as marvellous a thing in him, as if a man were able simultaneously to go through the demonstrations of two distinct problems in Euclid. Nor, strictly investigated, is there any incongruity in this comparison.
If the Sperm Whale be physiognomically a Sphinx, to the phrenologist his brain seems that geometrical circle which it is impossible to square.
The try-works are planted between the foremast and mainmast, the most roomy part of the deck. The timbers beneath are of a peculiar strength, fitted to sustain the weight of an almost solid mass of brick and mortar, some ten feet by eight square, and five in height. The foundation does not penetrate the deck, but the masonry is firmly secured to the surface by ponderous knees of iron bracing it on all sides, and screwing it down to the timbers. On the flanks it is cased with wood, and at top completely covered by a large, sloping, battened hatchway. Removing this hatch we expose the great try-pots, two in number, and each of several barrels’ capacity. When not in use, they are kept remarkably clean. Sometimes they are polished with soapstone and sand, till they shine within like silver punchbowls. During the night-watches some cynical old sailors will crawl into them and coil themselves away there for a nap. While employed in polishing them—one man in each pot, side by side—many confidential communications are carried on, over the iron lips. It is a place also for profound mathematical meditation. It was in the left hand try-pot of the Pequod, with the soapstone diligently circling round me, that I was first indirectly struck by the remarkable fact, that in geometry all bodies gliding along the cycloid, my soapstone for example, will descend from any point in precisely the same time.
In Chapter 129 (Captain Ahab to Pip):
“Weep so, and I will murder thee! have a care, for Ahab too is mad. Listen, and thou wilt often hear my ivory foot upon the deck, and still know that I am there. And now I quit thee. Thy hand!—Met! True art thou, lad, as the circumference to its centre. So: God for ever bless thee; and if it come to that,—God for ever save thee, let what will befall.”