Triangulating math, Mozart and “Moby-Dick”
For mathematician Sarah Hart, a close reading of “Moby-Dick” reveals not merely (per D.H. Lawrence) “one of the strangest and most wonderful books in the world” and “the greatest book of the sea ever written,” but also a work awash in mathematical metaphors.
“Herman Melville, he really liked mathematics — you can see it in his books,” Hart, a professor at Birkbeck, University of London, said during a February talk on “Mathematical Journeys into Fictional Worlds.”
“When he’s reaching for an allusion or a metaphor, he’ll often pick a mathematical one,” she said. “‘Moby-Dick’ has loads of lovely juicy mathematics in it.”
Near the beginning of the story, Ishmael, the narrator, describes the stingy landlord and his wares at Spouter-Inn: “Abominable are the tumblers into which he pours his poison. Though true cylinders without — within, the villainous green goggling glasses deceitfully tapered downward to a cheating bottom. Parallel meridians rudely pecked into the glass, surround these footpads’ goblets.”
And at the end, Captain Ahab praises the loyal cabin boy, Pip, with geometry: “True art thou, lad, as the circumference to its center.”
Hart explored this subject further with a paper, “Ahab’s Arithing. metic: The Mathematics of Moby-Dick,” recently published in the Journal of Humanistic Mathematics. She concluded that Melville “actively enjoyed mathematics and mathematical ideas, and that this shines through in his work.”
An exuberant enthusiasm for mathematics shines through Hart. Her talk in February was the latest in a series she is delivering on mathematical intersections in literature and music, presented online by Gresham College in London. Last spring, she was appointed the Gresham professor of geometry; established in 1597, it is the oldest mathematical chair in England.
Hart considers the twin vocations of her career to be researching mathematics (she specializes in group theory, the mathematics of symmetry) and communicating mathematics (she once gave a talk to 900 students on “How to Prove Absolutely Anything”).
The Gresham brief entails 18 public lectures, six each year over three years. Hart chose the theme “Mathematics, Culture and Creativity.”
“I am pathologically interested in everything,” she said from her home in Walthamstow, in East London. During lockdown, “everything” grew to include dabbling in lessons with her daughters, ages 10 and 14, on, among other things, palindromic numbers, origami, code cracking, geometric patterns, etymology and Latin.
Basically, Hart just likes play
“Was it Paul Klee who talked about ‘taking a line for a walk’?” she said. “I like to take an idea for a walk.”
Hart’s Gresham series debuted last fall with her lecture on the use of mathematical patterns and structures in music — for instance, with fractal compositions.
Hart also investigated the use of group theory and symmetry as a creative device in musical composition. The violin duet attributed to Mozart, “Der Spiegel” (“The Mirror”), demonstrates rotational symmetry. It is played simultaneously by two violinists, sitting across a table and looking at the same score; one plays from the beginning to the end, the other plays from the end to the beginning.
For her next installment, she considers applications of mathematical structures in literature, including the Oulipo group of French mathematicians and writers; the mathematicallyminded Argentine writer Jorge Luis Borges and his short story “The Library of Babel”; and Michael Crichton’s “Jurassic Park.”
She also discusses “The Luminaries,” by Eleanor Catton, winner of the 2013 Booker Prize. The chapters, she observed while reading, display a geometric progression, halving in length one to the next. She also noticed “a twelveness happening” — 12 chapters, and 12 signs of the zodiac each instantiated in one of the main characters.
The structure, by Hart’s reading, had a compelling effect. “It’s refining and refining and refining, gradually waning down, until it’s quite poignant by the end,” she said; the two main characters, the luminaries, seem trapped in their destinies. “It’s a feeling of inevitability, closing in the kernel of the love story at the center of the entire novel.”
Such constraints and structures are most successful when not imposed frivolously, she added: “That’s not what it’s about. And that’s not what mathematicians do. We don’t invent a structure for no reason, like some silly intellectual game. We find structures lying around, and we explore them.”
She is also enamored of the mathematical allusions applied by George Eliot (the pen name of Mary Ann Evans). Eliot, in her first novel, observed that Adam Bede seems “to find reassurance in the eternal truth of mathematics, consoling himself after his father’s death with the thought that ‘the square o’ four is sixteen, and you must lengthen your lever in proportion to your weight, is as true when a man’s miserable as when he’s happy.’”
Eliot also seemed to take solace from her own mathematical literacy. In 1849 Eliot, in “want of health,” described in a letter how she sustained herself: “I take walks, play on the piano, read Voltaire, talk to my friends, and just take a dose of mathematics every day to prevent my brain from becoming quite soft.”
Hart said: “Everybody should!”