Once Upon a Prime

Sarah Hart

8 annotations • data

First annotation on Jul 28th, 2025. Last on Aug 5th, 2025.

Chapter 1

There are many mathematical mnemonics that we may have learned at school for remembering things like the first few digits of "How I wish I could calculate pi": that's not me expressing a desire to calculate it's the mnemonic. The number of letters in each word tells you the next number in the decimal, which begins 3.141592. If you need more digits, a longer mnemonic is "How I need a drink, alcoholic in nature, after the heavy lectures involving quantum mechanics!" That one has been around for at least a century and is credited to the English physicist James Jeans. In fact, it's now a niche hobby to compose verse in "pilish," in which the word lengths are defined by the digits of 1

Chapter 2

In Vonnegut's graphs, the vertical axis measures good fortune and the horizontal axis measures time passing—a rising curve means improving fortunes, a falling curve means things are getting worse. In "Man in a Hole," for instance, we start with someone going along happily when suddenly disaster strikes, but everything works out wonderfully in the end. A novel in this category might be David Copperfield—or, to give it its full, glorious title, The Personal History, Adventures, Experience and Observation of David Copperfield the Younger of Blunderstone Rookery (Which He Never Meant to Publish on Any Account). The young David has a very happy childhood until he is seven, when his mother first marries beastly Mr. Murdstone, then soon afterward dies, leaving poor David orphaned. But after many reverses and trials, David eventually finds happiness.
This chapter takes its title from Hilbert Schenck's story "The Geometry of Narrative" (1983), in which a student suggests that simple plot "lines" are just the start. He finds a way to link Shakespeare's Hamlet to a four-dimensional "hypercube" by arguing that we should think of instances of a story within a story as adding a dimension.
As the author Amor Towles said in a 2021 interview,3 "Structure can be very valuable in artistic creation. Much as the rules of the sonnet are valuable to the poet, adopting the rules and trying to invent, within those rules, something that's new and different, the structure of a novel can do the same kind of thing."
In The Luminaries, each chapter is divided into a specific number of sections, and in every case, the number of sections, added to the number of the chapter, is the same: thirteen. Thus the first chapter has twelve sections, the second chapter has eleven sections, and by the time we get to the twelfth and final chapter, it has just one section. This kind of pattern, in which we see the same increase or decrease each time, as in the sequence 12, 11, 10, 9,…, is known in mathematics as an arithmetic progression. Hidden in the thirteenness of chapter number plus number of sections is a really simple trick to add up the total number of sections in the book.
The sense of the inescapability of our fates increases as the constraints become ever tighter with each chapter—we saw the literal spiraling-inward effect—drawing us into the final, tender scene between the doomed lovers in the last chapter, Part Twelve.
There are lots of different solutions to this card puzzle, but the precise number (1,152) wasn't known until the British mathematician Kathleen Ollerenshaw worked it out several centuries later. She was quite a woman. Born in 1912, she enjoyed mathematics very much as a child, and when she became deaf after an illness at age eight, she found that it was one of the few subjects (as they were taught at that time) in which her deafness did not impede her. During her long mathematical career she also produced the first academic paper setting forth a method to solve a Rubik's Cube from any starting position—this feat coming with the side effect of a thumb injury due to too much cube manipulation, an ailment described by Reader's Digest as the first known case of "mathematician's thumb." Oh, and she became lord mayor of Manchester and played ice hockey for England. Call me an old romantic, but I do like the fact that she married her childhood sweetheart, Robert Ollerenshaw, saying that she knew it must be love when he sent her a slide rule as a present.

Chapter 3

We can also notice that if we take Chapter 1 and Chapter 9 together, they fit together to form a microcosm of the whole, with exactly four copies of the "5 4 3 2 1" motif. And there we are: "A splendid hard diamond takes shape." It is a very elegant design. Indeed, Calvino himself said that Invisible Cities was one of the works with which he was most pleased, because in it he managed to say the "maximum number of things in the smallest number of words."