The Pleasures of Counting, by T. W. Körner, was recommended to me by my Chaos Theory professor Vidhu Prasad.#

The book is a mathematician's attempt to show that beautiful and interesting mathematics appears throughout virtually every field and that it's actually important. This is wrapped in, essentially, a history of math around the time of the two wars of the twentieth century.#

The book was very interesting with regards to the history of people and mathematical ideas I had not heard before, but when I came to the parts I understood well: fractals, group theory, algorithms, and cryptograhy; I could essentially only read for the clever quips.#

The biggest problem with the book, actually, was the author's unabashed socialism and constant mockery of liberty, as well as the most incredible example of The Fatal Conceit I've ever read at the end of the first part.#

Still I recommend the book.#

I thought this excerpt from the part of physics was very clever:#

Although it lies outside the main concerns of this chapter, I cannot resist including an application of number theory to biology. Some bamboos live for 80 years or more without flowering, then flower, set seed, covering the ground beneath thickly with seeds, and die. Other, more common bamboos flowers and seed more frequently but do so in synchrony, all seeding at the same time. At first sight this seems a curious and wasteful procedure since many more seeds are produced than could possibly produce new bamboos. The key to the riddle lies not in the bamboos themselves, but in the numerous insects and birds which can consume the seed s-- predators, as the biologists call them. The bamboos are providing so much seed in such a short time that the predators cannot eat all of it and some must survive.

Promising as this strategy of 'predator satiation' appears, it will not work if the bamboos seed every year because the seed eaters will then adjust their own breeding seasons so that their young can take advantage of the annual feast. Few species of bamboo flower more often than once in 15 or 20 years. There is a species of cicada in the Northern United States which follows a similar pattern, living underground as 'nymphs' for 17 years and then emerging above ground in millions and, in the space of a few weeks, completing their life cycle by becoming adult, mating, laying eggs and dying. A relate species in the South does the same but with a cycle time of 13 years.

Why do we have 13 and 17 year cicadas, but no cycles of 12, 14, 15, 16, or 18? Thirteen and 17 share a common property. They are large enough to exceed the life cycle of any predator, but they are also prime numbers (divisible by no integer smaller than themselves). Many potential predators have 2 to 5 year life cycles. Such cycles are not set by the availability of periodical cicadas (for they peak too often in years of non-emergence), but cicadas might be eagerly harvested when the cycles coincide. Consider a predator with a cycle of five years: if cicadas emerged every 15 years, each bloom would be hit by the predator. By cycling at a large prime number, cicadas minimise the number of coincidences (every 5 x 17 or 85 years, in this case). Thirteen and 17-year cycles cannot be tracked by any smaller number. (p. 107)