22 August, 2002
A History of Pi
Petr Beckmann
1971
202 pp, St. Martin's Press TPB
One of my labmates saw this book on my desk, and remarked sarcastically, "A bit of light reading?" In spite of the weighty title, this really is light reading. It's a breezy overview of the history of mathematics, with a focus on the study of pi (for the non-mathematically inclined, that's, the ratio of a circle's circumference to its diameter). It starts out with the mathematics of ancient Babylon, Egypt, Mesoamerica, and China, proceeds through the ancient Greeks and their geometry, the relatively stagnant periods of the Roman Empire and medieval times, the scientific and mathematical revolution of the 1600s and 1700s, Newton, Euler, and finally modern computational mathematics. I found it all rather interesting, but then again, I've always had a strong interest in the history of science (which is intimately connected to the history of math).
The book itself is a bit unusual. Beckman made no effort to write a formal, objective history, and he comes off as nothing so much as a borderline Usenet kook. His prejudices, while clearly stated (he loves Newton and Euler, and hates the Roman Empire, organized religion, and Communism) certainly influence his presentation of the material. To hear Beckmann tell it, the Romans, the Roman Catholic Church, and the Soviet Union never produced anything of any value or accomplished anything of interest, in mathematics or any other venture. While he touches on contributions of Asian and Arab contributions, he focusses almost exclusively on Western Europe. This is most notable in the way he focusses on the lack of mathematical advances in medieval Europe, rather than the great advances which were being made in the Islamic world during the same era. He interjects his narrative with random, opinionated asides on everything from the uselessness of the United Nations to the inherent value of science:
[Christiaan Huygens'] many discoveries included a principle of wave motion, which to this day is called Huygens' principle. He could not have known that the antennas of the radio stations tracking man's first flight to the moon would be calculated on the basis of that principle; any more than Apollonius of Perga, in the 3rd century B.C., could have known that the family of circles he discovered... would one day be the equipotentials of two parallel, cylindrical, electrical conductors. These are but two of hundreds of examples that one might quote in answer to the question what good comes from exploring the moon or studying non-Euclidean geometry. the question is often asked by people who count cents instead of dollars and dollars instead of satisfaction. Of late, this question is also being asked by the intellectual cripples who drivel about "too much technology," because technology has wounded them with the ultimate insult:the can't understand it any more.Some Victorian lady asked Michael Faraday (1791-1867) this question about his discovery of electromagnetic induction, and he answered, "Madam, what is the use of a newborn baby?"
I found this book a fun, light read, but I wouldn't recommend it to the general public, it's got a fair amount of math in it (nothing beyond what is taught in the average American high school), and Beckmann's opinionizing will not be appreciated by the easily-offended.