Book Review: Group Theory in the Bedroom and Other Mathematical Diversions by Brian Hayes

Popular Math at Its Very Best

Peter Flom
What a marvelous book! If you have any fondness for mathematics or computer programming, you will enjoy this collection of essays.

Group Theory in the Bedroom is a collection of essays by Brian Hayes; most of them were written as columns for American Scientist. There are 12 essays.

The first essay in Group Theory in the Bedroom is "Clock of Ages" about a truly marvelous clock built in Strasbourg. Not only does it keep fairly accurate time (considering when it was built) but it was built to last. It's designed to keep track of all sorts of things until the year 9999 (and there are instructions for what to do after that!). And it keeps track of lots of things - time, of course - but also local solar time and local lunar time. And the position of 5,000 stars, and the six inner planets and the phase of the moon. It marks Easter accurately. It keeps track of day of the year, but also the sidereal year (and it works for all the intricacies of leap years). Most amazingly, it does all this with brass gears and it was built in 1842. Brian Hayes uses this to get into the nature of programming, and the year 2000 crisis, and other things as well.

The second essay in Group Theory in the Bedroom is "Random Resources", and it's about the need for random numbers and how truly difficult it is to generate truly random numbers.

The third essay is "Follow the Money" about computer models of the economy, and how some very simple models can generate surprisingly complex behavior (or, sometimes, surprisingly simple behavior). More specifically, it asks what simple models can tell us about the distribution of wealth in human societies.

The fourth essay in Group Theory in the Bedroom is "Inventing the Genetic Code", and it's about efforts to figure out the four letters of the DNA alphabet translate into the 20 letters of the proteins. It turns out that nature is something of a kludge - the people who were trying to figure this out came up with much more elegant solutions than evolution did. (Although Hayes does not mention it, this seems like yet another argument against intelligent design).

The fifth essay is "Statistics of Deadly Quarrels", about efforts to model, statistically, the outbreaks of wars and insurrections and so on.

The sixth essay in Group Theory in the Bedroom is "Dividing the Continent" about the nature of the continental divide. This is the only chapter that I did not find interesting - but that says more about me than about the book.

Seventh, we have "On the Teeth of Wheels" about gears, the Stern Brocot tree, the Farey series, clock making, and early computers. The essential problem is how to make one gear turn a certain number of times when another gear turns once. But it gets complex, and mathematically fascinating.

The eighth essay in Group Theory in the Bedroom is "the Easiest Hard Problem" which uses the playground task of choosing up sides to get into the mathematics of partitioning, and the nature of "hard" and "easy" problems. The partitioning problem, simply put, is "Given a collection of objects of different weights, how do divide them into two groups, with the weights as equal as possible?"

Ninth, we have "Naming Names" about the surprisingly interesting problems of assigning names to things - from airports to phone numbers to license plates.

The tenth essay in Group Theory in the Bedroom is "Third Base" about computing in base 3, and in the fascinating "balanced ternary notation" which is base 3, but, rather than 0, 1, and 2, uses -1, 0 and 1. Both of these systems have very interesting properties!

Essay 11 is "Identity Crisis" about the complexities of the seemingly simple notion of =, in both mathematics and computer science.

The final essay is the title essay: "Group Theory in the Bedroom" and the real subject is, indeed, group theory, and how it can be used to figure out how to flip your mattress so that it wears as evenly as possible.

Overall, this book makes me want to read it again; and it makes me want to read more of Brian Hayes.

Published by Peter Flom

I am a statistician, working with a wide variety of clients, mostly researchers in psychology, education, medicine, social sciences and other fields. I also have given talks and written articles on learning...   View profile

To comment, please sign in to your Yahoo! account, or sign up for a new account.