Group Theory In The Bedroom

bit-player is a blog authored by Brian Hayes that I occasionally read. That is where I learnt about his latest book Group Theory In The Bedroom, And Other Mathematical Diversions. This book is a compilation of 12 essays he had written for the American Scientist magazine. Written for a scientifically oriented audience, I found most of the chapters to be fun and interesting. Brian has the gift of making complex ideas easy to understand by using simple analogies. He also goes deep into the history behind the science and such historical background is something I sorely miss in most math or science writing. To me, the humans and their stories are just as important as their ideas. I found this book to be an interesting read.

You can read almost all the chapters online since the original American Scientist articles are accessible. Find the links here. However, if you have access to the book through a friend or a library, I recommend that. This is because the articles in the book have been corrected, expanded and end with an Afterthoughts section.

The chapters which particularly engrossed me were:

Chapter 4: Inventing The Genetic Code - Watson discovered the DNA structure and found that it was made up of 4 nucleotide bases (ATGC). The next problem was to map these 4 to the 20 amino acids that make up all proteins. The chapter follows the various elegant solutions that scientists proposed for this mapping. In the end it was discovered that nature had eschewed elegance for a simple lookup table to do the mapping!

Chapter 7: On The Teeth Of Wheels - Before the world went digital, most computation was performed using gears. (Think of an analog watch.) With various examples, this chapter beautifully shows how number theory concepts are closely related to the design of gears. This chapter is sure to earn your respect for our early calculating machines that used gears.

Chapter 10: Third Base - If I have to pick a favorite chapter, this would be the one. Learn how base 3 is way better (and cooler) than base 2, base 10 and all others. At one time people even wanted to build a ternary computer!

Chapter 12: Group Theory In The Bedroom - What does the seasonal flipping of a bedroom mattress have to do with group theory? Read the chapter to find out. Group theory had always seemed extremely dry and pointless to me. This is probably the first time anyone has applied it in a fun way.

The book is full of delightful anecdotes, here’s one from the chapter Identity Crisis:

In 1948 John Archibald Wheeler, in a telephone conversation with his student Richard Feynman, proposed the delightful hypothesis that there is just one electron in the universe. The single particle shuttles forward and backward in time, weaving a fabulously tangled “world line.” At each point where the particle’s world line crosses the space-time plane that we perceive as “now,” it appears to us as an electron if it is moving forward in time and as a positron if it is going backward. The sum of all these appearances constructs the material universe. And that’s why all electrons have the same mass and charge: because they are all the same electron, always equal to itself.

More of my notes from this book can be found here.