Group Theory In The Bedroom

bit-player is a blog authored by Brian Hayes that I read occasionally. 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 long essays he had written for the American Scientist magazine. Written for a general 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 researches in-depth into the history behind the science, this is something I sorely miss in most math or science writing. The humans and their stories are just as important as their ideas. This book is an interesting read.

You can read almost all the chapters online since the original American Scientist articles are accessible. Find the links here. If you have access to the book however, I suggest you read that. 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 machines that calculate using 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.



I seem to be inadvertently reading only Booker winners, like Disgrace, which I borrowed from my friend and started reading during my travel in Vietnam. I had not heard of the author J.M. Coetzee and did not know that he had won a Nobel for Literature! The book deals with the disgrace of a man and the daughter he loves very much, set in post-Apartheid South Africa.

David Lurie is an old white man, a professor of English poetry and working on a book on Lord Byron. He has been divorced twice and is casual with satiating his sexual desires. He is thrown out of his university on charges of sexual harassment of one of his students who had consensual sex with him. Disgraced like this, he leaves town to live with his daughter Lucy who runs a dog kennel alone on a remote farm. David is a man of arrogance and ego, but he adjusts to the rural life helping Lucy and her friends with their dogs. But even his daughter’s idyllic life falls apart when some locals rape her and set him on fire. Father and daughter are left to workout their relationship and find their place in the changing racial landscape of Africa.

This is a tragic book where slowly, subtly and surely everyone’s life goes to hell. Coetzee’s prose is simple and interesting and kept me engaged even though I knew that the characters were in for a world of pain. Coetzee downplays the color of his characters, but most of their troubles stem from they being white in a post-Apartheid South Africa, a place where the natives seem to want payback for the misery they endured in the past. The lives of the characters are not settled even when the book ends. A lot of stuff in the book is left to the interpretation of the reader. For example, I am pretty sure the limping dog which David agrees to kill in the end is surely a metaphor for his own ego. If you have read this book, please do share your interpretations.

At 219 pages, this is a breezy read. A movie based on this book is now in the works. The Observer calls this the best novel of the last 25 years! I would not agree with that, but this is one haunting tale.

Related: After The Fall, NYTimes review of the book.

An excerpt:

(David and Lucy are discussing David’s fall from grace after his affair with a student.)

‘When you were small, when we were still living in Kenilworth, the people next door had a dog, a golden retriever. I don’t know whether you remember.’


‘It was a male. Whenever there was a bitch in the vicinity it would get excited and unmanageable, and with Pavlovian regularity the owners would beat it. This went on until the poor dog didn’t know what to do. At the smell of a bitch it would chase around the garden with its ears flat and its tail between its legs, whining, trying to hide.’

He pauses. ‘I don’t see the point,’ says Lucy. And indeed, what is the point?

‘There was something so ignoble in the spectacle that I despaired. One can punish a dog, it seems to me, for an offence like chewing a slipper. A dog will accept the justice of that: a beating for a chewing. But desire is another story. No animal will accept the justice of being punished for following its instincts.’

‘So males must be allowed to follow their instincts unchecked? Is that the moral?’

‘No, that is not the moral. What was ignoble about the Kenilworth spectacle was that the poor dog had begun to hate its own nature. It no longer needed to be beaten. It was ready to punish itself. At that point it would have been better to shoot it.’

‘Or to have it fixed.’

‘Perhaps. But at the deepest level I think it might have preferred being shot. It might have preferred that to the options it was offered: on the one hand, to deny its nature, on the other, to spend the rest of its days padding about the living-room, sighing and sniffing the cat and getting portly.’

‘Have you always felt this way, David?’

‘No, not always. Sometimes I have felt just the opposite. That desire is a burden we could well do without.’

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