The Mathematical Structure of the Human Sleep-Wake Cycle PDF

Over the past three years I have grown accustomed to the puzzled look which appears on people's faces when they hear that I am a mathematician who studies sleep.

They wonder, but are usually too polite to ask, what does mathematics have to do with sleep?

Instead they ask the questions that fascinate us all: Why do we have to sleep?

How much sleep do we really need? Why do we dream? These questions usually spark a lively discussion leading to the exchange of anecdotes, last night's dreams, and other personal information.

But they are questions about the func- tion of sleep and, interesting as they are, I shall have little more to say about them here.

The questions that have concerned me deal instead with the timing of sleep.

For those of us on a regular schedule, questions of timing may seem vacuous.

We go to bed at night and get up in the morning, going through a cycle of sleeping and waking every 24 hours.

Yet to a large extent, the cycle is imposed by the world around us.