Mathematical Structure of the Human Sleep-Wake Cycle

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 question...