Nature's Numbers by Ian Stewart

Author:Ian Stewart [Stewart, Ian]
Language: eng
Format: epub
ISBN: 9780786723928
Publisher: Basic Books

*The precise recipe is given in the Notes to The Collapse of Chaos, by Jack Cohen and Ian Stewart.

CHAPTER 7

THE RHYTHM OF LIFE

Nature is nothing if not rhythmic, and its rhythms are many and varied. Our hearts and lungs follow rhythmic cycles whose timing is adapted to our body’s needs. Many of nature’s rhythms are like the heartbeat: they take care of themselves, running “in the background.” Others are like breathing: there is a simple “default” pattern that operates as long as nothing unusual is happening, but there is also a more sophisticated control mechanism that can kick in when necessary and adapt those rhythms to immediate needs. Controllable rhythms of this kind are particularly common—and particularly interesting—in locomotion. In legged animals, the default patterns of motion that occur when conscious control is not operating are called gaits.

Until the development of high-speed photography, it was virtually impossible to find out exactly how an animal’s legs moved as it ran or galloped: the motion is too fast for the human eye to discern. Legend has it that the photographic technique grew out of a bet on a horse. In the 1870s, the railroad tycoon Leland Stanford bet twenty-five thousand dollars that at some times a trotting horse has all four feet completely off the ground. To settle the issue, a photographer, who was born Edward Muggeridge but changed his name to Eadweard Muybridge, photographed the different phases of the gait of the horse, by placing a line of cameras with tripwires for the horse to trot past. Stanford, it is said, won his bet. Whatever the truth of the story, we do know that Muybridge went on to pioneer the scientific study of gaits. He also adapted a mechanical device known as the zoetrope to display them as “moving pictures,” a road that in short order led to Hollywood. So Muybridge founded both a science and an art.

Most of this chapter is about gait analysis, a branch of mathematical biology that grew up around the questions “How do animals move?” and “Why do they move like that?” To introduce a little more variety, the rest is about rhythmic patterns that occur in entire animal populations, one dramatic example being the synchronized flashing of some species of fireflies, which is seen in some regions of the Far East, including Thailand. Although biological interactions that take place in individual animals are very different from those that take place in populations of animals, there is an underlying mathematical unity, and one of the messages of this chapter is that the same general mathematical concepts can apply on many different levels and to many different things. Nature respects this unity, and makes good use of it.

The organizing principle behind many such biological cycles is the mathematical concept of an oscillator—a unit whose natural dynamic causes it to repeat the same cycle of behavior over and over again. Biology hooks together huge “circuits” of oscillators, which interact with each other to create complex patterns of behavior. Such “coupled oscillator networks” are the unifying theme of this chapter.

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