21 Jun If we learn to reinvent the leg, all that will change (IAN STEWART)
As I walk along Braes Bayou, surrounded by wildlife, I realize that I am also surrounded by math.
For instance …
A lot of people walk their dogs along the paths. If you watch a walking dog, you quickly notice how rhythmic its movement is. Not when it stops to sniff at a tree or another dog, mind you; it’s rhythmic only when the dog is just bumbling happily along without a thought in its head. Tail wagging, tongue lolling, feet hitting the ground in a careless doggy dance.
What do the feet do?
When the dog is walking, there’s a characteristic pattern. Left rear, left front, right rear, right front. The foot-falls are equally spaced in time, like musical notes, four beats to the bar.
If the dog speeds up, its gait changes to a trot. Now diagonal pairs of legs—left rear and right front, then the other two—hit the ground together, in an alternating pattern of two beats to the bar. If two people walked one behind the other, exactly out of step, and you put them inside a cow costume, the cow would be trotting.
The dog is math incarnate. The subject of which it is an unwitting example is known as gait analysis; it has important applications in medicine: humans often have problems moving their legs properly, especially in infancy or old age, and an analysis of how they move can reveal the nature of the problem and maybe help cure it. Another application is to robotics: robots with legs can move in terrain that doesn’t suit robots with wheels, such as the inside of a nuclear power station, an army firing range, or the surface of Mars. If we can understand legged locomotion well enough, we can engineer reliable robots to decommission old power stations, locate unexploded shells and mines, and explore distant planets. Right now, we’re still using wheels for Mars rovers because that design is reliable, but the rovers are limited in where they can go. We’re not decommissioning nuclear power stations at all. But the U.S. Army does use legged robots for some tidying-up tasks on firing ranges.
If we learn to reinvent the leg, all that will change.
Letters to a Young Mathematician