"Archey lecture"- Auckland Museum Lecture for High-School students
From MathsDept
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THE 2007 ARCHEY LECTURE
THE PATTERN OF TINY FEET
Prof Ian Stewart FRS, Mathematics Institute, University of Warwick
Tuesday, October 9th 9am Auckland Museum Auditorium
The wheel is a familiar and ancient invention, but scientists are becoming convinced that legs are also going to be important in the future. Wheels need a flat surface to run on; there's little point in making wheels unless you also make roads. Robots that use legs would be able to operate in places where wheels don't work. The Mars Rovers, with their six wheels, are restricted to those parts of the surface of Mars that are relatively smooth, and slopes that are not too steep. A robot with legs would be able to go almost anywhere. And robots with legs are better for dangerous tasks like dismantling old nuclear power stations.
By looking at fossilised dinosaur footprints, and also by looking at the structure of their skeletons, scientists have also been able to work out how these gigantic beasts must have moved, and how quickly they could have traveled. It now seems that Tyrannosaurus rex was fairly slow --- a lot slower than the monster in Jurassic Park. And by analysing how people move, it is possible to spot problems before they become too serious, and deal with them.
Movement using legs poses new problems for engineers, scientists, and mathematicians. Wheels are much simpler. But in recent years, a lot of progress has been made in our understanding of how people and animals use their legs to move efficiently, and why particular patterns of movement occur. The timing patterns of legs when animals move are known as gaits and this is studied in a sub-branch of science called Gait Analysis which came into being about 130 years ago as the indirect consequence of a bet about a horse. It provides a fascinating application of the mathematics of rhythmic patterns.
It is generally thought that the basic rhythms of the main gaits are generated by a relatively simple network of nerve cells in the spinal column, called a Central Pattern Generator (CPG). Recently it has been discovered that the gait patterns provide clues to the structure of the CPG. In particular, the symmetries of the gaits are determined by the symmetries of the CPG.
Doctors are also interested in motion with legs, because that's what human beings use. They particularly need to understand how legs work in infants (where the legs are still developing) and in the elderly (where hip bones may have been replaced with metal ones).
The lecture will introduce the basic gaits for four-legged animals, discuss their symmetries, and explain what can be deduced about the CPG. No technical knowledge will be assumed, but there will be lots of pictures.
Prof Stewart has held visiting positions in Germany, New Zealand, and the USA, and is an adjunct professor at Houston. In 1995 he received the Michael Faraday Medal and in 1997 Prof Stewart gave the Royal Institution Christmas Lectures. He is winner of the 1999 Communications Award of the Joint Policy Board for Mathematics, and he was awarded the 2000 Gold Medal of the UK's Institute for Mathematics and Its Applications. His joint book The Science of Discworld was nominated for a Hugo award at the 2000 World science fiction convention. Jointly with M. Golubitsky he won the 2001 Balaguer Prize. He was elected a Fellow of the Royal Society in 2001, and won the Public Understanding of Science and Technology Award of the American Association for the Advancement of Science in 2002.
