‘What immortal hand or eye dare frame thy fearful symmetry?’ asked William Blake, referring to the tiger. Nature’s patterns are a source of inspiration and awe, and also of scientific problems. Have you ever wondered why tigers have stripes but leopards have spots? Did you know that some jet aircraft fly sideways? Or that snails are seldom left-handed? Did you realize that chaos can be used to design textiles? And have you ever tried to work out how a three-legged dog would walk?
Philosophers and scientists, from Plato to Dirac, have been so impressed by the patterns visible in the natural world that they have declared God a mathematician. The signature of a Dicing Deity is chaos, and the signature of a Geometer God is symmetry. Paradoxically, it is the breaking of symmetry that is responsible for many of nature’s patterns.
Fearful Symmetry will open your eyes to the broken symmetries that lie all around you, from the shapes of clouds to the drops of dew on a spider’s web, from the glittering facets of a diamond to the hoofbeats of the Alpine course, from centipedes to corn circles. It will take you into the depths of the atom, where broken symmetry controls the four basic forces of nature, and to the farthest reaches of the universe, where unimaginably large structures formed by millions of galaxies cast doubt upon current theories of the cosmos. It will bring you face-to-face with some of the deepest questions of modern science: the arrow of time, the handedness of life, and the origins of biological form.
Ian Stewart is Professor of Mathematics at the University of Warwick, and the author of over fifty books including Game, Set, and Math (Blackwell Publishers, 1989). He writes the Mathematical Recreations column in Scientific American and often appears in New Scientist and on radio. He is a research mathematician working on dynamical systems, aiming to develop practical applications of new ideas from pure mathematics. As a hobby he reads science fiction and keeps fish.
Martin Golubitsky is Cullen Distinguished Professor of Mathematics and Director of the Institute for Theoretical and Engineering Science at the University of Houston. He has written extensively both on how symmetries are useful when solving mathematical models and what implications these ideas have for experiments. Recently Golubitsky has concentrated his efforts on how symmetry and chaos combine to generate a new method for pattern formation. He is on the editorial boards of a number of scholarly journals.
Both authors were drawn together by a common interest in the application of new mathematical ideas to scientific problems, worked together for a year in Houston between 1983 and 1984, and have been collaborating intermittently on various projects ever since.