"Tiger, tiger, burning bright: In the forests of the night,
What immortal hand or eye: Could frame thy fearful symmetry?" -- William Blake
Fearful symmetry? William Blake, alluded to the beauty of the fearful tiger! Nature's patterns are a source of inspiration and awe; though with numerous scientific problems. Philosophers and scientists, impressed by the natural world's prevalent patterns, have declared God a master mathematician. King Ptolemy inquired, somewhat attentively, after Euclid had shown him his treatise on geometry, "Cannot the problems be made easier?" to which the geometer replied, "There is no royal road to geometry." This is true when applied to Symmetry, itself, a royal road leading us to divine wisdom, if we will but perceive its meaning and grasp its ideas . Have you ever wondered why tigers have stripes but leopards have spots? Did it ever occur to you that snails are seldom left-handed? If chaos is the signature of a Dicing Deity, then symmetry is the signature of a Geometer God.
Symmetry exists in all facets of life, and we see it as a manifestation of harmony and beauty by proportionality and balance that aesthetics imparts. This accessible book employs the mathematical concepts of symmetry to portray fascinating aspects of the physical and biological world. Paradoxically, it is the breaking of symmetry that is responsible for many of nature's patterns. Fearful Symmetry will zoom your focus on the broken symmetries that lie all around us, from the shapes in the clouds to the silken lines of a spider's web, from the hoof beats of a galloping horse to the sparkling surfaces of a diamond. It will take your imagination into the microsphere of the atom, where broken symmetry controls the quantum forces of nature; and to the farthest reaches of the galaxies, where black holes cast doubt on current theories of the universe. It will bring you face to face with the deepest mysteries of cosmic science: the origins of biological form, a Clue to the left-handed protein root of life on earth.
Almost a decade after his amazing historical overview of nonlinear science in, "Does God play dice?" comes Ian Stewart's "Is God a Geometer," full of brisk ideas and a fascinating expounding, while introducing the concept of Breaking Symmetry! The authors provide an introduction to symmetry within basic group theory in the early chapters, for readers who did not acquire a background in mathematics, but you don't need much mathematics to drive you through the book. Group Theory is a mathematical method by which aspects of molecular symmetry can be determined, revealing information about its properties like structure, spectra, and polarity. The following chapters explore the application of such ideas to various fields of natural forms, crystals, astronomy, molecular biology, and animal canter, trot, or walk. There is a discussion on the relationship between symmetry and chaos, and finally a philosophical debate on the extent to which symmetry is in the mind of the beholder, and does it mean us or the intelligent Designer?
Recently Golubitsky has focused his efforts on how symmetry and chaos combine to generate a new method for pattern formation. The two authors were drawn together by a common interest in the application of new mathematical concepts to scientific problems, working together for a year in Texas, collaborating on various projects ever since.