Symmetry: A Journey into the Patterns of Nature
Marcus du Sautoy
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Symmetry is all around us. Our eyes and minds are drawn to symmetrical objects, from the pyramid to the pentagon. Of fundamental significance to the way we interpret the world, this unique, pervasive phenomenon indicates a dynamic relationship between objects. In chemistry and physics, the concept of symmetry explains the structure of crystals or the theory of fundamental particles; in evolutionary biology, the natural world exploits symmetry in the fight for survival; and symmetry—and the breaking of it—is central to ideas in art, architecture, and music.
Combining a rich historical narrative with his own personal journey as a mathematician, Marcus du Sautoy takes a unique look into the mathematical mind as he explores deep conjectures about symmetry and brings us face-to-face with the oddball mathematicians, both past and present, who have battled to understand symmetry's elusive qualities. He explores what is perhaps the most exciting discovery to date—the summit of mathematicians' mastery in the field—the Monster, a huge snowflake that exists in 196,883-dimensional space with more symmetries than there are atoms in the sun.
What is it like to solve an ancient mathematical problem in a flash of inspiration? What is it like to be shown, ten minutes later, that you've made a mistake? What is it like to see the world in mathematical terms, and what can that tell us about life itself? In Symmetry, Marcus du Sautoy investigates these questions and shows mathematical novices what it feels like to grapple with some of the most complex ideas the human mind can comprehend.
Scientists talk about the left-handed universe, but no one really knows which wind is blowing to cause our amino acids to spin that way. The connections between symmetry and molecular structure led during the course of the twentieth century to a new dialogue between chemists, biologists and mathematicians. The other sciences began to tap into the power of mathematics to reveal the different shapes that were possible for these molecular configurations. Indeed, microbiologists discovered that some
is an example of how all these different triangles can be pieced together to approximate the sphere, the shape with ultimate symmetry. Fig. 73 A polyhedron made up of 120 equilateral triangles and 60 isosceles triangles. Klug and Caspar also came up with a different model for the formation of the shell of the polio virus. Again, symmetry came to the rescue as a way to collect the 180 protein pieces together. Just as the perfectly symmetrical sphere is the surface of minimum energy which a
But modern science has revealed that symmetry is key not only to the very tiny organisms of nature, but to one of the greatest mysteries of biology–the functioning of the mind itself. Mirrors in the mind Evolution has programmed us to be oversensitive to symmetry. Those that can spot a pattern with reflectional symmetry in the chaotic tangle of the jungle are more likely to survive. Symmetry in the undergrowth is either someone about to eat you or something you could eat. Our brains seem to
theory. If card D has a vowel on the other side, then the theory is false. It seems that our subconscious works according to a sort of symmetrical logic. It thinks that if the statement ‘if A then B’ is true, then so is its converse, the mirror image ‘if B then A’. In general, this is far from true. Logical deduction is usually very unsymmetrical. There is a whole school of psychology that tries to explain the mechanism of the subconscious in terms of this desire for a symmetrical logic. The
had been built. There were just two that remained out there in the mists: the Monster and Janko’s fourth group. The evidence for the existence of this pair was very convincing, but mathematicians still had the task of constructing something whose symmetries matched up with the numbers that were being predicted. Conway’s Atlas now contained extensive information about the Monster, even though the Cambridge team still weren’t sure that it really existed. One useful piece of information was the