4th
Symmetry: A ‘Key to Nature’s Secrets’
The five regular polyhedra. Plato argued in Timaeus that these were the shapes of the bodies making up the elements: earth consists of little cubes, while fire, air, and water are made of polyhedra with four, eight, and twenty identical faces, respectively. The fifth regular polyhedron, with twelve identical faces, was supposed by Plato to symbolize the cosmos.’ (Illustration Mike King)
“The Oxford English Dictionary tells us that symmetry is “the quality of being made up of exactly similar parts.” (…) A symmetry is a principle of invariance. That is, it tells us that something does not change its appearance when we make certain changes in our point of view—for instance, by rotating it or moving it. (…)
Laws of nature, in the modern sense of mathematical equations that tell us precisely what will happen in various circumstances, first appeared as the laws of motion and gravitation that Newton developed as a basis for understanding Kepler’s description of the solar system. From the beginning, Newton’s laws incorporated symmetry: the laws that we observe to govern motion and gravitation do not change their form if we reset our clocks, or if we change the point from which distances are measured, or if we rotate our entire laboratory so it faces in a different direction. (…)
It was already clear in the 1950s that the laws of nature, whatever they are, also respect symmetries of other kinds, having nothing directly to do with space and time. (…) Electromagnetic phenomena did not respect these symmetries: protons and some hyperons are electrically charged; neutrons and other hyperons are not. (…)
The recognition of accidental symmetry not only resolved the old puzzle about approximate symmetries; it also opened up exciting new possibilities. It turned out that there are certain symmetries that could not be violated in any theory that has the same particles and the same exact local symmetries as the Standard Model and that is simple enough to be renormalizable. (…)
There is an attractive theory, called chaotic inflation, according to which the universe began without any special spatial symmetries, in a completely chaotic state. Here and there by accident the fields pervading the universe were more or less uniform, and according to the gravitational field equations it is these patches of space that then underwent an exponentially rapid expansion, known as inflation, leading to something like our present universe, with all nonuniformities in these patches smoothed out by the expansion. In different patches of space the symmetries of the laws of nature would be broken in different ways. Much of the universe is still chaotic, and it is only in the patches that inflated sufficiently (and in which symmetries were broken in the right ways) that life could arise, so any beings who study the universe will find themselves in such patches. (…)
If it turns out that chaotic inflation is correct, then much of what we observe in nature will be due to the accident of our particular location, an accident that can never be explained, except by the fact that it is only in such locations that anyone could live.”
— Steven Weinberg, American theoretical physicist and Nobel laureate in Physics, Symmetry: A ‘Key to Nature’s Secrets’, The New York Review of Books, Oct 27, 2011
Marcus du Sautoy on Symmetry in Mathematics, and in Life | University of Oxford
In this fascinating lecture, Professor Marcus du Sautoy talks about his quest to discover Symmetry in Mathematics, and in Life. OUMNH 150th Anniversary.
Marcus du Sautoy is the Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford.
See also:
☞ Marcus du Sauto, “Finding Moonshine” lecture at Google’s Brussels office, 2010 (video)
☞ The Concept of Laws. The special status of the laws of mathematics and physics
