# Symmetry, Herman Weyl, from James Sogi

July 22, 2007 |

Herman Weyl's Symmetry, is a small book, modest in approach, but has huge ideas addressing core issues in philosophy, math and markets. He addresses symmetry from a generalized qualitative method, gives fascinating specific examples from biology, phylogeny, ontogeny, crystals, bee honeycombs, Egyptian, Greek, Persian, Sumerian art, math, physics and then generalizes to a an astonishing mathematical model right in line with the speculative approach with a multitude of trading applications. One of most fundamental ideas is that symmetry is more than just an aesthetic quality, but one of the core laws of the universe and leading to predictive application.

Symmetry arises from the very mapping of space and time and lies at the core of relativistic thought. Time is symmetry in the past and future revolving around the here and now relative to light and the point of observation. It is present in all higher life as bilateral symmetry. Life has laevo and dextro forms, a left and right. A regular symmetry in time is called rhythm in music. Art forms are filled with examples of symmetrical patterns in friezes, architecture, vases, floor tiles, in art. Symmetry is the basis of beauty and aesthetics. Curiously, in all life, my daughter tells me, DNA is left handed.

The quantitative model defines symmetries by defining the groups and examining the congruencies or mirror images in 2d or crystalline structures in 3d and reality in 4d or higher dimensions. The simple form of the bilateral congruencies, which applies to market common two axis lattice approaches is AB-BC: AC. By examining the mirror images, one can define the axis of rotation with obvious market application at 1/2a. Weyl examines transformations of the groups and claims that there are limited essentially different congruencies, which for markets can basically be described as patterns. The underlying characteristics can be rigorously defined.

In one of the most fascinating sections of the book, Weyl discusses the problem that the Pythagoreans guarded as a great secret and divides the schools of geometers from the algebraists. The essential problem is that algebra cannot solve the relation of a diagonal with its squares due to the irrationality of the square root of two, or curves due to pi, but solutions to that and many other problems can be solved with a ruler and compass. Weyl introduces Cartesian manipulation to solve the Pythagorean dilemma that was solved in in Universal Math using simple arithmetic and avoiding the irrational number problem.

Market symmetry is found in its basic microstructure of bid and ask. There is essential symmetry in the market negative correlation. The key is to find the axis of symmetry. Here is the key to investing, trading and identifying changes in cycles as well.

Weyl's method of defining auto morphisms Symmetry underlies Chair's examples such as Lobogola, cane investing, release, consummation, penumbras. No less important are the asymmetries of drift, vig, information. The market desires and demands symmetry. It is not satisfied until the moves are consummated. There is the symmetry of equal length of moves in the waves of various durations and in the retracements. Sometimes simple symmetries provide the greatest profits without resort to math but by use of two fingers.

## Bill Egan notes:

I have a different example for you. Drugs are asymmetric; highly symmetric molecules generally do not work well in optimization programs in drug discovery. I refer to the actual 2-D/3-D shape of the molecule.