What is the point of diamond theory -- Diamond Theory Forum

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Subject: What is the point of diamond theory
Author: Bob	[ Next Thread \| Previous Thread \| Next Message \| Previous Message ] Date Posted: 18:12:04 05/10/01 Thu What is the point of diamond theory? The pictures are pretty, but there are lots of pretty things to research in mathematics. Why is diamond theory more important than the other fields? Bob. [ Next Thread \| Previous Thread \| Next Message \| Previous Message ]

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[> Subject: Re: What is the point of diamond theory

Author:
Steve Cullinane
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Date Posted: 19:59:52 05/11/01 Fri

Dear Bob:

You ask what is the point of diamond theory.

Answer 1:

"...that profoundly serene and satisfying quality
which inheres in mathematics and in music and which may be described as the creation out of simple elements of a self-contained universe of forms."
- Edward Sapir, "The Grammarian and his Language," American Mercury 1:149-155, 1924

Answer 2:

As Weyl pointed out, symmetry is one of the most important concepts in mathematics (not to mention physics). Symmetry is often defined as invariance of some property under a group of transformations. Diamond theory is of aesthetic and pedagogical interest because what is invariant under its groups of tranformations is.... symmetry itself!

Answer 3:

Diamond theory provides insight (via the MOG of R. T. Curtis) into the structure of M24 -- the most interesting finite group, according to J. H. Conway.

I don't claim that diamond theory is more important than other fields, but that it forms a natural part of the fields of finite geometry, finite group theory, and combinatorics.

Yours truly, Steve Cullinane

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