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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