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The Diamond Theorem
Preprint
05 August 2013
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Summary
The mathematical discipline known as finite geometry was founded by Gino Fano in 1892. In 1962, Hans Freudenthal said of the axiomatic approach used by Fano (and later by Hilbert), "The bond with reality is cut." The diamond theorem may be viewed as restoring that bond. It describes a group of 322,560 permutations, later known as "the octad group," that now plays a role in speculative high-energy physics. See Moonshine, Superconformal Symmetry, and Quantum Error Correction .
Abstract
Finite projective geometry underlies the structure of the 35 square patterns in R. T. Curtis's Miracle Octad Generator, and also explains the surprising symmetry properties of some simple graphic designs.
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