Log24

Tuesday, June 17, 2014

Finite Relativity

Filed under: General,Geometry — Tags: , — m759 @ 11:00 AM

Continued.

Anyone tackling the Raumproblem  described here
on Feb. 21, 2014 should know the history of coordinatizations
of the 4×6 Miracle Octad Generator (MOG) array by R. T. Curtis
and J. H. Conway. Some documentation:

The above two images seem to contradict a statement by R. T. Curtis
in a 1989 paper.  Curtis seemed in that paper to be saying, falsely, that
his original 1973 and 1976 MOG coordinates were those in array M below—

This seemingly false statement involved John H. Conway's supposedly
definitive and natural canonical coordinatization of the 4×6 MOG
array by the symbols for the 24 points of the projective line over GF(23)—
{∞, 0, 1, 2, 3… , 21, 22}:

An explanation of the apparent falsity in Curtis's 1989 paper:

By "two versions of the MOG" Curtis seems to have meant merely that the
octads , and not the projective-line coordinates , in his earlier papers were
mirror images of the octads  that resulted later from the Conway coordinates,
as in the images below.

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