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.
