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Sunday, December 6, 2020

The Undoing

Filed under: General — m759 @ 10:16 PM

Today’s earlier post “Binary Coordinates” discussed a Dec. 6
revision to the Wikipedia article on PG(3,2), the projective
geometry of 3 dimensions over the 2-element field GF(2).

The revision, which improved the article, was undone later today
by a clueless retired academic, one William “Bill” Cherowitzo,
a professor emeritus of mathematics at U. of Colorado at Denver.
(See his article “Adventures of a Mathematician in Wikipedia-land,”
MAA Focus , December 2014/January 2015.)

See my earlier remarks on this topic . . . specifically, on this passage —

“A 3-(16,4,1) block design has 140 blocks
of size 4 on 16 points, such that each triplet
of points is covered exactly once. Pick any
single point, take only the 35 blocks
containing that point, and delete that point.
The 35 blocks of size 3 that remain comprise
a PG(3,2) on the 15 remaining points.”

As I noted on November 17, this is bullshit. Apparently Cherowitzo
never bothered to find out that an arbitrary  “3-(16,4,1) block design”
(an example of a Steiner quadruple system ) does not  yield a PG(3,2).

PG(3,2) is derived from the classical  3-(16,4,1) block design formed by the affine
space of 4 dimensions over GF(2).  That  design has 322,560 automorphisms.
In contrast, see a 3-(16,4,1) block design that is  automorphism-free.

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