Log24

Tuesday, July 7, 2026

Affine-Group Generation by Permutation of Parallel Subspaces

Filed under: General — Tags: , — m759 @ 6:38 pm

Compare Google AI Mode with Grok . . .

AI Mode says a conjecture on affine group generation in binary spaces is false, 
but Grok says it is true.  Which conclusion is correct? Does either AI actually
supply a valid proof for its conclusion?

https://x.com/i/grok/share/e6c7759afbe9437da3be55d6cafa8269

For Steiner's "language animals" . . . and now language models . . .

Logos

IMAGE- Current math.stackexchange.com logo and a 1984 figure from 'Notes on Groups and Geometry, 1978-1986'

Saturday, May 23, 2026

“Faltering Beginnings” . . . AI Benchmark

Filed under: General — Tags: — m759 @ 9:25 am

260523-Google-ideas-to-images-benchmark-test.jpg

260523-Google-ideas-to-images-benchmark-test-result.jpg

“The Zero Theorem” —
Faltering Beginnings . . . The Bucharest Version

Filed under: General — Tags: , , , , — m759 @ 12:05 am

For Christopher Nolan, a different perspective on the world of Odysseus.

Friday, May 22, 2026

“The Faltering Beginnings of Logic” — Phrase by Paul Valéry

Filed under: General — Tags: , , — m759 @ 12:16 pm

Vide  the May 2026  Notices of the American Mathematical Society . . .

For Mert Lawwill, Champion Motorcylist —
Zen and the Art of Metaphysics

Filed under: General — Tags: , , , — m759 @ 4:29 am

Lawwill reportedly died at 85 on May 6, 2026, in Meridian, Idaho.

From this journal on that date (Oz Space. . .

"And let us finally, then, observe the
parallel progress of the formations of thought
across the species of psychical onomatopoeia
of the primitives, and elementary symmetries
and contrasts, to the ideas of substances,
to metaphors, the faltering beginnings of logic,
formalisms, entities, metaphysical existences."

— Paul Valéry, Introduction to the Method of
    Leonardo da Vinci

Robert M. Pirsig,  Zen and the Art of Motorcycle Maintenance ,
Ch. 6 (italics are mine) —

“A classical understanding sees the world primarily as underlying form  itself.
A romantic understanding sees it primarily in terms of immediate appearance .”

Illustration

Diamond theorem illustrations

Thursday, May 21, 2026

Returning to Bunker Hill Community College . . .

Filed under: General — Tags: , , — m759 @ 8:31 am
 

Thursday, August 21, 2014

Nox  — m759 @ 1:00 AM

( A sequel to  Lux )

“By groping toward the light we are made to realize
how deep the darkness is around us.”

— Arthur Koestler, The Call Girls: A Tragi-Comedy ,
Random House, 1973, page 118

Robin Williams and the Stages of Math

i)   shock & denial
ii)  anger
iii) bargaining
iv) depression
v)  acceptance

A related description of the process —

“You know how sometimes someone tells you a theorem,
and it’s obviously false, and you reach for one of the many
easy counterexamples only to realize that it’s not a
counterexample after all, then you reach for another one
and another one and find that they fail too, and you begin
to concede the possibility that the theorem might not
actually be false after all, and you feel your world start to
shift on its axis, and you think to yourself: ‘Why did no one
tell me this before?’ “

— Tom Leinster yesterday at The n-Category Café

See as well yesterday's post on a
possibly true mathematical theorem,

Benchmarking the New Google Search Box.

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