Log24

Wednesday, August 15, 2018

An Exceptional Isomorphism

Filed under: General,Geometry — Tags: , , — m759 @ 5:40 AM

Why PSL(2,7) is isomorphic to GL(3.2)

From previous posts on this topic —

http://www.log24.com/log/pix18/180813-Structure_and_Sense-post-160606.gif

http://www.log24.com/log/pix18/180813-Knight_Moves-080116-page-top.gif

Tuesday, August 14, 2018

D8ing

Filed under: General,Geometry — Tags: , , , — m759 @ 12:06 AM

(Continued)

http://www.log24.com/log/pix18/180813-Ezra_Brown-PSL(2,7)-GL(2,3)-Oct-2009.jpg

http://www.log24.com/log/pix18/180814-Knight_Moves-archived-May_9_2008-500w.jpg

Thursday, August 9, 2018

Drama Queen in Yellow Dress

Filed under: General — Tags: — m759 @ 9:09 PM

http://www.log24.com/log/pix18/180809-Jessica_Jones-S1-E10-ca-28-min-in-500w.jpg

Related literature —

  http://www.log24.com/log/pix18/180809-White_Horse_Wings-As-if.jpg

Related video —

(Recall, in light of the previous post, that
Apollo is the lord of the dance.)

The Girl in the Yellow Dress
(from the Broadway musical "Contact")

True Grids

Filed under: General,Geometry — Tags: , — m759 @ 7:59 PM

From a search in this journal for "True Grid,"
a fanciful description of  the 3×3 grid —

"This is the garden of Apollo,
the field of Reason…."
John Outram, architect    

A fanciful instance of the 4×2 grid in
a scene from the film "The Master" —

IMAGE- Joaquin Phoenix, corridor scene in 'The Master'

A fanciful novel referring to the number 8,
and a not -so-fanciful reference:

http://www.log24.com/log/pix18/180809-The_EIght-and-coordinates-for-PSL(2,7)-actions-500w.jpg

Illustrated above are Katherine Neville's novel The Eight  and the
"knight" coordinatization of the 4×2 grid from a page on the exceptional
isomorphism between PSL(3,2) (alias GL(3,2)) and PSL(2,7) — groups
of, respectively, degree 7 and degree 8.

Literature related to the above remarks on grids:

Ross Douthat's New York Times  column yesterday purported, following
a 1946 poem by Auden, to contrast students of the humanities with
technocrats by saying that the former follow Hermes, the latter Apollo.

I doubt that Apollo would agree.

Wednesday, August 8, 2018

Synchronology

Filed under: General — Tags: , , — m759 @ 6:29 AM

Dates from math forums mentioned in the previous post

Dec. 7, 2016  and  Aug. 2, 2010.

Connoisseurs of synchonology may like to click on those dates.

8/8

Filed under: General,Geometry — Tags: , , , — m759 @ 6:00 AM

From mathoverflow.net on Dec. 7, 2016 —

The exceptional isomorphism between
PGL(3,2) and PSL(2,7): geometric origin?

Essentially the same question was asked earlier at

math.stackexchange.com on Aug. 2, 2010.

See also this  journal in November 2017 —

"Read something that means something."
                — New Yorker  ad

'Knight' octad labeling by the 8 points of the projective line over GF(7) .

Background — Relativity Problem in Log24.

Tuesday, August 7, 2018

Annals of E-Romance:

Filed under: General — Tags: , — m759 @ 2:22 AM

Smartphone Meets Laptop —

http://www.log24.com/log/pix18/180807-Jessica_Jones-S1-E13-AKA-Smile-smartphone-meets-laptop.jpg

Some related narrative from the previous post

“All right, Jessshica. It’s time to open the boxsssschhh.”

Monday, August 6, 2018

The Girl with Kaleidoscope Eyes

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

http://www.log24.com/log/pix18/180806-Lexicon-image-search.jpg

“All right, Jessshica. It’s time to open the boxsssschhh.”

“Gahh,” she said. She began to walk toward the box, but her heart failed her and she retreated back to the chair. “Fuck. Fuck.” Something mechanical purred. The seam she had found cracked open and the top of the box began to rise. She squeezed shut her eyes and groped her way into a corner, curling up against the concrete and plugging her ears with her fingers. That song she’d heard the busker playing on the train platform with Eliot, “Lucy in the Sky with Diamonds”; she used to sing that. Back in San Francisco, before she learned card tricks. It was how she’d met Benny: He played guitar. Lucy was the best earner, Benny said, so that was mainly what she sang. She must have sung it five times an hour, day after day. At first she liked it but then it was like an infection, and there was nothing she could do and nowhere she could go without it running across her brain or humming on her lips, and God knew she tried; she was smashing herself with sex and drugs but the song began to find its way even there. One day, Benny played the opening chord and she just couldn’t do it. She could not sing that fucking song. Not again. She broke down, because she was only fifteen, and Benny took her behind the mall and told her it would be okay. But she had to sing. It was the biggest earner. She kind of lost it and then so did Benny and that was the first time he hit her. She ran away for a while. But she came back to him, because she had nothing else, and it seemed okay. It seemed like they had a truce: She would not complain about her bruised face and he would not ask her to sing “Lucy.” She had been all right with this. She had thought that was a pretty good deal.

Now there was something coming out of a box, and she reached for the most virulent meme she knew. “Lucy in the sky!” she sang. “With diamonds!”

•   •   •

Barry, Max. Lexicon: A Novel  (pp. 247-248).
Penguin Publishing Group. Kindle Edition.

Related material from Log24 on All Hallows' Eve 2013

"Just another shake of the kaleidoscope" —

Related material:

Kaleidoscope Puzzle,  
Design Cube 2x2x2, and 
Through the Looking Glass: A Sort of Eternity.

Thursday, April 5, 2018

D8

Filed under: General — Tags: , — m759 @ 10:00 PM

The above title may be regarded as a poetic variant
of the title of Katherine Neville's 1988 novel The Eight .

Related material —

See also The Black Queen, a note from 2001.

Wednesday, April 4, 2018

D8ing the Joystick

Filed under: General — Tags: , — m759 @ 11:45 PM

Or: "Show me all  the blueprints!"
— A saying attributed to Howard Hughes.

Krysten Ritter narrates a podcast that asks 'R We D8ting?'

From the Blacklist episode in the previous post, "Date," blueprints
allegedly describing the boiler room in the Denver Mint —

Note the Thrust/Translation Controller Assembly (TTCA) at upper left
and the Attitude Controller Assembly (ACA) at lower right.

A NASA publication dated April 1, 1971, illustrates the Attitude Controller —

Krysten Ritter was born more than ten years later, in 1981.

For more on Attitude Control, see Boiler Room in this journal.

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