Log24

Saturday, May 8, 2021

A Tale of Two Omegas

Filed under: General — Tags: , — m759 @ 5:00 am

The Greek capital letter Omega, Ω, is customarily
used to denote a set that is acted upon by a group.
If the group is the affine group of 322,560
transformations of the four-dimensional
affine space over the two-element Galois field,
the appropriate Ω is the 4×4 grid above.

See the Cullinane diamond theorem .

If the group is the large Mathieu group  of
244,823,040 permutations of 24 things,
the appropriate Ω  is the 4×6 grid below.

See the Miracle Octad Generator  of R. T. Curtis.

Sunday, May 6, 2018

The Osterman Omega

Filed under: General,Geometry — Tags: , — m759 @ 5:01 pm

From "The Osterman Weekend" (1983) —

Counting symmetries of the R. T. Curtis Omega:

An Illustration from Shakespeare's birthday

Counting symmetries with the orbit-stabilizer theorem

Monday, January 12, 2015

Points Omega*

Filed under: General,Geometry — Tags: , , , — m759 @ 12:00 pm

The previous post displayed a set of
24 unit-square “points” within a rectangular array.
These are the points of the
Miracle Octad Generator  of R. T. Curtis.

The array was labeled  Ω
because that is the usual designation for
a set acted upon by a group:

* The title is an allusion to Point Omega , a novel by
Don DeLillo published on Groundhog Day 2010.
See “Point Omega” in this journal.

Sunday, September 18, 2011

Alpha and Omega

Filed under: General,Geometry — Tags: , — m759 @ 2:22 am

http://www.log24.com/log/pix11B/110918-AlphaAndOmega.jpg

A transcription—

"Now suppose that α  is an element of order 23 in M 24 ; we number the points of Ω
as the projective line , 0, 1, 2, … , 22 so that α : i i  + 1 (modulo 23) and fixes . In
fact there is a full L 2 (23) acting on this line and preserving the octads…."

— R. T. Curtis, "A New Combinatorial Approach to M 24 ,"
Mathematical Proceedings of the Cambridge Philosophical Society  (1976), 79: 25-42

Saturday, March 23, 2024

Alpha Bets

Filed under: General — Tags: , — m759 @ 6:31 am

"So you wanna play with magic?" — Katy Perry

Friday, August 19, 2022

The Guy Embedding

Filed under: General — Tags: , , — m759 @ 3:43 pm

M. J. T. Guy discovered that the lexicographic  version
of the Golay code contains, embedded within it, the
Miracle Octad Generator  (MOG)  of R. T. Curtis.

For 12 basis vectors of the lexicographic version, see below.

Basis vectors for the lexicographic version of the binary Golay code

For some context, click the embedded guy.

For a closely related, but simpler, mathematical
structure, see posts tagged The Omega Matrix.

Saturday, September 11, 2021

Reality for Academia

Filed under: General — Tags: — m759 @ 4:16 pm

The title of the previous post, "Ground Omega," suggests a related  nightmare . . .

A writer of fiction in the previous post

"When we say a thing is unreal, we mean it is too real…."

Old joke —

"What you mean 'we,' paleface?"

At Ground Omega  in the above My Hero Academia  site —

"The twenty-four students are split into six groups of four…."

I prefer the similar splittings of  the Curtis  Omega

Wednesday, May 26, 2021

Heavy Metaphor

Filed under: General — Tags: , — m759 @ 9:51 pm

Earlier posts that are also tagged "Points Omega" suggest some 
context for a May 19 New Republic  illustration.

      x -1/x
 

  See as well
"Flowers and Brown."

Sunday, July 28, 2019

Review

Filed under: General — m759 @ 11:18 am

From a news article featured on the American Mathematical Society
home page today

A joint Vietnam-USA mathematical meeting in Vietnam on
June 10-13, 2019:

This  journal on June 12, 2019:

Wednesday, June 12, 2019

The Osterman Haiku

Filed under: General — m759 @ 11:32 PM Edit This

Click on the book cover below for posts tagged "Haiku."

'Point Omega' by DeLillo

See also the Twentieth of May, 2008 —

Welcome to the Garden Club, Pilgrim.

Wednesday, June 12, 2019

The Osterman Haiku

Filed under: General — m759 @ 11:32 pm

Click on the book cover below for posts tagged "Haiku."

IMAGE- 'Point Omega' by DeLillo

Wednesday, October 24, 2018

The Cracked Potter

Filed under: General — Tags: , — m759 @ 1:52 pm

See also an embedded ad in The Atlantic  magazine, Sept. 2017.

Tuesday, October 23, 2018

Simplicity Versus Complexity

Filed under: General — m759 @ 7:13 pm

Simplicity  (Click for some complexity.)

Complexity  (Click for some simplicity.)

A passage from the 2011 book Idea Man  that was suggested by
a recent New Yorker  article on the book's author, the late Paul Allen —

Left-click image to enlarge.

Sunday, October 21, 2018

Simplicity

Filed under: General — m759 @ 11:00 am


 

Sunday, January 11, 2015

Real Beyond Artifice

Filed under: General,Geometry — Tags: , , , , , — m759 @ 7:20 pm

A professor at Harvard has written about
"the urge to seize and display something
real beyond artifice."

He reportedly died on January 3, 2015.

An image from this journal on that date:

Confession in 'The Seventh Seal'

Another Gitterkrieg  image:

 The 24-set   Ω  of  R. T. Curtis

Click on the images for related material.

Tuesday, August 26, 2014

Lux et Veritas

Filed under: General,Geometry — m759 @ 7:59 am

Omega by Lux:

Mathieu and Omega Steps

Omega by Curtis:

Sunday, July 4, 2010

Brightness at Noon (continued)

Filed under: General,Geometry — Tags: , — m759 @ 12:00 pm

Today's sermon mentioned the phrase "Omega number."

Other sorts of Omega numbers— 24 and 759— occur
in connection with the set named Ω by R. T. Curtis in 1976—

Image-- In a 1976 paper, R.T. Curtis names the 24-set of his Miracle Octad Generator 'Omega.'

— R. T. Curtis, "A New Combinatorial Approach to M24,"
Math. Proc. Camb. Phil. Soc. (1976), 79, 25-42

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