Friday, November 24, 2017

The Matrix Meets the Grid

Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 2:00 PM

The Matrix —

  The Grid

  Picturing the Witt Construction

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

Saturday, May 8, 2021

A Tale of Two Omegas

Filed under: General — 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.

Thursday, February 7, 2019

Geometry of the 4×4 Square: The Kummer Configuration

Filed under: General — Tags: , — m759 @ 12:00 AM

From the series of posts tagged Kummerhenge

A Wikipedia article relating the above 4×4 square to the work of Kummer —

A somewhat more interesting aspect of the geometry of the 4×4 square
is its relationship to the 4×6 grid underlying the Miracle Octad Generator
(MOG) of R. T. Curtis.  Hudson's 1905 classic Kummer's Quartic Surface
deals with the Kummer properties above and also foreshadows, without
explicitly describing, the finite-geometry properties of the 4×4 square as
a finite affine 4-space — properties that are of use in studying the Mathieu
group M24  with the aid of the MOG.

Sunday, September 3, 2017

Broomsday Revisited

Filed under: General,Geometry — m759 @ 9:29 AM

Ivars Peterson in 2000 on a sort of conceptual art —

" Brill has tried out a variety of grid-scrambling transformations
to see what happens. Aesthetic sensibilities govern which
transformation to use, what size the rectangular grid should be,
and which iteration to look at, he says. 'Once a fruitful
transformation, rectangle size, and iteration number have been
found, the artist is in a position to create compelling imagery.' "

"Scrambled Grids," August 28, 2000

Or not.

If aesthetic sensibilities lead to a 23-cycle on a 4×6 grid, the results
may not be pretty —

From "Geometry of the 4×4 Square."

See a Log24 post, Noncontinuous Groups, on Broomsday 2009.

Tuesday, May 8, 2012

Staging the Self

Filed under: General — m759 @ 9:29 AM

This post links to a column that
partially reveals the ending of
The Hunger Games  series of novels.

The title is from a column by Stanley Fish
on The Hunger Games  books in today's
online New York Times . The column
was posted at 9 PM EDT on May 7th, but I
did not see it until this morning.

Fish says—

"In the end… [spoiler details omitted]…
children… 'don’t know they play
on a graveyard'…."

For some literary background, see last night's post
on the May 7th, 2012, NY Times  obituaries as well
as the May 7th, 2006, Log24 post featuring 24 squares
arranged in a rectangular frame.

IMAGE- 4x6 grid

See also Frame Tales and, more generally,
The King and the Corpse.

"Et cetera, et cetera, et cetera." — Yul Brynner

Monday, November 27, 2017

The Golay Code via Witt’s Construction

Filed under: General,Geometry — Tags: — m759 @ 2:08 PM


Hansen, Robert Peter, "Construction and Simplicity of
the Large Mathieu Groups" (2011). Master's Theses. 4053. 

See also The Matrix Meets the Grid (Log24, Nov. 24).
More generally, see SPLAG in this journal.

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:

Another Gitterkrieg  image:

 The 24-set   Ω  of  R. T. Curtis

Click on the images for related material.

Monday, December 24, 2012

All Over Again

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

Octavio Paz —

"… the movement of analogy
begins all over once again."

See A Reappearing Number in this journal.


Figure 1 —

Background: MOG in this journal.

Figure 2 —

Image-- 'Then a miracle occurs' cartoon
Cartoon by S.Harris

Background —

Image-- Google search on 'miracle octad'-- top 3 results

Sunday, May 23, 2010

Annals of Conceptual Art

Filed under: General — Tags: , — m759 @ 2:02 AM

Josefine Lyche's
  "Theme and Variations" (Oslo, 2009)


Some images in reply—

  Frame Tale

Image by R. T. Curtis from 'Further Elementary Techniques...'

Click on images for further details.

"In the name of the former
and of the latter
and of their holocaust.

Finnegans Wake

Tuesday, July 10, 2007

Tuesday July 10, 2007

Filed under: General — m759 @ 8:00 AM
24 frames
in search of
a picture


Related material:


Friday, February 2, 2007

Friday February 2, 2007

Filed under: General — m759 @ 7:59 AM

Wednesday, May 24, 2006

Wednesday May 24, 2006

Filed under: General — m759 @ 3:00 PM
May 24

Related material:


Trinity and Counterpoint

Sunday, May 7, 2006

Sunday May 7, 2006

Filed under: General,Geometry — Tags: — m759 @ 3:00 AM

Bagombo Snuff Box
(in memory of
Burt Kerr Todd)

“Well, it may be the devil
or it may be the Lord
But you’re gonna have to
serve somebody.”

— “Bob Dylan”
(pseudonym of Robert Zimmerman),
quoted by “Bob Stewart”
on July 18, 2005

“Bob Stewart” may or may not be the same person as “crankbuster,” author of the “Rectangular Array Theorem” or “RAT.”  This “theorem” is intended as a parody of the “Miracle Octad Generator,” or “MOG,” of R. T. Curtis.  (See the Usenet group sci.math, “Steven Cullinane is a Crank,” July 2005, messages 51-60.)

“Crankbuster” has registered at Math Forum as a teacher in Sri Lanka (formerly Ceylon).   For a tall tale involving Ceylon, see the short story “Bagombo Snuff Box” in the book of the same title by Kurt Vonnegut, who has at times embodied– like Martin Gardner and “crankbuster“– “der Geist, der stets verneint.”

Here is my own version (given the alleged Ceylon background of “crankbuster”) of a Bagombo snuff box:

Related material:

Log24 entries of
April 16-30, 2005,

and the 5 Log24 entries
ending on Friday,
April 28, 2006.

Monday, April 25, 2005

Monday April 25, 2005

Filed under: General — m759 @ 10:31 AM

Mathematical Style:
Mac Lane Memorial, Part Trois

(See also Part I and Part II.)

“We have seen that there are many diverse styles that lead to success in mathematics. Choose one mathematician… from the ones we studied whose ‘mathematical style’ you find most rewarding for you…. Identify the mathematician and describe his or her mathematical style.”


— Sarah J. Greenwald,
take-home exam from
Introduction to Mathematics
at Appalachian State U.,
Boone, North Carolina

From today’s Harvard Crimson:

Ex-Math Prof Mac Lane, 95, Dies

[Saunders] Mac Lane was most famous for the ground-breaking paper he co-wrote with Samuel Eilenberg of Columbia in 1945 which introduced category theory, a framework to show how mathematical structures relate to each other. This branch of algebra has since influenced most mathematical fields and also has functions in philosophy and linguistics, but was first dismissed by many practical mathematicians as too abstract to be useful.

Gade University Professor of Mathematics Barry Mazur, a friend of the late Mac Lane, recalled that the paper had at first been rejected from a lower-caliber mathematical journal because the editor thought that it was “more devoid of content” than any other he had read.

“Saunders wrote back and said, ‘That’s the point,'” Mazur said. “And in some ways that’s the genius of it. It’s the barest, most Beckett-like vocabulary that incorporates the theory and nothing else.”

He likened it to a sparse grammar of nouns and verbs and a limited vocabulary that is presented “in such a deft way that it will help you understand any language you wish to understand and any language will fit into it.”

Beckett-like vocabulary
from April 24:


Also from Appalachian State University

(with illustration by Ingmar Bergman):

“In my hour of weakness,
that old enemy
tries to steal my soul.
But when he comes
like a flood to surround me
My God will step in
and a standard he’ll raise.”

Jesus Be a Fence

Related material:
The Crimson Passion

Sunday, April 24, 2005

Sunday April 24, 2005

Filed under: General — m759 @ 10:23 AM
April 24

Today’s sermon:


Sunday, June 15, 2003

Sunday June 15, 2003

Filed under: General,Geometry — Tags: — m759 @ 3:00 PM

Readings for Trinity Sunday

  1. Triune knot:
    Problems in Combinatorial Group Theory, 7 and 8, in light of the remark in Section 8.3 of Lattice Polygons and the Number 12 
  2. Cardinal Newman:
    Sermon 24
  3. Simon Nickerson:

For more on the structure
discussed by Nickerson, see

Raiders of the Lost Matrix:

For theology in general, see

Jews Telling Stories.

Tuesday, May 20, 2003

Tuesday May 20, 2003

Filed under: General — m759 @ 3:06 AM

Raiders of the Lost Matrix

“In general, a matrix is something that provides support or structure, especially in the sense of surrounding and/or shaping. It comes from the Latin word for ‘womb,’ itself derived from the Latin word for ‘mother,’ which is mater [as in alma mater].” — Wikipedia

For a mystical interpretation of the above matrix as it relates to the Hebrew words at the center of the official Yale seal, see Talmud


Powered by WordPress