Log24

Tuesday, November 19, 2024

Language Games:  Overarching Meets Upcoming

Filed under: General — Tags: , — m759 @ 6:58 am

Sunday, November 17, 2024

The Belgian Music Box

Filed under: General — Tags: , , , — m759 @ 6:51 am

From a search in this  journal for Ghent —

Related art —

Weyl, Symmetry, and the MOG
(HTML version of an earlier post)

Filed under: General — Tags: , — m759 @ 1:16 am

Some historical background for a new book by Robert T. Curtis,
The Art of Working with the Mathieu Group M24 

"Space is another example of an entity endowed with a structure.
Here the elements are points, and the structure is established
in terms of certain basic relations between points such as:
A, B, C lie on a straight line, AB is congruent CD, and the like.
What we learn from our whole discussion and what has indeed
become a guiding principle in modern mathematics is this lesson:
Whenever you have to do with a structure endowed entity Σ
try to determine its group of automorphisms
, the group of those
element-wise transformations which leave all structural relations
undisturbed. You can expect to gain a deep insight into the
constitution of Σ in this way. After that you may start to investigate
symmetric configurations of elements, i.e. configurations which are
invariant under a certain subgroup of the group of all automorphisms;
and it may be advisable, before looking for such configurations,
to study the subgroups themselves, e.g. the subgroup of those
automorphisms which leave one element fixed, or leave two distinct
elements fixed, and investigate what discontinuous or finite subgroups
there exist, and so forth."

— Hermann Weyl, Symmetry, Princeton University Press, 1952.
(Page 144 in the Princeton Science Library edition of 1989.)

4×4 Square
       
       
       
       

This square's automorphism group
has 322,560 transformations.

— The diamond theorem  of Steven H. Cullinane.

4×6 Rectangle
           
           
           
           

This rectangle's automorphism group
has 244,823,040 transformations.

— The Miracle Octad Generator  (MOG) of Robert T. Curtis.

The rectangle's automorphism group contains the
square's as a subgroup. The square's automorphism
group leaves invariant a set of 30 eight-subsquare sets
called affine hyperplanes. The rectangle's automorphism
group leaves invariant a set of 759 eight-subsquare sets
called octads.

View this post as a PDF.

Saturday, November 16, 2024

MORA for Lucy (A Memorable Watson)

Filed under: General — Tags: , — m759 @ 12:53 pm

Another interesting role for Liu — Head of MORA . . .

As for Mythological Oversight and Restoration . . .

Kaleidoscope, continued (August 11, 2005).

Related mythological material from August 11, 2005 —

Mysteries of the Rectangle :

Automorphism Groups: Examples for Weyl

Filed under: General — Tags: — m759 @ 3:17 am

View a PDF of this post.

Keywords: Weyl, symmetry, group, automorphism,
octad, MOG, Curtis, Cullinane.

Friday, November 15, 2024

Art Tales

Filed under: General — Tags: , — m759 @ 7:53 am

From a search in this journal for Arkani-Hamed —

This post was suggested by the title

"Visualizing a sacred city: London, art, and religion"

from today's 7 AM post.

Thursday, November 14, 2024

A Certain Character

Filed under: General — Tags: — m759 @ 9:50 am

"What we do may be small, but it has
  a certain character of permanence."

— G. H. Hardy, A Mathematician's Apology

Wednesday, November 13, 2024

Sigma Sweethearts

Filed under: General — Tags: — m759 @ 10:17 pm

Related reading — Valéry + group in this journal.

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