Log24

Sunday, December 3, 2023

Red Skull and the Tesseract Box

Filed under: General — Tags: — m759 @ 8:48 pm

Related art by Basquiat

Click on the above image for an Instagram description of its source.
See also related artistic remarks in this  journal on the date of that
Instagram description — October 17, 2022.

Wednesday, November 29, 2023

For a Labyrinth of Solitude

Filed under: General — Tags: , — m759 @ 11:24 am

Friday, November 24, 2023

Pioneering Pedagogy

Filed under: General — Tags: , — m759 @ 10:59 am

A Harvard Crimson  piece from Tuesday, November 21, 2023 —

See also "Pedagogy" in this  journal.

Wednesday, November 22, 2023

For E. Lily Yu* — Devs Setting

Filed under: General — Tags: , , , — m759 @ 12:49 pm
 

Friday, July 11, 2014

Spiegel-Spiel des Gevierts

Filed under: Uncategorized — m759 @ 12:00 PM

See Cube Symbology.

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

Da hats ein Eck 

* Author of Jewel Box: Stories  ( Erewhon Books, Oct. 24, 2023).

Tuesday, October 24, 2023

A Bond with Reality:  The Geometry of Cuts

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


Illustrations of object and gestures
from finitegeometry.org/sc/ —

Object

Gestures

An earlier presentation of the above
seven partitions of the eightfold cube:

Seven partitions of the 2x2x2 cube in a book from 1906

Related mathematics:

The use  of binary coordinate systems
as a conceptual tool

Natural physical  transformations of square or cubical arrays
of actual physical cubes (i.e., building blocks) correspond to
natural algebraic  transformations of vector spaces over GF(2).
This was apparently not previously known.

See "The Thing and I."

and . . .

Galois.space .

 

Related entertainment:

Or Matt Helm by way of a Jedi cube.

Friday, October 13, 2023

Hungarian Puzzle

Filed under: General — Tags: , , — m759 @ 8:25 pm

See "Cube Space" + Lovasz.

This search was suggested by . . .

The conclusion of Solomon Golomb's
"Rubik's Cube and Quarks,"
American Scientist , May-June 1982 —

Saturday, September 16, 2023

A Cube for Casaubon

Filed under: General — Tags: , , — m759 @ 1:25 pm

The 1955 Levi-Strauss 'canonic formula' in its original context of permutation groups

Later . . .

Affine groups on small binary spaces

Sunday, May 14, 2023

“The Structure of Space”

Filed under: General — Tags: , , , — m759 @ 1:44 am

The above title. by one Lee E. Mosley, is from 

"CreateSpace Independent Publishing Platform;
1st edition (June 4, 2017).
"

From the preface —

"So simple . . . ."

"Building blocks"? — See the literature of pop physics.

Natural companions to building blocks, are, of course, 
"permutation groups."

See the oeuvre  of physics writer John Baez —
For instance, in a Log24 post from the above Mosley
publication date — June 4, 2017 —

Friday, May 5, 2023

For St. Corky Lee

Filed under: General — Tags: , — m759 @ 6:23 am

Today's Google Doodle honors a Chinese-American photographer
who reportedly died on January 27, 2021.

From his dies natalis  (birth into heaven, in the Catholic tradition) —

See as well some background on a Chinese-related cube.

Saturday, April 8, 2023

Annals of Journalism

Filed under: General — Tags: , — m759 @ 12:27 pm

Update of 12:31 PM ET —

The time  of this post, 12:27 PM ET,
suggests a 12/27 flashback:

Click the above image for a related Log24 post of 15 years ago today.

related literary remark —

"Imagine Raiders of the Lost Ark  set in 20th-century London, and then
imagine it written by a man steeped not in Hollywood movies but in Dante
and the things of the spirit, and you might begin to get a picture…."

— Doug Thorpe in an Amazon.com book reviewnot  of Dark Materials.

Saturday, March 18, 2023

Zu diesem Themenkreis

Filed under: General — Tags: , , , — m759 @ 9:01 am

From last night's update to the previous post

The use  of binary coordinate systems
as a conceptual tool

Natural physical  transformations of square or cubical arrays
of actual physical cubes (i.e., building blocks) correspond to
natural algebraic  transformations of vector spaces over GF(2).
This was apparently not previously known.

See "The Thing and I."

From a post of May 1, 2016

Mathematische Appetithäppchen:
Faszinierende Bilder. Packende Formeln. Reizvolle Sätze

Autor: Erickson, Martin —

"Weitere Informationen zu diesem Themenkreis finden sich
unter http://​www.​encyclopediaofma​th.​org/​index.​php/​
Cullinane_​diamond_​theorem
und http://​finitegeometry.​org/​sc/​gen/​coord.​html ."

Friday, January 13, 2023

The “Diamond Space” of Mazzola

Filed under: General — Tags: , , , , — m759 @ 11:30 am

The Source —

Some similar notions from my own work . . .

The "Digraph" of Mazzola might correspond to a directed graph
indicating the structure of a permutation, as at right below —

Mazzola's "Formula" might correpond to a matrix and translation that
transform the above "Space" of eight coordinates, and his "Gesture"
to a different way of generating affine transformations of that space . . . 
as in my webpage "Cube Space, 1984-2003."

Tuesday, December 27, 2022

The Forms of Being

Filed under: General — Tags: , — m759 @ 1:25 pm

"If the window is this matrix of ambi- or multivalence,
and the bars of the windows-the grid-are what help us
to see, to focus on, this matrix, they are themselves 
the symbol of the symbolist work of art. They function as
the multilevel representation through which the work of art
can allude, and even reconstitute, the forms of Being."

Page 59, Rosalind Krauss, "Grids," MIT Press,
October , Vol. 9 (Summer, 1979), pp. 50-64

Related material —

Click the above image for a related Log24 post of 15 years ago today.

A related literary remark —

"Imagine Raiders of the Lost Ark  set in 20th-century London, and then
imagine it written by a man steeped not in Hollywood movies but in Dante
and the things of the spirit, and you might begin to get a picture…."

— Doug Thorpe in an Amazon.com book review, not  of Dark Materials.

Wednesday, November 30, 2022

Three Representations

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

'Cube Bricks, 1984,' by Steven H. Cullinane

Cube Bricks, 1984

See also Impenetrability .

Tuesday, November 29, 2022

Mere Synchronology

The date — January 9, 2010 — of the Guardian  book review
in the previous post was noted here by a top 40 music list
from that same date in an earlier year.

Update of 4:07 AM ET the same morning:

Fans of Cormac McCarthy's recent adventures in unreality
might enjoy interpreting the time — 3:25 AM ET — of this post
as the date  3/25, and comparing the logos, both revisited
and new, in a Log24 post from 3/25 . . .

Helen Mirren with plastic Gankyil .

. . . with the logo of a venue whose motto is

"Reality is not enough."

Monday, November 28, 2022

Groups, Spaces, and Ripoffs

Filed under: General — Tags: , — m759 @ 8:21 pm

"Rubik's Cube, and the simpler [2x2x2] Super Cube, represent
one form of mathematical and physical reality."

— Solomon W. Golomb, "Rubik's Cube and Quarks:
Twists on the eight corner cells of Rubik's Cube
provide a model for many aspects of quark behavior
,"
American Scientist , Vol. 70, No. 3 (May-June 1982), pp. 257-259 

From the last (Nov. 14, 2022) of the Log24 posts now tagged Groups and Spaces

From the first (June 21, 2010) of the Log24 posts now tagged Groups and Spaces

Wednesday, November 16, 2022

Core

Filed under: General — Tags: , , , — m759 @ 8:29 pm

Monday, October 17, 2022

From the November 2022 Notices of the A.M.S.

Filed under: General — Tags: , , , — m759 @ 9:28 am

"Geometric Group Theory" by Matt Clay, U. of Arkansas

"This article is intended to give an idea about how
the topology and geometry of a space influences
the algebraic structure of groups that act on it and
how this can be used to investigate groups."

Notices  homepage summary

A more precise description of the subject . . .

"The key idea in geometric group theory is to study
infinite groups by endowing them with a metric and
treating them as geometric spaces."

— AMS description of the 2018  treatise
Geometric Group Theory , by Drutu and Kapovich

See also "Geometric Group Theory" in this  journal.

The sort of thing that most interests me, finite  groups
acting on finite  structures, is not included in the above
description of Clay's article. That description only
applies to topological  spaces.  Topology is of little use
for finite  structures unless they are embedded* in 
larger spaces that are continuous, not discrete.

* As, for instance, the fifty-six 3-subsets of an 8-set are
embedded in the continuous space of The Eightfold Way .

Sunday, October 16, 2022

The Demianova Epiphany

Filed under: General — Tags: , , , — m759 @ 12:23 pm

The inspiration for the previous post

See as well Top and Bottom in this  journal.

Images for Siri

Filed under: General — Tags: , , — m759 @ 11:49 am

See also the Log24 posts of July 26, 2011, now tagged Images for Siri.

For Broomsday: Turning Eight

Filed under: General — Tags: , , — m759 @ 11:00 am

From a search in this journal for Quaternion + Rotation

Quaternion Group Models.

Wednesday, October 12, 2022

Spatial K

Filed under: General — Tags: , , , — m759 @ 7:11 am

Time and Chance  continues …

Cube symmetry subgroup of order 8 from 'Geometry and Symmetry,' Paul B. Yale, 1968, p.21

Wednesday, October 5, 2022

Physicality

Filed under: General — Tags: , — m759 @ 12:06 pm

"Battles argues that 'the experience of the physicality
of the book is strongest in large libraries,' and stand
among the glass cube at the center of the British Library,
the stacks upon stacks in Harvard’s Widener Library, or
the domed portico of the Library of Congress and tell me
any differently."

— Ed Simon, Binding the Ghost: Theology, Mystery, and
the Transcendence of Literature. 
Hardcover – April 19, 2022.

IMAGE- Construction of 'Heaven Descending' lattice

… And back to cube:

Related meditation:  Beer Summit.

Sunday, September 4, 2022

Dice and the Eightfold Cube

Filed under: General — Tags: , , , , — m759 @ 4:47 pm

At Hiroshima on March 9, 2018, Aitchison discussed another
"hexagonal array" with two added points… not at the center, as
in the Gell-Mann picture above, but rather at the ends  of one of
a cube's four diagonal axes of symmetry.

See some related illustrations below. 

Fans of the fictional "Transfiguration College" in the play
"Heroes of the Fourth Turning" may recall that August 6,
another Hiroshima date, was the Feast of the Transfiguration.

Iain Aitchison's 'dice-labelled' cuboctahedron at Hiroshima, March 2018

The exceptional role of  0 and  in Aitchison's diagram is echoed
by the occurence of these symbols in the "knight" labeling of a 
Miracle Octad Generator octad —

Transposition of  0 and  in the knight coordinatization 
induces the symplectic polarity of PG(3,2) discussed by 
(for instance) Anne Duncan in 1968.

Thursday, April 7, 2022

Blue Cube Group

Filed under: General — Tags: , , , — m759 @ 10:47 am

For more advanced students . . .

.

Saturday, April 2, 2022

Special Talents

Filed under: General — Tags: — m759 @ 7:47 pm

See Mimzy.xyz and Mimsy.xyz.

Friday, March 18, 2022

Found† in Space*

Filed under: General — Tags: , , , — m759 @ 9:42 pm

* See Box16.space, Box16.group, and Box16.art

Not so found See Waymark Prize .

Wednesday, March 9, 2022

Supercube Space

Filed under: General — Tags: , , — m759 @ 12:31 am

The new URL supercube.space forwards to http://box759.wordpress.com/.

The term supercube  is from a 1982 article by Solomon W. Golomb.

The related new URL supercube.group forwards to a page that
describes how the 2x2x2 (or eightfold, or "super") cube's natural
underlying automorphism group is Klein's simple group of order 168.

For further context, see the new URL supercube.art.

For some background, see the phrase Cube Space in this journal. 

Monday, September 13, 2021

“What a Swell Party This Is” — Cole Porter

Filed under: General — Tags: — m759 @ 4:59 pm

Using the Dreidel*

Filed under: General — Tags: , , — m759 @ 3:53 pm

The date of the Rubber Ducky article in the previous post was . . .

November 11, 2019.

Synchronology check:

* A phrase by Woody Allen (NY Times , May 5, 2011).

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