Log24

Saturday, August 27, 2011

Cosmic Cube*

Filed under: General,Geometry — Tags: , , — m759 @ 12:25 PM

IMAGE- Anthony Hopkins exorcises a Rubik cube

Prequel (Click to enlarge)

IMAGE- Galois vs. Rubik: Posters for Abel Prize, Oslo, 2008

Background —

IMAGE- 'Group Theory' Wikipedia article with Rubik's cube as main illustration and argument  by a cuber for the image's use

See also Rubik in this journal.

* For the title, see Groups Acting.

Tuesday, July 11, 2017

Dialogue from Plato’s Cave

Filed under: General — Tags: — m759 @ 10:15 AM

At  scifi.stackexchange.com

Why was the Cosmic Cube named the Tesseract 
in the Marvel movie series? Is there any specific reason 
for the name change? According to me, Cosmic Cube
seems a nice and cooler name.

— Asked March 14, 2013, by Dhwaneet Bhatt
    
At least it wasn't called 'The AllSpark.' 
It's not out of the realm of possibility. 

— Solemnity, March 14, 2013

Saturday, April 13, 2013

Narrative

Filed under: General — m759 @ 6:16 PM

Two friends from Brooklyn —

"… both marveled at early Ingmar Bergman movies."

One of the friends' "humor was inspired by
surrealist painters and Franz Kafka."

Wikipedia

"Most of Marvel's fictional characters operate in
a single reality known as the Marvel Universe…."

This journal yesterday

    

Related material:  The Cosmic Cube.

Thursday, September 13, 2012

Backstory

Filed under: General — m759 @ 2:00 AM

Yesterday's online Los Angeles Times  
on a film that inspired recent protests in Cairo—

The film… was shown on June 23
to an audience of less than 10
at a theater on Hollywood Boulevard,
a source familiar with the screening said….
The screening was at The Vine Theater,
which rents itself out for private screenings,
said one person involved in the theater.

An image from this journal on that same day, June 23

IMAGE- Rudolf Koch's version of the 'double cross' symbol

    Source: Rudolf KochThe Book of Signs

For some background on the symbol, see Damnation Morning.

See also Don Henley's Hollywood hymn "Garden of Allah."

Update of 8 PM Sept. 13, 2012—

Other sources give the film's screening date not as June 23,
2012, but rather as June 30, 2012. (BBC News, LAWEEKLY blogs)

The following post from this journal on that  date may or
may not have some religious relevance.

Saturday, June 30, 2012

Snares

Filed under: Uncategorized — m759 @ 7:20 PM

"… to snare the spirits of mankind in nets of magic"

— The aim of the artist, according to Thomas Wolfe

Related entertainment—

High-minded— Many Dimensions .

Not so high-minded— The Cosmic Cube .

Saturday, June 30, 2012

Snares

Filed under: General — m759 @ 7:20 PM

"… to snare the spirits of mankind in nets of magic"

— The aim of the artist, according to Thomas Wolfe 

Related entertainment—

High-minded— Many Dimensions .

Not so high-minded— The Cosmic Cube .

Sunday, January 22, 2012

The Presbyterian Exorcist

Filed under: General — Tags: — m759 @ 9:26 AM

(Backstory— Presbyterian in this journal)

Princeton University Press on a book it will publish in March—

Circles Disturbed  brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier–"Don't disturb my circles"–words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds–stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities.

Exercise— Discuss the above paragraph's vulgarity.

Discuss also the more robust vulgarity of Marvel Entertainment

Context— "Marvel" in this journal, and The Cosmic Cube.

Sunday, November 6, 2011

Design Sermon

Filed under: General,Geometry — m759 @ 11:00 AM

''Most people make the mistake of thinking design is what it looks like,''
says Steve Jobs, Apple's C.E.O. ''People think it's this veneer—
that the designers are handed this box and told, 'Make it look good!'
That's not what we think design is. It's not just what it looks like and feels like.
Design is how it works.''

— "The Guts of a New Machine," by Rob Walker,
New York Times Magazine , Sunday, Nov. 30, 2003

IMAGE- June 29, 2011, review of Zenna Henderson's 'The Anything Box'

See also, from the day of the above Anything Box  review—
St. Peter's Day, 2011— two Log24 posts—
The Shattered Mind and Rome After Dark.

Related boxes… Cosmic Cube and Design Cube.

Sunday, August 28, 2011

The Cosmic Part

Filed under: General,Geometry — Tags: — m759 @ 6:29 PM

Yesterday's midday post, borrowing a phrase from the theology of Marvel Comics,
offered Rubik's mechanical contrivance as a rather absurd "Cosmic Cube."

A simpler candidate for the "Cube" part of that phrase:

http://www.log24.com/log/pix10/100214-Cube2x2x2.gif

The Eightfold Cube

As noted elsewhere, a simple reflection group* of order 168 acts naturally on this structure.

"Because of their truly fundamental role in mathematics,
even the simplest diagrams concerning finite reflection groups
(or finite mirror systems, or root systems—
the languages are equivalent) have interpretations
of cosmological proportions."

Alexandre V. Borovik in "Coxeter Theory: The Cognitive Aspects"

Borovik has a such a diagram—

http://www.log24.com/log/pix11B/110828-BorovikM.jpg

The planes in Borovik's figure are those separating the parts of the eightfold cube above.

In Coxeter theory, these are Euclidean hyperplanes. In the eightfold cube, they represent three of seven projective points that are permuted by the above group of order 168.

In light of Borovik's remarks, the eightfold cube might serve to illustrate the "Cosmic" part of the Marvel Comics phrase.

For some related theological remarks, see Cube Trinity in this journal.

Happy St. Augustine's Day.

* I.e., one generated by reflections : group actions that fix a hyperplane pointwise. In the eightfold cube, viewed as a vector space of 3 dimensions over the 2-element Galois field, these hyperplanes are certain sets of four subcubes.

Friday, May 13, 2011

Apollo’s 13

Filed under: General,Geometry — Tags: — m759 @ 6:36 AM

Continued … See related previous posts.

IMAGE- The 13 symmetry axes of the cube

Those who prefer narrative to mathematics
may consult Wikipedia on The Cosmic Cube.

Tuesday, May 10, 2011

Groups Acting

Filed under: General,Geometry — Tags: — m759 @ 10:10 AM

The LA Times  on last weekend's film "Thor"—

"… the film… attempts to bridge director Kenneth Branagh's high-minded Shakespearean intentions with Marvel Entertainment's bottom-line-oriented need to crank out entertainment product."

Those averse to Nordic religion may contemplate a different approach to entertainment (such as Taymor's recent approach to Spider-Man).

A high-minded— if not Shakespearean— non-Nordic approach to groups acting—

"What was wrong? I had taken almost four semesters of algebra in college. I had read every page of Herstein, tried every exercise. Somehow, a message had been lost on me. Groups act . The elements of a group do not have to just sit there, abstract and implacable; they can do  things, they can 'produce changes.' In particular, groups arise naturally as the symmetries of a set with structure. And if a group is given abstractly, such as the fundamental group of a simplical complex or a presentation in terms of generators and relators, then it might be a good idea to find something for the group to act on, such as the universal covering space or a graph."

— Thomas W. Tucker, review of Lyndon's Groups and Geometry  in The American Mathematical Monthly , Vol. 94, No. 4 (April 1987), pp. 392-394

"Groups act "… For some examples, see

Related entertainment—

High-minded— Many Dimensions

Not so high-minded— The Cosmic Cube

http://www.log24.com/log/pix11A/110509-SpideySuperStories39Sm.jpg

One way of blending high and low—

The high-minded Charles Williams tells a story
in his novel Many Dimensions about a cosmically
significant cube inscribed with the Tetragrammaton—
the name, in Hebrew, of God.

The following figure can be interpreted as
the Hebrew letter Aleph inscribed in a 3×3 square—

http://www.log24.com/log/pix11A/110510-GaloisAleph.GIF

The above illustration is from undated software by Ed Pegg Jr.

For mathematical background, see a 1985 note, "Visualizing GL(2,p)."

For entertainment purposes, that note can be generalized from square to cube
(as Pegg does with his "GL(3,3)" software button).

For the Nordic-averse, some background on the Hebrew connection—

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