Log24

Friday, December 13, 2024

Design Cube

Filed under: General — m759 @ 6:41 pm

A 3D model of Solomon's Cube

The Warner Brothers version

Friday, February 2, 2024

Venice Beach Barbenheimer:  Design Cube News

Filed under: General — Tags: — m759 @ 11:12 am

See as well Froebel in this  journal.

Monday, October 2, 2023

Design Cube at Replit

Filed under: General — Tags: — m759 @ 8:10 pm

The Replit code development environment featured
in today's previous post has hosted, for some time now,
an embodiment of the design cube  from earlier posts —

Thursday, July 23, 2015

Design Cube

Filed under: General — m759 @ 8:24 pm

Broken Symmetries  in  Diamond Space —

Monday, November 5, 2012

Design Cubes

Filed under: General,Geometry — Tags: , — m759 @ 9:48 pm

Continued from April 2, 2012.

Some predecessors of the Cullinane design cubes of 1984
that lack the Cullinane cubes' symmetry properties

Kohs cubes (see 1920 article)
Wechsler cubes (see Wechsler in this journal), and
Horowitz  cubes (see links below).

Horowitz Design Cubes Package

Horowitz Design Cubes (1971)

1973 Horowitz Design Cubes Patent

Horowitz Biography

Monday, March 10, 2025

Face Planes Mindset Shift

Filed under: General — Tags: , , — m759 @ 4:58 pm

A rather different planes  solution from Log24 on March 7 —
See the illustrations in this journal on that date and . . .

"Note that in the Design Cube image above, the six faces are viewed
as suspended in space on three pairs of parallel planes, with the observer
viewing the parallel images only from the three directions front to back,
right to left,
and top to bottom.  In the WebSim row of six faces, the images
are pictured as they might be seen by an observer whose viewpoints vary
as he himself floats in space around the cube."

Related chrome  art —

Friday, March 7, 2025

2025: Space Odysseys

Filed under: General — Tags: — m759 @ 1:29 am

From a much more abstract space, an image from the
Log24 post Symmetry  of May 3, 2016 . . .

Webpage demonstrating symmetries of 'Solomon's Cube'

For a rotating 3D view from 2025, made with the help of AI, see . . .

Note that in the Design Cube image above, the six faces are viewed
as suspended in space on three pairs of parallel planes, with the observer
viewing the parallel images only from the three directions front to back,
right to left,
and top to bottom.  In the WebSim row of six faces, the images
are pictured as they might be seen by an observer whose viewpoints vary
as he himself floats in space around the cube.

Friday, September 1, 2023

Stella!

Filed under: General — Tags: , , — m759 @ 2:34 pm

An animated GIF that shows the basic unit for 
the "design cube" pages at finitegeometry.org —

From a post of Dec. 8, 2010, the (somewhat) related Stella Octangula —

http://www.log24.com/log/pix10B/101130-StellaIllusion.jpg

Monday, February 6, 2023

Interality Studies

Filed under: General — Tags: , , — m759 @ 12:26 pm
 

You, Xi-lin; Zhang, Peter. "Interality in Heidegger." 
The Free Library , April 1, 2015.  
. . . .

The term "interology" is meant as an interventional alternative to traditional Western ontology. The idea is to help shift people's attention and preoccupation from subjects, objects, and entities to the interzones, intervals, voids, constitutive grounds, relational fields, interpellative assemblages, rhizomes, and nothingness that lie between, outside, or beyond the so-called subjects, objects, and entities; from being to nothing, interbeing, and becoming; from self-identicalness to relationality, chance encounters, and new possibilities of life; from "to be" to "and … and … and …" (to borrow Deleuze's language); from the actual to the virtual; and so on. As such, the term wills nothing short of a paradigm shift. Unlike other "logoi," which have their "objects of study," interology studies interality, which is a non-object, a no-thing that in-forms and constitutes the objects and things studied by other logoi.
. . . .

Some remarks from this  journal on April 1, 2015 —

Manifest O

Tags:  

— m759 @ 4:44 AM April 1, 2015

The title was suggested by
http://benmarcus.com/smallwork/manifesto/.

The "O" of the title stands for the octahedral  group.

See the following, from http://finitegeometry.org/sc/map.html —

83-06-21 An invariance of symmetry The diamond theorem on a 4x4x4 cube, and a sketch of the proof.
83-10-01 Portrait of O  A table of the octahedral group O using the 24 patterns from the 2×2 case of the diamond theorem.
83-10-16 Study of O  A different way of looking at the octahedral group, using cubes that illustrate the 2x2x2 case of the diamond theorem.
84-09-15 Diamonds and whirls Block designs of a different sort — graphic figures on cubes. See also the University of Exeter page on the octahedral group O.

The above site, finitegeometry.org/sc, illustrates how the symmetry
of various visual patterns is explained by what Zhang calls "interality."

Monday, October 31, 2022

Folklore vs. Mathematics

Filed under: General — Tags: , , , — m759 @ 5:59 pm


Folklore —
 

Earlier in that same journal . . .

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


Mathematics —
 

Webpage demonstrating symmetries of 'Solomon's Cube'

Friday, May 6, 2022

Interality and the Bead Game

Filed under: General — Tags: , , , , — m759 @ 3:00 pm

WIkipedia on the URL suffix ".io" —

"In computer science, "IO" or "I/O" is commonly used
as an abbreviation for input/output, which makes the
.io domain desirable for services that want to be
associated with technology. .io domains are often used
for open source projects, application programming
interfaces ("APIs"), startup companiesbrowser games,
and other online services."

An association with the Bead Game from a post of April 7, 2018

IMAGE- 'Solomon's Cube'

Glasperlenspiel  passage quoted here in Summa Mythologica 

“"I suddenly realized that in the language, or at any rate
in the spirit of the Glass Bead Game, everything actually
was all-meaningful, that every symbol and combination of
symbols led not hither and yon, not to single examples,
experiments, and proofs, but into the center, the mystery
and innermost heart of the world, into primal knowledge.
Every transition from major to minor in a sonata, every
transformation of a myth or a religious cult, every classical
or artistic formulation was, I realized in that flashing moment,
if seen with a truly meditative mind, nothing but a direct route
into the interior of the cosmic mystery, where in the alternation
between inhaling and exhaling, between heaven and earth,
between Yin and Yang, holiness is forever being created.”

A less poetic meditation on the above 4x4x4 design cube —

"I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created."

See also a related remark by Lévi-Strauss in 1955

"…three different readings become possible:
left to right, top to bottom, front to back."

The recent use by a startup company of the URL "interality.io" suggests
a fourth  reading for the 1955 list of Lévi-Strauss — in and out
i.e., inner and outer group automorphisms —  from a 2011 post
on the birthday of T. S. Eliot :

A transformation:

Inner and outer group automorphisms

Click on the picture for details.

Thursday, February 10, 2022

“Kimi, Siri. Siri, Kimi.”

Filed under: General — Tags: — m759 @ 11:35 pm

From "Siri + Wechsler" in this journal —

For Little Man Tate —

IMAGE- Wechsler block-design cubes and related WAIS-R manual

Related material — Wechsler in this journal and
an earlier Siri Hustvedt art novel, from 2003 —

Mark and Lucille, Bill and Violet, Al and Regina,
etc., etc., etc. —

IMAGE- Siri Hustvedt on the name 'Wechsler' in 'What I Loved'

Related material —

Sunday, February 6, 2022

Animating the Savoir

Filed under: General — Tags: , — m759 @ 2:41 pm

                                             ". . . It is as if
We had come to an end of the imagination,
Inanimate in an inert savoir.

— Wallace Stevens, “The Plain Sense of Things

"In my end . . . ." — T. S. Eliot

Thursday, March 22, 2018

The Diamond Cube

Tags:  — m759 @ 11:32 AM 

. . . .

Here is an animated GIF that shows the basic unit
for the "design cube" pages at finitegeometry.org.

See a note from Sept. 15, 1984
 (perhaps the last day of life for Richard Brautigan).

Saturday, October 16, 2021

In Memory of Brian Goldner, dead on October 12th*

Filed under: General — m759 @ 7:16 am

"Before time began, there was the Cube." — Optimus Prime

See also Design Cube.

According to The Wall Street Journal … and possibly also
    dead on October 11th,  according to The New York Times .

Monday, August 6, 2018

The Girl with Kaleidoscope Eyes

Filed under: General,Geometry — Tags: , , — m759 @ 11:00 pm

http://www.log24.com/log/pix18/180806-Lexicon-image-search.jpg

“All right, Jessshica. It’s time to open the boxsssschhh.”

“Gahh,” she said. She began to walk toward the box, but her heart failed her and she retreated back to the chair. “Fuck. Fuck.” Something mechanical purred. The seam she had found cracked open and the top of the box began to rise. She squeezed shut her eyes and groped her way into a corner, curling up against the concrete and plugging her ears with her fingers. That song she’d heard the busker playing on the train platform with Eliot, “Lucy in the Sky with Diamonds”; she used to sing that. Back in San Francisco, before she learned card tricks. It was how she’d met Benny: He played guitar. Lucy was the best earner, Benny said, so that was mainly what she sang. She must have sung it five times an hour, day after day. At first she liked it but then it was like an infection, and there was nothing she could do and nowhere she could go without it running across her brain or humming on her lips, and God knew she tried; she was smashing herself with sex and drugs but the song began to find its way even there. One day, Benny played the opening chord and she just couldn’t do it. She could not sing that fucking song. Not again. She broke down, because she was only fifteen, and Benny took her behind the mall and told her it would be okay. But she had to sing. It was the biggest earner. She kind of lost it and then so did Benny and that was the first time he hit her. She ran away for a while. But she came back to him, because she had nothing else, and it seemed okay. It seemed like they had a truce: She would not complain about her bruised face and he would not ask her to sing “Lucy.” She had been all right with this. She had thought that was a pretty good deal.

Now there was something coming out of a box, and she reached for the most virulent meme she knew. “Lucy in the sky!” she sang. “With diamonds!”

•   •   •

Barry, Max. Lexicon: A Novel  (pp. 247-248).
Penguin Publishing Group. Kindle Edition.

Related material from Log24 on All Hallows' Eve 2013

"Just another shake of the kaleidoscope" —

Related material:

Kaleidoscope Puzzle,  
Design Cube 2x2x2, and 
Through the Looking Glass: A Sort of Eternity.

Sunday, April 8, 2018

Design

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

From a Log24 post of Feb. 5, 2009 —

Design Cube 2x2x2 for demonstrating Galois geometry

An online logo today —

See also Harry Potter and the Lightning Bolt.

 

Saturday, April 7, 2018

Sides

The FBI holding cube in "The Blacklist" —

" 'The Front' is not the whole story . . . ."

— Vincent Canby, New York Times  film review, 1976,
     as quoted in Wikipedia.

See also Solomon's Cube in this  journal.

IMAGE- 'Solomon's Cube'

Webpage demonstrating symmetries of 'Solomon's Cube'

Some may view the above web page as illustrating the
Glasperlenspiel  passage quoted here in Summa Mythologica 

“"I suddenly realized that in the language, or at any rate
in the spirit of the Glass Bead Game, everything actually
was all-meaningful, that every symbol and combination of
symbols led not hither and yon, not to single examples,
experiments, and proofs, but into the center, the mystery
and innermost heart of the world, into primal knowledge.
Every transition from major to minor in a sonata, every
transformation of a myth or a religious cult, every classical
or artistic formulation was, I realized in that flashing moment,
if seen with a truly meditative mind, nothing but a direct route
into the interior of the cosmic mystery, where in the alternation
between inhaling and exhaling, between heaven and earth,
between Yin and Yang, holiness is forever being created.”

A less poetic meditation on the above 4x4x4 design cube —

"I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created."

See also a related remark by Lévi-Strauss in 1955

"…three different readings become possible:
left to right, top to bottom, front to back."

Tuesday, March 27, 2018

Compare and Contrast

Filed under: General,Geometry — Tags: , , — m759 @ 4:28 pm

Weyl on symmetry, the eightfold cube, the Fano plane, and trigrams of the I Ching

Related material on automorphism groups —

The "Eightfold Cube" structure shown above with Weyl
competes rather directly with the "Eightfold Way" sculpture 
shown above with Bryant. The structure and the sculpture
each illustrate Klein's order-168 simple group.

Perhaps in part because of this competition, fans of the Mathematical
Sciences Research Institute (MSRI, pronounced "Misery') are less likely
to enjoy, and discuss, the eight-cube mathematical structure  above
than they are an eight-cube mechanical puzzle  like the one below.

Note also the earlier (2006) "Design Cube 2x2x2" webpage
illustrating graphic designs on the eightfold cube. This is visually,
if not mathematically, related to the (2010) "Expert's Cube."

Saturday, March 24, 2018

Sure, Whatever.

Filed under: General,Geometry — Tags: , , — m759 @ 11:13 am

The search for Langlands in the previous post
yields the following Toronto Star  illustration —

From a review of the recent film "Justice League" —

"Now all they need is to resurrect Superman (Henry Cavill),
stop Steppenwolf from reuniting his three Mother Cubes
(sure, whatever) and wrap things up in under two cinematic
hours (God bless)."

For other cubic adventures, see yesterday's post on A Piece of Justice 
and the block patterns in posts tagged Design Cube.

Thursday, March 22, 2018

The Diamond Cube

Filed under: General,Geometry — Tags: , , , — m759 @ 11:32 am

The Java applets at the webpage "Diamonds and Whirls"
that illustrate Cullinane cubes may be difficult to display.

Here instead is an animated GIF that shows the basic unit
for the "design cube" pages at finitegeometry.org.

Thursday, December 21, 2017

For Winter Solstice 2017

Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 10:30 am

A review —

Some context —

Webpage demonstrating symmetries of 'Solomon's Cube'

Wednesday, June 21, 2017

Concept and Realization

Filed under: General,Geometry — Tags: , , — m759 @ 1:12 pm

Remark on conceptual art quoted in the previous post

"…he’s giving the concept but not the realization."

A concept See a note from this date in 1983:

IMAGE- 'Solomon's Cube'

A realization  

Webpage demonstrating symmetries of 'Solomon's Cube'

Not the best possible realization, but enough for proof of concept .

Friday, December 2, 2016

Images from a Lumber Room*

Filed under: General — Tags: — m759 @ 7:20 am

An image search today for
"Design Cube" + Cullinane:
Click to enlarge (5.3 MB) —
    

* For the title, see St. Andrew's Day.

Thursday, December 1, 2016

What’s in a Name

Filed under: General,Geometry — m759 @ 11:23 pm

Design Cube 2x2x2 for demonstrating Galois geometry

   Backstory Aug. 21, 2016, and Quora.com.

Sunday, August 21, 2016

Imperium Emporium

Filed under: General,Geometry — m759 @ 11:30 pm

Design Cube 2x2x2 for demonstrating Galois geometry

Harry Potter with lightning-bolt scar

Harry Potter, star of the new film
"Imperium," with lightning-bolt
scar on his forehead

Tuesday, June 14, 2016

Model Kit

Filed under: General,Geometry — Tags: , , — m759 @ 12:14 pm

The title refers to the previous post, which quotes a 
remark by a poetry critic in the current New Yorker .

Scholia —

From the post Structure and Sense of June 6, 2016 —

Structure

Sense

A set of 7 partitions of the 2x2x2 cube that is invariant under PSL(2, 7) acting on the 'knight' coordinatization

From the post Design Cube of July 23, 2015 —

Broken Symmetries  in  Diamond Space 

Tuesday, May 3, 2016

Symmetry

A note related to the diamond theorem and to the site
Finite Geometry of the Square and Cube —

The last link in the previous post leads to a post of last October whose
final link leads, in turn, to a 2009 post titled Summa Mythologica .

Webpage demonstrating symmetries of 'Solomon's Cube'

Some may view the above web page as illustrating the
Glasperlenspiel  passage quoted here in Summa Mythologica 

“"I suddenly realized that in the language, or at any rate
in the spirit of the Glass Bead Game, everything actually
was all-meaningful, that every symbol and combination of
symbols led not hither and yon, not to single examples,
experiments, and proofs, but into the center, the mystery
and innermost heart of the world, into primal knowledge.
Every transition from major to minor in a sonata, every
transformation of a myth or a religious cult, every classical
or artistic formulation was, I realized in that flashing moment,
if seen with a truly meditative mind, nothing but a direct route
into the interior of the cosmic mystery, where in the alternation
between inhaling and exhaling, between heaven and earth,
between Yin and Yang, holiness is forever being created.”

A less poetic meditation on the above web page* —

"I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created."

Update of Sept. 5, 2016 — See also a related remark
by Lévi-Strauss in 1955:  "…three different readings
become possible: left to right, top to bottom, front
to back."

* For the underlying mathematics, see a June 21, 1983, research note.

Friday, October 9, 2015

Cube Design

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

For Aaron Sorkin and Walter Isaacson

Related material — 
Bauhaus CubeDesign Cube, and
Nabokov's Transparent Things .

Monday, July 27, 2015

The Ten

Filed under: General — Tags: — m759 @ 10:00 pm

The title refers to actress Kristen Wiig. (See Getcha.)

For Wiig, a scene from a 1968 Ingmar Bergman parody

'The Dove,' 1968, a Bergman parody

and parts of a post from Saturday night, July 18, 2015 —

Some related material from pure  mathematics — Design Cube (July 23).

Wednesday, April 1, 2015

Würfel-Märchen

Filed under: General,Geometry — Tags: , , , , — m759 @ 7:59 pm

Continued from yesterday, the date of death for German
billionaire philanthropist Klaus Tschira —

For Tschira in this journal, see Stiftung .

For some Würfel  illustrations, see this morning's post
Manifest O.  A related webpage —

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