Log24

Sunday, April 6, 2025

Solomon’s Cube at 3dthis.com

Filed under: General — m759 @ 3:35 am

The above cube is at  https://3dthis.com/player.htm?h=LTc5Mzg2NTk .

See as well the related diamond theorem unit cube  from yesterday.

Wednesday, January 15, 2025

Making a Textured Rotatable Solomon’s Cube

Filed under: General — m759 @ 4:32 am

Click image to see program at WebSim. To enlarge image click here.

The data file for the above cube is at
log24.com/log/pix25/Websim-SolCube-data.json.

(Right-click the above json link and choose "Save Link As.")

Wednesday, May 7, 2025

White Smoke This Week for Tom Hanks?

Filed under: General — Tags: — m759 @ 5:01 pm

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

IMAGE- Illuminati Diamond, pp. 359-360 in 'Angels & Demons,' Simon & Schuster Pocket Books 2005, 448 pages, ISBN 0743412397

Saturday, April 5, 2025

Fanciful Logic

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

The previous post suggests a review of what might,
fancifully, be called the Indiana Langdon  version
of the classic "duplication of the cube" problem.

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

In this version, the problem is to duplicate the static image
above as a rotatable 3D "diamond theorem unit cube" that
illustrates a design from 1984.

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.

Thursday, January 23, 2025

The Gotham/Getty problem: “Da hats ein Eck”

Filed under: General — Tags: , — m759 @ 7:42 am

Symbologist Robert Langdon views a corner of Solomon's Cube

This post was suggested by Dudeney's "Stonemason's Problem," which
in turn was suggested by the number "204" in the opening episode of
the new Apple TV Plus thriller "Prime Target."

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).

Sunday, November 19, 2023

Six Dimensions

Filed under: General — Tags: , — m759 @ 9:59 am

Heinlein:

"Sharpie, we have condensed six dimensions into four,
then we either work by analogy into six, or we have to use math
that apparently nobody but Jake and my cousin Ed understands.
Unless you can think of some way to project six dimensions into three–
you seem to be smart at such projections."

I closed my eyes and thought hard. "Zebbie, I don't think it can be done.
Maybe Escher could have done it."

Image-- Escher's 'Verbum'

Escher’s Verbum

Image-- Solomon's Cube

Solomon’s Cube

Wednesday, May 10, 2023

Saving the Appearances

Filed under: General — Tags: , , — m759 @ 2:18 pm

Douglas Hofstadter —

“… I realized that to me,
Gödel and Escher and Bach
were only shadows
cast in different directions by
some central solid essence.
I tried to reconstruct
the central object, and
came up with this book.”

Goedel Escher Bach cover

Related images —

Image-- Escher's 'Verbum'

Escher’s Verbum

Image-- Solomon's Cube

Solomon’s Cube

Thursday, April 20, 2023

Alphabet Meets Gestalt . . .

Filed under: General — Tags: , , — m759 @ 2:25 pm

Continued from April 18 .

"Working with words to create art
and working with your hands to create art
seem like two separate activities to me."

Cover artist, The New Yorker , on April 17

See also Alphabet Blocks in this  journal
as well as Escher's Verbum.

Image-- Escher's 'Verbum'

Escher’s Verbum

Image-- Solomon's Cube

Solomon’s Cube

Thursday, November 10, 2022

For Students of the Forked Tongue

Filed under: General — Tags: , , , — m759 @ 11:42 am

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

The above 1975 book by Robert Greer Cohn, Modes of Art, is
Volume I of a planned three-volume work.

The passage below is from a review of Cohn's Vol. II, Ways of Art — 

Franklin, Ursula (1987) "Book Review: A Critical Work II.
Ways of Art: Literature. Music, Painting in France 
,"
Grand Valley Review : Vol. 3: Iss. 1, Article 19. Available at: http://scholarworks.gvsu.edu/gvr/vol3/iss1/19 .

. . . .

Those not familiar with the author's epistemology should begin with Appendix A of Ways of Art , a schematic demonstration of his tetrapolar-polypolar-dialectic, especially as it concerns the development of the French novel within the European tradition. But this dialectic, which has antecedents in Kierkegaard, Mallarme and Joyce, underlies all art, because: "this dimensional pulsation, or tetrapolar (and polypolar) higher vibrancy is, in short, the stuff of life: life is vibrant in this more complex way as well as in the more bipolar sense" (7). Cohn shows that "far out enough" the male or linear and the female or circular, the male vertical and the female horizontal dimensions "tend to merge as in relativity theory" (19). Ways of Art  shows us the way through a historical becoming of art in its complex dialectic in which the metonymic (horizontal) axis constantly interrelates with the metaphoric (vertical). "Life is the mother, art the father" (vii); hence Cohn's quarrel with most contemporary Feminism, which is pronounced throughout the volume. Firmly grounded in its author's tetra-polypolar epistemology, this beautiful book becomes, however, at no point dryly abstract; it is the mature work of a true humanist who stands in clear and open opposition to the dehumanizing trend of "the quasi-scientific reductionism and abstract gimmickry of a great deal of current academic literary study, bellwethered by the structuralists, post-structuralists, and deconstructionists" (vi). Abundant footnotes constitute a substantial part of Ways of Art , on occasion developing insights almost into essays demonstrating crucial points along the general flow of the tradition from "Obscure Beginnings;' the opening chapter, to our "Contemporaries;' the last.

Cohn reminds us that "In the Beginning was the Word;' for the Judaeo-Christian tradition at least, which his study fervently embraces; thus, for example, in Appendix 0 on "The Dance of the Sexes;' he censures "those who live by slogans, camps, and peer-opinion, the countless little bastard cults which characterize an era which has massively veered away from our free and beautiful Greco-Judaeo-Christian tradition" (332). Cohn traces man's way and that of his myths and rituals culminating in his art from that beginning along the lines of Freud, Neumann and Cassirer, and many others, always demonstrating the underlying polypolar dialectical rhythm. Thus in "From Barbarism to Young Culture;' we follow the Celts to Druidic ritual, Hebrew beginnings to the Psalms, Dionysian ritual to Greek tragedy, and thence to the beginnings of French dramatic literature originating in the Quem quaeritis sequence of the medieval Mass. Along the way arises artistic symbolism, for Cohn synonymous with "effective poetry;' to finally "ripen in France as never before" (99). Table I (134) graphs this development from the twelfth to the late nineteenth and early twentieth centuries. The author traces the rise of the artistic vocation from its antecedents in the double function of bard and priest, with the figure of Ronsard at the crossroads of that dying institution and the nascent concept of personal glory. "The Enlightenment Vocation" is exemplified in Montaigne, who humanizes the French cultural elite and points the way to French classicism and, farther down the road, after the moral collapse with the outgoing reign of Louis XIV, toward the Age of Reason. Clearly the most significant figure of the French Enlightenment for all of Western civilization is Rousseau, and Cohn beautifully shows us why this is so. Subsequently, "the nineteenth-century stage of the writer's journey will lead, starting from the crossroads of Rousseau, primarily in these two directions: the imperialistic and visionary prose of Balzac, the equally ambitious poetry of Mallarme", brothers under the skin" (199). And these two paths will then be reconciled in Proust's monumental A la recherche du temps perdu .

. . . .

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'

Saturday, June 25, 2022

Gödel, Escher, Bach

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

Image-- Escher's 'Verbum'

Escher’s Verbum

Image-- Solomon's Cube

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, March 5, 2020

Pythagorean Letter Meets Box of Chocolates

Filed under: General — Tags: , , , , — m759 @ 10:30 am

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 

Monday, November 11, 2019

Time and Chance

Filed under: General — Tags: , , , , — m759 @ 2:49 pm

http://www.log24.com/log/pix10B/101202-DreidelAndStone.jpg

The misleading image at right above is from the cover of
an edition of Charles Williams's classic 1931 novel 
Many Dimensions  published in 1993 by Wm. B. Eerdmans.

Compare and constrast —

Goedel Escher Bach cover

Cover of a book by Douglas Hofstadter

IMAGE- 'Solomon's Cube'

An Invariance of Symmetry

Monday, September 9, 2019

ART WARS at Harvard: The Wertham Professorship

Filed under: General — Tags: , — m759 @ 8:38 pm

See as well an obituary for Mrs. Wertham from 1987.

Related art —

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 

For further details, search the Web for "Wertham Professor" + Eck.

Sunday, July 15, 2018

Jewish Oases

Filed under: General,Geometry — Tags: , , — m759 @ 10:06 pm

"… Lincoln Plaza Cinemas, the Juilliard String Quartet,
and the Strand Book Store remained  oases
for cultural and intellectual stimulation."

John S. Friedman in The Forward , Jan. 21, 2018

Read more: 

https://forward.com/culture/392483/
how-fred-bass-dan-talbot-robert-mann
-shaped-new-york-culture/

From  the Oasis  in Steven Spielberg's "Ready Player One" (2018) —

I prefer, from a Log24 search for Flux Capacitor

Symbologist Robert Langdon views a corner of Solomon's Cube

From "Raiders of the Lost Images" —

"The cube shape of the lost Mother Box,
also known as the Change Engine,
is shared by the Stone in a novel by
Charles Williams, Many Dimensions .
See the Solomon's Cube webpage."

Thursday, June 7, 2018

For Dan Brown

Filed under: General,Geometry — Tags: , , , — m759 @ 1:09 pm

See also Eightfold Trinity in this  journal.

Symbologist Robert Langdon views a corner of Solomon's Cube

Saturday, May 19, 2018

Flux Capacitor

Filed under: General,Geometry — Tags: , , , — m759 @ 4:13 pm

For Tom Hanks and Dan Brown —

Symbologist Robert Langdon views a corner of Solomon's Cube

From "Raiders of the Lost Images" —

"The cube shape of the lost Mother Box,
also known as the Change Engine,
is shared by the Stone in a novel by
Charles Williams, Many Dimensions .
See the Solomon's Cube webpage."

See as well a Google search for flux philosophy
https://www.google.com/search?q=flux+philosophy.

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, January 16, 2018

The Pentagram Papers

Filed under: General,Geometry — Tags: , , — m759 @ 9:16 am

Other intersection-points-counting material —

The Finkelstein Talisman:

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

See also Hanks + Cube in this journal —

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

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'

Monday, July 24, 2017

Penguin Classics Deluxe Edition

Filed under: General,Geometry — Tags: , — m759 @ 9:00 am

The above title was suggested by a film trailer quoted here Saturday

" Jeremy Irons' dry Alfred Pennyworth:
'One misses the days when one's biggest concerns
were exploding wind-up penguins.' "

"Penguin Classics Deluxe Edition" describes, among other books,
an edition of the I Ching  published on December 1, 2015.

Excerpt from this journal on that date

Tuesday, December 1, 2015

Verhexung

Filed under: Uncategorized — m759 @ 9:00 PM 

(Continued)

"The positional meaning of a symbol derives from
its relationship to other symbols in a totality, a Gestalt,
whose elements acquire their significance from the
system as a whole."

— Victor Turner, The Forest of Symbols , Ithaca, NY,
Cornell University Press, 1967, p. 51, quoted by
Beth Barrie in "Victor Turner."

(Turner pioneered the use of the term "symbology,"
a term later applied by Dan Brown to a fictional
scholarly pursuit at Harvard.)

. . . .

Related material —

IMAGE by Cullinane- 'Solomon's Cube' with 64 identical, but variously oriented, subcubes, and six partitions of these 64 subcubes

The I Ching's underlying group has 1,290,157,424,640 permutations.

Thursday, June 22, 2017

Face Henge

Filed under: General,Geometry — Tags: , , — m759 @ 3:07 pm

With a hat tip to Vinnie Mancuso

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 .

Wednesday, March 29, 2017

Art Space Illustrated

Another view of the previous post's art space  —

IMAGE by Cullinane- 'Solomon's Cube' with 64 identical, but variously oriented, subcubes, and six partitions of these 64 subcubes

More generally, see Solomon's Cube in Log24.

See also a remark from Stack Exchange in yesterday's post Backstory,
and the Stack Exchange math logo below, which recalls the above 
cube arrangement from "Affine groups on small binary spaces" (1984).

IMAGE- Current math.stackexchange.com logo and a 1984 figure from 'Notes on Groups and Geometry, 1978-1986'

Friday, March 10, 2017

Transformers

Filed under: General,Geometry — Tags: , — m759 @ 1:00 pm

Or:  Y  for Yale  continued

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

See also Transformers in this journal and Y for Yale.

Thursday, March 2, 2017

Stories

Filed under: General,Geometry — Tags: , , — m759 @ 12:48 pm

"We tell ourselves stories in order to live." — Joan Didion

The New York Times Magazine  online today —

"As a former believer and now a nonbeliever, Carrère,
seeking answers, sets out, in The Kingdom , to tell
the story of the storytellers. He is trying to understand
what it takes to be able to tell a story, any story.
And what he finds, once again, is that you have to find
your role in it."

Wyatt Mason in The New York Times Magazine ,
     online March 2, 2017 

Like Tom Hanks?

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

Click image for related posts.

Sunday, February 26, 2017

Poetic Order

Filed under: General,Geometry — Tags: , — m759 @ 1:06 pm

Transformations acting on Solomon's Cube
furnish a model of poetic order.

Some backstory for Hollywood —

Hollywood analogue to Solomon's Cube in 'Transformers'

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