Log24

Saturday, February 10, 2024

Gilded Cage Meets Crimson Abyss

Filed under: General — Tags: , — m759 @ 6:54 pm

"… as if into a crimson abyss …." —

Sunday, December 17, 2023

Sternwürfel 101 — “A Full Course of Instruction”

Filed under: General — Tags: , — m759 @ 2:57 pm

See also . . .

https://writing.upenn.edu/epc/authors/joris/todtnauberg.html

and Sternwürfel  in this  journal.

Wednesday, December 13, 2023

Director’s Exit

Filed under: General — Tags: , — m759 @ 2:45 pm

For St. Lucy's Day . . . Vide  another post now tagged "Cube School."

Chaos and Boundaries

Filed under: General — Tags: , , — m759 @ 2:21 pm

Another approach to chaos within boundaries: The I Ching —

Sunday, December 10, 2023

Wrestling

Filed under: General — Tags: — m759 @ 4:20 pm

This afternoon's New York Times  requiem by Ari L. Goldman for
"a scholar who wrestled with the interplay of tradition and modernity"
suggests a link to another such scholar I personally find more interesting . . .

But seriously . . .

Filed under: General — Tags: , , — m759 @ 3:27 pm

Erin’s Barron’s:  Skye High

Filed under: General — Tags: — m759 @ 1:23 am

More realistic views, near Erin Burnett's ancestral Isle of Skye —

"Lustworthy!" — Instagram

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

Tuesday, November 28, 2023

Red Riding Hood: The Katowice Version

Filed under: General — Tags: , , — m759 @ 3:47 pm

Comment:

The above date — Jan. 3, 2021 — suggests posts now tagged "Ice Stone."

See also the comments below (click to enlarge).

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.

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 ."

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

Filed under: General — Tags: , , — m759 @ 3:25 am

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, but
rather at the ends  of a cube's diagonal axis 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 .

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).

Duck Sup

Filed under: General — Tags: , — m759 @ 3:27 pm

Cube Space Revisited

Filed under: General — Tags: , , , , — m759 @ 3:02 pm

The above Quanta  article mentions

"Maryna Viazovska’s 2016 discovery of the most efficient
ways of packing spheres in dimensions eight and 24."

From a course to be taught by Viazovska next spring:

The Lovasz reference suggests a review of my own webpage
Cube Space, 1984-2003.

See as well a review of Log24 posts on Packing.

Tuesday, August 31, 2021

Annals of Geometry

Filed under: General — Tags: , , — m759 @ 2:21 pm

A passage by Max Jammer quoted in yesterday's post
A Brief Introduction to Ideas suggests further remarks:

There are geometries in which lengths are not invariant 
because they are not  relevant — for instance, projective 
geometry,  finite  geometry, and of course finite projective 
geometry.

See the annus mirabilis  introduction to that subject 
cited by Jammer in yesterday's Brief Introduction —

Monday, March 29, 2021

Graduate School

Filed under: General — Tags: , — m759 @ 5:37 pm

Also on 18 November 2010 —

Sunday, March 21, 2021

Mathematics and Narrative: The Unity

Filed under: General — Tags: , , — m759 @ 10:25 pm

“To conquer, three boxes* have to synchronize and join together into the Unity.”

―Wonder Woman in Zack Snyder’s Justice League

See also The Unity of Combinatorics  and The Miracle Octad Generator.

* Cf.  Aitchison’s Octads

Mind the Gaps…

Filed under: General — Tags: , , — m759 @ 1:18 pm

Continues from March 17.

See as well some remarks on Chinese  perspective
in the Log24 post “Gate” of June 13, 2013.

Wednesday, March 17, 2021

Mind the Gaps

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

Katherine Neville's 'The Eight,' edition with knight on cover, on her April 4 birthday

Page from 'The Paradise of Childhood,' 1906 edition

Thursday, February 25, 2021

Compare and Contrast

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

“… What is your dream—your ideal?  What is your News from Nowhere,
or, rather, What is the result of the little shake your hand has given to
the old pasteboard toy with a dozen bits of colored glass for contents?
And, most important of all, can you present it in a narrative or romance
which will enable me to pass an idle hour not disagreeably? How, for instance,
does it compare in this respect with other prophetic books on the shelf?”

— Hudson, W. H.. A Crystal Age  (p. 2). Open Road Media. Kindle Edition.

See as well . . .

The lexicographic Golay code
contains, embedded within it,
the Miracle Octad Generator.

Wednesday, February 24, 2021

Annals of Dim Antiquity

Filed under: General — Tags: , — m759 @ 2:20 pm

“Twenty-four glyphs, each one representing not a letter, not a word,
but a concept, arranged into four groups, written in Boris’s own hand,
an artifact that seemed to have resurrected him from the dead. It was
as if he were sitting across from Bourne now, in the dim antiquity of
the museum library.

This was what Bourne was staring at now, written on the unfolded
bit of onionskin.”

The Bourne Enigma , published on June 21, 2016

Passing, on June 21, 2016, into a higher dimension —

For those who prefer Borges to Bourne —

Sunday, February 21, 2021

Cube Woo

Filed under: General — Tags: , — m759 @ 7:01 pm

"Before time began, there was the Cube."
— Hassenfeld Brothers merchandising slogan

Monday, February 15, 2021

Raiders of the Lost Building Blocks

Filed under: General — Tags: — m759 @ 11:22 am

In memory of a Dead Sea Scrolls scholar who
reportedly died on December 29, 2020, here are
links to two Log24 posts from that date:
I Ching  Geometry  and Raiders of the Lost Coordinates.

Tuesday, December 29, 2020

I Ching  Geometry

Filed under: General — Tags: , , — m759 @ 11:04 am

"Before time began, there was the Cube."
Hassenfeld Brothers cinematic merchandising slogan

Sunday, December 27, 2020

Knight Move for Trevanian

Filed under: General — Tags: — m759 @ 11:42 pm

Knight move” remark from The Eiger Sanction

“I like to put people on myself by skipping logical steps
in the conversation until they’re dizzy.”

The following logical step — a check of the date Nov. 18, 2017
was omitted in the post Futon Dream  on this year’s St. Stephen’s Day.

For further context, see James Propp in this journal.

Wednesday, September 23, 2020

Geometry of Even Subsets

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

Various posts here on the geometry underlying the Mathieu group M24
are now tagged with the phrase “Geometry of Even Subsets.”

For example, a post with this diagram . . .

Monday, September 21, 2020

Zelig-Like?

Filed under: General — Tags: , — m759 @ 10:46 pm

“On their way to obscurity, the Simulmatics people
played minor parts in major events, appearing Zelig-like
at crucial moments of 1960s history.”

James Gleick reviewing a new book by Jill Lepore

Saturday, September 19, 2020

The Summerfield Prize

Filed under: General — Tags: , , — m759 @ 3:01 pm

"Like Coleridge" . . .

Related material:  Bloomsday 2006.

Cube School

Filed under: General — Tags: — m759 @ 3:16 am

The new domain http://cube.school
points to posts tagged Cube School here.

Thursday, September 17, 2020

Structure and Mutability . . .

Continues in The New York Times :

“One day — ‘I don’t know exactly why,’ he writes — he tried to
put together eight cubes so that they could stick together but
also move around, exchanging places. He made the cubes out
of wood, then drilled a hole in the corners of the cubes to link
them together. The object quickly fell apart.

Many iterations later, Rubik figured out the unique design
that allowed him to build something paradoxical:
a solid, static object that is also fluid….” — Alexandra Alter

Another such object: the eightfold cube .

Thursday, September 10, 2020

Raiders of . . .

Filed under: General — Tags: , — m759 @ 11:34 pm

Wednesday, September 9, 2020

Portrait with Holocron

Filed under: General — Tags: , , — m759 @ 11:08 pm

Novus Ordo Seclorum — Harold Bloom and the Tetrahedral Model of PG(3,2)

Sith Holocron in 'Star Wars Rebels'

For a Jedi  holocron of sorts, see this  journal on the above YouTube date

Thursday, July 9, 2020

The Enigma Glyphs

Filed under: General — Tags: , , — m759 @ 5:53 am

IMAGE- The Diamond Theorem

For those who  prefer fiction —

“Twenty-four glyphs, each one representing not a letter, not a word,
but a concept, arranged into four groups, written in Boris’s own hand,
an artifact that seemed to have resurrected him from the dead. It was
as if he were sitting across from Bourne now, in the dim antiquity of
the museum library.

This was what Bourne was staring at now, written on the unfolded
bit of onionskin.”

— “Robert Ludlum’s”  The Bourne Enigma , published on June 21, 2016

Passing, on June 21, 2016, into a higher dimension —

Sunday, July 5, 2020

It’s Still the Same Old Story …

Filed under: General — Tags: , , — m759 @ 4:29 pm

“He recounted the story of Adam and Eve, who were banished
from paradise because of their curiosity. Their inability to resist
the temptation of the forbidden fruit. Which itself was a metaphorical
stand-in for knowledge and power. He urged us to find the restraint
needed to resist the temptation of the cube—the biblical apple
in modern garb. He urged us to remain in Eden until we were able
to work out the knowledge the apple offered, all by ourselves.”

— Richards, Douglas E.. The Enigma Cube  (Alien Artifact Book 1)
(pp. 160-161). Paragon Press, 2020. Kindle Edition.

The biblical apple also appears in the game, and film, Assassin’s Creed .

Related material —

See the cartoon version of Alfred North Whitehead in the previous post,
and some Whitehead-related projective geometry —

Enigma Variations

Filed under: General — Tags: , — m759 @ 2:24 pm

The previous post reported, perhaps inaccurately, a publication
date of February 13, 2020, for the novel The Enigma Cube .

A variant publication date, Jan. 21,  2020, is reported below.

This journal on that  date —

The Enigma Cube

Filed under: General — Tags: , — m759 @ 5:03 am

Promotional material —

“Did you buckle up?” —  Harlan Kane

The publication date of The Enigma Cube  reported above was February 13, 2020.

Related material — Log24 posts around that date now tagged The Reality Bond.

Saturday, May 23, 2020

Eightfold Geometry: A Surface Code “Unit Cell”

Filed under: General — Tags: , , — m759 @ 1:50 am

A unit cell in 'a lattice geometry for a surface code'

The resemblance to the eightfold cube  is, of course,
completely coincidental.

Some background from the literature —

Friday, May 22, 2020

Surface Code News

Filed under: General — Tags: , — m759 @ 5:50 pm

From a paper cited in the above story:

“Fig. 4   A lattice geometry for a surface code.” —

The above figure suggests a search for “surface code” cube :

Related poetic remarks — “Illumination of a surface.”

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, February 24, 2020

For “Time Cube” Fans

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

See also Time Cube elsewhere in this  journal.

Friday, February 21, 2020

To and Fro, Back and …

Filed under: General — Tags: , , , — m759 @ 11:44 pm

Also on January 27, 2017 . . .

For other appearances of John Hurt here,
see 1984 Cubes.

Update of 12:45 AM Feb. 22 —

A check of later obituaries reveals that Hurt may well
have died on January 25, 2017, not January 27 as above.

Thus the following remarks may be more appropriate:

Not to mention what, why, who, and how.

Sunday, September 29, 2019

Stage Direction: “Comments Off.”

Filed under: General — Tags: , , — m759 @ 11:29 am

The previous post dealt with “magic” cubes, so called because of the
analogous “magic” squares. Douglas Hofstadter has written about a
different, physical , object, promoted as “the  Magic Cube,” that Hofstadter
felt embodied “a deep invariant”:

Wednesday, July 10, 2019

Artifice* of Eternity …

Filed under: General — Tags: , , , — m759 @ 10:54 am

… and Schoolgirl Space

"This poem contrasts the prosaic and sensual world of the here and now
with the transcendent and timeless world of beauty in art, and the first line,
'That is no country for old men,' refers to an artless world of impermanence
and sensual pleasure."

— "Yeats' 'Sailing to Byzantium' and McCarthy's No Country for Old Men :
Art and Artifice in the New Novel,"
Steven Frye in The Cormac McCarthy Journal ,
Vol. 5, No. 1 (Spring 2005), pp. 14-20.

See also Schoolgirl Space in this  journal.

* See, for instance, Lewis Hyde on the word "artifice" and . . .

Tuesday, July 9, 2019

Schoolgirl Space: 1984 Revisited

Filed under: General — Tags: , , , , — m759 @ 9:24 pm

Cube Bricks 1984 —

An Approach to Symmetric Generation of the Simple Group of Order 168

From "Tomorrowland" (2015) —

From John Baez (2018) —

See also this morning's post Perception of Space 
and yesterday's Exploring Schoolgirl Space.

Perception of Space

Filed under: General — Tags: , , , — m759 @ 10:45 am

(Continued)

The three previous posts have now been tagged . . .

Tetrahedron vs. Square  and  Triangle vs. Cube.

Related material —

Tetrahedron vs. Square:

Labeling the Tetrahedral Model  (Click to enlarge) —

Triangle vs. Cube:

and, from the date of the above John Baez remark —

Dreamtimes

Filed under: General — Tags: , , — m759 @ 4:27 am

“I am always the figure in someone else’s dream. I would really rather
sometimes make my own figures and make my own dreams.”

— John Malkovich at squarespace.com, January 10, 2017

Also on that date . . .

.

Monday, July 8, 2019

Exploring Schoolgirl Space

See also "Quantum Tesseract Theorem" and "The Crosswicks Curse."

Sunday, July 7, 2019

Schoolgirl Problem

Filed under: General — Tags: , , , — m759 @ 11:18 pm

Anonymous remarks on the schoolgirl problem at Wikipedia —

"This solution has a geometric interpretation in connection with 
Galois geometry and PG(3,2). Take a tetrahedron and label its
vertices as 0001, 0010, 0100 and 1000. Label its six edge centers
as the XOR of the vertices of that edge. Label the four face centers
as the XOR of the three vertices of that face, and the body center
gets the label 1111. Then the 35 triads of the XOR solution correspond
exactly to the 35 lines of PG(3,2). Each day corresponds to a spread
and each week to a packing
."

See also Polster + Tetrahedron in this  journal.

There is a different "geometric interpretation in connection with
Galois geometry and PG(3,2)" that uses a square  model rather
than a tetrahedral  model. The square  model of PG(3,2) last
appeared in the schoolgirl-problem article on Feb. 11, 2017, just
before a revision that removed it.

Saturday, June 8, 2019

Art Object, continued and continued

Filed under: General — Tags: , , — m759 @ 1:21 pm

Notes on a remark by Chuanming Zong

See as well posts mentioning "An Object of Beauty."

Update of 12 AM June 11 — A screenshot of this post 
is now available at  http://dx.doi.org/10.17613/hqk7-nx97 .

Tuesday, May 21, 2019

Inside the White Cube

Filed under: General — Tags: , , , — m759 @ 11:01 am

(Continued)

Monday, May 13, 2019

Star Cube

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

"Before time began . . . ." — Optimus Prime

Doris Day at the Hudson Rock

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

" 'My public image is unshakably that of
America’s wholesome virgin, the girl next door,
carefree and brimming with happiness,' 
she said in Doris Day: Her Own Story
a 1976 book . . . ."

From "Angels & Demons Meet Hudson Hawk" (March 19, 2013) —

From the March 1 post "Solomon and the Image," a related figure —

Friday, March 1, 2019

Solomon and the Image

Filed under: General — Tags: , , , — m759 @ 2:27 am

"Maybe an image is too strong
Or maybe is not strong enough."

— "Solomon and the Witch,"
      by William Butler Yeats

Wednesday, October 24, 2018

Shadowlands

Filed under: General — Tags: , , — m759 @ 4:38 am

The previous post suggests a review.

Following the above reference to March 30, 2016 —

Following the above reference to Lovasz —

Saturday, August 25, 2018

“Waugh, Orwell. Orwell, Waugh.”

Filed under: General,Geometry — Tags: , , , — m759 @ 4:00 pm

Suggested by a review of Curl on Modernism —

http://www.log24.com/log/pix18/180825-Ballard-on-Modernism.gif

Related material —

Waugh + Orwell in this journal and

Cube Bricks 1984

An Approach to Symmetric Generation of the Simple Group of Order 168

Wednesday, June 27, 2018

Taken In

Filed under: General,Geometry — Tags: , , , — m759 @ 9:36 am

A passage that may or may not have influenced Madeleine L'Engle's
writings about the tesseract :

From Mere Christianity , by C. S. Lewis (1952) —

"Book IV – Beyond Personality:
or First Steps in the Doctrine of the Trinity"
. . . .

I warned you that Theology is practical. The whole purpose for which we exist is to be thus taken into the life of God. Wrong ideas about what that life is, will make it harder. And now, for a few minutes, I must ask you to follow rather carefully.

You know that in space you can move in three ways—to left or right, backwards or forwards, up or down. Every direction is either one of these three or a compromise between them. They are called the three Dimensions. Now notice this. If you are using only one dimension, you could draw only a straight line. If you are using two, you could draw a figure: say, a square. And a square is made up of four straight lines. Now a step further. If you have three dimensions, you can then build what we call a solid body, say, a cube—a thing like a dice or a lump of sugar. And a cube is made up of six squares.

Do you see the point? A world of one dimension would be a straight line. In a two-dimensional world, you still get straight lines, but many lines make one figure. In a three-dimensional world, you still get figures but many figures make one solid body. In other words, as you advance to more real and more complicated levels, you do not leave behind you the things you found on the simpler levels: you still have them, but combined in new ways—in ways you could not imagine if you knew only the simpler levels.

Now the Christian account of God involves just the same principle. The human level is a simple and rather empty level. On the human level one person is one being, and any two persons are two separate beings—just as, in two dimensions (say on a flat sheet of paper) one square is one figure, and any two squares are two separate figures. On the Divine level you still find personalities; but up there you find them combined in new ways which we, who do not live on that level, cannot imagine.

In God's dimension, so to speak, you find a being who is three Persons while remaining one Being, just as a cube is six squares while remaining one cube. Of course we cannot fully conceive a Being like that: just as, if we were so made that we perceived only two dimensions in space we could never properly imagine a cube. But we can get a sort of faint notion of it. And when we do, we are then, for the first time in our lives, getting some positive idea, however faint, of something super-personal—something more than a person. It is something we could never have guessed, and yet, once we have been told, one almost feels one ought to have been able to guess it because it fits in so well with all the things we know already.

You may ask, "If we cannot imagine a three-personal Being, what is the good of talking about Him?" Well, there isn't any good talking about Him. The thing that matters is being actually drawn into that three-personal life, and that may begin any time —tonight, if you like.

. . . .

But beware of being drawn into the personal life of the Happy Family .

https://www.jstor.org/stable/24966339

"The colorful story of this undertaking begins with a bang."

And ends with

Martin Gardner on Galois

"Galois was a thoroughly obnoxious nerd,
suffering from what today would be called
a 'personality disorder.'  His anger was
paranoid and unremitting."

Wednesday, June 6, 2018

Geometry for Goyim

Filed under: General,Geometry — Tags: , , , — m759 @ 12:45 pm

Mystery box  merchandise from the 2011  J. J. Abrams film  Super 8  —

A mystery box that I prefer —

Box containing Froebel's Third Gift-- The Eightfold Cube

Click image for some background.

See also Nicht Spielerei .

Thursday, March 29, 2018

“Before Creation Itself . . .”

Filed under: General,Geometry — Tags: , , , — m759 @ 10:13 am

From the Diamond Theorem Facebook page —

A question three hours ago at that page

“Is this Time Cube?”

Notes toward an answer —

And from Six-Set Geometry in this journal . . .

Saturday, March 24, 2018

Slight?

Filed under: General,Geometry — Tags: , — m759 @ 12:30 pm

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.

Friday, March 23, 2018

Reciprocity

Filed under: General,Geometry — Tags: , — m759 @ 7:00 pm

Copy editing — From Wikipedia

"Copy editing (also copy-editing or copyediting, sometimes abbreviated ce)
is the process of reviewing and correcting written material to improve accuracy,
readability, and fitness for its purpose, and to ensure that it is free of error,
omission, inconsistency, and repetition. . . ."

An example of the need for copy editing:

Related material:  Langlands and Reciprocity in this  journal.

Piece Prize

Filed under: General,Geometry — Tags: , , — m759 @ 6:15 pm

The Waymark Prize from 'A Piece of Justice' (1995) by Jill Paton Walsh

The Waymark Prize Mystery - 'A Piece of Justice' (1995) p. 138

From the Personal to the Platonic

Filed under: General,Geometry — Tags: , , — m759 @ 11:01 am

On the Oslo artist Josefine Lyche —

"Josefine has taken me through beautiful stories,
ranging from the personal to the platonic
explaining the extensive use of geometry in her art.
I now know that she bursts into laughter when reading
Dostoyevsky, and that she has a weird connection
with a retired mathematician."

Ann Cathrin Andersen
    http://bryggmagasin.no/2017/behind-the-glitter/

Personal —

The Rushkoff Logo

— From a 2016 graphic novel by Douglas Rushkoff.

See also Rushkoff and Talisman in this journal.

Platonic —

The Diamond Cube.

Compare and contrast the shifting hexagon logo in the Rushkoff novel above 
with the hexagon-inside-a-cube in my "Diamonds and Whirls" note (1984).

Thursday, March 22, 2018

In Memoriam

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

Also on March 18, 2015 . . .

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.

Wednesday, March 7, 2018

Unite the Seven.

Filed under: General,Geometry — Tags: , , , — m759 @ 10:31 am


Related material —

The seven points of the Fano plane within 

The Eightfold Cube.
 

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


"Before time began . . . ."

  — Optimus Prime

Monday, January 22, 2018

Hollywood Moment

Matt B. Roscoe and Joe Zephyrs, both of Missoula, Montana, authors of article on quilt block symmetries

A death on the date of the above symmetry chat,
Wednesday, August 17, 2016

'Love Story' director dies

An Hispanic Hollywood moment:

Ojo de Dios —

Click for related material.

For further Hispanic entertainment,
see Ben Affleck sing 
"Aquellos Ojos Verdes "
in "Hollywoodland."

Saturday, November 18, 2017

Cube Space Continued

Filed under: General,Geometry — Tags: , — m759 @ 4:44 am

James Propp in the current Math Horizons  on the eightfold cube

James Propp on the eightfold cube

For another puerile approach to the eightfold cube,
see Cube Space, 1984-2003 (Oct. 24, 2008).

Wednesday, September 13, 2017

Summer of 1984

The previous two posts dealt, rather indirectly, with
the notion of "cube bricks" (Cullinane, 1984) —

Group actions on partitions —

Cube Bricks 1984 —

An Approach to Symmetric Generation of the Simple Group of Order 168

Another mathematical remark from 1984 —

For further details, see Triangles Are Square.

Tuesday, September 12, 2017

Think Different

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

The New York Times  online this evening

"Mr. Jobs, who died in 2011, loomed over Tuesday’s
nostalgic presentation. The Apple C.E.O., Tim Cook,
paid tribute, his voice cracking with emotion, Mr. Jobs’s
steeple-fingered image looming as big onstage as
Big Brother’s face in the classic Macintosh '1984' commercial."

James Poniewozik 

Review —

Thursday, September 1, 2011

How It Works

Filed under: Uncategorized — Tags:  — m759 @ 11:00 AM 

"Design is how it works." — Steven Jobs (See Symmetry and Design.)

"By far the most important structure in design theory is the Steiner system S(5, 8, 24)."
 — "Block Designs," by Andries E. Brouwer

. . . .

See also 1984 Bricks in this journal.

Chin Music

Filed under: General,Geometry — Tags: , — m759 @ 9:45 pm

Related image suggested by "A Line for Frank" (Sept. 30, 2013) —

Tuesday, June 20, 2017

Epic

Continuing the previous post's theme  

Group actions on partitions

Cube Bricks 1984 —

An Approach to Symmetric Generation of the Simple Group of Order 168

Related material — Posts now tagged Device Narratives.

Wednesday, June 7, 2017

Three Things at Once

Filed under: General,Geometry — Tags: , — m759 @ 1:28 pm

Rosalind Krauss in 1979

Nanavira Thera in 1959

Cambridge University Press in 1999 —

See also Cube Bricks.

Sunday, June 4, 2017

In Memory of the Time Cube Page*

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

From this journal on August 18, 2015, "A Wrinkle in Terms" —

For two misuses by John Baez of the phrase “permutation group”
at the n-Category Café, see “A Wrinkle in the Mathematical Universe
and “Re: A Wrinkle…” —

“There is  such a thing as a permutation group.”
— Adapted from A Wrinkle in Time , by Madeleine L’Engle

* See RIP, Time Cube at gizmodo.com (September 1, 2015).

Wednesday, April 12, 2017

Contracting the Spielraum

The contraction of the title is from group actions on
the ninefold square  (with the center subsquare fixed)
to group actions on the eightfold cube.

From a post of June 4, 2014

At math.stackexchange.com on March 1-12, 2013:

Is there a geometric realization of the Quaternion group?” —

The above illustration, though neatly drawn, appeared under the
cloak of anonymity.  No source was given for the illustrated group actions.
Possibly they stem from my Log24 posts or notes such as the Jan. 4, 2012,
note on quaternion actions at finitegeometry.org/sc (hence ultimately
from my note “GL(2,3) actions on a cube” of April 5, 1985).

Tuesday, April 4, 2017

White Cube

Filed under: General — Tags: , , — m759 @ 12:21 pm

Inside the White Cube” —

“We have now reached
a point where we see
not the art but the space first….
An image comes to mind
of a white, ideal space
that, more than any single picture,
may be the archetypal image
of 20th-century art.”

http://www.log24.com/log/pix09/090205-cube2x2x2.gif

“Space: what you
damn well have to see.”

— James Joyce, Ulysses  

Thursday, November 3, 2016

Triple Cross

(Continued See the title in this journal, as well as Cube Bricks.)

Cube Bricks 1984 —

An Approach to Symmetric Generation of the Simple Group of Order 168
Related material —

Dirac and Geometry in this journal,
Kummer's Quartic Surface in this journal,
Nanavira Thera in this journal, and
The Razor's Edge  and Nanavira Thera.

See as well Bill Murray's 1984 film "The Razor's Edge"

Movie poster from 1984 —

"A thin line separates
love from hate,
success from failure,
life from death."

Three other dualities, from Nanavira Thera in 1959 —

"I find that there are, in every situation,
three independent dualities…."

(Click to enlarge.)

Tuesday, October 4, 2016

Westworld

Filed under: General — Tags: — m759 @ 10:27 am

The title refers to a Log24 post of 9:45 AM ET Sunday, Oct. 2.

From the "Westworld" post of Sunday, Oct. 2 —

"It was rather like watching a play."

QED.

Sunday, October 2, 2016

Westworld

Filed under: General,Geometry — Tags: , — m759 @ 9:45 am

On a new HBO series that opens at 9 PM ET tonight —

Watching Westworld , you can sense a grand mythology unfolding before your eyes. The show’s biggest strength is its world-building, an aspect of screenwriting that many television series have botched before. Often shows will rush viewers into plot, forgetting to instill a sense of place and of history, that you’re watching something that doesn’t just exist in a vacuum but rather is part of some larger ecosystem. Not since Lost  can I remember a TV show so committed to immersing its audience into the physical space it inhabits. (Indeed, Westworld  can also be viewed as a meta commentary on the art of screenwriting itself: brainstorming narratives, building characters, all for the amusement of other people.)

Westworld  is especially impressive because it builds two worlds at once: the Western theme park and the futuristic workplace. The Western half of Westworld  might be the more purely entertaining of the two, with its shootouts and heists and chases through sublime desert vistas. Behind the scenes, the theme park’s workers show how the robot sausage is made. And as a dystopian office drama, the show does something truly original.

Adam Epstein at QUARTZ, October 1, 2016

"… committed to immersing its audience
  into the physical space it inhabits…."

See also, in this journal, the Mimsy Cube

"Mimsy Were the Borogoves,"
classic science fiction story:

"… he lifted a square, transparent crystal block, small enough to cup in his palm– much too small to contain the maze of apparatus within it. In a moment Scott had solved that problem. The crystal was a sort of magnifying glass, vastly enlarging the things inside the block. Strange things they were, too. Miniature people, for example– They moved. Like clockwork automatons, though much more smoothly. It was rather like watching a play."

A Crystal Block —

Cube, 4x4x4

Friday, September 30, 2016

Desmic Midrash

Filed under: General — Tags: , , — m759 @ 9:19 am

The author of the review in the previous post, Dara Horn, supplies
below a midrash on "desmic," a term derived from the Greek desmé
( δέσμη: bundle, sheaf , or, in the mathematical sense, pencil —
French faisceau ), which is related to the term desmos , bond …

(The term "desmic," as noted earlier, is relevant to the structure of
Heidegger's Sternwürfel .)

The Horn midrash —

(The "medieval philosopher" here is not the remembered pre-Christian
Ben Sirah (Ecclesiasticus ) but the philosopher being read — Maimonides:  
Guide for the Perplexed , 3:51.)

Here of course "that bond" may be interpreted as corresponding to the
Greek desmos  above, thus also to the desmic  structure of the
stellated octahedron, a sort of three-dimensional Star of David.

See "desmic" in this journal.

Thursday, September 29, 2016

Articulation

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

Cassirer vs. Heidegger at Harvard —

A remembrance for Michaelmas —

A version of Heidegger’s “Sternwürfel ” —

From Log24 on the upload date for the above figure —

Wednesday, September 28, 2016

Star Wars

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

See also in this journal "desmic," a term related
to the structure of Heidegger's Sternwürfel .

Scholia

Filed under: General — Tags: , — m759 @ 2:48 pm

Heidegger- 'The world's darkening never reaches to the light of being'

Scholia —

D. H. Lawrence quote from 'Kangaroo'

South Australia goes dark

Tuesday, April 5, 2016

“Puzzle Cube of a Novel”

Filed under: General,Geometry — Tags: , , — m759 @ 2:00 am

"To know the mind of the creator"

Or that of Orson Welles

Related material — Cube Coloring.

Monday, April 4, 2016

Cube for Berlin

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

Foreword by Sir Michael Atiyah —

"Poincaré said that science is no more a collection of facts
than a house is a collection of bricks. The facts have to be
ordered or structured, they have to fit a theory, a construct
(often mathematical) in the human mind. . . . 

 Mathematics may be art, but to the general public it is
a black art, more akin to magic and mystery. This presents
a constant challenge to the mathematical community: to
explain how art fits into our subject and what we mean by beauty.

In attempting to bridge this divide I have always found that
architecture is the best of the arts to compare with mathematics.
The analogy between the two subjects is not hard to describe
and enables abstract ideas to be exemplified by bricks and mortar,
in the spirit of the Poincaré quotation I used earlier."

— Sir Michael Atiyah, "The Art of Mathematics"
in the AMS Notices , January 2010

Judy Bass, Los Angeles Times , March 12, 1989 —

"Like Rubik's Cube, The Eight  demands to be pondered."

As does a figure from 1984, Cullinane's Cube —

The Eightfold Cube

For natural group actions on the Cullinane cube,
see "The Eightfold Cube" and
"A Simple Reflection Group of Order 168."

See also the recent post Cube Bricks 1984

An Approach to Symmetric Generation of the Simple Group of Order 168

Related remark from the literature —

http://www.log24.com/log/pix11B/110918-Felsner.jpg

Note that only the static structure is described by Felsner, not the
168 group actions discussed by Cullinane. For remarks on such
group actions in the literature, see "Cube Space, 1984-2003."

(From Anatomy of a Cube, Sept. 18, 2011.)

Wednesday, March 30, 2016

Hungarian Algorithm

Filed under: General — Tags: — m759 @ 12:00 am

“Of all the Hungarian friends I’ve ever had
I can’t remember one who didn’t want me to think of him
as a king of con men.”

” ‘The omelet, you know that, don’t you? Sure. It’s a classic.
An omelet, it’s in our Hungarian cookbook.
“To make an omelet,” it says “first, steal an egg.” ‘ ”

— Orson Welles, in his last completed film.

See also Lovasz in this journal.

Thursday, December 17, 2015

Hint of Reality

From an article* in Proceedings of Bridges 2014

As artists, we are particularly interested in the symmetries of real world physical objects.

Three natural questions arise:

1. Which groups can be represented as the group of symmetries of some real-world physical object?

2. Which groups have actually  been represented as the group of symmetries of some real-world physical object?

3. Are there any glaring gaps – small, beautiful groups that should have a physical representation in a symmetric object but up until now have not?

The article was cited by Evelyn Lamb in her Scientific American  
weblog on May 19, 2014.

The above three questions from the article are relevant to a more
recent (Oct. 24, 2015) remark by Lamb:

" finite projective planes [in particular, the 7-point Fano plane,
about which Lamb is writing] 
seem like a triumph of purely 
axiomatic thinking over any hint of reality…."

For related hints of reality, see Eightfold Cube  in this journal.

* "The Quaternion Group as a Symmetry Group," by Vi Hart and Henry Segerman

Friday, August 7, 2015

Parts

Filed under: General,Geometry — Tags: , — m759 @ 2:19 am

Spielerei  —

"On the most recent visit, Arthur had given him
a brightly colored cube, with sides you could twist
in all directions, a new toy that had just come onto
the market."

— Daniel Kehlmann, F: A Novel  (2014),
     translated from the German by
     Carol Brown Janeway

Nicht Spielerei  —

A figure from this journal at 2 AM ET
on Monday, August 3, 2015

Also on August 3 —

FRANKFURT — "Johanna Quandt, the matriarch of the family
that controls the automaker BMW and one of the wealthiest
people in Germany, died on Monday in Bad Homburg, Germany.
She was 89."

MANHATTAN — "Carol Brown Janeway, a Scottish-born
publishing executive, editor and award-winning translator who
introduced American readers to dozens of international authors,
died on Monday in Manhattan. She was 71."

Related material —  Heisenberg on beauty, Munich, 1970                       

Thursday, May 7, 2015

Paradigm for Pedagogues

Filed under: General,Geometry — Tags: , — m759 @ 7:14 pm

Illustrations from a post of Feb. 17, 2011:

Plato’s paradigm in the Meno —

http://www.log24.com/log/pix11/110217-MenoFigure16bmp.bmp

Changed paradigm in the diamond theorem (2×2 case) —

http://www.log24.com/log/pix11/110217-MenoFigureColored16bmp.bmp

Ultron: By the Book

Filed under: General,Geometry — Tags: , — m759 @ 6:45 pm

If The New York Times interviewed Ultron for its
Sunday Book Review "By the Book" column —

What books are currently on your night stand?

Steve Fuller's Thomas Kuhn: A Philosophical History for Our Times

Gerald Holton's Thematic Origins of Scientific Thought

John Gray's The Soul of the Marionette

Lede

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

"Who is Ultron? What is he?"

See too the previous post and Cube of Ultron.

Wednesday, May 6, 2015

Soul

Filed under: General,Geometry — Tags: , , , — m759 @ 4:30 pm

Nonsense…

See Gary Zukav, Harvard ’64, in this journal.

and damned  nonsense —

“Every institution has a soul.”

— Gerald Holton in Harvard Gazette  today

Commentary —

“The Ferris wheel came into view again….”
Malcom Lowry, Under the Volcano

See also Holton in a Jan. 1977 interview:

“If people have souls, and I think a few have, it shows….”

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 —

Manifest O

Filed under: General,Geometry — Tags: , , — m759 @ 4:44 am

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.

Sunday, December 28, 2014

Cube of Ultron

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

The Blacklist “Pilot” Review

"There is an element of camp to this series though. Spader is
quite gleefully channeling Anthony Hopkins, complete with being
a well educated, elegant man locked away in a super-cell.
Speaking of that super-cell, it’s kind of ridiculous. They’ve got him
locked up in an abandoned post office warehouse on a little
platform with a chair inside  a giant metal cube that looks like
it could have been built by Tony Stark. And as Liz approaches
to talk to him, the entire front of the cube  opens and the whole
thing slides back to leave just the platform and chair. Really? 
FUCKING REALLY ? "

Kate Reilly at Geekenstein.com (Sept. 27, 2013)

Wednesday, September 17, 2014

Raiders of the Lost Articulation

Tom Hanks as Indiana Langdon in Raiders of the Lost Articulation :

An unarticulated (but colored) cube:

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

A 2x2x2 articulated cube:

IMAGE- Eightfold cube with detail of triskelion structure

A 4x4x4 articulated cube built from subcubes like
the one viewed by Tom Hanks above:

Image-- Solomon's Cube

Solomon’s Cube

Friday, August 29, 2014

Raum

Filed under: General,Geometry — Tags: , , — m759 @ 8:00 am

A possible answer to the 1923 question of Walter Gropius, “Was ist Raum?“—

See also yesterday’s Source of the Finite and the image search
on the Gropius question in last night’s post.

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