“Before time began, there was the Cube.”
— Hassenfeld Brothers merchandising slogan
Sunday, February 21, 2021
Saturday, September 19, 2020
Cube School
The new domain http://cube.school
points to posts tagged Cube School here.
Sunday, July 5, 2020
The Enigma Cube
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.
Monday, February 24, 2020
For “Time Cube” Fans
Tuesday, May 21, 2019
Monday, May 13, 2019
Thursday, March 22, 2018
The Diamond Cube
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.
Saturday, November 18, 2017
Cube Space Continued
James Propp in the current Math Horizons on the eightfold cube —
For another puerile approach to the eightfold cube,
see Cube Space, 1984-2003 (Oct. 24, 2008).
Sunday, June 4, 2017
In Memory of the Time Cube Page*
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).
Tuesday, April 4, 2017
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.”
“Space: what you
damn well have to see.”
— James Joyce, Ulysses
Tuesday, April 5, 2016
“Puzzle Cube of a Novel”
Monday, April 4, 2016
Cube for Berlin
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 —
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 —
Related remark from the literature —
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.)
Sunday, December 28, 2014
Cube of Ultron
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)
Monday, May 19, 2014
Cube Space
A sequel to this afternoon’s Rubik Quote:
“The Cube was born in 1974 as a teaching tool
to help me and my students better understand
space and 3D. The Cube challenged us to find
order in chaos.”
— Professor Ernő Rubik at Chrome Cube Lab
(Click image below to enlarge.)
Thursday, January 24, 2013
Cube Space
For the late Cardinal Glemp of Poland,
who died yesterday, some links:
Friday, December 28, 2012
Cube Koan
From Don DeLillo's novel Point Omega — I knew what he was, or what he was supposed to be, a defense intellectual, without the usual credentials, and when I used the term it made him tense his jaw with a proud longing for the early weeks and months, before he began to understand that he was occupying an empty seat. "There were times when no map existed to match the reality we were trying to create." "What reality?" "This is something we do with every eyeblink. Human perception is a saga of created reality. But we were devising entities beyond the agreed-upon limits of recognition or interpretation. Lying is necessary. The state has to lie. There is no lie in war or in preparation for war that can't be defended. We went beyond this. We tried to create new realities overnight, careful sets of words that resemble advertising slogans in memorability and repeatability. These were words that would yield pictures eventually and then become three-dimensional. The reality stands, it walks, it squats. Except when it doesn't." He didn't smoke but his voice had a sandlike texture, maybe just raspy with age, sometimes slipping inward, becoming nearly inaudible. We sat for some time. He was slouched in the middle of the sofa, looking off toward some point in a high corner of the room. He had scotch and water in a coffee mug secured to his midsection. Finally he said, "Haiku." I nodded thoughtfully, idiotically, a slow series of gestures meant to indicate that I understood completely. "Haiku means nothing beyond what it is. A pond in summer, a leaf in the wind. It's human consciousness located in nature. It's the answer to everything in a set number of lines, a prescribed syllable count. I wanted a haiku war," he said. "I wanted a war in three lines. This was not a matter of force levels or logistics. What I wanted was a set of ideas linked to transient things. This is the soul of haiku. Bare everything to plain sight. See what's there. Things in war are transient. See what's there and then be prepared to watch it disappear." |
What's there—
This view of a die's faces 3, 6, and 5, in counter-
clockwise order (see previous post) suggests a way
of labeling the eight corners of a die (or cube):
123, 135, 142, 154, 246, 263, 365, 456.
Here opposite faces of the die sum to 7, and the
three faces meeting at each corner are listed
in counter-clockwise order. (This corresponds
to a labeling of one of MacMahon's* 30 colored cubes.)
A similar vertex-labeling may be used in describing
the automorphisms of the order-8 quaternion group.
For a more literary approach to quaternions, see
Pynchon's novel Against the Day .
* From Peter J. Cameron's weblog:
"The big name associated with this is Major MacMahon,
an associate of Hardy, Littlewood and Ramanujan,
of whom Robert Kanigel said,
His expertise lay in combinatorics, a sort of
glorified dice-throwing, and in it he had made
contributions original enough to be named
a Fellow of the Royal Society.
Glorified dice-throwing, indeed…"
Sunday, August 5, 2012
Cube Partitions
The second Logos figure in the previous post
summarized affine group actions on partitions
that generate a group of about 1.3 trillion
permutations of a 4x4x4 cube (shown below)—
Click for further details.
Thursday, July 26, 2012
Solomon’s Seal
(Mathematics and Narrative, continued)
Narrative—
The Ring and The Stone from yesterday’s post, and…
“In Medieval Jewish, Christian and Islamic legends,
the Seal of Solomon was a magical signet ring
said to have been possessed by King Solomon….”
— Wikipedia article, Seal of Solomon
Mathematics—
A fact related to the mathematical
“Solomon’s seal” described above by Bell:
The reference to Edge is as follows—
[3] Edge, W. L., Quadrics over GF(2) and
their relevance for the cubic surface group,
Canadian J. Maths. 11 (1959) ….
(This reference relates Hirschfeld’s remarks
quoted above to the 64-point affine space
illustrated below (via the associated
63-point projective space PG (5, 2)).
Sunday, February 5, 2012
Wednesday, January 11, 2012
Cuber
“Examples galore of this feeling must have arisen in the minds of the people who extended the Magic Cube concept to other polyhedra, other dimensions, other ways of slicing. And once you have made or acquired a new ‘cube’… you will want to know how to export a known algorithm , broken up into its fundamental operators , from a familiar cube. What is the essence of each operator? One senses a deep invariant lying somehow ‘down underneath’ it all, something that one can’t quite verbalize but that one recognizes so clearly and unmistakably in each new example, even though that example might violate some feature one had thought necessary up to that very moment. In fact, sometimes that violation is what makes you sure you’re seeing the same thing , because it reveals slippabilities you hadn’t sensed up till that time….
… example: There is clearly only one sensible 4 × 4 × 4 Magic Cube. It is the answer; it simply has the right spirit .”
— Douglas R. Hofstadter, 1985, Metamagical Themas: Questing for the Essence of Mind and Pattern (Kindle edition, locations 11557-11572)
See also Many Dimensions in this journal and Solomon’s Cube.
Friday, December 30, 2011
Quaternions on a Cube
The following picture provides a new visual approach to
the order-8 quaternion group's automorphisms.
Click the above image for some context.
Here the cube is called "eightfold" because the eight vertices,
like the eight subcubes of a 2×2×2 cube,* are thought of as
independently movable. See The Eightfold Cube.
See also…
- The 1985 note from which the above figures were drawn
- Visualizing GL(2,p)
- Quaternions in an Affine Galois Plane
Related material: Robin Chapman and Karen E. Smith
on the quaternion group's automorphisms.
* See Margaret Wertheim's Christmas Eve remarks on mathematics
and the following eightfold cube from an institute she co-founded—

© 2005 The Institute for Figuring
Photo by Norman Brosterman
fom the Inventing Kindergarten
exhibit at The Institute for Figuring
(co-founded by Margaret Wertheim)
Sunday, September 18, 2011
Anatomy of a Cube
R.D. Carmichael’s seminal 1931 paper on tactical configurations suggests
a search for later material relating such configurations to block designs.
Such a search yields the following—
“… it seems that the relationship between
BIB [balanced incomplete block ] designs
and tactical configurations, and in particular,
the Steiner system, has been overlooked.”
— D. A. Sprott, U. of Toronto, 1955
The figure by Cullinane included above shows a way to visualize Sprott’s remarks.
For the group actions described by Cullinane, see “The Eightfold Cube” and
“A Simple Reflection Group of Order 168.”
Update of 7:42 PM Sept. 18, 2011—
From a Summer 2011 course on discrete structures at a Berlin website—
A different illustration of the eightfold cube as the Steiner system S(3, 4, 8)—
Note that only the static structure is described by Felsner, not the
168 group actions discussed (as above) by Cullinane. For remarks on
such group actions in the literature, see “Cube Space, 1984-2003.”
Saturday, August 27, 2011
Cosmic Cube*
Prequel — (Click to enlarge)
Background —
See also Rubik in this journal.
* For the title, see Groups Acting.
Friday, June 24, 2011
The Cube
Click the above image for some background.
Related material:
Skateboard legend Andy Kessler,
this morning's The Gleaming,
and But Sometimes I Hit London.
Monday, June 21, 2010
Cube Spaces
Cubic models of finite geometries
display an interplay between
Euclidean and Galois geometry.
Example 1— The 2×2×2 Cube—
also known as the eightfold cube—
Group actions on the eightfold cube, 1984—
Version by Laszlo Lovasz et al., 2003—
Lovasz et al. go on to describe the same group actions
as in the 1984 note, without attribution.
Example 2— The 3×3×3 Cube
A note from 1985 describing group actions on a 3×3 plane array—
Undated software by Ed Pegg Jr. displays
group actions on a 3×3×3 cube that extend the
3×3 group actions from 1985 described above—
Pegg gives no reference to the 1985 work on group actions.
Example 3— The 4×4×4 Cube
A note from 27 years ago today—
As far as I know, this version of the
group-actions theorem has not yet been ripped off.
Thursday, October 22, 2009
Chinese Cubes
From the Bulletin of the American Mathematical Society, Jan. 26, 2005:
What is known about unit cubes
by Chuanming Zong, Peking University
Abstract: Unit cubes, from any point of view, are among the simplest and the most important objects in n-dimensional Euclidean space. In fact, as one will see from this survey, they are not simple at all….
From Log24, now:
What is known about the 4×4×4 cube
by Steven H. Cullinane, unaffiliated
Abstract: The 4×4×4 cube, from one point of view, is among the simplest and the most important objects in n-dimensional binary space. In fact, as one will see from the links below, it is not simple at all.
The Klein Correspondence, Penrose Space-Time, and a Finite Model
Related material:
Monday’s entry Just Say NO and a poem by Stevens,
Thursday, March 5, 2020
Pythagorean Letter Meets Box of Chocolates
Friday, July 11, 2014Spiegel-Spiel des GeviertsFiled under: Uncategorized — m759 @ 12:00 PM See Cube Symbology. |
Monday, November 11, 2019
Time and Chance
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 —
Cover of a book by Douglas Hofstadter
Monday, September 9, 2019
ART WARS at Harvard: The Wertham Professorship
See as well an obituary for Mrs. Wertham from 1987.
Related art —
Friday, July 11, 2014
|
For further details, search the Web for "Wertham Professor" + Eck.
Sunday, July 15, 2018
Jewish Oases
"… 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 …
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
Saturday, May 19, 2018
Flux Capacitor
For Tom Hanks and Dan Brown —
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.
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
Other intersection-points-counting material —
See also Hanks + Cube in this journal —
Thursday, December 21, 2017
Monday, July 24, 2017
Penguin Classics Deluxe Edition
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
|
Related material —
Thursday, June 22, 2017
Wednesday, June 21, 2017
Concept and Realization
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:
A realization —
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 —
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).
Friday, March 10, 2017
Transformers
Thursday, March 2, 2017
Stories
"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?
Click image for related posts.
Sunday, February 26, 2017
Poetic Order
Transformations acting on Solomon's Cube
furnish a model of poetic order.
Some backstory for Hollywood —
Saturday, February 18, 2017
Solid Symmetry (continued)
See Hanks + Cube in this journal … For instance …
Friday, July 11, 2014
|
Verbum
The Log24 version (Nov. 9, 2005, and later posts) —
VERBUM
|
See also related material in the previous post, Transformers.
Monday, October 3, 2016
Ein Eck
Friday, July 11, 2014
|
Friday, August 5, 2016
Sleight of Post
From an earlier Log24 post —
Friday, July 11, 2014
|
From a post of the next day, July 12, 2014 —
"So there are several different genres and tones
jostling for prominence within Lexicon :
a conspiracy thriller, an almost abstract debate
about what language can do, and an ironic
questioning of some of the things it’s currently used for."
— Graham Sleight in The Washington Post
a year earlier, on July 15, 2013
For the Church of Synchronology, from Log24 on the next day —
From a post titled Circles on the date of Marc Simont's death —
See as well Verhexung in this journal.
Thursday, July 14, 2016
Symmetries and Correspondences
The title is that of a large-scale British research project
in mathematics. On a more modest scale …
"Hanks + Cube" in this journal —
Tuesday, June 21, 2016
The Central Structure
“The central poem is the poem of the whole,
The poem of the composition of the whole”
— Wallace Stevens, “A Primitive like an Orb”
The symmetries of the central four squares in any pattern
from the 4×4 version of the diamond theorem extend to
symmetries of the entire pattern. This is true also of the
central eight cubes in the 4×4×4 Solomon’s cube .
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 .
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.
Wednesday, April 20, 2016
Symmetric Generation of a Simple Group
The reference in the previous post to the work of Guitart and
The Road to Universal Logic suggests a fiction involving
the symmetric generation of the simple group of order 168.
See The Diamond Archetype and a fictional account of the road to Hell …
The cover illustration below has been adapted to
replace the flames of PyrE with the eightfold cube.
For related symmetric generation of a much larger group, see Solomon’s Cube.
Wednesday, December 2, 2015
Saturday, April 25, 2015
Ghosts and Shadows
For Poetry Month
From the home page of Alexandre Borovik:
Book in progress: Shadows of the Truth
This book (to be published soon) can be viewed
as a sequel to Mathematics under the Microscope ,
but with focus shifted on mathematics as it was
experienced by children (well, by children who
became mathematicians). The cover is designed
by Edmund Harriss.
See also Harriss's weblog post of Dec. 27, 2008, on the death
of Harold Pinter: "The Search for the Truth Can Never Stop."
This suggests a review of my own post of Dec. 3, 2012,
"The Revisiting." A figure from that post:
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:
A 2x2x2 articulated cube:
A 4x4x4 articulated cube built from subcubes like
the one viewed by Tom Hanks above:
Saturday, July 12, 2014
Mars Package
“For me it is a sign that we have fundamentally different
conceptions of the work of the intelligence services.”
— Germany’s Chancellor Angela Merkel in
theguardian.com, Saturday, 12 July 2014, 14.32 EDT
Another sort of service, thanks to Dan Brown and Tom Hanks:
Friday, July 11, 2014 |
Sequel
A sequel to the 1974 film
Thunderbolt and Lightfoot :
Contingent and Fluky
Some variations on a thunderbolt theme:
These variations also exemplify the larger
Verbum theme:
A search today for Verbum in this journal yielded
a Georgetown University Chomskyite, Professor
David W. Lightfoot.
"Dr. Lightfoot writes mainly on syntactic theory,
language acquisition and historical change, which
he views as intimately related. He argues that
internal language change is contingent and fluky,
takes place in a sequence of bursts, and is best
viewed as the cumulative effect of changes in
individual grammars, where a grammar is a
'language organ' represented in a person's
mind/brain and embodying his/her language
faculty."
Some syntactic work by another contingent and fluky author
is related to the visual patterns illustrated above.
See Tecumseh Fitch in this journal.
For other material related to the large Verbum cube,
see posts for the 18th birthday of Harry Potter.
That birthday was also the upload date for the following:
See esp. the comments section.
Friday, July 11, 2014
Spiegel-Spiel des Gevierts
Friday, May 9, 2014
Models of Everything
“The About page contains detailed descriptions of the project….”
— The Illustris project on constructing a model of the universe
For the mathematics of a simpler traditional Chinese model
of everything, see
- Geometry of the I Ching ,
- Solomon’s Cube, and the
- Diamond Space about page.
Thursday, March 27, 2014
Diamond Space
Definition: A diamond space — informal phrase denoting
a subspace of AG(6, 2), the six-dimensional affine space
over the two-element Galois field.
The reason for the name:
Click to enlarge.
Saturday, April 21, 2012
Finding a Form
In "Contact," Dr. Arroway is shown the key to the Primer—
In this journal, fictional symbologist Robert Langdon is shown a cube—
"Confusion is nothing new." — Song lyric
Wednesday, April 18, 2012
Adam in Eden
…. and John Golding, an authority on Cubism who "courted abstraction"—
"Adam in Eden was the father of Descartes." — Wallace Stevens
Fictional symbologist Robert Langdon and a cube—
From a Log24 post, "Eightfold Cube Revisited,"
on the date of Golding's death—
A related quotation—
"… quaternions provide a useful paradigm
for studying the phenomenon of 'triality.'"
— David A. Richter's webpage Zometool Triality
See also quaternions in another Log24 post
from the date of Golding's death— Easter Act.
Monday, April 16, 2012
Carroll Thanks the Academy
Gary Gutting, "Arguing About Language," in "The Stone,"
The New York Times philosophy column, yesterday—
There's a sense in which we speak language
and a sense in which, in Mallarmé's famous phrase,
“language itself speaks.”
Famous? A Google Book Search for
"language itself speaks" Mallarmé
yields 2 results, neither helpful.
But a Google Book Search for
"language itself speaks" Heidegger
yields "about 312 results."
A related search yields the following—
Paul Valéry, encountering Un Coup de Dés in Mallarmé’s worksheets in 1897, described the text as tracing the pattern of thought itself:
It seemed to me that I was looking at the form and pattern of a thought, placed for the first time in finite space. Here space itself truly spoke, dreamed, and gave birth to temporal forms….
… there in the same void with them, like some new form of matter arranged in systems or masses or trailing lines, coexisted the Word! (Leonardo 309*)
* The page number is apparently a reference to The Collected Works of Paul Valéry: Leonardo, Poe, Mallarmé , translated by Malcolm Cowley and James R. Lawler, Princeton University Press, 1972. (As a temporal form, "309" might be interpreted as a reference to 3/09, March 9, the date of a webpage on the Void.)
For example—
Background:
Deconstructing Alice
and Symbology.
Wednesday, September 1, 2010
September Morn
For Alyssa Milano —
(Click here for cheesy Neil Diamond background music.)
For some related philosophical remarks, see Deconstructing Alice
and the new Pythagorean thriller The Thousand.
Wednesday, June 16, 2010
Brightness at Noon
David Levine's portrait of Arthur Koestler (see Dec. 30, 2009) —
See also this morning's post as well as
Monday's post quoting George David Birkhoff —
"If I were a Leibnizian mystic… I would say that…
God thinks multi-dimensionally — that is,
uses multi-dimensional symbols beyond our grasp."
Geometry of Language
(Continued from April 23, 2009, and February 13, 2010.)
Paul Valéry as quoted in yesterday’s post:
“The S[elf] is invariant, origin, locus or field, it’s a functional property of consciousness” (Cahiers, 15:170 [2: 315])
The geometric example discussed here yesterday as a Self symbol may seem too small to be really impressive. Here is a larger example from the Chinese, rather than European, tradition. It may be regarded as a way of representing the Galois field GF(64). (“Field” is a rather ambiguous term; here it does not, of course, mean what it did in the Valéry quotation.)
From Geometry of the I Ching—
The above 64 hexagrams may also be regarded as
the finite affine space AG(6,2)— a larger version
of the finite affine space AG(4,2) in yesterday’s post.
That smaller space has a group of 322,560 symmetries.
The larger hexagram space has a group of
1,290,157,424,640 affine symmetries.
From a paper on GL(6,2), the symmetry group
of the corresponding projective space PG(5,2),*
which has 1/64 as many symmetries—
For some narrative in the European tradition
related to this geometry, see Solomon’s Cube.
* Update of July 29, 2011: The “PG(5,2)” above is a correction from an earlier error.
Tuesday, May 4, 2010
Mathematics and Narrative, continued
Romancing the
Non-Euclidean Hyperspace
Backstory —
Mere Geometry, Types of Ambiguity,
Dream Time, and Diamond Theory, 1937
For the 1937 grid, see Diamond Theory, 1937.
The grid is, as Mere Geometry points out, a non-Euclidean hyperspace.
For the diamonds of 2010, see Galois Geometry and Solomon’s Cube.
Friday, March 19, 2010
Garden of Forking Paths
Saturday, March 6, 2010
Deconstructing Alice
Alyssa is Wonderland
Manohla Dargis in The New York Times yesterday—
“Of course the character of Carroll’s original Alice is evident in each outrageous creation she dreams up in ‘Wonderland’ and in the sequel, ‘Through the Looking-Glass,’ which means that she’s a straight man to her own imagination. (She is Wonderland.)”
From Inside the White Cube—
“The sacramental nature of the space becomes clear, and so does one of the great projective laws of modernism: as modernism gets older, context becomes content. In a peculiar reversal, the object introduced into the gallery ‘frames’ the gallery and its laws.”
From Yogi Berra–
“When you come to a fork in the road, take it.”
Related material: For Baron Samedi and…
Thursday, February 18, 2010
Theories: An Outline
Truth, Geometry, Algebra
The following notes are related to A Simple Reflection Group of Order 168.
1. According to H.S.M. Coxeter and Richard J. Trudeau
“There is a pleasantly discursive treatment of Pontius Pilate’s unanswered question ‘What is truth?’.”
— Coxeter, 1987, introduction to Trudeau’s The Non-Euclidean Revolution
1.1 Trudeau’s Diamond Theory of Truth
1.2 Trudeau’s Story Theory of Truth
2. According to Alexandre Borovik and Steven H. Cullinane
2.1 Coxeter Theory according to Borovik
2.1.1 The Geometry–
Mirror Systems in Coxeter Theory
2.1.2 The Algebra–
Coxeter Languages in Coxeter Theory
2.2 Diamond Theory according to Cullinane
2.2.1 The Geometry–
Examples: Eightfold Cube and Solomon’s Cube
2.2.2 The Algebra–
Examples: Cullinane and (rather indirectly related) Gerhard Grams
Summary of the story thus far:
Diamond theory and Coxeter theory are to some extent analogous– both deal with reflection groups and both have a visual (i.e., geometric) side and a verbal (i.e., algebraic) side. Coxeter theory is of course highly developed on both sides. Diamond theory is, on the geometric side, currently restricted to examples in at most three Euclidean (and six binary) dimensions. On the algebraic side, it is woefully underdeveloped. For material related to the algebraic side, search the Web for generators+relations+”characteristic two” (or “2“) and for generators+relations+”GF(2)”. (This last search is the source of the Grams reference in 2.2.2 above.)
Tuesday, January 26, 2010
Symbology
From this journal:
Friday December 5, 2008Mirror-Play of
the Fourfold For an excellent commentary View selected pages Play and the Aesthetic Dimension (Mihai I. Spariosu, Related material: – and Theme and Variations. |
Transition to the
Garden of Forking Paths–
(See For Baron Samedi)–
The Found Symbol
and Dissemination, by Jacques Derrida,
translated by Barbara Johnson,
London, Athlone Press, 1981–
Pages 354-355
On the mirror-play of the fourfold
Pages 356-357
Shaking up a whole culture
Pages 358-359
Cornerstone and crossroads
Pages 360-361
A deep impression embedded in stone
Pages 362-363
A certain Y, a certain V
Pages 364-365
The world is Zeus's play
Page 366
It was necessary to begin again
Saturday, January 23, 2010
For Baron Samedi
Annals of Deconstruction —
Click on image for background.
Related material
for Baron Samedi —
The Found Symbol
Saturday, November 14, 2009
Mathematics and Narrative, continued:
A graphic novel reviewed in the current Washington Post features Alfred North Whitehead and Bertrand Russell–
Related material:
Whitehead on Fano’s finite projective three-space:
“This is proved by the consideration of a three dimensional geometry in which there are only fifteen points.”
—The Axioms of Projective Geometry , Cambridge University Press, 1906
Further reading:
See Solomon’s Cube and the link at the end of today’s previous entry, then compare and contrast the above portraits of Whitehead and Russell with Charles Williams’s portraits of Sir Giles Tumulty and Lord Arglay in the novel Many Dimensions .
Thursday, September 17, 2009
Thursday September 17, 2009
Wednesday, September 16, 2009
Saturday, September 5, 2009
Saturday September 5, 2009
Burning Man
(Cover slightly changed.)
Background —
SAT
Part I:
Part II:
![]() |
Part III:
From August 25th —
"Boo, boo, boo,
square root of two."
Saturday, December 6, 2008
Saturday December 6, 2008
Another Show
A footprint from Germany:
Germany Python-urllib |
/504856559/item.html | 12/6/2008 1:21 PM |
The link in the above footprint leads
to an entry of July 5, 2006.
The access method:
The urllib Module“The Python urllib module implements a fairly high-level abstraction for making any web object with a URL act like a Python file: i.e., you open it, and get back an object….” |
of the object fetched by Python,
see Anti-Christmas 2007.
For a larger and more sophisticated
relative of that object,
see Solomon’s Cube and
the related three presents
from the German link’s target:
1. Many Dimensions 2. Boggle 3. My Space |
Saturday, May 10, 2008
Monday, July 23, 2007
Monday July 23, 2007
is 18 today.

Greetings.
“The greatest sorcerer (writes Novalis memorably)
would be the one who bewitched himself to the point of
taking his own phantasmagorias for autonomous apparitions.
Would not this be true of us?”
–Jorge Luis Borges, “Avatars of the Tortoise”
“El mayor hechicero (escribe memorablemente Novalis)
sería el que se hechizara hasta el punto de
tomar sus propias fantasmagorías por apariciones autónomas.
¿No sería este nuestro caso?”
–Jorge Luis Borges, “Los Avatares de la Tortuga“
At Midsummer Noon:“In Many Dimensions (1931)
Williams sets before his reader the
mysterious Stone of King Solomon,
an image he probably drew from
a brief description in Waite’s
The Holy Kabbalah (1929) of
a supernatural cubic stone
on which was inscribed
‘the Divine Name.’”
![]() Related material:
|
It is not enough to cover the rock with leaves. We must be cured of it by a cure of the ground Or a cure of ourselves, that is equal to a cure Of the ground, a cure beyond forgetfulness. And if we ate the incipient colorings – Wallace Stevens, “The Rock” |
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.”

“shadows” of a sort,
derived from a different
“central object”:
Tuesday, April 3, 2007
Tuesday April 3, 2007
Our Judeo-Christian
Heritage –
Lottery
Hermeneutics
Part I: Judeo
The Lottery 12/9/06 | Mid-day | Evening |
New York | 036
See |
331
See 3/31— “square crystal” and “the symbolism could not have been more perfect.” |
Pennsylvania | 602
See 6/02— Walter Benjamin |
111
See 1/11— “Related material:
|
Part II: Christian
The Lottery 4/3/07 | Mid-day | Evening |
New York | 115
See 1/15— |
017
See |
Pennsylvania | 604
See |
714
See |
Related material:
It is perhaps relevant to
this Holy Week that the
date 6/04 (2006) above
refers to both the Christian
holy day of Pentecost and
to the day of the
facetious baccalaureate
of the Class of 2006 in
the University Chapel
at Princeton.
For further context for the
Log24 remarks of that same
date, see June 1-15, 2006.
Sunday, December 10, 2006
Sunday December 10, 2006
Time and Chance
on the 90th Birthday
of Kirk Douglas,
star of
“The Garden of Allah“
The Lottery 12/9/06 | Mid-day | Evening |
New York | 036
See |
331
See 3/31— “square crystal” and “the symbolism could not have been more perfect.” |
Pennsylvania | 602
See 6/02— Walter Benjamin |
111
See 1/11— “Related material: |

Thursday, October 5, 2006
Thursday October 5, 2006
(Title of an interview with
the late Paul Halmos, mathematician)
From a 1990 interview:
“What’s the best part of being a mathematician? I’m not a religious man, but it’s almost like being in touch with God when you’re thinking about mathematics. God is keeping secrets from us, and it’s fun to try to learn some of the secrets.”
I personally prefer Annie Dillard on God:
“… if Holy the Firm is matter at its dullest, Aristotle’s materia prima, absolute zero, and since Holy the Firm is in touch with the Absolute at base, then the circle is unbroken. And it is…. Holy the Firm is in short the philosopher’s stone.”
Some other versions of
the philosopher’s stone:
April 28, 2004:
This last has the virtue of
being connected with Halmos
via his remarks during the
“In Touch with God” interview:
“Combinatorics, the finite case, is where the genuine, deep insight is.”
See also the remark of Halmos that serves as an epigraph to Theme and Variations.
the 4×9 black rectangle
has also served
at least one interpreter
as a philosopher’s stone,
and is also the original
“Halmos tombstone.”
Wednesday, September 20, 2006
Wednesday September 20, 2006
Public Space
“… the Danish cartoons crisis last March showed ‘two world views colliding in public space with no common point of reference.'”
— George Carey, Archbishop of Canterbury from 1991 to 2002, quoted in today’s London Times.
Related material:
Geometry and Christianity
(Google search yielding
“about 1,540,000” results)
Geometry and Islam
(Google search yielding
“about 1,580,000” results)

A Public Space
— Motto of
Plato’s Academy
Log24 on Feb. 15, 2006:
If we replace the Chinese word “I” (change, transformation) with the word “permutation,” the relevance of Western mathematics (which some might call “the Logos“) to the I Ching (“Changes Classic”) beomes apparent.
Related material:
Hitler’s Still Point, Jung’s Imago, Solomon’s Cube, Geometry of the I Ching, and Globe Award. |
For the relevance of Plato to
Islam, see David Wade’s
Pattern in Islamic Art
and a Google search on
Plato and Islam
(“about 1,680,000” results).
— Heraclitus of Ephesus, about 500 B.C.
Wednesday, July 5, 2006
Wednesday July 5, 2006
And now, from
the author of Sphere…
He beomes aware of something else… some other presence.
“Anybody here?” he says.
I am here.
He almost jumps, it is so loud. Or it seems loud. Then he wonders if he has heard anything at all.
“Did you speak?”
No.
How are we communicating? he wonders.
The way everything communicates with everything else.
Which way is that?
Why do you ask if you already know the answer?
— Sphere, by Michael Crichton, Harvard ’64
“… when I went to Princeton things were completely different. This chapel, for instance– I remember when it was just a clearing, cordoned off with sharp sticks. Prayer was compulsory back then, and you couldn’t just fake it by moving your lips; you had to know the words, and really mean them. I’m dating myself, but this was before Jesus Christ.”
— Baccalaureate address at Princeton, Pentecost 2006, reprinted in The New Yorker, edited by David Remnick, Princeton ’81
Related figures:
For further details,
see Solomon’s Cube
and myspace.com/affine.
For further details,
see Jews on Buddhism
and
Adventures in Group Theory.
“In this way we are offered
a formidable lesson
for every Christian community.”
Pope Benedict XVI
on Pentecost,
June 4, 2006,
St. Peter’s Square.
Saturday, June 17, 2006
Saturday June 17, 2006
game that many people can play.”
— Freeman Dyson in the current
New York Review of Books
Part I:
The Game
Part II:
Many People
For further details,
see Solomon’s Cube
and myspace.com/affine.
“The rock cannot be broken.
It is the truth.”
— Wallace Stevens
Wednesday, May 10, 2006
Wednesday May 10, 2006
“… 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.”
The Number of the Beast

The above screenshot shows a
moveable JavaScript display
of a space of six dimensions
(over the 2-element field).
(To see how the display works,
try the Kaleidoscope Puzzle first.)
This is a crazy world and
the only way to enjoy it
is to treat it as a joke.”
Compare and contrast:
Solomon’s Cube, the five
Log24 entries ending on 3/14,
and the
American Mathematical Society
on Mathematical Imagery.
Related material:
A more extensive excerpt from
The Number of the Beast, and
Thursday, March 9, 2006
Thursday March 9, 2006
Finitegeometry.org Update
(Revised May 21, 2006)
Finitegeometry.org now has permutable JavaScript views of the 2x2x2 and 4x4x4 design cubes. Solomon’s Cube presented a claim that the 4x4x4 design cube retains symmetry under a group of about 1.3 trillion transformations. The JavaScript version at finitegeometry.org/sc/64/view/ lets the reader visually verify this claim. The reader should first try the Diamond 16 Puzzle. The simpler 2x2x2 design cube, with its 1,344 transformations, was described in Diamonds and Whirls; the permutable JavaScript version is at finitegeometry.org/sc/8/view/.
Wednesday, January 4, 2006
Wednesday January 4, 2006
In memory of Humphrey Carpenter, author of The Inklings, who attended The Dragon School. Carpenter died a year ago today.
“Lewis began with a number of haunted images….”
“The best of the books are the ones… where the allegory is at a minimum and the images just flow.”
“‘Everything began with images,’ Lewis wrote….”

From Paul Preuss,
Broken Symmetries
(see previous entry):
From
Verbum Sat Sapienti?
Wednesday, November 9, 2005
Thursday, February 25, 2021
Compare and Contrast
“… 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
“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 —
Monday, February 15, 2021
Raiders of the Lost Building Blocks
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
Sunday, December 27, 2020
Knight Move for Trevanian
“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
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?
“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
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
Wednesday, September 9, 2020
Portrait with Holocron
Thursday, July 9, 2020
The Enigma Glyphs
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 …
“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
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 —
Saturday, May 23, 2020
Eightfold Geometry: A Surface Code “Unit Cell”
The resemblance to the eightfold cube is, of course,
completely coincidental.
Some background from the literature —
Friday, May 22, 2020
Surface Code News
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.”
Friday, February 21, 2020
To and Fro, Back and …
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.”
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 …
… 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
Cube Bricks 1984 —
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
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
“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
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
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 .
Monday, May 13, 2019
Doris Day at the Hudson Rock
" '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
"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
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.”
Suggested by a review of Curl on Modernism —
Related material —
Waugh + Orwell in this journal and …
Wednesday, June 6, 2018
Geometry for Goyim
Mystery box merchandise from the 2011 J. J. Abrams film Super 8 —
A mystery box that I prefer —
Click image for some background.
See also Nicht Spielerei .
Thursday, March 29, 2018
“Before Creation Itself . . .”
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
Sure, Whatever.
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.