"Before time began, there was the Cube."
— Optimus Prime
"Spiel ist nicht Spielerei."
— Friedrich Froebel
Friday, February 2, 2024
Monday, January 15, 2024
Storylines Colliding: The Cornfield Paradox
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Monday, January 1, 2024
Molly’s Date
The Des Moines Register 2018 story pictured at lower right in
the previous post featured one Molly Vincent. A holiday greeting
on her LinkedIn page leads to . . .
Also on the above YouTube date —
Related reading — "Weird Pharaonic Monument" —
"Before time began, there was the Cube." — Optimus Prime
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Monday, December 25, 2023
“Weird Pharaonic Monument”
Epigraph for Cormac McCarthy —
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"When I got to high school the first place I went was to the library. It was just a small room with a desk and maybe a thousand books. Maybe not that. But among them was a volume of Berkeley. I dont know what it was doing there. Probably because Berkeley was a bishop. Well. Almost certainly because Berkeley was a bishop. But I sat in the floor and I read A New Theory of Vision. And it changed my life. I understood for the first time that the visual world was inside your head. All the world, in fact. I didnt buy into his theological speculations but the physiology was beyond argument. I sat there for a long time. Just letting it soak in."
— McCarthy, Cormac. Stella Maris (p. 39). |
From this journal on April 18, 2023 —
" NY Times columnist's advice to the recent Harvard donor of $300 million —
'At least make them build you some weird pharaonic monument.' "
Illustration suggested by my own high-school library reading many years ago —
Click to enlarge:
"Before time began, there was the Cube." — Optimus Prime
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Wednesday, December 13, 2023
Director’s Exit
For St. Lucy's Day . . . Vide another post now tagged "Cube School."
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Sunday, December 10, 2023
Erin’s Barron’s: Skye High
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Tuesday, December 5, 2023
Wednesday, November 22, 2023
For E. Lily Yu* — Devs Setting
Friday, July 11, 2014
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* Author of Jewel Box: Stories ( Erewhon Books, Oct. 24, 2023).
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Sunday, November 19, 2023
Six Dimensions
"Sharpie, we have condensed six dimensions into four,
then we either work by analogy into six, or we have to use math
that apparently nobody but Jake and my cousin Ed understands.
Unless you can think of some way to project six dimensions into three–
you seem to be smart at such projections."
I closed my eyes and thought hard. "Zebbie, I don't think it can be done.
Maybe Escher could have done it."
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Friday, November 17, 2023
Classicism Continued: An Apotheosis of Modernity
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From Chapter 23, "Poetry," by Adam Parkes, in Writing in 1910–11, the English poet and critic T. E. Hulme claimed that the two major traditions in poetry, romanticism and classicism, were as different as a well and a bucket. According to the romantic party, Hulme explained, humankind is “intrinsically good, spoilt by circumstance”; that is, our nature is “a well, a reservoir full of possibilities.” For the classical party, however, human nature is “like a bucket”; it is “intrinsically limited, but disciplined by order and tradition to something fairly decent” (Hulme 1987: 117). But it was not only that romanticism and classicism were as dissimilar as a well and a bucket; their contents were different, too. To draw water from the well of romanticism was, in effect, to pour a “pot of treacle over the dinner table,” while the classical bucket was more likely to be full of little stones – or jewels, perhaps. Romanticism, in Hulme’s view, was the result of displaced religious fervor; it represented the return of religious instincts that the “perverted rhetoric of Rationalism” had suppressed, so that “concepts that are right and proper in their own sphere are spread over, and so mess up, falsify and blur the clear outlines of human experience” (Hulme 1987: 118). Classicism, by contrast, traded in dry goods – dry, hard goods, to be precise. Hulme left little doubt as to which side he was on. “It is essential to prove,” he argued, “that beauty may be in small, dry things. The great aim is accurate, precise and definite description. . . . I prophesy that a period of dry, hard, classical verse is coming” (Hulme 1987: 131–3). If by “dry, hard, classical verse” Hulme meant poems looking like the fragments of Sappho, he didn’t have to wait long to see his prophecy fulfilled.
The hard sand breaks,
Far off over the leagues of it, 228
playing on the wide shore, So wrote Hilda Doolittle in “Hermes of the Ways,” the first poem that she signed “H. D., Imagiste” at the behest of her fellow American expatriate Ezra Pound. From Pound’s perspective, the Imagist movement that he co-founded in 1912 with H. D. and the English poet Richard Aldington was finished well before the First World War began in August 1914; throughout this war-torn decade, however, Imagism continued to spawn the poetry of “small, dry things” whose coming Hulme had predicted a few years before. Indeed, modernist poets weren’t content merely to break down the extended heroic narratives – the “spilt religion,” as Hulme put it – of their treacly nineteenthcentury predecessors; they insisted on breaking down small things into ever-smaller particles and subparticles. This logic of disintegration is clearly at work in poems like “Hermes of the Ways,” where each line is metrically unique, creating a sense of perpetual freshness – an apotheosis of modernity, as it were. REFERENCE Hulme, T. E. (1987). Speculations: Essays on Humanism and the Philosophy of Art, ed. Herbert Read. London and New York: Routledge and Kegan Paul. First published 1924. |
Compare and contrast:
Jeremy Gray,
Plato's Ghost: The Modernist Transformation of Mathematics,
Princeton University Press, first edition Sept. 22, 2008 —
"Here, modernism is defined as an autonomous body of ideas,
having little or no outward reference, placing considerable emphasis
on formal aspects of the work and maintaining a complicated—
indeed, anxious— rather than a naïve relationship with the
day-to-day world, which is the de facto view of a coherent group
of people, such as a professional or discipline-based group
that has a high sense of the seriousness and value of what it is
trying to achieve. This brisk definition…."
(Quoted at the webpage Solomon's Cube.)
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Sunday, November 12, 2023
“Cum grano salis”
The above title is from the Black Mass performed by Boris Karloff
in a classic 1934 horror film. An illustration —
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Friday, November 10, 2023
Altman’s Monster* Version of Musk’s Grok Logo
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Tuesday, November 7, 2023
If It’s Tuesday . . .
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Tuesday, October 24, 2023
A Bond with Reality: The Geometry of Cuts
Illustrations of object and gestures
from finitegeometry.org/sc/ —
Object
Gestures
An earlier presentation of the above
seven partitions of the eightfold cube:
|
|
Related mathematics:
|
The use of binary coordinate systems
Natural physical transformations of square or cubical arrays See "The Thing and I." |
and . . .
Related entertainment:
Or Matt Helm by way of a Jedi cube.
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Monday, October 23, 2023
Friday, October 13, 2023
Hungarian Puzzle
See "Cube Space" + Lovasz.
This search was suggested by . . .
The conclusion of Solomon Golomb's
"Rubik's Cube and Quarks,"
American Scientist , May-June 1982 —
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Artbox.group
This new URL will forward to http://m759.net/wordpress/?s=Solomon+Cube.
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Lightbox for a Friday the 13th
For a different sort of Lightbox, more closely associated with
the number 13, see instances in this journal of . . .
(Adapted from Encyclopaedia Britannica,
Eleventh Edition (1911), Crystallography .)
"Before time began . . . ." — Optimus Prime
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Saturday, September 30, 2023
Café Society
Some less esoteric café alternatives … the ".cafe" domains
cubespace, foursquare, metamorph, and namespace.
And then there is a Morocco café domain for Marcela —
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Monday, September 25, 2023
Cool Kids’ Vocabulary: Anthropic
https://www.merriam-webster.com/dictionary/anthropic —
"Questions abound about how the various proposals intersect with
anthropic reasoning and the infamous multiverse idea."
— Natalie Wolchover, WIRED, 16 June 2019
A more recent, and notable, use of "anthropic" :
https://techcrunch.com/2023/09/25/
amazon-to-invest-up-to-4-billion-in-ai-startup-anthropic/ —
"As part of the investment agreement, Anthropic will use
Amazon’s cloud giant AWS as a primary cloud provider for
mission-critical workloads . . . ."
The cloud giant appeared here recently :
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Friday, September 22, 2023
Figurate Space
For the purpose of defining figurate geometry , a figurate space might be
loosely described as any space consisting of finitely many congruent figures —
subsets of Euclidean space such as points, line segments, squares,
triangles, hexagons, cubes, etc., — that are permuted by some finite group
acting upon them.
Thus each of the five Platonic solids constructed at the end of Euclid's Elements
is itself a figurate space, considered as a collection of figures — vertices, edges,
faces — seen in the nineteenth century as acted upon by a group of symmetries .
More recently, the 4×6 array of points (or, equivalently, square cells) in the Miracle
Octad Generator of R. T. Curtis is also a figurate space . The relevant group of
symmetries is the large Mathieu group M24 . That group may be viewed as acting
on various subsets of a 24-set… for instance, the 759 octads that are analogous
to the faces of a Platonic solid. The geometry of the 4×6 array was shown by
Curtis to be very helpful in describing these 759 octads.
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Thursday, September 21, 2023
For TOS, the Talent Operating System, an adapted song lyric:
“Beams could get no keener reception in a beamery”
|
Graphic design from April 1, 2018 —
Later, in 2019 — An undated webpage says . . . "…we’re officially announcing the launch of the new Beamery brand."
"A logo, a name, an idea: Meet the Bexa"
|
This flashback to March 7, 2022,
was suggested by a marrific date.
Fans of metadata may consult, in this journal,
the above metadata date — November 20, 2019.
Comments Off on For TOS, the Talent Operating System, an adapted song lyric:
“Beams could get no keener reception in a beamery”
“Beams could get no keener reception in a beamery”
Tuesday, September 19, 2023
Mystery Box
Sarah Larson in The New Yorker yesterday —
"Having revealed itself, the Perelman Performing Arts Center (PAC NYC),
designed by Joshua Ramus and his firm, REX, retains an air of mystery:
it’s a giant marble-sheathed cube, beige and opaque by day and warmly
aglow by night, fronted by a two-story staircase that evokes the approach
to a Mayan temple or the gangway to an alien spacecraft. What’s inside?"
Always an interesting question . . .
From "Made for Love" (2021) — Lyle Herringbone:
See as well yesterday's post
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Thursday, September 14, 2023
Wednesday, September 13, 2023
Edgelord School
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Monday, May 8, 2017
New Pinterest Board
|
The face at lower left above is that of an early Design edgelord.
A product of that edgelord's school —
See a design by Prince-Ramus in today's New York Times —
Remarks quoted here on the above San Diego date —
A related void —
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Saturday, September 9, 2023
“Fez” as Metaphor in Nowak* and in Levinson**
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"We need the word 'metaphor' for the whole double unit, and to use it sometimes for one of the two components in separation from the other is as injudicious as that other trick by which we use 'the meaning' here sometimes for the work that the whole double unit does and sometimes for the other component–the tenor, as I am calling it–the underlying idea or principal subject which the vehicle or figure means. It is not surprising that the detailed analysis of metaphors, if we attempt it with such slippery terms as these, sometimes feels like extracting cube-roots in the head."
— I. A. Richards, The Philosophy of Rhetoric . |
* Nowak: See the central image in "An Art Director's Top Nine," Log24 yesterday.
** Levinson: See Variety on the "Euphoria" character.
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Friday, September 1, 2023
Stella!
An animated GIF that shows the basic unit for
the "design cube" pages at finitegeometry.org —
From a post of Dec. 8, 2010, the (somewhat) related Stella Octangula —
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Friday, August 25, 2023
On the Night Road from Marfa
"I’m really interested in exploring space."
— New Yorker cover artist for the Aug. 28, 2023, issue.
Related cinematic art . . .
From a search in this journal for Nocturnal —
For some Bright Art Blocks Moments , see Cube Epiphany .
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Thursday, August 10, 2023
Lines and Shadows (title taken from Wambaugh)
Lines
"Listen to the wind blow, down comes the night
Running in the shadows, damn your love, damn your lies"
— Fleetwood Mac, "The Chain"
Shadows
Related YouTube and Log24 date: Sept. 27, 2018 —
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Monday, July 24, 2023
Topdot Art
The new URL topdot.art refers to depictions of
the top dot (or point, or vertex) in a vertex-edge diagram
of a square, cube, or hypercube that has been rotated
so that the bottom dot (or point, or vertex), represented by
all-zero coordinates in a labeling, is at the bottom …
and the top dot (or point, or vertex), represented by
all-one coordinates in a labeling, is at the top.
See (for instance) the Log24 post Physicality (Oct. 5, 2022).
Related philosophical remarks: Einheit .
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Friday, July 21, 2023
Sunday, July 2, 2023
Badlands Philosophy
This afternoon's Windows lockscreen is Badlands National Park —
From this morning's post, a phrase from Schopenhauer —
"Apparent Design in the Fate of the Individual."
An apparent design in the philosophy of Optimus Prime —
"Before time began, there was the Cube" —
Click the image for further remarks.
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Saturday, July 1, 2023
Mechanical Plaything (Hinged) vs. Conceptual Art (Unhinged)
"Infinity Cube" … hinged plaything, for sale —
"Eightfold Cube" … un hinged concept, not for sale—
See as well yesterday's Trickster Fuge ,
and a 1906 discussion of the eightfold cube:
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Wednesday, June 21, 2023
Annals of Magical Thinking: The Rushmore Embedding
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Saturday, June 10, 2023
Green, Orange, Black
The colors surrounding Watson's body in the above
"bandeau" photo suggest a review. A search in this journal
for Green+Orange+Black yields . . .
In the above image, the "hard core of objectivity" is represented
by the green-and-white eightfold cube. The orange and black are,
of course, the Princeton colors.
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Sunday, June 4, 2023
The Galois Core
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Friday, June 2, 2023
Geometric Entertainment
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Reichenbach’s Fell Swoop
See The Eightfold Cube and . . .
Art is magic delivered from
the lie of being truth.
— Theodor Adorno, Minima moralia,
London, New Left Books, 1974, p. 222
(First published in German in 1951.)
The director, Carol Reed, makes…
impeccable use of the beauty of black….
— V. B. Daniel on The Third Man
I see your ironical smile.
— Hans Reichenbach
Adorno, The Third Man, and Reichenbach
are illustrated below (l. to r.) above the names of
cities with which they are associated.
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Thursday, June 1, 2023
Antwerp Revisited: Diamond Space
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Tuesday, May 30, 2023
The Tour
In memory of a co-founder of Hollywood's "Magic Castle"
who reportedly died at 92 on Sunday . . .
From posts that were tagged "Blake Tour" on Sunday —
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Sunday, May 14, 2023
“The Structure of Space”
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 —
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Wednesday, May 10, 2023
Saving the Appearances
“… I realized that to me,
Gödel and Escher and Bach
were only shadows
cast in different directions by
some central solid essence.
I tried to reconstruct
the central object, and
came up with this book.”
Related images —
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Friday, May 5, 2023
For St. Corky Lee
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.
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Thursday, April 20, 2023
Alphabet Meets Gestalt . . .
Continued from April 18 .
"Working with words to create art
and working with your hands to create art
seem like two separate activities to me."
— Cover artist, The New Yorker , on April 17
See also Alphabet Blocks in this journal
as well as Escher's Verbum.
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|
Comments Off on Alphabet Meets Gestalt . . .
Saturday, April 8, 2023
Annals of Journalism
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.
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.
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Thursday, April 6, 2023
A Literary Supplement
Religious remarks in the Times Literary Supplement
issue dated April 7, 2023 (Good Friday) suggest a
review of other remarks — from July 1, 2019 —now
tagged The Exploded Cube. Some will prefer more useful
types of explosions.
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Sunday, March 19, 2023
For Your Consideration
Mank, Baez, Collins — A trip back to Christmas Eve, 2021.
Related art (via Baez) for Josefine Lyche —
See also Lyche in Log24 posts tagged Star Cube.
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Saturday, March 18, 2023
Blocking Groups*
Kitty in Uncanny X-Men #168 (April 1983)
"Try Bing Chat, Kitty."
* A Harvard phrase for a process analogous to that of the Hogwarts Sorting Hat.
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Zu diesem Themenkreis
From last night's update to the previous post —
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The use of binary coordinate systems
Natural physical transformations of square or cubical arrays See "The Thing and I." |
From a post of May 1, 2016 —
|
Mathematische Appetithäppchen: Autor: Erickson, Martin —
"Weitere Informationen zu diesem Themenkreis finden sich |
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Friday, March 17, 2023
Bing Chat Continues
Update at 9 PM ET March 17: A related observation by SHC —
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."
Comments Off on Bing Chat Continues
Sunday, March 12, 2023
Monday, February 13, 2023
The Adelson Shadow
Related search results —
From a different Adelson, in a Log24 post from 2003 —
Related geometric entertainment —
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Friday, February 10, 2023
Interstices and Symmetry
Call a 4×4 array labeled with 4 copies each
of 4 different symbols a foursquare.
The symmetries of foursquares are governed
by the symmetries of their 24 interstices —
(Cullinane, Diamond Theory, 1976.)
From Log24 posts tagged Mathieu Cube —
A similar exercise might involve the above 24 interstices of a 4×4 array.
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Monday, February 6, 2023
Interality Studies
|
You, Xi-lin; Zhang, Peter. "Interality in Heidegger."
The term "interology" is meant as an interventional alternative to traditional Western ontology. The idea is to help shift people's attention and preoccupation from subjects, objects, and entities to the interzones, intervals, voids, constitutive grounds, relational fields, interpellative assemblages, rhizomes, and nothingness that lie between, outside, or beyond the so-called subjects, objects, and entities; from being to nothing, interbeing, and becoming; from self-identicalness to relationality, chance encounters, and new possibilities of life; from "to be" to "and … and … and …" (to borrow Deleuze's language); from the actual to the virtual; and so on. As such, the term wills nothing short of a paradigm shift. Unlike other "logoi," which have their "objects of study," interology studies interality, which is a non-object, a no-thing that in-forms and constitutes the objects and things studied by other logoi. |
Some remarks from this journal on April 1, 2015 —
Manifest O
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| 83-06-21 | An invariance of symmetry The diamond theorem on a 4x4x4 cube, and a sketch of the proof. |
| 83-10-01 | Portrait of O A table of the octahedral group O using the 24 patterns from the 2×2 case of the diamond theorem. |
| 83-10-16 | Study of O A different way of looking at the octahedral group, using cubes that illustrate the 2x2x2 case of the diamond theorem. |
| 84-09-15 | Diamonds and whirls Block designs of a different sort — graphic figures on cubes. See also the University of Exeter page on the octahedral group O. |
The above site, finitegeometry.org/sc, illustrates how the symmetry
of various visual patterns is explained by what Zhang calls "interality."
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Friday, January 27, 2023
The Stone
Here stands the mean, uncomely stone,
’Tis very cheap in price!
The more it is despised by fools,
The more loved by the wise.
— https://jungcurrents.com/
the-story-of-the-stone-at-bollingen
Not so cheap:
Identical copies of the above image are being offered for sale
on three websites as representing a Masonic "cubic stone."
None of the three sites say where, exactly, the image originated.
Image searches for "Masonic stone," "Masonic cube," etc.,
fail to yield any other pictures that look like the above image —
that of a 2x2x2 array of eight identical subcubes.
For purely mathematical — not Masonic — properties of such
an array, see "eightfold cube" in this journal.
The websites offering to sell the questionable image —
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Getty —
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Alamy —
https://www.alamy.com/
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Photo12 —
https://www.photo12.com/en/image/
No price quoted on public page:
|
Comments Off on The Stone
Sunday, January 22, 2023
Preform
Sometimes the word "preform" is not a misspelling.
"… there are present in every psyche forms which are unconscious
but nonetheless active — living dispositions, ideas in the Platonic sense,
that preform and continually influence our thoughts and feelings and actions."
The Source: Jung on a facultas praeformandi . . .
Illustration —
"A primordial image . . . .
the axial system of a crystal"
For those who prefer a Jewish approach to these matters —
(Post last updated at about 2:10 PM ET on Jan. 23, 2023.)
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“Preform an affine transformation”
"Before time began, there was the Cube." — Transformers (2007)
Related literature:
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Saturday, January 21, 2023
Monday, January 16, 2023
Saturday, January 14, 2023
Châtelet on Weil — A “Space of Gestures”
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From Gilles Châtelet, Introduction to Figuring Space Metaphysics does have a catalytic effect, which has been described in a very beautiful text by the mathematician André Weil: Nothing is more fertile, all mathematicians know, than these obscure analogies, these murky reflections of one theory in another, these furtive caresses, these inexplicable tiffs; also nothing gives as much pleasure to the researcher. A day comes when the illusion vanishes: presentiment turns into certainty … Luckily for researchers, as the fogs clear at one point, they form again at another.4 André Weil cuts to the quick here: he conjures these 'murky reflections', these 'furtive caresses', the 'theory of Galois that Lagrange touches … with his finger through a screen that he does not manage to pierce.' He is a connoisseur of these metaphysical 'fogs' whose dissipation at one point heralds their reforming at another. It would be better to talk here of a horizon that tilts thereby revealing a new space of gestures which has not as yet been elucidated and cut out as structure. 4 A. Weil, 'De la métaphysique aux mathématiques', (Oeuvres, vol. II, p. 408.) |
For gestures as fogs, see the oeuvre of Guerino Mazzola.
For some clearer remarks, see . . .
Illustrations of object and gestures
from finitegeometry.org/sc/ —
Object
Gestures
An earlier presentation
of the above seven partitions
of the eightfold cube:
|
|
Related material: Galois.space .
Comments Off on Châtelet on Weil — A “Space of Gestures”
Friday, January 13, 2023
The “Diamond Space” of Mazzola
The Source —
Some similar notions from my own work . . .
The "Digraph" of Mazzola might correspond to a directed graph
indicating the structure of a permutation, as at right below —
Mazzola's "Formula" might correpond to a matrix and translation that
transform the above "Space" of eight coordinates, and his "Gesture"
to a different way of generating affine transformations of that space . . .
as in my webpage "Cube Space, 1984-2003."
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Wednesday, January 11, 2023
Raiders of the Lost Dark
A sequel to the previous post, "How the Darkness Gets In" —
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Tuesday, December 27, 2022
The Forms of Being
"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.
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Monday, December 26, 2022
Super-8 Box
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Friday, December 23, 2022
“Was ist Raum?” — Bauhaus Founder Walter Gropius
"Was ist Raum, wie können wir ihn
erfassen und gestalten?"
The Theory and
Organization of the
Bauhaus (1923)
A relevant illustration:
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).
These references will not appeal to those who enjoy modernism as a religion.
(For such a view, see Rosalind Krauss on grids and another writer's remarks
on the religion's 100th anniversary this year.)
Some related nihilist philosophy from Cormac McCarthy —
"Forms turning in a nameless void."
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Wednesday, November 30, 2022
Three Representations
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Tuesday, November 29, 2022
Mere Synchronology
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."
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Monday, November 28, 2022
Groups, Spaces, and Ripoffs
"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 —
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Thursday, November 10, 2022
For Students of the Forked Tongue
The above 1975 book by Robert Greer Cohn, Modes of Art, is
Volume I of a planned three-volume work.
The passage below is from a review of Cohn's Vol. II, Ways of Art —
|
Franklin, Ursula (1987) "Book Review: A Critical Work II. . . . . Those not familiar with the author's epistemology should begin with Appendix A of Ways of Art , a schematic demonstration of his tetrapolar-polypolar-dialectic, especially as it concerns the development of the French novel within the European tradition. But this dialectic, which has antecedents in Kierkegaard, Mallarme and Joyce, underlies all art, because: "this dimensional pulsation, or tetrapolar (and polypolar) higher vibrancy is, in short, the stuff of life: life is vibrant in this more complex way as well as in the more bipolar sense" (7). Cohn shows that "far out enough" the male or linear and the female or circular, the male vertical and the female horizontal dimensions "tend to merge as in relativity theory" (19). Ways of Art shows us the way through a historical becoming of art in its complex dialectic in which the metonymic (horizontal) axis constantly interrelates with the metaphoric (vertical). "Life is the mother, art the father" (vii); hence Cohn's quarrel with most contemporary Feminism, which is pronounced throughout the volume. Firmly grounded in its author's tetra-polypolar epistemology, this beautiful book becomes, however, at no point dryly abstract; it is the mature work of a true humanist who stands in clear and open opposition to the dehumanizing trend of "the quasi-scientific reductionism and abstract gimmickry of a great deal of current academic literary study, bellwethered by the structuralists, post-structuralists, and deconstructionists" (vi). Abundant footnotes constitute a substantial part of Ways of Art , on occasion developing insights almost into essays demonstrating crucial points along the general flow of the tradition from "Obscure Beginnings;' the opening chapter, to our "Contemporaries;' the last. Cohn reminds us that "In the Beginning was the Word;' for the Judaeo-Christian tradition at least, which his study fervently embraces; thus, for example, in Appendix 0 on "The Dance of the Sexes;' he censures "those who live by slogans, camps, and peer-opinion, the countless little bastard cults which characterize an era which has massively veered away from our free and beautiful Greco-Judaeo-Christian tradition" (332). Cohn traces man's way and that of his myths and rituals culminating in his art from that beginning along the lines of Freud, Neumann and Cassirer, and many others, always demonstrating the underlying polypolar dialectical rhythm. Thus in "From Barbarism to Young Culture;' we follow the Celts to Druidic ritual, Hebrew beginnings to the Psalms, Dionysian ritual to Greek tragedy, and thence to the beginnings of French dramatic literature originating in the Quem quaeritis sequence of the medieval Mass. Along the way arises artistic symbolism, for Cohn synonymous with "effective poetry;' to finally "ripen in France as never before" (99). Table I (134) graphs this development from the twelfth to the late nineteenth and early twentieth centuries. The author traces the rise of the artistic vocation from its antecedents in the double function of bard and priest, with the figure of Ronsard at the crossroads of that dying institution and the nascent concept of personal glory. "The Enlightenment Vocation" is exemplified in Montaigne, who humanizes the French cultural elite and points the way to French classicism and, farther down the road, after the moral collapse with the outgoing reign of Louis XIV, toward the Age of Reason. Clearly the most significant figure of the French Enlightenment for all of Western civilization is Rousseau, and Cohn beautifully shows us why this is so. Subsequently, "the nineteenth-century stage of the writer's journey will lead, starting from the crossroads of Rousseau, primarily in these two directions: the imperialistic and visionary prose of Balzac, the equally ambitious poetry of Mallarme", brothers under the skin" (199). And these two paths will then be reconciled in Proust's monumental A la recherche du temps perdu . . . . . |
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Tuesday, November 1, 2022
From “Goethe on All Souls’ Day”
The above title is that of a Log24 post on St. Cecilia's Day in 2017
that quoted some earlier All Souls' Day remarks from Berlin.
From that post —
Exercise: Explain why the lead article in the November issue of
Notices of the American Mathematical Society misquotes Weyl
and gives the misleading impression that the example above,
the eightfold cube , might be part of the mathematical pursuit
known as geometric group theory .
Background: Earlier instances here of the phrase "geometric group theory."
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Monday, October 31, 2022
Folklore vs. Mathematics
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Wednesday, October 12, 2022
Wednesday, October 5, 2022
Physicality
"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.
… And back to cube:
Related meditation: Beer Summit.
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Thursday, September 29, 2022
The 4×6 Problem*
The exercise posted here on Sept. 11, 2022, suggests a
more precisely stated problem . . .
The 24 coordinate-positions of the 4096 length-24 words of the
extended binary Golay code G24 can be arranged in a 4×6 array
in, of course, 24! ways.
Some of these ways are more geometrically natural than others.
See, for instance, the Miracle Octad Generator of R. T. Curtis.
What is the size of the largest subcode C of G24 that can be
arranged in a 4×6 array in such a way that the set of words of C
is invariant under the symmetry group of the rectangle itself, i.e. the
four-group of the identity along with horizontal and vertical reflections
and 180-degree rotation.
Recent Log24 posts tagged Bitspace describe the structure of
an 8-dimensional (256-word) code in a 4×6 array that has such
symmetry, but it is not yet clear whether that "cube-motif" code
is a Golay subcode. (Its octads are Golay, but possibly not all its
dodecads; the octads do not quite generate the entire code.)
Magma may have an answer, but I have had little experience in
its use.
* Footnote of 30 September 2022. The 4×6 problem is a
special case of a more general symmetric embedding problem.
Given a linear code C and a mapping of C to parts of a geometric
object A with symmetry group G, what is the largest subcode of C
invariant under G? What is the largest such subcode under all
such mappings from C to A?
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Wednesday, September 28, 2022
Bitspace Note
Update of 5:20 AM ET on Sept. 29. 2022 —
The octads of the [24, 8, 8] cube-motif code
can be transformed by the permutation below
into octads recognizable, thanks to the Miracle
Octad Generator (MOG) of R. T. Curtis, as
belonging to the Golay code.
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The Madness of Art
The title is by Henry James.*
For examples, see the Sept. 19 webpage below . . .
… and, in this journal, posts from that same date now tagged Cube Codes.
*
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Friday, September 16, 2022
Symmetric Generation
The above is about a subspace of the
24-dimensional vector space over GF(2)
. . . "An entire world of just 24 squares,"
to adapt a phrase from other Log24
posts tagged "Promises."
Update of 1:45 AM ET Sept. 18, 2022 —
It seems* from a Magma calculation that
the resemblance of the above extended
cube-motif code to the Golay code is only
superficial.
Without the highly symmetric generating codewords that were added
to extend its dimension from 8 to 12, the cube-motifs code apparently
does , like the Golay code, have nonzero weights of only 8, 12, 16, and 24 —
Perhaps someone can prove there is no way that adding more generating
codewords can turn the cube-motif code into the Golay code.
* The "seems" is because I have not yet encountered any of these
relatively rare (42 out of 4096) purported weight-4 codewords. Their
apparent existence may be due to an error in my typing of 0's and 1's.
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Wednesday, September 14, 2022
Tuesday, September 13, 2022
A Helpful Survey of the Literature
Some background for the exercise of 9/11 —
Vera Pless, "More on the uniqueness of the Golay codes,"
Discrete Mathematics 106/107 (1992) 391-398 —
"Several people [1-2,6] have shown that
any set of 212 binary vectors of length 24,
distance ≥ 8, containing 0, must be the
unique (up to equivalence) [24,12,8] Golay code."
[1] P. Delsarte and J.M. Goethals, "Unrestricted codes
with the Golay parameters are unique,"
Discrete Math. 12 (1975) 211-224.
[2] A. Neumeier, private communication, 1990.
[6] S.L. Snover, "The uniqueness of the
Nordstrom-Robinson and the Golay binary codes,"
Ph.D. Thesis, Dept. of Mathematics,
Michigan State Univ., 1973.
Related images —
"Before time began, there was the Cube."
"Remember, remember the fifth of November"
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“We Got This Covered”
The previous post's quotation of the word "leitmotif" suggests a review:
See as well Sunday's post "Raiders of the Lost Space."
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Saturday, September 10, 2022
Orthogonal Latin Triangles
From a 1964 recreational-mathematics essay —
Note that the first two triangle-dissections above are analogous to
mutually orthogonal Latin squares . This implies a connection to
affine transformations within Galois geometry. See triangle graphics
in this journal.
Update of 4:40 AM ET —
Other mystical figures —
"Before time began, there was the Cube."
— Optimus Prime in "Transformers" (Paramount, 2007)
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Saturday, September 3, 2022
1984 Revisited
Note the three quadruplets of parallel edges in the 1984 figure above.
The above Gates article appeared earlier, in the June 2010 issue of
Physics World , with bigger illustrations. For instance —
Exercise: Describe, without seeing the rest of the article,
the rule used for connecting the balls above.
Wikipedia offers a much clearer picture of a (non-adinkra) tesseract —
And then, more simply, there is the Galois tesseract —
For parts of my own world in June 2010, see this journal for that month.
The above Galois tesseract appears there as follows:
See also the Klein correspondence in a paper from 1968
in yesterday's 2:54 PM ET post.
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Wednesday, August 17, 2022
Cold Comfort Dam
"And, as with all retold tales that are in people's hearts,
there are only good and bad things and black and white
things and good and evil things and no in-between anywhere."
— John Steinbeck, author's epigraph to The Pearl
From the Season 4 finale of Westworld :
uploading Dolores's pearl at Hoover Dam —
For those who prefer greater theological simplicity . . .
Optimus Prime on a different Hoover Dam figure, that of
the AllSpark: "Before time began, there was the Cube."
Simplifying even more . . .
“A set having three members is a single thing
wholly constituted by its members but distinct from them.
After this, the theological doctrine of the Trinity as
‘three in one’ should be child’s play.”
– Max Black, Caveats and Critiques: Philosophical Essays
in Language, Logic, and Art , Cornell U. Press, 1975
As above, Black's theology forms a cube.
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Monday, August 1, 2022
Enowning
Related material — The Eightfold Cube.
See also . . .
"… 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."
— Sir Michael Atiyah, “The Art of Mathematics”
in the AMS Notices , January 2010
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Review
From Log24 posts tagged Art Space —
From a paper on Kummer varieties,
arXiv:1208.1229v3 [math.AG] 12 Jun 2013,
“The Universal Kummer Threefold,” by
Qingchun Ren, Steven V Sam, Gus Schrader,
and Bernd Sturmfels —
Two such considerations —
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Sunday, July 31, 2022
For Camp Sontag*
|
"We need the word 'metaphor' for the whole double unit, and to use it sometimes for one of the two components in separation from the other is as injudicious as that other trick by which we use 'the meaning' here sometimes for the work that the whole double unit does and sometimes for the other component–the tenor, as I am calling it–the underlying idea or principal subject which the vehicle or figure means. It is not surprising that the detailed analysis of metaphors, if we attempt it with such slippery terms as these, sometimes feels like extracting cube-roots in the head."
— I. A. Richards, The Philosophy of Rhetoric .
The above quotation was appropriated from |
* See yesterday's post Summer Camp.
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Tuesday, July 12, 2022
“Tell it Skewb” continues.
Previously on Log24:
"Tell it Skewb." — Motto adapted from Emily Dickinson.
On further investigation . . .
From the above Sanfilippo date —
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Object Lesson: The Quelling
"The successful artist shares with the politician
a recurrent temptation to indulge in emotional claptrap.
Bernard Bosanquet in Three Lectures on Aesthetic (1915)
proposed that this urge to chase after tears or laughter
could be quelled by attaching the art-emotion to a particular object
and not a set of reactions. His consequent definition of art was
'feeling expressed for expression’s sake.' Notice, however, that
this is something only the deranged would dream of wanting in
real life. Our everyday expressions of feeling are spontaneous and
practical; they are never 'for expression’s sake.' By contrast,
aesthetic feeling is self-sufficient."
— David Bromwich in The Nation, July 11, 2022
A Particular Object —
"Tell it Skewb." — Motto adapted from Emily Dickinson.
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Monday, July 4, 2022
Wednesday, June 29, 2022
Techie Wordplay: “Lynx”
"As of 2022, it is the oldest web browser still being maintained,,,,"
"The speed benefits of text-only browsing are most apparent
when using low bandwidth internet connections, or older computer
hardware that may be slow to render image-heavy content."
— Wikipedia [“Older” link added.]
And then there is . . .
See as well the LYNX of Oslo artist Josefine Lyche.
Update of June 30, 2022 —
Lyche, whose art often incorporates mathematical notions,
has not yet, as far as I know, explored the Borromean link
(three rings, linked mutually but not pairwise) in her art.
Remarks by a different math fan, Evelyn Lamb —
"I have had a thing for the Borromean rings for years now.
There’s something so poetic about them. The three rings
are strong together, but they fall apart if any one of them
is removed. Alternatively, the three rings are trapped together
until one of them leaves and sets the others free. I’m kind of
surprised there isn’t a Wisława Szymborska poem or
Tom Stoppard play that explores the metaphorical possibilities
in the Borromean rings." — Scientific American , Sept. 30, 2016.
See also the Lamb date Sept. 30, 2016, as well as work
by Lyche, in Log24 posts tagged Star Cube.
Related material — The Log24 post Borromean Generators.
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Monday, June 27, 2022
Dealing With Cubism
Continued from April 12, 2022.
"It’s important, as art historian Reinhard Spieler has noted,
that after a brief, unproductive stay in Paris, circa 1907,
Kandinsky chose to paint in Munich. That’s where he formed
the Expressionist art group Der Blaue Reiter (The Blue Rider) —
and where he avoided having to deal with cubism."
— David Carrier,
Remarks by Louis Menand in The New Yorker today —
"The art world isn’t a fixed entity.
It’s continually being reconstituted
as new artistic styles emerge."
(Adapted from Encyclopaedia Britannica,
Eleventh Edition (1911), Crystallography .)
"Before time began, there was the Cube."
— Optimus Prime
See as well Verbum (February 18, 2017).
Related dramatic music —
"Westworld Season 4 begins at Hoover Dam,
with William looking to buy the famous landmark.
What does he consider to be 'stolen' data that is inside?"
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Saturday, June 25, 2022
Sunday, June 12, 2022
Piercing the Twelve*
From "When Novelists Become Cubists," by Andre Furlani—
"The architectonics of a narrative," Davenport says,
"are emphasized and given a role to play in dramatic effect
when novelists become Cubists; that is, when they see
the possibilities of making a hieroglyph, a coherent symbol,
an ideogram of the total work. A symbol comes into being
when an artist sees that it is the only way to get all the meaning in."
* See "Starlight Like Intuition" by Delmore Schwartz.
The "Twelve" of the title may be regarded as cube edges.
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Friday, May 27, 2022
Plan 9 from Disney
"With the Tablet of Ahkmenrah and the Cube of Rubik,
my power will know no bounds!"
— Kahmunrah in a novelization of Night at the Museum:
Battle of the Smithsonian , Barron's Educational Series
Scholium —
Abstracting from narrative to structure, and from structure
to pure number, the Tablet of Ahkmenrah represents the
number 9 and the Cube of Rubik represents the number 27.
Returning from pure abstract numbers to concrete representations,
9 yields the structures in Log24 posts tagged Triangle.graphics,
and 27 yields a Galois cube .
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Tuesday, May 24, 2022
Playing the Palace
From a Jamestown (NY) Post-Journal article yesterday on
"the sold-out 10,000 Maniacs 40th anniversary concert at
The Reg Lenna Center Saturday" —
" 'The theater has a special place in our hearts. It’s played
a big part in my life,' Gustafson said.
Before being known as The Reg Lenna Center for The Arts,
it was formerly known as The Palace Theater. He recalled
watching movies there as a child…."
This, and the band's name, suggest some memories perhaps
better suited to the cinematic philosophy behind "Plan 9 from
Outer Space."
"With the Tablet of Ahkmenrah and the Cube of Rubik,
my power will know no bounds!"
— Kahmunrah in a novelization of Night at the Museum:
Battle of the Smithsonian , Barron's Educational Series
The above 3×3 Tablet of Ahkmenrah image comes from
a Log24 search for the finite (i.e., Galois) field GF(3) that
was, in turn, suggested by last night's post "Making Space."
See as well a mysterious document from a website in Slovenia
that mentions a 3×3 array "relating to nine halls of a mythical
palace where rites were performed in the 1st century AD" —
Comments Off on Playing the Palace
Friday, May 6, 2022
Interality and the Bead Game
WIkipedia on the URL suffix ".io" —
"In computer science, "IO" or "I/O" is commonly used
as an abbreviation for input/output, which makes the
.io domain desirable for services that want to be
associated with technology. .io domains are often used
for open source projects, application programming
interfaces ("APIs"), startup companies, browser games,
and other online services."
An association with the Bead Game from a post of April 7, 2018 —
|
Glasperlenspiel passage quoted here in Summa Mythologica —
“"I suddenly realized that in the language, or at any rate A less poetic meditation on the above 4x4x4 design cube —
"I saw that in the alternation between front and back, See also a related remark by Lévi-Strauss in 1955:
"…three different readings become possible: |
The recent use by a startup company of the URL "interality.io" suggests
a fourth reading for the 1955 list of Lévi-Strauss — in and out —
i.e., inner and outer group automorphisms — from a 2011 post
on the birthday of T. S. Eliot :
A transformation:
Click on the picture for details.
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Interality and the I Ching
See "Flusser and the I Ching," by Peter Zhang.
Zhang has written extensively on the concept of "interality,"
a term coined by his colleague Geling Shang.
For interality as the mathematics underlying the natural
automorphism group of the I Ching, see my own work.
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Sunday, May 1, 2022
Jailbait Puzzle for Moon Knight
The pane number of interest — 15 or 14 ? —
depends on your perspective.
Related cinematic art of Oscar Isaac —
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Wednesday, April 27, 2022
Dealing with Cubism …
Comments Off on Dealing with Cubism …
Sunday, April 17, 2022
Easter for Aitchison*
* See other posts tagged Aitchison in this journal.
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Wednesday, April 13, 2022
Dealing with Cubism continues . . .
Comments Off on Dealing with Cubism continues . . .
Tuesday, April 12, 2022
Dealing with Cubism
"It’s important, as art historian Reinhard Spieler has noted,
that after a brief, unproductive stay in Paris, circa 1907,
Kandinsky chose to paint in Munich. That’s where he formed
the Expressionist art group Der Blaue Reiter (The Blue Rider) —
and where he avoided having to deal with cubism."
— David Carrier,
Images from an earlier Christmas Day, in 2005 —
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Friday, April 8, 2022
Wednesday, March 30, 2022
Monday, March 28, 2022
The Omega Oracle
"Design is how it works ." — Steve Jobs. See interality.org.
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Saturday, March 26, 2022
Box Geometry: Space, Group, Art (Work in Progress)
| Name Tag | .Space | .Group | .Art |
|---|---|---|---|
| Box4 |
2×2 square representing the four-point finite affine geometry AG(2,2). (Box4.space) |
S4 = AGL(2,2) (Box4.group) |
(Box4.art) |
| Box6 |
3×2 (3-row, 2-column) rectangular array representing the elements of an arbitrary 6-set. |
S6 | |
| Box8 | 2x2x2 cube or 4×2 (4-row, 2-column) array. | S8 or A8 or AGL(3,2) of order 1344, or GL(3,2) of order 168 | |
| Box9 | The 3×3 square. | AGL(2,3) or GL(2,3) | |
| Box12 | The 12 edges of a cube, or a 4×3 array for picturing the actions of the Mathieu group M12. | Symmetries of the cube or elements of the group M12 | |
| Box13 | The 13 symmetry axes of the cube. | Symmetries of the cube. | |
| Box15 |
The 15 points of PG(3,2), the projective geometry of 3 dimensions over the 2-element Galois field. |
Collineations of PG(3,2) | |
| Box16 |
The 16 points of AG(4,2), the affine geometry of 4 dimensions over the 2-element Galois field. |
AGL(4,2), the affine group of |
|
| Box20 | The configuration representing Desargues's theorem. | ||
| Box21 | The 21 points and 21 lines of PG(2,4). | ||
| Box24 | The 24 points of the Steiner system S(5, 8, 24). | ||
| Box25 | A 5×5 array representing PG(2,5). | ||
| Box27 |
The 3-dimensional Galois affine space over the 3-element Galois field GF(3). |
||
| Box28 | The 28 bitangents of a plane quartic curve. | ||
| Box32 |
Pair of 4×4 arrays representing orthogonal Latin squares. |
Used to represent elements of AGL(4,2) |
|
| Box35 |
A 5-row-by-7-column array representing the 35 lines in the finite projective space PG(3,2) |
PGL(3,2), order 20,160 | |
| Box36 | Eurler's 36-officer problem. | ||
| Box45 | The 45 Pascal points of the Pascal configuration. | ||
| Box48 | The 48 elements of the group AGL(2,3). | AGL(2,3). | |
| Box56 |
The 56 three-sets within an 8-set or |
||
| Box60 | The Klein configuration. | ||
| Box64 | Solomon's cube. |
— Steven H. Cullinane, March 26-27, 2022
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Friday, March 25, 2022
The Diamantova Logo
From the "Mathematics and Narrative" link in the previous post —
An image reposted here on March 12, 2022, the reported date of death
for Vera Diamantova —
Helen Mirren with plastic Gankyil .
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Thursday, March 24, 2022
Westview via Spelman
Images reposted here on March 9 . . .
the reported date of death for film director John Korty —
The quotation is from a professor of mathematics at Spelman College.
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Monday, March 21, 2022
Candidate for the Waymark Prize
The previous post suggests a review of
a Log24 post from August 22, 2020 —
From a web page —
From YouTube, for the Church of Synchronology —
For some context, see Holocron in this journal.
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Sunday, March 13, 2022
Black Art
"… Mathematics may be art, but to the general public it is
a black art, more akin to magic and mystery."
— Sir Michael Atiyah, quoted here on April 4, 2016.
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Saturday, March 12, 2022
Geometric Theology: Logos vs. Antilogos
In a 1999 Yale doctoral dissertation,
"Diabolical Structures in the Poetics of Nikolai Gogol,"
the term "antilogos" occurs 70 times.
Students of poetic structures may compare and contrast . . .
Logos
Antilogos
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Thursday, March 10, 2022
Space Group Art
Supercube.space, supercube.group, supercube.art.
See also the Supercube channel at are.na.
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Wednesday, March 9, 2022
“Cunning Mashup”
See also the previous post and the new URL cube.salon
that forwards to posts containing the following offensive remark:
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Monday, March 7, 2022
Logos: Beamery vs. Eightfold
Logos as tab icons —
Logos in context —
Related graphic design from April 1, 2018 —
Later, in 2019 —
An undated webpage says . . .
"…we’re officially announcing the launch of the new Beamery brand."
"A logo, a name, an idea: Meet the Bexa"
— https://beamery.com/resources/blogs/were-launching-beamerys-new-brand
(metadata: itemprop="datePublished" content="2019-11-20T19:00:00")
This logo design was described elsewhere —
"Beamery's new mark–The Bexa. The Bexa contains the negative space
of 3 Bs rotating clockwise within a hexagon shape to capture Beamery's
3 pillars of the Talent Operating System." — Ben Stafford for Focus Lab
"All things serve the Beamery."
— Slogan adapted from Stephen King.
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Saturday, March 5, 2022
Word and World*
This afternoon's post with the phrase
"Eternal Word Meets Eternal World"
suggests a book —
A search in this journal for "world within" yields . . .
|
"Instead of the 'static spacetime jewel' of blockworld that is often invoked by eternalists to help their readers conceptualize of what a blockworld would 'look like' from the outside, now imagine that a picture on a slide is being projected onto the surface of this space-time jewel. From the perspective of one inside the jewel, one might ask 'Why is this section blue while this section is black?,' and from within the jewel, one could not formulate an answer since one could not see the entire picture projected on the jewel; however, from outside the jewel, an observer (some analogue of Newton's God, perhaps, looking down on his 'sensorium' from the 5th dimension) could easily see the pattern and understand that all of the 'genuinely fortuitous' events inside the space-time jewel are, in fact, completely determined by the pattern in the projector." — "Genuine Fortuitousness, Relational Blockworld, Realism, and Time" (pdf), by Daniel J. Peterson, Honors Thesis, Swarthmore College, December 13, 2007, footnote 55, page 114 |
A related image from pure mathematics —
* The title is thanks to William Gass.
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Monday, February 14, 2022
Artbusters: Cubism
" Welcher Art ist die ursprüngliche Einheit,
daß sie sich in diese Scheidung auseinanderwirft,
und in welchem Sinn sind die Geschiedenen
hier als Wesung der Ab-gründigkeit gerade einig?
Hier kann es sich nicht um irgend eine »Dialektik«
handeln, sondern nur um die Wesung des Grundes
(der Wahrheit also) selbst."
"Before time began, there was the Cube." — Optimus Prime
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Saturday, February 12, 2022
Das Geheimnis der Einheit
Thomas Mann on "the mystery of the unity" —
"Denn um zu wiederholen, was ich anfangs sagte:
in dem Geheimnis der Einheit von Ich und Welt,
Sein und Geschehen, in der Durchschauung des
scheinbar Objectiven und Akzidentellen als
Veranstaltung der Seele glaube ich den innersten Kern
der analytischen Lehre zu erkennen." (GW IX 488)
An Einheit-Geheimnis that is perhaps* more closely related
to pure mathematics** —
"What is the nature of the original unity
that throws itself apart in this separation,
and in what sense are the separated ones
here as the essence of the abyss?
Here it cannot be a question of any kind of 'dialectic,'
but only of the essence of the ground
(that is, of truth) itself." [Tr. by Google]
" Welcher Art ist die ursprüngliche Einheit,
daß sie sich in diese Scheidung auseinanderwirft,
und in welchem Sinn sind die Geschiedenen
hier als Wesung der Ab-gründigkeit gerade einig?
Hier kann es sich nicht um irgend eine »Dialektik«
handeln, sondern nur um die Wesung des Grundes
(der Wahrheit also) selbst."
* Or perhaps not .
** For a relevant Scheidung , see Eightfold Cube.
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Friday, February 11, 2022
For Space Groupies
A followup to Wednesday's post Deep Space —
Related material from this journal on July 9, 2019 —
Cube Bricks 1984 —
From "Tomorrowland" (2015) —
From other posts tagged 1984 Cubes —
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Thursday, February 10, 2022
“Kimi, Siri. Siri, Kimi.”
From "Siri + Wechsler" in this journal —
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For Little Man Tate —
Related material — Wechsler in this journal and
Mark and Lucille, Bill and Violet, Al and Regina,
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Related material —
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