Finesse —
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Sunday December 10, 2006 m759 @ 9:00 PM
“Function defined form, expressed in a pure geometry
– J. G. Ballard on Modernism
“The greatest obstacle to discovery is not ignorance –
— Daniel J. Boorstin, |
Geometrie —
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.
"Weight limit 10 tons… Except local deliveries" —
Conclusion: the book is a mine of information, but
you sure have to dig for it. — Paul R. Halmos,
review of Topological Dynamics , November 1955
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"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" |
|
Gottschalk Review —
W. H. Gottschalk and G. A. Hedlund, Topological Dynamics, The ending of the review — The most striking virtue of the book is its organization. The authors' effort to arrange the exposition in an efficient order, and to group the results together around a few central topics, was completely successful; they deserve to be congratulated on a spectacular piece of workmanship. The results are stated at the level of greatest available generality, and the proofs are short and neat; there is no unnecessary verbiage. The authors have, also, a real flair for the "right" generalization; their definitions of periodicity and almost periodicity, for instance, are very elegant and even shed some light on the classical concepts of the same name. The same is true of their definition of a syndetic set, which specializes, in case the group is the real line, to Bohr's concept of a relatively dense set. The chief fault of the book is its style. The presentation is in the brutal Landau manner, definition, theorem, proof, and remark following each other in relentless succession. The omission of unnecessary verbiage is carried to the extent that no motivation is given for the concepts and the theorems, and there is a paucity of illuminating examples. The striving for generality (which, for instance, has caused the authors to treat uniform spaces instead of metric spaces whenever possible) does not make for easy reading. The same is true of the striving for brevity; the shortest proof of a theorem is not always the most perspicuous one. There are too many definitions, especially in the first third of the book; the reader must at all times keep at his finger tips a disconcerting array of technical terminology. The learning of this terminology is made harder by the authors' frequent use of multiple statements, such as: "The term {asymptotic } {doubly asymptotic } means negatively {or} {and} positively asymptotic." Conclusion: the book is a mine of information, but you sure have to dig for it. — PAUL R. HALMOS |
On Doctor Strange in Spider-Man: No Way Home —
"This all-powerful wizard really used 'Scooby-Doo' as a verb
meaning 'successfully pull off a series of physical challenges
against monsters who are real.' What in the dad-trying-to-
relate-to-his-distant-son hell? That's like pumping someone up
to kick a game-winning field goal by saying 'Charlie Brown this crap.'"
— Vinnie Mancuso at Collider , November 17, 2021
But seriously . . .
From posts tagged Frankfurter —
"Scooby-Doo this ."
The above image suggests a review of Sigaud in this journal and of . . .
Related material from the Web —
"Anubis, easily recognizable as an anthropomorphized jackal or dog,
was the Egyptian god of the afterlife and mummification. He helped
judge souls after their death and guided lost souls into the afterlife.
So, was he evil? No, and in fact just the opposite. In ancient Egyptian
mythology the ultimate evil was chaos. Nearly all of Egyptian mythology
was focused around maintaining the cycles of cosmic order that kept
chaos at bay. Few things were as significant in this goal as the rituals
maintaining the cycle of life, death, and afterlife. Therefore, Anubis was
not evil but rather one of the most important gods who kept evil out of Egypt."
— Christopher Muscato at Study.com
"On a crisp Fall morning…." — The late Maureen Howard, writer of fiction.
Non-fiction: Feb. 19, 2022,
https://news.yahoo.com/frances-haugen-
on-meta-headquarters-122958675.html —
FRANCES HAUGEN: To give you a sense of how absurd the space is,
so Facebook is obsessed with 15 and 30-minute meetings. It's like they're
very efficient, everyone's– they're obsessed with the word crisp, like are
your documents crisp, is your explanation crisp? The space is so large that
I would regularly walk 15 minutes, 10, 15 minutes to go to a 30-minute meeting.
And again, fiction . . .
See other posts now so tagged.
Hudson's Rosenhain tetrads, as 20 of the 35 projective lines in PG(3,2),
illustrate Desargues's theorem as a symmetry within 10 pairs of squares
under rotation about their main diagonals:
See also "The Square Model of Fano's 1892 Finite 3-Space."
The remaining 15 lines of PG(3,2), Hudson's Göpel tetrads, have their
own symmetries . . . as the Cremona-Richmond configuration.
See as well the life of a real astrophysicist.
Update of 12:26 PM ET March 15:
Vide other posts now tagged The Rosenhain Symmetry.
"I’ve lived five years on the edge of the continent,
and over those years I’ve shed one skin and grown into another."
— Steinhauer, Olen. All the Old Knives (p. 222).
St. Martin's Publishing Group. Kindle Edition.
(Hardcover first edition: Minotaur Books, March 10, 2015.)
So to speak.
"… 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.
* Recent role of Ewan McGregor, the camerlengo of Dan Brown.
** Mashup of the C. S. Lewis wardrobe and the previous post.
The "branding" part of this post's title and tag —
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The scene went from bad to worse. The camerlengo’s torn cassock, having been only laid over his chest by Chartrand, began to slip lower. For a moment, Langdon thought the garment might hold, but that moment passed. The cassock let go, sliding off his shoulders down around his waist. The gasp that went up from the crowd seemed to travel around the globe and back in an instant. Cameras rolled, flashbulbs exploded. On media screens everywhere, the image of the camerlengo’s branded chest was projected, towering and in grisly detail. Some screens were even freezing the image and rotating it 180 degrees. The ultimate Illuminati victory. Langdon stared at the brand on the screens. Although it was the imprint of the square brand he had held earlier, the symbol now made sense. Perfect sense. The marking’s awesome power hit Langdon like a train. Orientation. Langdon had forgotten the first rule of symbology. When is a square not a square? He had also forgotten that iron brands, just like rubber stamps, never looked like their imprints. They were in reverse. Langdon had been looking at the brand’s negative ! As the chaos grew, an old Illuminati quote echoed with new meaning: ‘A flawless diamond, born of the ancient elements with such perfection that all those who saw it could only stare in wonder.’ Langdon knew now the myth was true. Earth, Air, Fire, Water. The Illuminati Diamond. — Dan Brown, Angels & Demons |
I prefer Modal Nietzsche.
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
Cable was born in Akeley, Pennsylvania, in 1932 and graduated
from Warren High School in nearby Warren PA in 1950.
The "online remembrance" is at the Meadville Tribune.
Members of the Church of Synchronology may consult this journal's
posts on the date of Cable's reported death.
The Stonecutter
|
This post is in honor of Thandiwe Newton, intimacy coordinator.
The title of the previous post suggests a search for
Shubnikov in this journal. That search yields a 1999
Yale doctoral dissertation,
"Diabolical Structures in the Poetics of Nikolai Gogol."
A related image:
From "Made for Love" (2021) — Lyle Herringbone:
Supercube.space, supercube.group, supercube.art.
See also the Supercube channel at are.na.
In Memoriam:
Widely quoted description of Russia —
"A gas station with nukes."
See also . . . The Tenet Prom.
See also the previous post and the new URL cube.salon
that forwards to posts containing the following offensive remark:
The new URL supercube.space forwards to http://box759.wordpress.com/.
The term supercube is from a 1982 article by Solomon W. Golomb.
The related new URL supercube.group forwards to a page that
describes how the 2x2x2 (or eightfold, or "super") cube's natural
underlying automorphism group is Klein's simple group of order 168.
For further context, see the new URL supercube.art.
For some background, see the phrase Cube Space in this journal.
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."
— 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.
By the Daniel J. Peterson whose Swarthmore honors thesis was quoted
here last night —
"What, then, is the relationship between theory-relative symmetries
(physical symmetries) and theory-independent symmetries
(overarching symmetries)? My statement of this problem is
a bit abstract, so let’s look at an example: classical Newtonian gravity
and classical electromagnetism . . . ."
— Prospects for a New Account of Time Reversal
by Daniel J. Peterson, Ph.D. dissertation, U. Mich., 2013, p. 16.
Another 2013 approach to the word "overarching" and sytmmetries —
Other terms of interest: Tenet , Nolanism , and Magic for Liars .
This afternoon's post with the phrase
"Eternal Word Meets Eternal World"
suggests a book —
A search in this journal for "world within" yields . . .
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"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.
The name of the author in the above search result suggests . . .
See as well yesterday's Art for Jokers .
Eternal Word Meets Eternal World.
Related words … Posts tagged Meta.
Clay himself might prefer Chicks for Hicks.
From earlier today . . .
"Eyes that look like heaven,
lips like cherry wine . . . .
My heart's on fire . . . ."
For a similar phrase, see
"When things look bleak critically for the DC brand,
the bat-signal is always there."
"… in the Logic of Scientific Discovery Popper introduces
the technical concept of a 'basic statement' or 'basic proposition,'
which he defines as a statement which can serve as a premise
in an empirical falsification and which takes the singular existential
form 'There is an X at Y .' Basic statements are important because
they can formally contradict universal statements, and accordingly
play the role of potential falsifiers."
— https://plato.stanford.edu/entries/popper/
The parquet floor supporting Lily Collins in today's noon-hour post
suggests a search in this journal for parquet.
A resulting quote from Henry James —
"… the high party-walls,
on the other side of which
grave hôtels stood off for privacy,
spoke of survival, transmission, association,
a strong indifferent persistent order."
As do the three Dark Materials images in the search.
Giddy up a oom papa oom papa mow mow
Giddy up a oom papa oom papa mow mow
G7 C
Hi-yo silver away
"In Zuckerberg's metaverse, humans are represented by legless avatars."
Elsewhere . . .
Click for some context.
Related reading:
Instagram two days ago —
Compelled to Layer
"From the moment he penciled his first sketch
for the new Grand Rapids Art Museum (GRAM)
in Grand Rapids, Mich., architect Kulapat Yantrasast
was inspired by more than art. A native of Thailand
and a partner in the Los Angeles firm Workshop
Hakomori Yantrasast (wHY), Yantrasast, 39, felt
compelled to layer the building's primary role—
as a place for displaying art—with activities that
would naturally attract people. " [Link added.]
— https://www.architectmagazine.com/design/
buildings/gram-green_o , October 4, 2007
See Sith Pyramid and Jedi Cube .
Related reading . . .
Pyramid:
https://www.theguardian.com/commentisfree/
2022/feb/27/vladimir-putin-russia-ukraine-power
Cube:
"To enter into the world of Putin’s favorite philosophers
is to enter a world full of melodrama, mysticism and
grandiose eschatological visions."
— David Brooks in the online New York Times on March 3, 2014
Scholium:
This journal on the above NY Times date —
From a New York Times obituary online today —
“He was an absolutely brilliant reader
at taking what seemed to be the knots,
or the impenetrability, or the downright
insanity of a piece of writing, and just
saying, ‘Hey, guys, that’s the point.’”
See as well Humpty Dumpty and unit e .
https://en.wikisource.org/wiki/
A_History_of_Mathematics/
Recent_Times/Theory_of_Functions —
See also Gopel in this journal.
Another illustration of the difference between data and metadata —
A Google image search for Göpel inscape —
Data :
(Click for the full 11.7 MB version
of this data .)
Meta data :
Related film dialogue —
"Media is nothing but neuro-trigger response and viral conditioning."
"Wait, what are you two talking about?"
"Cat videos."
(Continued from other posts tagged Date Time.)
Metadata Verse — An image description —"That Fat Cat Sat."
Related image titled What is Metadata? —
From the current online New Yorker , a barnyard elegy:
From the top of the New Yorker homepage tonight:
Locking the barn door after the chandelier is gone —
(Click to enlarge.)
The above White Goddess new-edition publication date: Oct. 8, 2013.
This journal on that date —
"Please wait as your operating system is initiated."
"The class is objectively characterized, but not
the individual coordinate assignment."
Tell it to Watchduck, Hermann.
See a related remark by Quack5quack in Raiders of the Lost Coordinates.
An image linked to* in Mapping Problem Continued (Log24, 16 July 2012) —
* The link is on the phrase "may be deduced."
The geometry of the 4×4 square may be associated with the name
Galois, as in "the Galois tesseract," or similarly with the name Kummer.
Here is a Google image search using the latter name —
(Click to enlarge.)
"FILE – Retired Sandinista Gen. Hugo Torres poses for portrait
at his home, in Managua, Nicaragua, May 2, 2018."
— Photo caption from a Feb. 12 Washington Post obituary
Also on May 2, 2018 —
Related theology —
Tuesday, February 23, 2016
|
"There is such a thing as a tesseract."
— Mrs. Whatsit in A Wrinkle in Time (1962)
"Simplify, simplify." — Henry David Thoreau in Walden (1854)
|
A Jungian on this six-line figure:
“They are the same six lines that exist in the I Ching…. Now observe the square more closely: four of the lines are of equal length, the other two are longer…. For this reason symmetry cannot be statically produced and a dance results.” |
"Stories are the only way people can absorb information
in any depth" — Stephen Lussier, retired De Beers executive
Related story — De Beer's Consolidated Mine
“Nothing Lasts Forever” will screen at Berlinale
on February 12th at 9 pm at Cubix 7, February 17th
at 9 pm at Cubix 5 and 6, and February 18th at 6 pm
at Cubix 5 and 6. — https://moveablefest.com
See as well "Story Theory of Truth" in this journal.
"The Cable Guy isn't necessarily the first one you would expect
to make a comeback, but that's exactly what he has done
this Sunday during the big game."
Related material — Cable Girl —
" 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
|
From The Atlantic on February 10, 2022 —
"Facebook Has a Superuser-Supremacy Problem" —
What else is new?
From this journal on June 5, 2019 —
Also on June 5, 2019 —
This journal on the above date —
The New York Times yesterday reported that the above dancer,
no longer very young, died on February 3, 2022.
Some Log24 flashback images reposted on that date —
See as well two Dec. 22, 2002, posts
now tagged Trifecta —
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.
"… out of all things there comes a unity,
and out of a unity all things . . . . "
— Heraclitus, according to de Beer quoting McKirahan
An image we may regard as illustrating
the group-identity symbol "e" for "Einheit " —
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 —
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.
But seriously . . .
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,
|
Related material —
Some personal memories triggered by the above —
The novel The Lathe of Heaven , the film "Paper Towns," and
the images in Instance of a Fingerpost (Log24, July 24, 2015).
Related illustration from a search in this journal for Wechsler —
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Above: Dr. Harrison Pope, Harvard professor of psychiatry,
demonstrates the use of the Wechsler Adult Intelligence Scale (WAIS)
“block design” subtest.
— From a Log24 search for “Harrison Pope.”
Conwell, 1910 —
(In modern notation, Conwell is showing that the complete
projective group of collineations and dualities of the finite
3-space PG (3,2) is of order 8 factorial, i.e. "8!" —
In other words, that any permutation of eight things may be
regarded as a geometric transformation of PG (3,2).)
Later discussion of this same "Klein correspondence"
between Conwell's 3-space and 5-space . . .
A somewhat simpler toy model —
Related fiction — "The Bulk Beings" of the film "Interstellar."
For your consideration: "Nightmare Alley" Oscar nominations —
Costume design, production design, cinematography, Best Picture.
See as well the introduction by Nick Tosches to the novel .
A touch I personally like: Over the end credits, Hoagy Carmichael's
"Stardust" plays. From related remarks (here abridged) by poet
David Lehman on November 22, 2015 (the feast of St. Cecilia) —
"Every year on this day I think unfailingly of three things:
— that today is Hoagy Carnichael's birthday ….
— that if time were elastic I would write a series of
popular history novels ….
— that paranoid conspiracy theories … are based on
our fundamental inability to understand events.
From this journal on November 22, 2015 —
On reading about DNA:
"Suddenly it was clear to me
that all the beautiful complexity of life
had simplicity at its core," he says.
"This is the kind of thing mathematicians love."
— Eric Lander in "The 2004 TIME 100 — Our list
of the most influential people in the world today"
The date on the above TIME piece is Monday,
Apr. 26, 2004. Remarks in this journal on that date
are now tagged Directions Out.
Warren (PA) Public Library's Instagram
on January 21, 2022 —
Morphart —
Morph Art — from Raiders of the Lost Coordinates
"There is such a thing as a 4-set."
— Saying adapted from a 1962 young-adult novel.
In memory of Hale Trotter, a mathematician who reportedly
died at Princeton, N.J., on Jan. 17, 2022.
Other perspectives —
“The carnival is an incredibly close-knit, hermetic society.”
— Guillermo del Toro, director and co-writer of
the new remake of "Nightmare Alley"
Dialogue from that remake —
STAN — How do you ever get a guy to geek?
CLEM — Oh- I ain’t going to crap you up. It ain’t easy.
"There is such a thing as a four-set."
— Saying adapted from a 1962 young-adult novel
". . . It is as if
We had come to an end of the imagination,
Inanimate in an inert savoir.”
— Wallace Stevens, “The Plain Sense of Things”
"In my end . . . ." — T. S. Eliot
|
Thursday, March 22, 2018
The Diamond Cube
|
See a note from Sept. 15, 1984
(perhaps the last day of life for Richard Brautigan).
The online New York Times today reporting a Jan. 29 death:
"Mr. Dylan asked Mr. Lay to back him on the title track
of his album “Highway 61 Revisited.” In addition to
playing drums, Mr. Lay played a toy whistle on the song’s
memorable opening."
— Richard Sandomir, Feb. 5, 2022, 2:06 p.m. ET
The above link yields a March 11, 2019, YouTube upload:
Some may prefer the theology of Hexagram 61.
“‘Oracle, why did you write
The Grasshopper Lies Heavy?
What are we supposed to learn?'”
— Philip K. Dick
“She began throwing the coins.“
Other remarks from the above
YouTube upload date — March 11, 2019 —
Shown below is an illustration from "The Puzzle Layout Problem" —
Exercise: Using the above numerals 1 through 24
(with 23 as 0 and 24 as ∞) to represent the points
∞, 0, 1, 2, 3 … 22 of the projective line over GF(23),
reposition the labels 1 through 24 in the above illustration
so that they appropriately* illustrate the cube-parts discussed
by Iain Aitchison in his March 2018 Hiroshima slides on
cube-part permutations by the Mathieu group M24.
A note for Northrop Frye —
Interpenetration in the eightfold cube — the three midplanes —
A deeper example of interpenetration:
Aitchison has shown that the Mathieu group M24 has a natural
action on the 24 center points of the subsquares on the eightfold
cube's six faces (four such points on each of the six faces). Thus
the 759 octads of the Steiner system S(5, 8, 24) interpenetrate
on the surface of the cube.
* "Appropriately" — I.e. , so that the Aitchison cube octads correspond
exactly, via the projective-point labels, to the Curtis MOG octads.
From The Dumbing-Down —
The above image appeared here on August 5, 2021.
From an instagram post on that same date
that might be titled "The Wising-Up" —
New York Times eulogy today for "a wizard of movement and words"—
See as well the previous post and Ballet Blanc .
Engineering image uploaded on Sept. 4, 2015 —
Art image from this journal on that date —
See as well "Novel Engineering."
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