For the Church of Synchronology —
See also this journal on July 17, 2014, and March 28, 2017.
Saturday, April 15, 2017
Quanta Dating
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Friday, April 14, 2017
Hudson and Finite Geometry
The above four-element sets of black subsquares of a 4×4 square array
are 15 of the 60 Göpel tetrads , and 20 of the 80 Rosenhain tetrads , defined
by R. W. H. T. Hudson in his 1905 classic Kummer's Quartic Surface .
Hudson did not view these 35 tetrads as planes through the origin in a finite
affine 4-space (or, equivalently, as lines in the corresponding finite projective
3-space).
In order to view them in this way, one can view the tetrads as derived,
via the 15 two-element subsets of a six-element set, from the 16 elements
of the binary Galois affine space pictured above at top left.
This space is formed by taking symmetric-difference (Galois binary)
sums of the 15 two-element subsets, and identifying any resulting four-
element (or, summing three disjoint two-element subsets, six-element)
subsets with their complements. This process was described in my note
"The 2-subsets of a 6-set are the points of a PG(3,2)" of May 26, 1986.
The space was later described in the following —
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Thursday, April 13, 2017
Wednesday, April 12, 2017
Contracting the Spielraum
The contraction of the title is from group actions on
the ninefold square (with the center subsquare fixed)
to group actions on the eightfold cube.
From a post of June 4, 2014 …
At math.stackexchange.com on March 1-12, 2013:
“Is there a geometric realization of the Quaternion group?” —
The above illustration, though neatly drawn, appeared under the
cloak of anonymity. No source was given for the illustrated group actions.
Possibly they stem from my Log24 posts or notes such as the Jan. 4, 2012,
note on quaternion actions at finitegeometry.org/sc (hence ultimately
from my note “GL(2,3) actions on a cube” of April 5, 1985).
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Expanding the Spielraum
"Cézanne ignores the laws of classical perspective . . . ."
— Voorhies, James. “Paul Cézanne (1839–1906).”
In Heilbrunn Timeline of Art History . New York:
The Metropolitan Museum of Art, 2000–. (October 2004)
Some others do not.
This is what I called "the large Desargues configuration"
in posts of April 2013 and later.
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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
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Monday, April 3, 2017
Saturday, April 1, 2017
Art Space
Click image for some backstory.
“Whatever he drew was the platonic ideal
of what a cartoon should look like.”
— Bob Mankoff on Jack Ziegler, who reportedly
died on Wednesday, March 29, 2017.
See also "Hexagram 64 in Context," March 16, 2017.
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Wednesday, March 29, 2017
The Crimson Abyss
"And as the characters in the meme twitch into the abyss
that is the sky, this meme will disappear into whatever
internet abyss swallowed MySpace."
—Staff writer Kamila Czachorowski, Harvard Crimson , March 29
1984 —
2010 —
Logo design for Stack Exchange Math by Jin Yang
Recent posts now tagged Crimson Abyss suggest
the above logo be viewed in light of a certain page 29 —
"… as if into a crimson abyss …." —
Update of 9 PM ET March 29, 2017:
Prospero's Children was first published by HarperCollins,
London, in 1999. A statement by the publisher provides
an instance of the famous "much-needed gap." —
"This is English fantasy at its finest. Prospero’s Children
steps into the gap that exists between The Lion, the Witch
and the Wardrobe and Clive Barker’s Weaveworld , and
is destined to become a modern classic."
Related imagery —
See also "Hexagram 64 in Context" (Log24, March 16, 2017).
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Design Abyss
Hexagram 29,
The Abyss (Water)
This post was suggested by an August 6, 2010, post by the designer
(in summer or fall, 2010) of the Stack Exchange math logo (see
the previous Log24 post, Art Space Illustrated) —
In that post, the designer quotes the Wilhelm/Baynes I Ching to explain
his choice of Hexagram 63, Water Over Fire, as a personal icon —
"When water in a kettle hangs over fire, the two elements
stand in relation and thus generate energy (cf. the
production of steam). But the resulting tension demands
caution. If the water boils over, the fire is extinguished
and its energy is lost. If the heat is too great, the water
evaporates into the air. These elements here brought in
to relation and thus generating energy are by nature
hostile to each other. Only the most extreme caution
can prevent damage."
See also this journal on Walpurgisnacht (April 30), 2010 —
|
Hexagram 29:
|
Hexagram 30:
"Hates California,
|
A thought from another German-speaking philosopher —
"Die Philosophie ist ein Kampf gegen die Verhexung
unsres Verstandes durch die Mittel unserer Sprache."
See also The Crimson 's abyss in today's 4:35 AM post Art Space, Continued.
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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).
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Art Space, Continued
"And as the characters in the meme twitch into the abyss
that is the sky, this meme will disappear into whatever
internet abyss swallowed MySpace."
—Staff writer Kamila Czachorowski, Harvard Crimson today
From Log24 posts tagged Art Space —
From a recent 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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Tuesday, March 28, 2017
Bit by Bit
From Log24, "Cube Bricks 1984" —
Also on March 9, 2017 —
For those who prefer graphic art —
Broken Symmetries in Diamond Space —
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Backstory
Click here to enlarge. Click the image for the source page.
The "this page" reference is to …
Finite Geometry of the Square and Cube.
Also from March 14, 2017 —
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Sunday, December 6, 2015
Form and Idea
"Those early works are succinct and uncompromising
in how they give shape to the philosophical perplexities
of form and idea…."
J. J. Charlesworth, artnet news, Dec. 16, 2014
"Form" and "idea" are somewhat synonymous,
as opposed to "form" and "substance." A reading:
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Wednesday, April 22, 2015
Purely Aesthetic
G. H. Hardy in A Mathematician's Apology —
|
What ‘purely aesthetic’ qualities can we distinguish in such theorems as Euclid’s or Pythagoras’s? I will not risk more than a few disjointed remarks. In both theorems (and in the theorems, of course, I include the proofs) there is a very high degree of unexpectedness, combined with inevitability and economy. The arguments take so odd and surprising a form; the weapons used seem so childishly simple when compared with the far-reaching results; but there is no escape from the conclusions. There are no complications of detail—one line of attack is enough in each case; and this is true too of the proofs of many much more difficult theorems, the full appreciation of which demands quite a high degree of technical proficiency. We do not want many ‘variations’ in the proof of a mathematical theorem: ‘enumeration of cases’, indeed, is one of the duller forms of mathematical argument. A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way. |
Related material:
-
A post at noon on Sunday, April 19, 2015, with a link,
"Ageometretos medeis eisito," to an image search
for "large Desargues configuration" that includes …
-
A review, dated April 20, 2015, of "After Hours at the
Harvard Art Museums" in The Harvard Crimson -
An article, also dated April 20, 2015, in Harvard Magazine
titled "Harvard Installs 'Triangle Constellation'"
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Tuesday, February 3, 2015
Expanding the Spielraum
A short poem by several authors:
"The role of
the 16 singular points
on the Kummer surface
is now played by
the 64 singular points
on the Kummer threefold."
— From Remark 2.4 on page 9 of
"The Universal Kummer Threefold,"
by Qingchun Ren, Steven V Sam,
Gus Schrader, and Bernd Sturmfels,
http://arxiv.org/abs/1208.1229v3,
August 6, 2012 — June 12, 2013.
See also "Expanded Field" in this journal.
Illustration from "Sunday School," July 20, 2014.
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Tuesday, April 1, 2014
For April 1
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Friday, March 7, 2014
Kummer Varieties
The Dream of the Expanded Field continues…
From Klein's 1893 Lectures on Mathematics —
"The varieties introduced by Wirtinger may be called Kummer varieties…."
— E. Spanier, 1956
From this journal on March 10, 2013 —
From a recent 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 —
Update of 10 PM ET March 7, 2014 —
The following slides by one of the "Kummer Threefold" authors give
some background related to the above 64-point vector space and
to the Weyl group of type E7, W (E7):
The Cayley reference is to "Algorithm for the characteristics of the
triple ϑ-functions," Journal für die Reine und Angewandte
Mathematik 87 (1879): 165-169. <http://eudml.org/doc/148412>.
To read this in the context of Cayley's other work, see pp. 441-445
of Volume 10 of his Collected Mathematical Papers .
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Tuesday, January 21, 2014
Class of 64
A NY Times researcher from this morning’s previous post
tweeted last fall about art forgery and China.
Related material — Art Cube.
Illustration from December 25, 2013.
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Wednesday, December 25, 2013
Rotating the Facts
"She never looked up while her mind rotated the facts,
trying to see them from all sides, trying to piece them
together into theory. All she could think was that she
was flunking an IQ test."
— Steve Martin, An Object of Beauty
"So you should not feel so all alone…"
— Adapted song lyric
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Saturday, April 6, 2013
Seize the Dia
On this journal:
"he seems to repeat stuff compulsively punctuated with citing others and berating them for note taken nor credit given of his precedence .. but like i said, he more than makes up for that, dredging up and dusting off his all time faves like a super expensive store keeper who moves a piece only once a decade"
— "poetpiet" on Feb. 23, 2013
This suggests moving a piece linked to here
(in an update; scroll down) a decade ago.
Photo source: http://evanfazio.com/public-relations-lessons-from-the-chess-board/
The New York Times Magazine cover story
a decade ago, on Sunday, April 6, 2003:
"The artists demanded space
in tune with their aesthetic."
— "The Dia Generation,"
by Michael Kimmelman
Related material: Occupy Space in this journal.
Sunday, May 22, 2011
Asterisk*
A year ago today—
Art Space
|
Pictorial version |
|
| “Space: what you damn well have to see.” – James Joyce, Ulysses |
|
* See Vonnegut.
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Wednesday, March 16, 2011
Time and Chance (continued)
Accidental Time and Space
New York Lottery today— midday 987, evening 522.
Time
The midday 987 may be interpreted as "…nine, eight, seven, …."—
"The countdown as we know it, 10-9-8-u.s.w.,
was invented by Fritz Lang in 1929 for
the Ufa film Die Frau im Mond . He put it into
the launch scene to heighten the suspense.
'It is another of my damned "touches,"' Fritz Lang said."
Space
The evening 522 suggests the date 5/22. From that date last year—
Art Space (2:02 AM EDT)
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Pictorial version |
|
“Space: what you damn well have to see.”
– James Joyce, Ulysses
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Sunday, February 20, 2011
Sermon
From Galleri MGM in Oslo —
Josefine Lyche "Why do we remember the past, but not the future?" "If you want a vision of the future, imagine a boot stamping on a human face – forever." Galleri MGM is pleased to present the second solo exhibition by Josefine Lyche (b.1973). Lyche presents a body of work consisting of sculptures and a wall painting, as well as a series of new paperwork, all using geometrical abstractions and light as a medium. Her work dissolves boundaries between fiction and documentation, depicting how fantasies and dreams collide with and yet help determine the shape of reality. Theme and variations is a term most commonly used in the music genre as a musical form in which the fundamental musical idea, or theme, is repeated in altered form or accompanied in a different manner. The exhibition explores geometric shapes and solids and revisits work of artists like Robert Morris and Ellsworth Kelly, giving it a disco treatment of glitter, neon and gloss. The mathematical, science-fiction and new age references incorporated in the works comments on the ambivalent foretelling of utopian hope and dystopian vision of a near, yet unknown future. The transmission between past and future is shown in the sculpture "The Omega Point" a portal that leads in or out of time and space. … |
A connection to today's earlier post, Sunday School— The Oslo Version, from Friday, May 21, 2010.
Lyche's "Omega Point" portal, together with her last name, suggested three posts from the following Saturday morning— which later proved to be the date of Martin Gardner's death—
Art Space, Through the Lyche Gate and The Lyche Gate Asterisk.
For some further religious remarks, see November 9th, 2010— A Theory of Pure Design.
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Friday, June 4, 2010
ART WARS continued
Today's New York Times—
Art Review
Painting Thin Air, Sometimes in Bright Blue
(“Yves Klein: With the Void, Full Powers”
runs through Sept. 12 at the Hirshhorn.)
Related material—
Search this journal for klein + paris.
See also Art Space (May 22, 2010)—
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Pictorial version |
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Saturday, May 22, 2010
Art Space
From an interview with artist Josefine Lyche (see previous post) dated March 11, 2009—
– Can you name a writer or book, fiction or theory that has inspired your works?
– Right now I am reading David Foster Wallace, which is great and inspiring. Others would be Aleister Crowley, Terence McKenna, James Joyce, J.L Borges, J.D Ballard, Stanislaw Lem, C. S. Lewis and Plato to mention some. Books, both fiction and theory are a great part of my life and work.
This journal on the date of the interview had a post about a NY Times story, ”Paris | A Show About Nothing."
Related images—
|
Pictorial version |
|
“Space: what you damn well have to see.”
– James Joyce, Ulysses
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