Log24

Saturday, September 27, 2025

Four-Color Monolith

Filed under: General — Tags: , , , — m759 @ 12:59 pm

Those who find Kubrick's black 2001 monolith too dark
may prefer a more colorful image, taken from yesterday's
post on the Klein correspondence

http://www.log24.com/log/pix11/110412-IconicArt.jpg

When?

Going to dark bed there was a square round 
Sinbad the Sailor roc’s auk’s egg
in the night of the bed of all the auks of the rocs
of Darkinbad the Brightdayler.

Where?

Black disc from end of Ch. 17 in Ulysses

— Ulysses , conclusion of Chapter 17.

Friday, September 13, 2024

Starbrick Art

Filed under: General — Tags: , — m759 @ 4:47 am

“Looking carefully at Golay’s code
is like staring into the sun.”

— Richard Evan Schwartz

The monolith at the beginning of '2001'

Twelve basis vectors, in lexicographic order, for the binary Golay-code space

Friday, May 8, 2026

Function Decomposition and the Klein Quadric

Filed under: General — Tags: — m759 @ 7:48 am

"Grid models" in finite geometry include the 4-row 2-column
"brick space" arrays of the R. T. Curtis Miracle Octad Generator.

The remarks below on grid models suggested this post's title,
"Function Decomposition and the Klein Quadric." The result of
applying the Cullinane decomposition theorem to the final 
remarks in Cameron's Parallelisms of Complete Designs

http://m759.net/wordpress/?s=Brick+Color+Monolith .

Connecting Diverse Mathematical Fields
The grid model acts as a unifying framework for several other abstract concepts:
  • The Klein Quadric: The correspondence extends to higher dimensions via the Klein correspondence. This maps the 35 lines of  PG(3,2) (the grid structures) to 35 points on the Klein quadric in a 5-dimensional projective space, PG(5,2). This connects the combinatorial partitions of the grid to the geometry of quadric surfaces.
  • Latin Squares: The model provides a geometric interpretation of combinatorial design. The concept of orthogonality between Latin squares corresponds to the geometric concept of skewness (non-intersecting lines) in PG(3,2).
  • Walsh Functions: The symmetries and binary additions inherent in the line diagrams reflect the structure of Walsh functions, which are orthogonal functions used in digital signal processing and discrete harmonic analysis.
  • Ring Theory: The patterns can be organized algebraically to form "diamond rings," which are isomorphic to rings of matrices over the field GF(4), linking the visual design to abstract algebra and function decomposition.
Summary
The 4×4 grid model acts as a "kaleidoscope" of mathematical structure. Just as a kaleidoscope rearranges simple elements into symmetric patterns, this grid rearranges simple binary tiles to reveal the invariant structures of finite geometries, sporadic groups, and error-correcting codes. It transforms what appears to be a simple problem of tiling into a visualization of the affine 4-space over GF(2)

Sunday, April 10, 2011

Bedeviled

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

From tonight's online New York Times

John McCracken, Sculptor of Geometric Forms, Dies at 76

McCracken died in Manhattan on Friday, April 8.

From Christopher Knight in tonight's online LA Times

… the works embody perceptual and philosophical conundrums. The colored planks stand on the floor like sculptures….

McCracken was bedeviled by Stanley Kubrick's famously obscure science-fiction epic, "2001: A Space Odyssey," with its iconic image of an ancient monolith floating in outer space. The 1968 blockbuster was released two years after the artist made his first plank.

"At the time, some people thought I had designed the monolith or that it had been derived from my work," he told art critic Frances Colpitt of the coincidence in a 1998 interview.

Two photos of McCracken's 1967 Black Plank  seem relevant—

November 28, 2010 (Click to enlarge)

http://www.log24.com/log/pix11/110410-McCrackenPlank1967400w.jpg

December 28, 2010 (Click to enlarge)

http://www.log24.com/log/pix11/110410-McCracken-NatGallery-NothingToSeeHere-400w.jpg

Material that an artist might view as related, if only synchronistically—

Two posts in this journal on the dates the photos were taken—
The Embedding on November 28 and Dry Bones on December 28.

The photos are of an exhibition titled "There is nothing to see here" at the
National Gallery of Art, October 30, 2010-April 24, 2011 —

Click to enlarge.

http://www.log24.com/log/pix11/110410-NothingToSee-400w.jpg

For related nihilism from the National Gallery, see "Pictures of Nothing" in this journal.

Some less nihilistic illustrations—

The Meno  Embedding

Plato's Diamond embedded in The Matrix

A photo by one of the artists whose work is displayed above beside McCracken's—

http://www.log24.com/log/pix11/110410-Sugimoto-AndoChurch.jpg

"Accentuate the Positive."
 — Clint Eastwood

Sunday, February 15, 2009

Sunday February 15, 2009

Filed under: General,Geometry — Tags: , , — m759 @ 11:00 am
From April 28, 2008:
 

Religious Art

The black monolith of
Kubrick's 2001 is, in
its way, an example
of religious art.

Black monolith, proportions 4x9

One artistic shortcoming
(or strength– it is, after
all, monolithic) of
that artifact is its
resistance to being
analyzed as a whole
consisting of parts, as
in a Joycean epiphany.

The following
figure does
allow such
  an epiphany.

A 2x4 array of squares

One approach to
 the epiphany:

"Transformations play
  a major role in
  modern mathematics."
– A biography of
Felix Christian Klein

See 4/28/08 for examples
of such transformations.

 
Related material:
 

From Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, pp. 117-118:

"… his point of origin is external nature, the fount to which we come seeking inspiration for our fictions. We come, many of Stevens's poems suggest, as initiates, ritualistically celebrating the place through which we will travel to achieve fictive shape. Stevens's 'real' is a bountiful place, continually giving forth life, continually changing. It is fertile enough to meet any imagination, as florid and as multifaceted as the tropical flora about which the poet often writes. It therefore naturally lends itself to rituals of spring rebirth, summer fruition, and fall harvest. But in Stevens's fictive world, these rituals are symbols: they acknowledge the real and thereby enable the initiate to pass beyond it into the realms of his fictions.

Two counter rituals help to explain the function of celebration as Stevens envisions it. The first occurs in 'The Pediment of Appearance,' a slight narrative poem in Transport to Summer. A group of young men enter some woods 'Hunting for the great ornament, The pediment of appearance.' Though moving through the natural world, the young men seek the artificial, or pure form, believing that in discovering this pediment, this distillation of the real, they will also discover the 'savage transparence,' the rude source of human life. In Stevens's world, such a search is futile, since it is only through observing nature that one reaches beyond it to pure form. As if to demonstrate the degree to which the young men's search is misaligned, Stevens says of them that 'they go crying/The world is myself, life is myself,' believing that what surrounds them is immaterial. Such a proclamation is a cardinal violation of Stevens's principles of the imagination. For in 'Notes Toward a Supreme Fiction' he tells us that

... the first idea was not to shape the clouds
In imitation. The clouds preceded us.      

There was a muddy centre before we breathed.
There was a myth before the myth began,
Venerable and articulate and complete.      

From this the poem springs: that we live in a place
That is not our own and, much more, not ourselves
And hard it is in spite of blazoned days.      

We are the mimics.

                                (Collected Poems, 383-84)

Believing that they are the life and not the mimics thereof, the world and not its fiction-forming imitators, these young men cannot find the savage transparence for which they are looking. In its place they find the pediment, a scowling rock that, far from being life's source, is symbol of the human delusion that there exists a 'form alone,' apart from 'chains of circumstance.'

A far more productive ritual occurs in 'Sunday Morning.'…."

For transformations of a more
specifically religious nature,
see the remarks on
Richard Strauss,
"Death and Transfiguration,"
(Tod und Verklärung, Opus 24)

in Mathematics and Metaphor
on July 31, 2008, and the entries
of August 3, 2008, related to the
 death of Alexander Solzhenitsyn.

Sunday, October 26, 2003

Sunday October 26, 2003

Filed under: General — m759 @ 3:17 am

ART WARS for

Trotsky’s Birthday

Part I:
Symbols

From my entry of July 26, 2003, in memory
of Marathon Man director John Schlesinger:

Bright Star and Dark Lady

“Mexico is a solar country — but it is also a black country, a dark country. This duality of Mexico has preoccupied me since I was a child.”

Octavio Paz,
quoted by Homero Aridjis

Bright Star

Amen.

Dark Lady

For the meaning of the above symbols, see
Kubrick’s 1x4x9 monolith in 2001,
the Halmos tombstone in Measure Theory,
and the Fritz Leiber Changewar stories.

No se puede vivir sin amar.


Part II:
Sunday in the Park with Death

  To Leon from Diego —
Details of a mural,
A Dream of a Sunday Afternoon
in Alameda Park,
Fresco, 1947-48,
Alameda Hotel, Mexico City:

Three’s a Crowd:

Symbol:


Thursday, September 4, 2003

Thursday September 4, 2003

Filed under: General — m759 @ 2:42 am

Monolith

“Music can name the unnameable
and communicate the unknowable.”

— Quotation attributed to Leonard Bernstein

“Finally we get to Kubrick’s ultimate trick….  His secret is in plain sight…. The film is the monolith. In a secret that seems to never have been seen by anyone: the monolith in the film has the same exact dimensions as the movie screen on which 2001 was projected.”

—  Alchemical Kubrick 2001, by Jay Weidner 

My entry of Saturday, August 30,
included the following illustration:

My entry of Monday, September 1,
concluded with the black monolith.

“There is little doubt that the black monolith
in 2001 is the Philosopher’s Stone.”

—  Alchemical Kubrick 2001, by Jay Weidner 

 The philosopher Donald Davidson
died on Saturday, August 30.

The New York Times says that as an undergraduate, Davidson “persuaded Harvard to let him put on ‘The Birds’ by Aristophanes and played the lead, Peisthetairos, which meant memorizing 700 lines of Greek. His friend and classmate Leonard Bernstein, with whom he played four-handed piano, wrote an original score for the production.”

Perhaps they are still making music together.

Saturday, July 26, 2003

Saturday July 26, 2003

Filed under: General — Tags: , — m759 @ 5:29 am

Funeral March

John Schlesinger dead at 77;
‘Midnight Cowboy’ director

 
Anthony Breznican
Associated Press
Jul. 26, 2003 12:00 AM

LOS ANGELES – Oscar-winning director John Schlesinger, who daringly brought gay characters into mainstream cinema with Midnight Cowboy and tapped into nightmares with the teeth-drilling torture of Marathon Man, died Friday at 77.

The British-born filmmaker…. died about 5:30 a.m….

Schlesinger also directed The Day of the Locust, based on a novel by Nathanael West.

See Heaven, Hell, and Hollywood and

Dogma Part II: Amores Perros.

From the latter:

“Then you know your body’s sent,
Don’t care if you don’t pay rent,
Sky is high and so am I,
If you’re a viper — a vi-paah.”

The Day of the Locust,
    by Nathanael West (1939),
    New Directions paperback,
    1969, page 162

This song may be downloaded at

Pot Culture, 1910-1960.

That same site begins with a traditional Mexican song…

La cucaracha, la cucaracha,
 ya no puede caminar,
 porque no quiere,
 porque le falta
 marihuana que fumar.
” 

(“The cockroach, the cockroach,
 can’t walk anymore,
 because he doesn’t want to,
 because he has no
 marihuana to smoke.”)

This suggests an appropriate funeral march for John Schlesinger:

“Ya murió la cucaracha, ya la llevan a enterrar…”La Cucaracha

Those attending Schlesinger’s wake, as opposed to his funeral, may wish to perform other numbers from the Pot Culture page, which offers a variety of “viper” songs.

Bright Star and Dark Lady

“Mexico is a solar country — but it is also a black country, a dark country. This duality of Mexico has preoccupied me since I was a child.”

Octavio Paz,
quoted by Homero Aridjis

Bright Star

Amen.

 

Dark Lady

For the meaning of the above symbols, see
Kubrick’s 1x4x9 monolith in 2001,
the Halmos tombstone in Measure Theory,
and the Fritz Leiber Changewar stories.

No se puede vivir sin amar.

Concluding Unscientific Postscript:

Oh, yes… the question of
Heaven or Hell for John Schlesinger… 

Recall that he also directed the delightful
Cold Comfort Farm and see
last year’s entry for this date.

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