Log24

Monday, September 1, 2014

Mathematics, Not Theology

Filed under: Uncategorized — m759 @ 5:00 PM

(Continued)

“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

IMAGE- The Trinity of Max Black (a 3-set, with its eight subsets arranged in a Hasse diagram that is also a cube)

“There is  such a thing as a three-set.”
— Saying adapted from a novel by Madeleine L’Engle

Bone-Clock Intruders

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“For those who like this sort of thing,
this is the sort of thing they like.”

Sunday, August 31, 2014

Sunday School

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The Folding

Cynthia Zarin in The New Yorker , issue dated April 12, 2004—

“Time, for L’Engle, is accordion-pleated. She elaborated,
‘When you bring a sheet off the line, you can’t handle it
until it’s folded, and in a sense, I think, the universe can’t
exist until it’s folded — or it’s a story without a book.’”

The geometry of the 4×4 square array is that of the
3-dimensional projective Galois space PG(3,2).

This space occurs, notably, in the Miracle Octad Generator (MOG)
of R. T. Curtis (submitted to Math. Proc. Camb. Phil. Soc.  on
15 June 1974).  Curtis did not, however, describe its geometric
properties. For these, see the Cullinane diamond theorem.

Some history:

Curtis obtained the 4×4 space by “folding” three 1×8 binary
sequences into three 4×2 binary arrays. The original 1×8 sequences
came from the method of Turyn (1967) described by van Lint in his
book Coding Theory  (Springer Lecture Notes in Mathematics,
No. 201 
, first edition published in 1971). Two of the three 4×2 arrays
form each 4×4 square array within the MOG. This construction did not
suggest any discussion of the geometric properties of the square arrays.

Saturday, August 30, 2014

Physics and Theology

Filed under: Uncategorized — m759 @ 7:00 PM

The titles of the previous three posts refer to
Hermann Weyl’s 1918 book Raum, Zeit, Materie
(Space, Time, Matter).

This suggests a look at a poetically parallel 1950 title —
The Lion, the Witch and the Wardrobe —
and at its underlying philosophy:

I am among “those who do not know that this great myth became Fact.”
I do, however, note that some other odd things have become fact.
Those who wish more on this topic may consult:

Friday, August 29, 2014

Materie

Filed under: Uncategorized — m759 @ 9:29 AM

(A sequel to Raum  and  Zeit )

See also Christmas Eve, 2012.

“It’s going to be accomplished
in steps, this establishment
of the talented….”

To Ride Pegasus , by
Anne McCaffrey (Radcliffe ’47)

Zeit

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( A sequel to Raum )

The author reportedly died on August 14, 2014. See a post from that date.

Raum

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A possible answer to the 1923 question of Walter Gropius, “Was ist Raum?“—

See also yesterday’s Source of the Finite and the image search
on the Gropius question in last night’s post.

Thursday, August 28, 2014

Brutalism Revisited

Filed under: Uncategorized — m759 @ 11:59 PM

Yesterday’s 11 AM post was a requiem for a brutalist architect.

Today’s LA Times  has a related obituary:

“Architectural historian Alan Hess, who has written several books on
Mid-Century Modern design, said Meyer didn’t have a signature style,
‘which is one reason he is not as well-known as some other architects
of the period. But whatever style he was working in, he brought a real
sense of quality to his buildings.’

A notable example is another bank building, at South Beverly Drive
and Pico Boulevard, with massive concrete columns, a hallmark of
the New Brutalism style. ‘This is a really good example of it,’ Hess said.”

— David Colker, 5:43 PM LA time, Aug. 28, 2014

A related search, suggested by this morning’s post Source of the Finite:

(Click to enlarge.)

Source of the Finite

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“Die Unendlichkeit  ist die uranfängliche Tatsache: es wäre nur
zu erklären, woher das Endliche  stamme….”

— Friedrich Nietzsche, Das Philosophenbuch/Le livre du philosophe
(Paris: Aubier-Flammarion, 1969), fragment 120, p. 118

Cited as above, and translated as “Infinity is the original fact;
what has to be explained is the source of the finite….” in
The Production of Space , by Henri Lefebvre. (Oxford: Blackwell,
1991 (1974)), p.  181.

This quotation was suggested by the Bauhaus-related phrase
“the laws of cubical space” (see yesterday’s Schau der Gestalt )
and by the laws of cubical space discussed in the webpage
Cube Space, 1984-2003.

For a less rigorous approach to space at the Harvard Graduate
School of Design, see earlier references to Lefebvre in this journal.

Wednesday, August 27, 2014

Not Quite

Filed under: Uncategorized — m759 @ 12:00 PM

Click image to enlarge.

Altar

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“To every man upon this earth,
Death cometh soon or late.
And how can man die better
Than facing fearful odds,
For the ashes of his fathers,
and the temples of his gods…?”

— Macaulay, quoted in the April 2013 film “Oblivion

“Leave a space.” — Tom Stoppard, “Jumpers”

Related material: The August 16, 2014, sudden death in Scotland
of an architect of the above Cardross seminary, and a Log24 post,
Plato’s Logos, from the date of the above photo: June 26, 2010.

See also…

IMAGE- T. Lux Feininger on 'Gestaltung'

Here “eidolon” should instead be “eidos .”

An example of eidos — Plato’s diamond (from the Meno ) —

http://www.log24.com/log/pix10A/100607-PlatoDiamond.gif

Schau der Gestalt

Filed under: Uncategorized — m759 @ 5:01 AM

(Continued from Aug. 19, 2014)

“Christian contemplation is the opposite
of distanced consideration of an image:
as Paul says, it is the metamorphosis of
the beholder into the image he beholds
(2 Cor 3.18), the ‘realisation’ of what the
image expresses (Newman). This is
possible only by giving up one’s own
standards and being assimilated to the
dimensions of the image.”

— Hans Urs von Balthasar,
The Glory of the Lord:
A Theological Aesthetics,

Vol. I: Seeing the Form
[ Schau der Gestalt ],
Ignatius Press, 1982, p. 485

A Bauhaus approach to Schau der Gestalt :

I prefer the I Ching ‘s approach to the laws of cubical space.

Tuesday, August 26, 2014

Le Pianiste

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Bryan Cranston won an Emmy for lead actor in a drama series Monday…”

“Tu es le pianiste….” — Log24 post 641

Lux et Veritas

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Omega by Lux:

Omega by Curtis:

Exotic Sphere

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Two images from posts tagged ‘Objects of Beauty‘ —

“And be these juggling fiends no more believed,
That palter with us in a double sense….”

Later

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Related material:  March 20, 2013.

Monday, August 25, 2014

A Challenging Story:

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Symplectic Macbeth

Lead on, McDuff:

Plato Thanks the Academy

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(Continued)

See Shadowlands in this journal.
The film so titled was directed by Richard Attenborough,
President of the Royal Academy of Dramatic Art,
who reportedly died on Sunday, August 24, 2014.

It’s all in Plato, all in Plato:
bless me, what do  they
teach them at these schools!”
— C. S. Lewis

Sunday, August 24, 2014

Richard Attenborough

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Richard Samuel Attenborough, Baron AttenboroughCBE
(
… 29 August 1923 – 24 August 2014) was an English actor,
film director, producer and entrepreneur. He was the President of
the 
Royal Academy of Dramatic Art (RADA).” — Wikipedia

Symplectic Structure…

Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

In the Miracle Octad Generator (MOG):

The above details from a one-page note of April 26, 1986, refer to the
Miracle Octad Generator of R. T. Curtis, as it was published in 1976:

http://www.log24.com/log/pix10A/100514-Curtis1976MOG.jpg

From R. T. Curtis (1976). A new combinatorial approach to M24,
Mathematical Proceedings of the Cambridge Philosophical Society ,
79, pp 25-42. doi:10.1017/S0305004100052075.

The 1986 note assumed that the reader would be able to supply, from the
MOG itself, the missing top row of each heavy brick.

Note that the interchange of the two squares in the top row of each
heavy brick induces the diamond-theorem correlation.

Note also that the 20 pictured 3-subsets of a 6-set in the 1986 note
occur as paired complements  in two pictures, each showing 10 of the
3-subsets.

This pair of pictures corresponds to the 20 Rosenhain tetrads  among
the 35 lines of PG(3,2), while the picture showing the 2-subsets
corresponds to the 15 Göpel tetrads  among the 35 lines.

See Rosenhain and Göpel tetrads in PG(3,2). Some further background:

The Blue Path

Filed under: Uncategorized — m759 @ 2:56 AM

A song for those who prefer the red path: Abracadabra.

IMAGE- Abracadabra 4x6

Saturday, August 23, 2014

Monolith

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Unity 

Roman numeral I
as well as capital I

(Not signifying nothing.)

The Scottish Play…

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Meets Clark Gable —

Signifying Nothing.

Explicatio

Filed under: Uncategorized — m759 @ 2:20 AM

(The title is from a post of July 8, 2010.)

“What is important is the ability to tell stories through character.”

Diana Gabaldon, author of the Outlander  series of novels

An image from the bottom line of images in the previous post:

In memory of Scottish folk singer Jean Redpath,
who reportedly died on Thursday, August 21:

See also this journal on August 21.

Friday, August 22, 2014

The Bottom Line

Filed under: Uncategorized — m759 @ 11:30 PM

The bottom three lines of an image search:

For a meditation on the bottom line, see Mary Gaitskill’s story
“The Agonized Face.” See also George C. Scott reciting from
the Scottish play in The Exorcist III.

Review

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Image search for “symplectic structure” + “35 lines” —

Click for larger (2.5 MB) image.

Thursday, August 21, 2014

Remember me to…

Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

Herald Square.

The Folding

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See Madeleine + Folded.

An illustration (click to enlarge) —

Related material: Posts from the above upload date, 10/1/10.

Nox

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( A sequel to Lux )

“By groping toward the light we are made to realize
how deep the darkness is around us.”

— Arthur Koestler, The Call Girls: A Tragi-Comedy ,
Random House, 1973, page 118

Robin Williams and the Stages of Math

i)   shock & denial
ii)  anger
iii) bargaining
iv) depression
v)  acceptance

A related description of the process —

You know how sometimes someone tells you a theorem,
and it’s obviously false, and you reach for one of the many
easy counterexamples only to realize that it’s not a
counterexample after all, then you reach for another one
and another one and find that they fail too, and you begin
to concede the possibility that the theorem might not
actually be false after all, and you feel your world start to
shift on its axis, and you think to yourself: ‘Why did no one
tell me this before?’ “

— Tom Leinster yesterday at The n-Category Café

Tuesday, August 19, 2014

Lux

Filed under: Uncategorized — m759 @ 7:00 PM

(As opposed to an alleged bearer  of lux  .)

IMAGE- T. Lux Feininger on 'Gestaltung'

(Here “eidolon” should instead be “eidos.”)

An example of Gestaltung :

This journal on the day of Feininger’s death, and the day before —

The 256 Code (Thursday, July 7, 2011) and Nordstrom-Robinson Automorphisms.

Grid

Filed under: Uncategorized — m759 @ 2:56 AM

In memory of one who sent in the clowns:

See also Plan 9 in this journal, as well as Saturday’s posts.

Sunday, August 17, 2014

Flashback…

Filed under: Uncategorized — m759 @ 11:01 AM

To Feb. 11, 2012:

“News and Traffic. Sports and Weather. These were his acid terms
for the life he’d left behind, more than two years of living with
the tight minds that made the war. It was all background noise,
he said, waving a hand. He liked to wave a hand in dismissal.”

— DeLillo, Don (2010-02-02), Point Omega 

Send in the Clowns.   (Click to enlarge.)

The above flashback was suggested by Lev Grossman’s verb “trafficked”
in yesterday’s posts, and by the song lyric “show us the way to
the next little girl.”

Saturday, August 16, 2014

The Grossman Chronicles

Filed under: Uncategorized — Tags: — m759 @ 10:16 PM

“Shakespeare, Dante, Milton, Homer: those writers trafficked in
witches and fairies and ghosts and monsters. Why shouldn’t I?”

Novelist Lev Grossman in The New York Times  this afternoon

Grossman’s father was the poet Allen Grossman.

See that Grossman in this journal, as well as a search for Holy Water.

Les Prédateurs

Filed under: Uncategorized — Tags: — m759 @ 10:30 AM

For the Thin White Duke —
The Next Whiskey Bar:

Saturday, August 16, 2014, 6:00 pm in UTC+02
at LYNX 760 in Oslo, Norway.

Friday, August 15, 2014

August Ninth Death

Filed under: Uncategorized — m759 @ 11:59 PM

In memory of a Manhattan real-estate developer
who reportedly died on August 9, 2014 —
a post from that date a year earlier.

Click on the Tower for further details.

The Omega Matrix

Filed under: Uncategorized — m759 @ 11:00 PM

(Continued)

The webpage Rosenhain and Göpel Tetrads in PG(3,2)
has been updated to include more material on symplectic structure.

Thursday, August 14, 2014

Analects

Filed under: Uncategorized — m759 @ 11:59 PM

“Mr. Ryckmans translated, into English, the ‘Analects,’
the collection of sayings attributed to Confucius.”

— A New York Times  obituary this evening

See also this morning’s post on Confucius.

Full Frontal Aesthetics

Filed under: Uncategorized — m759 @ 7:59 PM

A prequel to today’s noon post

Rosalind Krauss in “Grids” —

“The physical qualities of the surface, we could say,
are mapped onto the aesthetic dimensions of
the same surface. And those two planes—
the physical and the aesthetic— are demonstrated
to be the same plane…. the bottom line of the grid is
a naked and determined materialism.”

A writer I prefer:

Barsotti’s classic illustrated:

The naked and determined Annette Bening in “The Grifters” —

Bottom Line

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“. . . the bottom line of the grid is a naked and determined materialism.”

— Rosalind Krauss, quoted by Josefine Lyche

See also http://www.dailymotion.com/video/
x164rmi_britt-ekland-nude-wicker-man-1973_people.

MIT Mystery

Filed under: Uncategorized — m759 @ 11:00 AM

Robin Williams and the Stages of Grief

A weblog post from Jan. 25, 2014 (click image to enlarge)—

Clues for a Mystery   (Click links for more details)—

Clue 1:  A June 11,* 2014, math death.

Clue 2:  The answer is a surname.

Midrash for Will Hunting:

See Nanavira Thera at Wikipedia and space notes from September 2012.

* According to a (perhaps inaccurate) math department.
June 10, according to other sources cited by the department.

Intelligent Opening?

Filed under: Uncategorized — m759 @ 9:15 AM

“The Pope’s visit to South Korea is the first part of a very intelligent
opening to Asia,” said Lionel Jensen, associate professor of East Asian
Languages and Cultures at the University of Notre Dame.
— Madison Park, CNN this morning

A not-so-intelligent opening —

“Could it be that the familiar and beloved figure of Confucius
was invented by Jesuit priests? In Manufacturing Confucianism,
Lionel M. Jensen reveals this very fact….”

Duke University Press

For some background, see an Atlantic Monthly  article from 1999,
Confucius and the Scholars,” by Charlotte Allen.

Wednesday, August 13, 2014

Symplectic Structure continued

Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

Some background for the part of the 2002 paper by Dolgachev and Keum
quoted here on January 17, 2014 —

Related material in this journal (click image for posts) —

Stranger than Dreams*

Filed under: Uncategorized — m759 @ 12:00 AM

Illustration from a discussion of a symplectic structure 
in a 4×4 array quoted here on January 17, 2014 —

See symplectic structure in this journal.

* The final words of Point Omega , a 2010 novel by Don DeLillo.
See also Omega Matrix in this journal.

Tuesday, August 12, 2014

Point Omega

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Continues

Update of 9:29 PM ET (Click to enlarge.) —

Adapted from a Facebook page.

Monkey Business

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Welcome to the Ape Stuff.

Monday, August 11, 2014

The Wicca Man*

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Don’t forget to send us your strip!

* A reference to mathematician Peter J. Cameron as Lord Summerisle.

Raiding Minsky’s

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In honor of Emil Post and Robin Williams:

With Honors

Filed under: Uncategorized — m759 @ 7:59 PM

Continued from June 5, 2003.

Complete the sentence: “The son of a bitch stole my _______. ”

Syntactic/Symplectic

Filed under: Uncategorized — m759 @ 4:00 PM

(Continued from August 9, 2014.)

Syntactic:

Symplectic:

“Visual forms— lines, colors, proportions, etc.— are just as capable of
articulation , i.e. of complex combination, as words. But the laws that govern
this sort of articulation are altogether different from the laws of syntax that
govern language. The most radical difference is that visual forms are not
discursive 
. They do not present their constituents successively, but
simultaneously, so the relations determining a visual structure are grasped
in one act of vision.”

– Susanne K. LangerPhilosophy in a New Key

For examples, see The Diamond-Theorem Correlation
in Rosenhain and Göpel Tetrads in PG(3,2).

This is a symplectic  correlation,* constructed using the following
visual structure:

IMAGE- A symplectic structure -- i.e. a structure that is symplectic (meaning plaited or woven).

* Defined in (for instance) Paul B. Yale, Geometry and Symmetry ,
Holden-Day, 1968, sections 6.9 and 6.10.

Sunday, August 10, 2014

That Old Devil Moon

Filed under: Uncategorized — m759 @ 9:00 PM

“Something in your eyes I see
Soon begins bewitching me”

Knight Moves

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Some illustrations:

Springer logo - A chess knight

Chess Knight
(in German, Springer)

See also…

Katherine Neville's 'The Eight,' edition with knight on cover, on her April 4 birthday

More technically (click image for details):

Sermon

Filed under: Uncategorized — m759 @ 11:00 AM

From The Mathematics of Language:
10th and 11th  Biennial Conference….
Berlin,  Springer, 2010 —

Creation Myths of Generative Grammar
and the Mathematics of Syntactic Structures
by Geoffrey K. Pullum, University of Edinburgh

Abstract

Syntactic Structures  (Chomsky [6])  is widely believed to have laid
the foundations of a cognitive revolution in linguistic science, and
to have presented (i) the first use in linguistics of powerful new ideas
regarding grammars as generative systems, (ii) a proof that English
was not a regular language, (iii) decisive syntactic arguments against
context-free phrase structure grammar description, and (iv) a
demonstration of how transformational rules could provide a formal
solution to those problems. None of these things are true. This paper
offers a retrospective analysis and evaluation.”

Saturday, August 9, 2014

Syntactic/Symplectic

Filed under: Uncategorized — m759 @ 3:00 PM

Syntactic  Structure —

See the Lightfoot of today’s previous post:

Symplectic  Structure —

See the plaited, or woven, structure of  August 6:

IMAGE- A symplectic structure -- i.e. a structure that is symplectic (meaning plaited or woven).

See also Deep  Structure  (Dec. 9, 2012).

Operation Lightfoot*

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“In 1977, Golan directed Operation Thunderbolt….”

Hollywood Reporter  obituary

* See a search for Lightfoot  in this journal.

Friday, August 8, 2014

Succès de Scandale

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Ten Years

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A Late Quartet

01:13:08.25,01:13:12.35
(STRING QUARTET PLAYING
SLOW, LUSH MELODY)

01:13:22.59,01:13:26.23
They’re fucking sixteenths,
Steve, stop milking them.

01:13:26.36,01:13:29.78
Folks, disagree,
but do it nicely, and please…

01:13:30.47,01:13:33.38
…try not to get caught up in mistakes.

01:13:35.17,01:13:38.21
When I was your age,
I met the great Pablo Casals.

01:13:38.34,01:13:40.85
I was so intimidated
I could barely speak.

01:13:40.98,01:13:43.19
He must have sensed this, because…

01:13:43.31,01:13:46.99
…instead of a chat,
he asked me to play.

01:13:47.12,01:13:49.93
He requested the prelude
to the Fourth Bach suite.

01:13:51.62,01:13:54.80
I focused, took a deep breath,
began, the notes started to flow,

01:13:54.93,01:13:58.67
the music’s in the air, and it was
the worst music I ever made.

01:13:58.80,01:14:00.28
(STUDENTS CHUCKLE)

01:14:01.13,01:14:05.44
I played so badly,
I got halfway through and had to stop.

01:14:05.57,01:14:07.71
“Bravo,” he said, “Well done.”

01:14:08.94,01:14:13.85
Then, he asked me to play the allemande.
“A second chance,” I think to myself.

01:14:15.48,01:14:17.05
I never played worse.

01:14:18.48,01:14:22.06
“Wonderful. Splendid,” he praised me.

01:14:22.19,01:14:26.73
And when I left that night,
I felt terrible about my performance,

01:14:26.86,01:14:30.50
but what really bothered me
wasn’t my playing, it was Casals.

01:14:30.63,01:14:32.30
The insincerity.

01:14:33.90,01:14:36.50
Years later, I met him in Paris

01:14:36.63,01:14:40.41
and by then I was professional,
we played together.

01:14:40.54,01:14:45.08
We became acquaintances,
and one evening, over a glass of wine…

01:14:46.94,01:14:51.32
…I confessed to him what I thought
of his horseshit all those years ago.

01:14:51.45,01:14:53.22
(LAUGHTER)

01:14:55.12,01:14:59.09
And he got angry. His demeanor changed,
he grabbed his cello,

01:14:59.22,01:15:02.50
“Listen,” he said.
And he played this phrase.

01:15:03.63,01:15:07.58
(PLAYS DYNAMIC, DRAMATIC PHRASE)

01:15:19.08,01:15:22.06
“Didn’t you play that? Fingering.

01:15:22.18,01:15:25.96
You did.
It was novel to me. It was good.

01:15:26.08,01:15:31.09
And here, didn’t you attack
this passage with an up-bow like this?”

01:15:45.14,01:15:49.08
Casals emphasized the good stuff,
the things he enjoyed.

01:15:50.87,01:15:55.65
He encouraged. And for the rest,
leave that to the morons,

01:15:55.78,01:16:00.85
or whatever it is in Spanish,
who judge by counting faults.

01:16:00.98,01:16:03.62
“I can be grateful,
and so must you be,” he said,

01:16:03.75,01:16:09.03
“for even one singular phrase,
one transcendent moment.”

01:16:09.33,01:16:10.33
Hmm?

01:16:11.40,01:16:16.64
- Wow.
- Yeah, wow. Pablo Casals. Champion.

01:16:17.90,01:16:21.82
Once more, with feeling please. Feeling!

01:16:25.21,01:16:29.05
(SLOW, LUSH MELODY RESUMES)

See also a video of this scene and a post from this date ten years ago.

Forty Years

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Thursday, August 7, 2014

The Omega Mystery

Filed under: Uncategorized — m759 @ 11:00 PM

See a post,  The Omega Matrix, from the date of her death.

Related material:

“When Death tells a story, you really have to listen.”
— Cover of The Book Thief

A scene from the film of the above book —

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

— Richard Evan Schwartz

Some context — “Mathematics, Magic, and Mystery” —
See posts tagged April Awareness 2014.

Abuse of Language

Filed under: Uncategorized — m759 @ 12:00 AM

From Wikipedia — Abuse of language —

“… in mathematics, a use of terminology in a way that is not formally correct
but that simplifies exposition or suggests the correct intuition.”

The phrase “symplectic structure” in the previous post
was a deliberate abuse of languageThe real definition:

Wednesday, August 6, 2014

Symplectic Structure*

Filed under: Uncategorized — Tags: — m759 @ 1:00 PM

From Gotay and Isenberg, “The Symplectization of Science,”
Gazette des Mathématiciens  54, 59-79 (1992):

“… what is the origin of the unusual name ‘symplectic’? ….
Its mathematical usage is due to Hermann Weyl who,
in an effort to avoid a certain semantic confusion, renamed
the then obscure ‘line complex group’ the ‘symplectic group.’
… the adjective ‘symplectic’ means ‘plaited together’ or ‘woven.’
This is wonderfully apt….”

IMAGE- A symplectic structure -- i.e. a structure that is symplectic (meaning plaited or woven)

The above symplectic  structure** now appears in the figure
illustrating the diamond-theorem correlation in the webpage
Rosenhain and Göpel Tetrads in PG(3,2).

Some related passages from the literature:

http://www.log24.com/log/pix10B/100915-SteinbergOnChevalleyGroups.jpg

* The title is a deliberate abuse of language .
For the real definition of 
“symplectic structure,” see (for instance)
“Symplectic Geometry,” by Ana Cannas da Silva (article written for
Handbook of Differential Geometry, vol 2.)

** See Steven H. Cullinane, Inscapes III, 1986

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