Log24

Tuesday, May 28, 2019

Quaternion at Candlebrow

Filed under: General — Tags: — m759 @ 11:00 AM

From a Groundhog Day post in 2009 —

The Candlebrow Conference
in Pynchon's Against the Day:

The conferees had gathered here from all around the world…. Their spirits all one way or another invested in, invested by, the siegecraft of Time and its mysteries.

"Fact is, our system of so-called linear time is based on a circular or, if you like, periodic phenomenon– the earth's own spin. Everything spins, up to and including, probably, the whole universe. So we can look to the prairie, the darkening sky, the birthing of a funnel-cloud to see in its vortex the fundamental structure of everything–"

Quaternion in finite geometry
Quaternion  by  S. H. Cullinane

"Um, Professor–"….

… Those in attendance, some at quite high speed, had begun to disperse, the briefest of glances at the sky sufficing to explain why. As if the professor had lectured it into being, there now swung from the swollen and light-pulsing clouds to the west a classic prairie "twister"….

… In the storm cellar, over semiliquid coffee and farmhouse crullers left from the last twister, they got back to the topic of periodic functions….

"Eternal Return, just to begin with. If we may construct such functions in the abstract, then so must it be possible to construct more secular, more physical expressions."

"Build a time machine."

"Not the way I would have put it, but if you like, fine."

Vectorists and Quaternionists in attendance reminded everybody of the function they had recently worked up….

"We thus enter the whirlwind. It becomes the very essence of a refashioned life, providing the axes to which everything will be referred. Time no long 'passes,' with a linear velocity, but 'returns,' with an angular one…. We are returned to ourselves eternally, or, if you like, timelessly."

"Born again!" exclaimed a Christer in the gathering, as if suddenly enlightened.

Above, the devastation had begun.

"As if the professor had lectured it into being . . . ."

See other posts now tagged McLuhan Time.

Wednesday, March 6, 2013

Midnight in Pynchon*

Filed under: General,Geometry — m759 @ 12:00 AM

"It is almost as though Pynchon wishes to
repeat the grand gesture of Joyce’s Ulysses…."

Vladimir Tasic on Pynchon's Against the Day

Related material:

Tasic's Mathematics and the Roots of Postmodern Thought  
and Michael Harris's "'Why Mathematics?' You Might Ask"

*See also Occupy Galois Space and Midnight in Dostoevsky.

Friday, December 28, 2012

Cube Koan

Filed under: General,Geometry — Tags: , , , — m759 @ 4:56 AM
 

From Don DeLillo's novel Point Omega —

I knew what he was, or what he was supposed to be, a defense intellectual, without the usual credentials, and when I used the term it made him tense his jaw with a proud longing for the early weeks and months, before he began to understand that he was occupying an empty seat. "There were times when no map existed to match the reality we were trying to create."

"What reality?"

"This is something we do with every eyeblink. Human perception is a saga of created reality. But we were devising entities beyond the agreed-upon limits of recognition or interpretation. Lying is necessary. The state has to lie. There is no lie in war or in preparation for war that can't be defended. We went beyond this. We tried to create new realities overnight, careful sets of words that resemble advertising slogans in memorability and repeatability. These were words that would yield pictures eventually and then become three-dimensional. The reality stands, it walks, it squats. Except when it doesn't."

He didn't smoke but his voice had a sandlike texture, maybe just raspy with age, sometimes slipping inward, becoming nearly inaudible. We sat for some time. He was slouched in the middle of the sofa, looking off toward some point in a high corner of the room. He had scotch and water in a coffee mug secured to his midsection. Finally he said, "Haiku."

I nodded thoughtfully, idiotically, a slow series of gestures meant to indicate that I understood completely.

"Haiku means nothing beyond what it is. A pond in summer, a leaf in the wind. It's human consciousness located in nature. It's the answer to everything in a set number of lines, a prescribed syllable count. I wanted a haiku war," he said. "I wanted a war in three lines. This was not a matter of force levels or logistics. What I wanted was a set of ideas linked to transient things. This is the soul of haiku. Bare everything to plain sight. See what's there. Things in war are transient. See what's there and then be prepared to watch it disappear."

What's there—

This view of a die's faces 3, 6, and 5, in counter-
clockwise order (see previous post) suggests a way
of labeling the eight corners  of a die (or cube):

123, 135, 142, 154, 246, 263, 365, 456.

Here opposite faces of the die sum to 7, and the
three faces meeting at each corner are listed
in counter-clockwise order. (This corresponds
to a labeling of one of MacMahon's* 30 colored cubes.)
A similar vertex-labeling may be used in describing 
the automorphisms of the order-8 quaternion group.

For a more literary approach to quaternions, see
Pynchon's novel Against the Day .

* From Peter J. Cameron's weblog:

  "The big name associated with this is Major MacMahon,
   an associate of Hardy, Littlewood and Ramanujan,
   of whom Robert Kanigel said,

His expertise lay in combinatorics, a sort of
glorified dice-throwing, and in it he had made
contributions original enough to be named
a Fellow of the Royal Society.

   Glorified dice-throwing, indeed…"

Friday, October 7, 2011

Enigma Variations

Filed under: General — Tags: — m759 @ 9:00 PM

For Yom Kippur

1. New York Lottery

http://www.log24.com/log/pix11C/111007-AlmeidaInscape.jpg

2. Image— Almeida and Inscape

3. Against the Day , page 453

Rebecca Goldstein and a Cullinane quaternion

4. Image— Argument for the Existence of Rebecca

Some literary and cinematic background—

http://www.log24.com/log/pix11/110114-AlderTilleyColored.gif


"Are you the butterfly… ?"

Sunday, May 29, 2011

A Mathematical Operation

Filed under: General — m759 @ 12:00 AM

Against the Day

http://www.log24.com/log/pix11A/110528-AgainstTheDay.jpg

    New York Lottery, May 28, 2011—

http://www.log24.com/log/pix11A/110528-NYlottery.jpg

Page 548

General Boulanger
That the General was 'reactionary' and that the C of C bureaucracy had a 'defiant residue' of Boulangism, continues the characterization of the organization for which the Chums 'work'.

See p. 543 above, regarding a 2007 book in which Boulanger is called the 'father of fascism'.

timbres fictifs
French: fictive postage stamps. Cf "Lot 49".
Yes, stamps mean something in Pynchon's works; here, it seems important that these stamps are characterized as frauds.

Page 935

transform
A mathematical operation that "maps" a relation from one domain to another.

Here, "Belgian Congo" maps to "Balkan Penninsula". By 1912, everyone at Yz-le-Bans would be familiar with Conrad's Heart of Darkness , if not with other descriptions of the atrocities of exploitation of indigenous people in Congo. The conversation here and to follow describes the dawning realization of the imperialist exploitation of Eastern Europe by European powers. (Zora Neale Hurston famously commented that Hitler did in Europe what Europeans had been doing in Africa for a century. Cf. The Hereros sections in V .). It begins with railroads and "other straight line" constructions.

The themes of ATD might also "map" to current events in another warzone, where a contemporary Great Game is being played out.

common in dreams
Such as Frank's and Reef's. And/or, dreams require interpretation.

Wednesday, November 10, 2010

Scavenger Hunt

Filed under: General — m759 @ 3:09 AM

A description in Pynchon's Against the Day  of William Rowan Hamilton's October 16th, 1843, discovery of quaterions—

"The moment, of course, is timeless. No beginning, no end, no duration, the light in eternal descent, not the result of conscious thought but fallen onto Hamilton, if not from some Divine source then at least when the watchdogs of Victorian pessimism were sleeping too soundly to sense, much less frighten off, the watchful scavengers of Epiphany."

New York Lottery yesterday, on Hermann Weyl's birthday— Midday 106, Evening 865.

http://www.log24.com/log/pix10B/101110-WeylAndDiamond.jpg

Here 106 suggests 1/06, the date of Epiphany, and 865 turns out to be the title number of Weyl's Symmetry  at Princeton University Press—

http://press.princeton.edu/titles/865.html.

Symmetry and quaternions are, of course, closely related.

Tuesday, February 2, 2010

Time After Time

Filed under: General — m759 @ 12:00 AM

Godmother and Cinderella

http://www.log24.com/log/pix10/100202-StreepAdams.jpg

Meryl Streep and Amy Adams in "Julie & Julia"

The image is from gossipsauce.com on August 2, 2009.

For a darker Godmother/Cinderella pair,
see the film discussed in this journal
on that same date (Lughnasa 2009).

A thought from Pynchon's Against the Day quoted here on Groundhog Day a year ago today

“We thus enter the whirlwind. It becomes the very essence of a refashioned life, providing the axes to which everything will be referred. Time no long ‘passes,’ with a linear velocity, but ‘returns,’ with an angular one…. We are returned to ourselves eternally, or, if you like, timelessly.”

“Born again!” exclaimed a Christer in the gathering, as if suddenly enlightened.

Tuesday, February 3, 2009

Tuesday February 3, 2009

Filed under: General — m759 @ 7:59 AM

Everything and Nothing

"I know what 'nothing' means…."

— Joan Didion, Play It As It Lays, Farrar, Straus and Giroux, 1990 paperback, page 214

"In 1935, near the end of a long affectionate letter to his son George in America, James Joyce wrote: 'Here I conclude. My eyes are tired. For over half a century they have gazed into nullity, where they have found a lovely nothing.'"

— Lionel Trilling, "James Joyce in His Letters," Commentary, 45, no. 2 (Feb. 1968), abstract

"The quotation is from The Letters of James Joyce, Volume III, ed. Richard Ellman (New York, 1966), p. 359. The original Italian reads 'Adesso termino. Ho gli occhi stanchi. Da più di mezzo secolo scrutano nel nulla dove hanno trovato un bellissimo niente.'"

— Lionel Trilling: Criticism and Politics, by William M. Chace, Stanford U. Press, 1980, page 198, Note 4 to Chapter 9

"Space: what you damn well have to see."

— James Joyce, Ulysses

"What happens to the concepts of space and direction if all the matter in the universe is removed save a small finite number of particles?"

— "On the Origins of Twistor Theory," by Roger Penrose

"… we can look to the prairie, the darkening sky, the birthing of a funnel-cloud to see in its vortex the fundamental structure of everything…"

Against the Day, by Thomas Pynchon (See previous entry.)

"A strange thing then happened."

L. Frank Baum

Monday, February 2, 2009

Monday February 2, 2009

Filed under: General,Geometry — m759 @ 10:30 AM

Against the Day

is a novel by Thomas Pynchon
published on Nov. 21, 2006, in
hardcover, and in paperback on
Oct. 30, 2007 (Devil's Night).

Perhaps the day the title
refers to is one of the above
dates… or perhaps it is–

Groundhog Day

The Candlebrow Conference
in Pynchon's Against the Day:

The conferees had gathered here from all around the world…. Their spirits all one way or another invested in, invested by, the siegecraft of Time and its mysteries.

"Fact is, our system of so-called linear time is based on a circular or, if you like, periodic phenomenon– the earth's own spin. Everything spins, up to and including, probably, the whole universe. So we can look to the prairie, the darkening sky, the birthing of a funnel-cloud to see in its vortex the fundamental structure of everything–"

Quaternion in finite geometry
Quaternion by
S. H. Cullinane

"Um, Professor–"….

… Those in attendance, some at quite high speed, had begun to disperse, the briefest of glances at the sky sufficing to explain why. As if the professor had lectured it into being, there now swung from the swollen and light-pulsing clouds to the west a classic prairie "twister"….

… In the storm cellar, over semiliquid coffee and farmhouse crullers left from the last twister, they got back to the topic of periodic functions….

"Eternal Return, just to begin with. If we may construct such functions in the abstract, then so must it be possible to construct more secular, more physical expressions."

"Build a time machine."

"Not the way I would have put it, but if you like, fine."

Vectorists and Quaternionists in attendance reminded everybody of the function they had recently worked up….

"We thus enter the whirlwind. It becomes the very essence of a refashioned life, providing the axes to which everything will be referred. Time no long 'passes,' with a linear velocity, but 'returns,' with an angular one…. We are returned to ourselves eternally, or, if you like, timelessly."

"Born again!" exclaimed a Christer in the gathering, as if suddenly enlightened.

Above, the devastation had begun.

 
Related material:
Yesterday's entry and
Pynchon on Quaternions.

Happy birthday,
James Joyce.

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