Log24

Saturday, February 28, 2009

Saturday February 28, 2009

Filed under: General,Geometry — Tags: — m759 @ 8:00 am
Mathematics
and Narrative
continued

Narrative:

xxx

Mathematics:

"It must be remarked that these 8 heptads are the key to an elegant proof…."

— Philippe Cara, "RWPRI Geometries for the Alternating Group A8," in Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference, (July 2000), Springer, 2001, ed. Aart Blokhuis, James W. P. Hirschfeld, Dieter Jungnickel, and Joseph A. Thas, pp. 61-97
 

Mathematics:

"Regular graphs are considered, whose automorphism groups are permutation representations P of the orthogonal groups in various dimensions over GF(2). Vertices and adjacencies are defined by quadratic forms, and after graphical displays of the trivial isomorphisms between the symmetric groups S2, S3, S5, S6 and corresponding orthogonal groups, a 28-vertex graph is constructed that displays the isomorphism between S8 and O6 + (2)."

— J. Sutherland Frame in "Orthogonal Groups over GF(2) and Related Graphs," Springer Lecture Notes in Mathematics vol. 642, Theory and Applications of Graphs (Proceedings, Michigan, May 11–15, 1976), edited by Y. Alavi and D. R. Lick, pp. 174-185

"One has O+(6) ≅ S8, the symmetric group of order 8!…."

— "Siegel Modular Forms and Finite Symplectic Groups," by Francesco Dalla Piazza and Bert van Geemen, May 5, 2008, preprint. This paper gives some context in superstring theory for the following work of Frame:

[F1] J.S. Frame, The classes and representations of the group of 27 lines and 28 bitangents, Annali
di Mathematica Pura ed Applicata, 32 (1951) 83–119.
[F2] J.S. Frame, Some characters of orthogonal groups over the field of two elements, In: Proc. of the
Second Inter. Conf. on the Theory of Groups, Lecture Notes in Math., Vol. 372, pp. 298–314,
Springer, 1974.
[F3] J. S. Frame, Degree polynomials for the orthogonal groups over GF(2), C. R. Math. Rep. Acad.
Sci. Canada 2 (1980) 253–258.

Friday, February 27, 2009

Friday February 27, 2009

Filed under: General,Geometry — Tags: , — m759 @ 7:35 pm
Time and Chance
continued

Today's Pennsylvania lottery numbers suggest the following meditations…

Midday:  Lot 497, Bloomsbury Auctions May 15, 2008– Raum und Zeit (Space and Time), by Minkowski, 1909. Background: Minkowski Space and "100 Years of Space-Time."*

Evening: 5/07, 2008, in this journal– "Forms of the Rock."

Related material:

A current competition at Harvard Graduate School of Design, "The Space of Representation," has a deadline of 8 PM tonight, February 27, 2009.

The announcement of the competition quotes the Marxist Henri Lefebvre on "the social production of space."

A related quotation by Lefebvre (cf. 2/22 2009):

"… an epoch-making event so generally ignored that we have to be reminded of it at every moment. The fact is that around 1910 a certain space was shattered… the space… of classical perspective and geometry…."

— Page 25 of The Production of Space (Blackwell Publishing, 1991)

This suggests, for those who prefer Harvard's past glories to its current state, a different Raum from the Zeit 1910.

In January 1910 Annals of Mathematics, then edited at Harvard, published George M. Conwell's "The 3-space PG(3, 2) and Its Group." This paper, while perhaps neither epoch-making nor shattering, has a certain beauty. For some background, see this journal on February 24, 2009.†

    * Ending on Stephen King's birthday, 2008
     † Mardi Gras

Friday February 27, 2009

Filed under: General — Tags: — m759 @ 10:12 am
Lasting Significance


Wittgenstein’s Lasting Significance, edited by Max Kölbel and Bernhard Weiss, published by Routledge, 2004–

Page 168:

“Wittgenstein told Norman Malcolm that ‘a serious and good philosophical work could be written that would consist entirely of jokes (without being facetious)’ (Malcolm 1999: 64).”

Malcolm, N. (1999) “Wittgenstein: A Memoir,” in F.A. Flowers (ed.) Portraits of Wittgenstein, vol. 3, Bristol: Thoemmes Press, pp. 60-112

The lasting significance here is perhaps in the page numbers.

Or perhaps in a name…

Roger Cohen, Ash Wednesday, 2009
 

Thursday, February 26, 2009

Thursday February 26, 2009

Filed under: General — m759 @ 8:04 pm
If you liked Badiou
(previous 5 entries),
you’ll love Zizek!

Thursday February 26, 2009

Filed under: General — Tags: — m759 @ 9:00 am
Truth and
Consequences:

From Roger Cohen
to Alain Badiou
to Wallace Stevens

“That summer of ’68, I was in a vast crowd in London’s sunlit Hyde Park listening to Pink Floyd’s free concert:

One inch of love is one inch of shadow
Love is the shadow that ripens the wine
Set the controls for the heart of the sun!

Right on! Anything seemed possible….”

— Roger Cohen, May 28, 2008, on 1968,
   “The Year That Changed the World“

“Much of Badiou’s life has been shaped by his dedication to the consequences of the May 1968 revolt in Paris.”

— European Graduate School biography

“The Event of Truth,”
European Graduate School video:

Video, Badiou on Truth

Quoted by Badiou at
European Graduate School,
August 2002:

We live in a constellation
Of patches and of pitches,
Not in a single world,
In things said well in music,
On the piano and in speech,
As in a page of poetry—
Thinkers without final thoughts
In an always incipient cosmos.
The way, when we climb a mountain,
Vermont throws itself together.

— Wallace Stevens,
    from “July Mountain”

Or Pennsylvania:

http://www.log24.com/log/pix09/090226-View.jpg

'One inch of love, one inch of ashes'-- Li Shangyin
 

Thursday February 26, 2009

Filed under: General — m759 @ 12:30 am
Happy birthday to
the late Johnny Cash.

Thursday February 26, 2009

Filed under: General — m759 @ 12:00 am
Midnight

“Dead time lasts for one hour– from half an hour before midnight to half an hour after midnight. The half-hour before midnight is for doin’ good. The half-hour after midnight is for doin’ evil….”

— Glenna Whitley, “Voodoo Justice“

Cover of 'Theory and the Common from Marx to Badiou,' by Patrick McGee (2009)

From the Curriculum Vitae
of Patrick McGee:

“Theory and the Common
 from Marx to Badiou
    (Palgrave 2009, scheduled for
   March 31 publication)”

Thanks for the warning.

From the publisher:

Using a method that combines analysis, memoir, and polemic, McGee writes experimentally about a series of thinkers who ruptured linguistic and social hierarchies, from Marx, to Gramsci, to Badiou.

About the Author

Patrick McGee is McElveen Professor of English at Louisiana State University, Baton Rouge. 

Table of Contents

Related Categories

Found in: Cultural Theory, Literary Theory & Criticism, Ethics

Wednesday, February 25, 2009

Wednesday February 25, 2009

Filed under: General — m759 @ 11:30 pm
STICKS NIX HICK PIX

in the Garden
of Good and Evil


“Dead time lasts for one hour– from half an hour before midnight to half an hour after midnight. The half-hour before midnight is for doin’ good.”

— Glenna Whitley, “Voodoo Justice,” The New York Times, March 20, 1994

'Variety' with 1935 headline 'STICKS NIX HICK PIX'

Click for details.


Wednesday February 25, 2009

Filed under: General — m759 @ 12:00 pm
Ideas of Reference
for Ash Wednesday

Happy trails to you…

http://www.log24.com/log/pix09/090225-Trails.jpg
 
The image “http://www.log24.com/log/pix09/090224-PAlotteryMardiGras.jpg” cannot be displayed, because it contains errors.

These numbers from yesterday
(Mardi Gras, 2009) are random,
yet have a particular
meaning for me and
perhaps one other person.

http://www.log24.com/log/pix09/090225-VachelLindsay.jpg
                     — Google Book Search

Tuesday, February 24, 2009

Tuesday February 24, 2009

Filed under: General,Geometry — Tags: , , , , , , — m759 @ 1:00 pm
 
Hollywood Nihilism
Meets
Pantheistic Solipsism

Tina Fey to Steve Martin
at the Oscars:
"Oh, Steve, no one wants
 to hear about our religion
… that we made up."

Tina Fey and Steve Martin at the 2009 Oscars

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

… 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.


Superficially the young men's philosophy seems to resemble what Wikipedia calls "pantheistic solipsism"– noting, however, that "This article has multiple issues."

As, indeed, does pantheistic solipsism– a philosophy (properly called "eschatological pantheistic multiple-ego solipsism") devised, with tongue in cheek, by science-fiction writer Robert A. Heinlein.

Despite their preoccupation with solipsism, Heinlein and Stevens point, each in his own poetic way, to a highly non-solipsistic topic from pure mathematics that is, unlike the religion of Martin and Fey, not made up– namely, the properties of space.

Heinlein:

"Sharpie, we have condensed six dimensions into four, then we either work by analogy into six, or we have to use math that apparently nobody but Jake and my cousin Ed understands. Unless you can think of some way to project six dimensions into three– you seem to be smart at such projections."
    I closed my eyes and thought hard. "Zebbie, I don't think it can be done. Maybe Escher could have done it."

Stevens:

A discussion of Stevens's late poem "The Rock" (1954) in Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 120:

For Stevens, the poem "makes meanings of the rock." In the mind, "its barrenness becomes a thousand things/And so exists no more." In fact, in a peculiar irony that only a poet with Stevens's particular notion of the imagination's function could develop, the rock becomes the mind itself, shattered into such diamond-faceted brilliance that it encompasses all possibilities for human thought: 

The rock is the gray particular of man's life,
The stone from which he rises, up—and—ho,
The step to the bleaker depths of his descents ...

The rock is the stern particular of the air,
The mirror of the planets, one by one,
But through man's eye, their silent rhapsodist,

Turquoise the rock, at odious evening bright
With redness that sticks fast to evil dreams;
The difficult rightness of half-risen day.

The rock is the habitation of the whole,
Its strength and measure, that which is near,
     point A
In a perspective that begins again

At B: the origin of the mango's rind.

                    (Collected Poems, 528)

Stevens's rock is associated with empty space, a concept that suggests "nothingness" to one literary critic:

B. J. Leggett, "Stevens's Late Poetry" in The Cambridge Companion to Wallace Stevens— On the poem "The Rock":

 

"… the barren rock of the title is Stevens's symbol for the nothingness that underlies all existence, 'That in which space itself is contained'….  Its subject is its speaker's sense of nothingness and his need to be cured of it."

 

This interpretation might appeal to Joan Didion, who, as author of the classic novel Play It As It Lays, is perhaps the world's leading expert on Hollywood nihilism.

More positively…

Space is, of course, also a topic
in pure mathematics…
For instance, the 6-dimensional
affine space (or the corresponding
5-dimensional projective space)

The 4x4x4 cube

over the two-element Galois field
can be viewed as an illustration of
Stevens's metaphor in "The Rock."

Heinlein should perhaps have had in mind the Klein correspondence when he discussed "some way to project six dimensions into three." While such a projection is of course trivial for anyone who has taken an undergraduate course in linear algebra, the following remarks by Philippe Cara present a much more meaningful mapping, using the Klein correspondence, of structures in six (affine) dimensions to structures in three.

Cara:

Philippe Cara on the Klein correspondence
Here the 6-dimensional affine
space contains the 63 points
of PG(5, 2), plus the origin, and
the 3-dimensional affine
space contains as its 8 points
Conwell's eight "heptads," as in
Generating the Octad Generator.

Monday, February 23, 2009

Monday February 23, 2009

Filed under: General — m759 @ 2:22 pm
Another Manic Monday—
McGee and Smee 

Project MUSE —

… and interpretations, “any of the
Zingari shoolerim [gypsy schoolchildren]
may pick a peck of kindlings yet from the
sack of auld hensyne” (FW 112.4-8). …

— Patrick McGee, “Reading Authority:
Feminism and Joyce,” MFS: Modern
Fiction Studies— Volume 35, Number 3,
Fall 1989, pp. 421-436, The Johns Hopkins
University Press

McGee Thanks the Academy:

“The ulterior motive behind this essay [“Reading Authority,” above], the purpose for which I seize this occasion, concerns the question or problem of authority. I stress at the outset my understanding of authority as the constructed repository of value or foundation of a system of values, the final effect of fetishism– in this case, literary fetishism. [Cf. Marx, Das Kapital] Reading– as in the phrase ‘reading authority’– should be grasped as the institutionally determined act of constructing authority….”

Wikipedia:

“[In Peter Pan] Smee is Captain Hook’s right-hand man… Barrie describes him as ‘Irish’ and ‘a man who stabbed without offence‘….”

Background: In yesterday’s morning entry, James Joyce as Jesuit, with “Dagger Definitions.”

A different Smee appears as an art critic in yesterday’s afternoon entry “Design Theory.”–

Smee Stabs Without Offence:

“Brock, who has a brisk mind, is a man on a mission. He read mathematical economics and political philosophy at Princeton (he has five degrees in all) and is the founder and president of Strategic Economic Decisions Inc., a think tank specializing in applying the economics of uncertainty to forecasting and risk assessment.

But phooey to all that; Brock has deeper things to think about. He believes he has cracked the secret of beautiful design. He even has equations and graphs to prove it.”

A Jesuit in Portrait of the Artist as a Young Man:

“When may we expect to have something from you on the esthetic question?”

Beckett Bethicketted:

“Our entanglement in the wilderness of Finnegans Wake is exemplified by the neologism ‘Bethicket.’ This word condenses a range of possible meanings and reinforces a diversity of possible syntactic interpretations. Joyce seems to allude to Beckett, creating a portmanteau word that melds ‘Beckett’ with ‘thicket’ (continuing the undergrowth metaphor), ‘thick’ (adding mental density to floral density)…. As a single word ‘Bethicket’ contains the confusion that its context suggests. On the one hand, ‘Bethicket me for a stump of a beech’ has the sound of a proverbial expletive that might mean something like ‘I’ll be damned’ or ‘Well, I’ll be a son of a gun.’….”

— Stephen Dilks

Winslet, Penn, and Cruz at the Oscars, 2009

At the Oscars, 2009

Related material:

Frame Tales and Dickung

Sunday, February 22, 2009

Sunday February 22, 2009

Filed under: General,Geometry — m759 @ 4:07 pm
Themes and
Variations
Horace Brock with his collection at the Boston Museum of Fine Arts


The Boston Globe today on a current Museum of Fine Arts exhibit of works collected by one Horace Brock–

“Designed objects, Brock writes, can be broken down into ‘themes’ and ‘transformations.’ A theme is a motif, such as an S-curve; a transformation might see that curve appear elsewhere in the design, but stretched, rotated 90 degrees, mirrored, or otherwise reworked.

Aesthetic satisfaction comes from an apprehension of how those themes and transformations relate to each other, or of what Brock calls their ‘relative complexity.’ Basically– and this is the nub of it– ‘if the theme is simple, then we are most satisfied when its echoes are complex… and vice versa.'”

Related material:

Theme

Diamond theme

and Variations

Variations on the diamond theme

See also earlier tributes to
Hollywood Game Theory

Chess game in The Thomas Crown Affair

and Hollywood Religion:

http://www.log24.com/log/pix09/090222-SoundOfSilence.jpg

For some variations on the
above checkerboard theme, see
Finite Relativity and
 A Wealth of Algebraic Structure.

Sunday February 22, 2009

Filed under: General — Tags: , — m759 @ 11:00 am

Design at Harvard:
Natural or Unnatural?

Logo of Harvard Graduate School of Design compared to the 'natural' sign

From the Harvard Graduate School of Design–

Call for Entries: The Space of Representation

DEADLINE FEBRUARY 27, 2009 8PM EST

"According to Henri Lefebvre, the social production of space has three components: spatial practice, the representation of space, and the space of representation. The latter two are integral to both design and the review process."

Also according to Henri Lefebvre:

An 'epoch-making event' from Lefebvre, 'The Production of Space'

This is clearly nonsense.
It is also, like much else at Harvard,
damned Marxist  nonsense.

I recommend instead  
James Joyce on space —

Dagger Definitions

From 'Ulysses,' 1922 first edition, page 178-- 'dagger definitions'

Saturday, February 21, 2009

Saturday February 21, 2009

Filed under: General — m759 @ 10:10 am
The Graduate

Today’s New York Times:

New York Times executive Mary Jacobus dies at 52

The Times goes on to say…

“A native of Buffalo, Ms. Jacobus
graduated from Le Moyne College
in Syracuse.”

She died yesterday.

A quotation from
yesterday’s entries
may be relevant:

“Men’s curiosity searches past and future
And clings to that dimension. But to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint….”

— T. S. Eliot, Four Quartets

  
In memory of Mary Jacobus-- Clint Eastwood sings 'Accentuate the Positive'

Related material:

From a previous appearance
of the Eastwood meditation
in this journal:

Masks of comedy and tragedy

Click on image
for details.

Friday, February 20, 2009

Friday February 20, 2009

Filed under: General,Geometry — Tags: , , — m759 @ 11:01 pm

The Cross
of Constantine

mentioned in
this afternoon's entry
"Emblematizing the Modern"
was the object of a recent
cinematic chase sequence
(successful and inspiring)
starring Mira Sorvino
at the Metropolitan
Museum of Art.

In memory of
Dr. Hunter S. Thompson,
dead by his own hand
on this date
four years ago —

Rolling Stone memorial to Dr. Hunter S. Thompson

Click for details.

There is
another sort of object
we may associate with a
different museum and with
a modern Constantine …
See "Art Wars for MoMA"
(Dec. 14, 2008).

This object, modern
rather than medieval,
is the ninefold square:

The ninefold square

It may suit those who,
like Rosalind Krauss
(see "Emblematizing"),
admire the grids of modern art
but view any sort of Christian
cross with fear and loathing.

For some background that
Dr. Thompson might appreciate,
see notes on Geometry and Death
in this journal, June 1-15, 2007,
and the five Log24 entries
 ending at 9 AM Dec. 10. 2006,
which include this astute
observation by J. G. Ballard:

"Modernism's attempt to build a better world with the aid of science and technology now seems almost heroic. Bertolt Brecht, no fan of modernism, remarked that the mud, blood and carnage of the first world war trenches left its survivors longing for a future that resembled a white-tiled bathroom."

Selah.

Friday February 20, 2009

Filed under: General — Tags: , — m759 @ 6:00 pm
A Kind of Cross

Descartes portrait

"For every kind of vampire,
there is a kind of cross."

— Thomas Pynchon in  
Gravity's Rainbow

Descartes's Cross

Click for source.

Related material:

A memorial service
held at 2 PM today at the
U.S. Space & Rocket Center
in Huntsville, Alabama, and
 today's previous entry.

Friday February 20, 2009

Filed under: General,Geometry — Tags: , , — m759 @ 2:01 pm
Emblematizing
 the Modern 

The following meditation was
inspired by the recent fictional
recovery, by Mira Sorvino
in "The Last Templar,"
of a Greek Cross —
"the Cross of Constantine"–
and by the discovery, by
art historian Rosalind Krauss,
of a Greek Cross in the
art of Ad Reinhardt.

http://www.log24.com/log/pix09/090220-CrossOfDescartes.jpg

The Cross of Descartes  

Note that in applications, the vertical axis
of the Cross of Descartes often symbolizes
the timeless (money, temperature, etc.)
while the horizontal axis often symbolizes time.


T.S. Eliot:

"Men’s curiosity searches past and future
And clings to that dimension. But to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint…."


There is a reason, apart from her ethnic origins, that Rosalind Krauss (cf. 9/13/06) rejects, with a shudder, the cross as a key to "the Pandora's box of spiritual reference that is opened once one uses it." The rejection occurs in the context of her attempt to establish not the cross, but the grid, as a religious symbol:
 

"In suggesting that the success [1] of the grid
is somehow connected to its structure as myth,
I may of course be accused of stretching a point
beyond the limits of common sense, since myths
are stories, and like all narratives they unravel
through time, whereas grids are not only spatial
to start with, they are visual structures
that explicitly reject a narrative
or sequential reading of any kind.

[1] Success here refers to
three things at once:
a sheerly quantitative success,
involving the number of artists
in this century who have used grids;
a qualitative success through which
the grid has become the medium
for some of the greatest works
of modernism; and an ideological
success, in that the grid is able–
in a work of whatever quality–
to emblematize the Modern."

— Rosalind Krauss, "Grids" (1979)

Related material:

Time Fold and Weyl on
objectivity and frames of reference.

See also Stambaugh on
The Formless Self
as well as
A Study in Art Education
and
Jung and the Imago Dei.

Thursday, February 19, 2009

Thursday February 19, 2009

Filed under: General — Tags: — m759 @ 7:07 am

A Sunrise
for Sunrise

“If we open any tract– Plastic Art and Pure Plastic Art or The Non-Objective World, for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter. They are talking about Being or Mind or Spirit.  From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.”

— Rosalind Krauss, “Grids”

Yesterday’s entry featured a rather simple-minded example from Krauss of how the ninefold square (said to be a symbol of Apollo)

The 3x3 grid

may be used to create a graphic design– a Greek cross, which appears also in crossword puzzles:

Crossword-puzzle design that includes Greek-cross elements

Illustration by
Paul Rand
(born Peretz Rosenbaum)

A more sophisticated example
of the ninefold square
in graphic design:

“That old Jew
gave me this here.”
— A Flag for Sunrise  

The 3x3 grid as an organizing frame for Chinese calligraphy. Example-- the character for 'sunrise'
From Paul-Rand.com

Wednesday, February 18, 2009

Wednesday February 18, 2009

Filed under: General — Tags: , , , , — m759 @ 11:30 am

Raiders of
the Lost Well

“The challenge is to
keep high standards of
scholarship while maintaining
showmanship as well.”

— Olga Raggio, a graduate of the Vatican library school and the University of Rome who, at one point in her almost 60 years with the Metropolitan Museum of Art, organized “The Vatican Collections,” a blockbuster show. Dr. Raggio died on January 24.

The next day, “The Last Templar,” starring Mira Sorvino, debuted on NBC.

Mira Sorvino in 'The Last Templar'
“The story, involving the Knights Templar, the Vatican, sunken treasure, the fate of Christianity and a decoding device that looks as if it came out of a really big box of medieval Cracker Jack, is the latest attempt to combine Indiana Jones derring-do with ‘Da Vinci Code’ mysticism.”

— The New York Times

Sorvino in “The Last Templar”
at the Church of the Lost Well:

Mira Sorvino at the Church of the Lost Well in 'The Last Templar'

“One highlight of Secretary of State Hillary Clinton’s first overseas trip will be a stop in China. Her main mission in Beijing will be to ensure that US-China relations under the new Obama administration get off to a positive start.”

— Stephanie Ho, Voice of America Beijing bureau chief, today

Symbol of The Positive,
from this journal
on Valentine’s Day:

'Enlarge' symbol from USA Today

“Stephanie started at the Voice of America as an intern in 1991. She left briefly to attend film school in London in 2000. Although she didn’t finish, she has always wanted to be a film school dropout, so now she’s living one of her dreams.

Stephanie was born in Ohio and grew up in California. She has a bachelor’s degree in Asian studies with an emphasis on Chinese history and economics, from the University of California at Berkeley.”

“She is fluent in
Mandrin Chinese.”
—VOA

As is Mira Sorvino.

Chinese character for 'well' and I Ching Hexagram 48, 'The Well'

Those who, like Clinton, Raggio, and
Sorvino’s fictional archaeologist in
“The Last Templar,” prefer Judeo-
Christian myths to Asian myths,
may convert the above Chinese
“well” symbol to a cross
(or a thick “+” sign)
by filling in five of
the nine spaces outlined
by the well symbol.

In so doing, they of course
run the risk, so dramatically
portrayed by Angelina Jolie
as Lara Croft, of opening
Pandora’s Box.

(See Rosalind Krauss, Professor
of Art and Theory at Columbia,
for scholarly details.)

Rosalind Krauss

Krauss

Greek Cross, adapted from painting by Ad Reinhardt

The Krauss Cross

Tuesday, February 17, 2009

Tuesday February 17, 2009

Filed under: General,Geometry — Tags: , , , , — m759 @ 1:06 pm

Diamond-Faceted:
Transformations
of the Rock

A discussion of Stevens's late poem "The Rock" (1954) in Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 120:

For Stevens, the poem "makes meanings of the rock." In the mind, "its barrenness becomes a thousand things/And so exists no more." In fact, in a peculiar irony that only a poet with Stevens's particular notion of the imagination's function could develop, the rock becomes the mind itself, shattered into such diamond-faceted brilliance that it encompasses all possibilities for human thought: 

The rock is the gray particular of man's life,
The stone from which he rises, up—and—ho,
The step to the bleaker depths of his descents ...

The rock is the stern particular of the air,
The mirror of the planets, one by one,
But through man's eye, their silent rhapsodist,

Turquoise the rock, at odious evening bright
With redness that sticks fast to evil dreams;
The difficult rightness of half-risen day.

The rock is the habitation of the whole,
Its strength and measure, that which is near,
     point A
In a perspective that begins again

At B: the origin of the mango's rind.

                    (Collected Poems, 528)

A mathematical version of
this poetic concept appears
in a rather cryptic note
from 1981 written with
Stevens's poem in mind:

http://www.log24.com/log/pix09/090217-SolidSymmetry.jpg

For some explanation of the
groups of 8 and 24
motions referred to in the note,
see an earlier note from 1981.

For the Perlis "diamond facets,"
see the Diamond 16 Puzzle.

For a much larger group
of motions, see
Solomon's Cube.

As for "the mind itself"
and "possibilities for
human thought," see
Geometry of the I Ching.

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.
 

Saturday, February 14, 2009

Saturday February 14, 2009

Filed under: General — Tags: — m759 @ 9:29 pm
The Devil
in the Details

 

Here are clearer pictures of
the Einstein-Gutkind letter
discussed here February 7.

The pictures are from
the Bloomsbury Auctions site.

http://www.log24.com/log/pix09/Einstein-Gutkind1954-1.jpg

http://www.log24.com/log/pix09/Einstein-Gutkind1954-2.jpg

The Bloomsbury Auctions caption for these images is as follows:

303. Einstein (Albert, theoretical physicist, 1879-1955) Autograph Letter signed to Eric B. Gutkind, in German, 1½pp. & envelope, 4to, Princeton, 3rd January 1954, thanking him for a copy of his book and expressing his view of God and Judaism, [The word God is for me nothing more than the expression and product of human weaknesses, the Bible a collection of honorable, but still primitive legends which are nevertheless pretty childish… . For me the Jewish religion like all other religions is an incarnation of the most childish superstitions. And the Jewish people to whom I gladly belong and with whose mentality I have a deep affinity have no different quality for me than all other people…], folds, slightly browned ; and a photograph of Gutkind, v.s., v.d.

est. £6000 – £8000

Einstein’s view of God and Judaism.
 Eric B. Gutkind (1877-1965), philosopher; author of Choose Life: The Biblical Call to Revolt, 1952.
Albert Einstein – see also lot 497

Sold for £170000
Sale 649, 15th May 2008

Here is a close reading of the part of the letter itself that Bloomsbury gives in English, transcribed from the above images.

Line-by-line transcription of paragraph 2, starting at line 4 of that paragraph:                        

                   ... Das Wort Gott ist für mich nichts als Ausdruck
und Produkt menschlicher Schwächen, die Bibel eine Sammlung
ehrwürdiger, aber doch reichlich primitiver Legenden. Keine noch
so feinsinnige Auslegung kann (für mich) etwas daran ändern.
Diese verfeinerten Auslegungen sind naturgemäß höchst mannigfaltig
und haben so gut wie nichts mit dem Urtext zu schaffen. Für
mich ist die unverfälschte jüdische Religion, wie alle anderen
Religionen, eine Inkarnation des primitiven Aberglaubens. Und das
jüdische Volk, zu dem ich gern gehöre und mit dessen Mentalität ich
tief verwachsen bin, hat für mich doch keine andersartige
Qualität als alle anderen Völker. So weit meine Erfahrung reicht,
ist es auch um nichts besser als andere menschliche Gruppierungen,
wenn es auch durch Mangel an Macht gegen die schlimmsten
Auswüchse gesichert ist. Ansonsten kann ich nichts "Auserwähltes"
an ihm wahrnehmen.

The Guardian of May 13, 2008 stated that the following was "translated from German by Joan Stambaugh"–

... The word God is for me nothing more than the expression
and product of human weaknesses, the Bible a collection
of honourable, but still primitive legends which are nevertheless pretty childish. No
interpretation no matter how subtle can (for me) change this.
These subtilised interpretations are highly manifold
according to their nature and have almost nothing to do with the original text. For
me the Jewish religion like all other
religions is an incarnation of the most childish [German: primitiven] superstitions. And the
Jewish people to whom I gladly belong and with whose mentality I
have a deep affinity have no different
quality for me than all other people. As far as my experience goes,
they are also no better than other human groups,
although they are protected from the worst
cancers by a lack of power. Otherwise I cannot see anything 'chosen'
about them.

Phrases by Stambaugh that do not appear in the German text are highlighted.

Stambaugh, a philosophy professor, is the author of a work on Buddhism, The Formless Self. For some related material on young men who "go crying 'The world is myself, life is myself'" in May, see Wallace Stevens's "The Pediment of Appearance."
 

Saturday February 14, 2009

Filed under: General — m759 @ 12:00 pm
“Somewhere in the
   heart of Rome”

— Sinatra, 1954  

'Man and His Symbols,' by Carl Jung and others

USA Today:

Geithner has some success
with world stage debut

Bernanke and Geithner at Rome G7 on Valentine's Day

'Enlarge' symbol from USA Today

Click for commentary.

Friday, February 13, 2009

Friday February 13, 2009

Filed under: General — m759 @ 7:36 pm
Fire and Ice
 
http://www.log24.com/log/pix09/090213-NYTfront.jpg

Prologue from
Answers.com:

bombardier
The member of a
combat aircraft crew who
operates the bombsight
and drops the bombs.

February 13, 2009 — Toronto
Press Release

Bombardier confirms a Dash 8 Q400 aircraft was involved in an accident near Buffalo, New York on February 12. We extend our sympathies to the families of those who perished in this accident. Bombardier has dispatched a product safety and technical team to the site to assist the National Transportation Safety Board with their investigation.

Until such time as the investigators release any information or findings, Bombardier cannot comment further or speculate on the cause of this accident.

Bombardier Q400 product information is available on www.q400.com.

Today in History, by
The Associated Press

On this date…
in 1945, during World War II,
Allied planes began bombing
the German city of Dresden.

For the rest of the story,
see Kurt Vonnegut
and Robert Frost.

Friday February 13, 2009

Filed under: General — m759 @ 9:26 am
Childish Things
(continued from Feb. 7)

DENNIS OVERBYE

in The New York Times of May 16, 2008
(quoted here on that date):

“From the grave, Albert Einstein poured gasoline on the culture wars between science and religion this week.

A letter the physicist wrote in 1954 to the philosopher Eric Gutkind, in which he described the Bible as ‘pretty childish’….”

This morning’s New York Times:

Plane crash near Buffalo on Lincoln-Darwin bicentennial


The plane crashed at about 10:20 PM.

Meanwhile…

Yesterday evening in Springfield (as scheduled):

6:20 PM THE PRESIDENT arrives in Springfield, IL
 
7:00 PM THE PRESIDENT delivers remarks at the 102nd Abraham Lincoln Association Annual Banquet

8:30 PM THE PRESIDENT departs from Springfield, IL

Religious summary by
Buffalo Springfield:

“Stop, children,
what’s that sound?
Everybody look
what’s going down.”

Friday February 13, 2009

Filed under: General — m759 @ 12:00 am
Happy birthday to
King Friday XIII
and friend:

Mr. Rogers and King Friday XIII

Yesterday, by the way,
was Georgia Day
in Savannah.

'Midnight in the Garden of Good and Evil' and 'I Put a Spell on You'

“I Put a Spell on You”
— Nina Simone,
title of autobiograpy


“The voodoo priestess looked across the table at her wealthy client, a man on trial for murder: ‘Now, you know how dead time works. Dead time lasts for one hour– from half an hour before midnight to half an hour after midnight. The half-hour before midnight is for doin’ good. The half-hour after midnight is for doin’ evil….'”

— Glenna Whitley, “Voodoo Justice,” The New York Times, March 20, 1994

Thursday, February 12, 2009

Thursday February 12, 2009

Filed under: General — Tags: , , — m759 @ 11:11 am
Headliners

Today, many observe
the 200th anniversary
of the birth of two
noted philosophers
of death:
Charles Darwin and
Abraham Lincoln.

A fitting headline:

FAUST VIVIFIES DEATH
(Harvard Crimson ,
February 7, 2008)

Happy birthday,
Cotton Mather.

Robert Stone,
A Flag for Sunrise :

Willow on tombstone from Lachlan Cranswick's homepage in Melbourne, Australia

"Our secret culture is as frivolous as a willow on a tombstone. It's a wonderful thing– or it was. It was strong and dreadful, it was majestic and ruthless. It was a stranger to pity. And it's not for sale, ladies and gentlemen."

Wednesday, February 11, 2009

Wednesday February 11, 2009

Filed under: General — m759 @ 9:48 am
Happy Birthday

Leslie Nielsen in two classic roles

For details, see
yesterday’s entries.

Tuesday, February 10, 2009

Tuesday February 10, 2009

Filed under: General — m759 @ 11:07 pm
Numbers

“Most crime dramas
have a gimmick.”

— March 2009 Notices of the
American Mathematical Society

Feb. 10,
2009		 PA NY
Midday 106 407
Evening 829 216


“Brams… uses elementary ideas from game theory to create situations between a Person (P) and God (Supreme Being, SB) and discusses how each reacts to the other in these model scenarios….”

Revelation Game payoff matrix

(The number-pairs here reflect
relative values of the situations
the author assigns to SB and to P.)

Related Material

on theology and drama —
the two Log24 entries on
Stephen King’s birthday, 2008.

Tuesday February 10, 2009

Filed under: General — m759 @ 7:11 pm
Coming Soon!

National Treasure logo

Trailer:

FinancialStability.gov site at 7 p.m. ET Feb. 10, 2009

“Now, here’s my plan…”

“‘What plan?’ asked Bert Ely, an Alexandria, Va., banking consultant. ‘The devil is in the details, and the details are hiding in the bushes or deep underground.’

The Dow, which was down only about 70 points before Geithner’s speech, fell sharply as soon as he began talking.”

— Walter Hamilton in The Los Angeles Times today

Monday, February 9, 2009

Monday February 9, 2009

Filed under: General,Geometry — m759 @ 12:12 pm
The Vision Thing

The British Academy Awards last night showed two Paul Newman clips:

"Sometimes nothin' can be a real cool hand."

"Boy, I got vision and the rest of the world wears bifocals."

Related material: This journal, September 2008.

As for bifocals…

 

Ben Franklin
 
Pennsylvania Lottery
 
PA Lottery Feb. 8, 2009-- Midday 017, Evening 717
Versus
7/17:

 

Aion —
A symbol
   of the self —

Four-diamond symbol of the self from Jung's 'Aion'

 

Sunday, February 8, 2009

Sunday February 8, 2009

Filed under: General,Geometry — m759 @ 11:00 am
The Sound of Silence

Memorial sermon for John von Neumann, who died on Feb. 8,  1957

See also yesterday’s entry
on philosophy professor
Joan Stambaugh and the
fabrication of a now-famous saying
   falsely attributed to Einstein–
that the Bible is “pretty childish.”

Stambaugh advocates
a Zen form of nihilism.

The 4×4 space illustrated
above is a Western form
of the the Sunyata, or
emptiness, discussed by
Stambaugh in
The Formless Self.

It appeared in this journal
on the feast day this year
of St. John Neumann.

Saturday, February 7, 2009

Saturday February 7, 2009

Filed under: General,Geometry — m759 @ 2:02 pm
Childish Things

(continued from Thursday's
"Through the Looking Glass")

DENNIS OVERBYE

in The New York Times of May 16, 2008
(quoted here on that date):

"From the grave, Albert Einstein poured gasoline on the culture wars between science and religion this week.

A letter the physicist wrote in 1954 to the philosopher Eric Gutkind, in which he described the Bible as 'pretty childish' and scoffed at the notion that the Jews could be a 'chosen people,' sold for $404,000 at an auction in London. That was 25 times the presale estimate."

Einstein did not, at least in the place alleged, call the Bible "childish." Proof:

(Click for larger version.)
 
Proof that Einstein did not call the Bible 'childish'

The image of the letter is
from the Sept./Oct. 2008
Search Magazine.

By the way, today is
the birthday of G. H. Hardy.

Here is an excerpt from his
thoughts on childish things:

"What 'purely aesthetic' qualities can we distinguish in such theorems as Euclid's or Pythagoras's?…. 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."

Eightfold (2x2x2) cube

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

— James Joyce, Ulysses  

Friday, February 6, 2009

Friday February 6, 2009

Filed under: General — m759 @ 4:00 am
Eternal City


Today’s New York Times:

“Olga Raggio was born in Rome on Feb. 5, 1926, to a Russian mother and an Italian father. She earned a diploma from the Vatican library school in 1947 and a Ph.D. from the University of Rome in 1949.”

“… Raggio, an internationally known scholar and curator who in almost 60 years with the Metropolitan Museum of Art organized some of its best-known exhibitions, scoured the world for treasure and coaxed rarely seen artworks from places as far flung as the Vatican and as close at hand as a New Jersey abbey, died on Jan. 24 in the Bronx. She was 82 and lived in Manhattan.”

Quoted here on the date of Raggio’s death:

“Death is not earnest in the same way the eternal is. To the earnestness of death belongs precisely that capacity for awakening, that resonance of a profound mockery which, detached from the thought of the eternal, is an empty and often brash jest, but together with the thought of the eternal is just what it should be, utterly different from the insipid solemness which least of all captures and holds a thought with tension like that of death.”

— Soren Kierkegaard, Works of Love, Harper Torchbooks, 1964, p. 324

Related material:

  February 2, 3, and 4 as well as
  February 5 (Raggio’s birthday).

Thursday, February 5, 2009

Thursday February 5, 2009

Filed under: General,Geometry — Tags: , , , , , — m759 @ 1:00 pm

Through the
Looking Glass:
A Sort of Eternity

From the new president’s inaugural address:

“… in the words of Scripture, the time has come to set aside childish things.”

The words of Scripture:

9 For we know in part, and we prophesy in part.
10 But when that which is perfect is come, then that which is in part shall be done away.
11 When I was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things.
12 For now we see through a glass, darkly, but then face to face: now I know in part; but then shall I know even as also I am known. 

— First Corinthians 13

“through a glass”—

[di’ esoptrou].
By means of
a mirror [esoptron].

Childish things:

Froebel's third gift, the eightfold cube
© 2005 The Institute for Figuring
Photo by Norman Brosterman
fom the Inventing Kindergarten
exhibit at The Institute for Figuring
(co-founded by Margaret Wertheim) 

Not-so-childish:

Three planes through
the center of a cube
that split it into
eight subcubes:
Cube subdivided into 8 subcubes by planes through the center
Through a glass, darkly:

A group of 8 transformations is
generated by affine reflections
in the above three planes.
Shown below is a pattern on
the faces of the 2x2x2 cube
that is symmetric under one of
these 8 transformations–
a 180-degree rotation:

Design Cube 2x2x2 for demonstrating Galois geometry

(Click on image
for further details.)

But then face to face:

A larger group of 1344,
rather than 8, transformations
of the 2x2x2 cube
is generated by a different
sort of affine reflections– not
in the infinite Euclidean 3-space
over the field of real numbers,
but rather in the finite Galois
3-space over the 2-element field.

Galois age fifteen, drawn by a classmate.

Galois age fifteen,
drawn by a classmate.

These transformations
in the Galois space with
finitely many points
produce a set of 168 patterns
like the one above.
For each such pattern,
at least one nontrivial
transformation in the group of 8
described above is a symmetry
in the Euclidean space with
infinitely many points.

For some generalizations,
see Galois Geometry.

Related material:

The central aim of Western religion– 

"Each of us has something to offer the Creator...
the bridging of
 masculine and feminine,
 life and death.
It's redemption.... nothing else matters."
-- Martha Cooley in The Archivist (1998)

The central aim of Western philosophy–

 Dualities of Pythagoras
 as reconstructed by Aristotle:
  Limited Unlimited
  Odd Even
  Male Female
  Light Dark
  Straight Curved
  ... and so on ....

“Of these dualities, the first is the most important; all the others may be seen as different aspects of this fundamental dichotomy. To establish a rational and consistent relationship between the limited [man, etc.] and the unlimited [the cosmos, etc.] is… the central aim of all Western philosophy.”

— Jamie James in The Music of the Spheres (1993)

“In the garden of Adding
live Even and Odd…
And the song of love’s recision
is the music of the spheres.”

— The Midrash Jazz Quartet in City of God, by E. L. Doctorow (2000)

A quotation today at art critic Carol Kino’s website, slightly expanded:

“Art inherited from the old religion
the power of consecrating things
and endowing them with
a sort of eternity;
museums are our temples,
and the objects displayed in them
are beyond history.”

— Octavio Paz,”Seeing and Using: Art and Craftsmanship,” in Convergences: Essays on Art and Literature (New York: Harcourt Brace Jovanovich 1987), 52

From Brian O’Doherty’s 1976 Artforum essays– not on museums, but rather on gallery space:

“Inside the 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.”

http://www.log24.com/log/pix09/090205-cube2x2x2.gif

“Space: what you
damn well have to see.”

— James Joyce, Ulysses  

Wednesday, February 4, 2009

Wednesday February 4, 2009

Filed under: General — Tags: , — m759 @ 1:23 pm
Overkill
 
In memory of
James Joyce and of
Patrick McGoohan.
who both died on
a January 13th —
Scene from 'The Seventh Seal' on McLuhan book cover
Baby Blues cartoon on global positioning systems

 

Related material:

The phrase
"Habitat Global Village"
in the previous entry.

Marshall McLuhan was
apparently the originator
of the phrase
"global village."

The phrase, coined by McLuhan,
 a Catholic, should be associated
more with Rome than
with Americus, Georgia.

"The association is the idea."
— Ian Lee, The Third Word War

Number Six meets Global Village
 

Wednesday February 4, 2009

Filed under: General — m759 @ 5:18 am
Enter

'Times Talks' at The New York Times

Click on images below
for further details.

Millard Fuller and John Updike in the New York Times obituaries

John Updike discusses his sequel to 'The Witches of Eastwick'

“A strange thing then happened.”

— L. Frank Baum

Tuesday, February 3, 2009

Tuesday February 3, 2009

Filed under: General — m759 @ 7:11 pm
Roger Cohen’s Version

From this afternoon’s footprints:

Israel
A		 /438080412/item/?
Your Site		 2/3/2009
3:34 PM

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 — Tags: , — 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.

Sunday, February 1, 2009

Sunday February 1, 2009

Filed under: General,Geometry — Tags: — m759 @ 9:00 am

"For every kind of vampire,
there is a kind of cross."
— Gravity's Rainbow

Quaternion in finite geometry

Quaternion

Happy St. Bridget's Day.

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