Log24

Friday, November 30, 2012

Point

Filed under: General — Tags: — m759 @ 12:31 pm

"….mirando il punto  
a cui tutti li tempi son presenti"

— Dante, Paradiso , XVII, 17-18

 For instance

IMAGE- Three films from Christmas 1963 (IMDb): Captain Newman, MD; The Prize; Love with the Proper Stranger

Click image for higher quality.

Title

Filed under: General — m759 @ 12:26 am

The title of yesterday's 11:22 PM post was "The Place of the Lion."

This is also the title of a novel by Charles Williams.

See, too, Midsummer Eve's Dream and Midsummer Night 2007.

Thursday, November 29, 2012

The Place of the Lion

Filed under: General — m759 @ 11:22 pm

For C. S. Lewis, who was born on this date in 1898,
and Natalie Wood, who died on this date in 1981

"He was accustomed to receiving manuscripts from strangers…."
— C. P. Snow on mathematician G. H. Hardy

"Whoever you are— I have always depended on
the kindness of strangers." — A Streetcar Named Desire

From this journal on September 24, 2012

"A single self-transcendence" — Aldous Huxley

From an anonymous author at the website Kill Devil Hill

"This little story… has that climactic moment of 
heightened awareness…. This is a moment where
two individuals become one, empowering them
to transcend the limitations of their own individual
frailty and society. It's an epiphany, an almost
divine spark. It is an experience when one plus one
don't equal two, but something far greater."

Kill Devil Hills also appears in a 1983 film—

"Suppose it were possible to transfer
from one mind to another
the experience of another person."

— Trailer for "Brainstorm" (1983),
the last film of Natalie Wood

Lines of Symbols

Filed under: General,Geometry — Tags: — m759 @ 3:00 pm

C. P. Snow on G. H. Hardy, in Snow's foreword to A Mathematician's Apology

"One morning early in 1913, he found, among the letters on his breakfast table, a large untidy envelope decorated with Indian stamps. When he opened it, he found sheets of paper by no means fresh, on which, in a non-English holograph, were line after line of symbols. Hardy glanced at them without enthusiasm. He was by this time, at the age of thirty-six, a world famous mathematician: and world famous mathematicians, he had already discovered, are unusually exposed to cranks. He was accustomed to receiving manuscripts from strangers, proving the prophetic wisdom of the Great Pyramid, the revelations of the Elders of Zion, or the cryptograms that Bacon has inserted in the plays of the so-called Shakespeare."

Some related material (click to enlarge)—

The author links to, but does not name, the source of the above
"line after line of symbols." It is "Visualizing GL(2,p)." See that webpage
for some less esoteric background.

See also the two Wikipedia articles Finite geometry and Hesse configuration
and an image they share—

IMAGE- Image from Wikipedia articles 'Finite geometry' and 'Hesse configuration.'

The Hesse here is not Hermann, but Otto.

Conceptual Art

Filed under: General,Geometry — m759 @ 12:09 pm

Quotes from the Bremen site
http://dada.compart-bremen.de/ 
 

IMAGE- Steven H. Cullinane, diamond theorem, from 'Diamond Theory,' Computer Graphics and Art, Vol. 2 No. 1, Feb. 1977, pp. 5-7

" 'compArt | center of excellence digital art' is a project
at the University of Bremen, Germany. It is dedicated
to research and development in computing, design,
and teaching. It is supported by Rudolf Augstein Stiftung,
the University of Bremen, and Karin und Uwe Hollweg Stiftung."

See also Stiftung in this journal.

Wednesday, November 28, 2012

Synesis

Filed under: General — Tags: , — m759 @ 2:00 pm

From a New York Times  weblog last night—

The Reconstruction of Rome
By ROBERT BEASER

The New York Times , Nov. 27, 2012, 9:00 PM

Logic Pro software enables us to layer complex
technolike tracks and simulate meta, sampled orchestras—
fake orchestras that have on more than one occasion
fooled a jury of the most discriminating composers
into thinking it was the real thing. …

Several decades of cultural relativism has helped to
hasten the decline of the dominance of Western canon….

This next generation is becoming adept at taking small
bits of information, unformed, and assembling it
into larger asynchronous maps, of nonlinear order. 

IT from BITS*

These failures of number agreement—
orchestras… it,  decades… has,  bits… it —
suggest a look at synesis.

Synesis is a traditional grammatical/rhetorical term
derived from Greek σύνεσις (originally meaning "unification,
meeting, sense, conscience, insight, realization, mind, reason").
A constructio kata synesin  (or constructio ad sensum  in Latin)
means a grammatical construction in which a word takes
the gender or number not of the word with which it should
regularly agree, but of some other word implied in that word.
It is effectively an agreement of words with the sense,
instead of the morphosyntactic form. Example:
"If the band are popular, they will play next month." —Wikipedia

The conclusion of Wikipedia's synesis article is of particular interest:

See also…. Elohim , a Hebrew word whose number varies.

* A nod to the late John Archibald Wheeler

Annals of Religion

Filed under: General — Tags: — m759 @ 2:56 am

IMAGE- 'Candlestick of Death' in Michener's 'The Source'
IMAGE- An Oscar for 'Chicago'

Diamond Theory

Filed under: General,Geometry — Tags: — m759 @ 2:18 am

A pdf of a 1977 three-page article with this title
has been added at finitegeometry.org/sc.

Tuesday, November 27, 2012

Raiders of the Lost Lottery

Filed under: General — m759 @ 2:06 pm

Today's midday New York Lottery: 444 and 5222.

See Deuteronomy  4:44 and 5:2-22.

Counterexample

Filed under: General,Geometry — Tags: — m759 @ 12:25 pm

The non-Coxeter simple reflection group of order 168
is a counterexample to the statement that
"Every finite reflection group is a Coxeter group."

The counterexample is based on a definition of "reflection group"
that includes reflections defined over finite fields.

Today I came across a 1911 paper that discusses the counterexample.
Of course, Coxeter groups were undefined in 1911, but the paper, by
Howard H. Mitchell, discusses the simple order-168 group as a reflection group .

(Naturally, Mitchell's definition of "reflection" and his statement that

"The discussion of the binary groups
applies also to the case p = 2."

should be approached with care.)

A review of this topic might be appropriate for Jessica Fintzen's 2012 fall tutorial at Harvard
on reflection groups and Coxeter groups. The syllabus for the tutorial states that
"finite Coxeter groups correspond precisely to finite reflection groups." This statement
is based on Fintzen's definition of "reflection group"—

"Reflection groups are— as their name indicates—
groups generated by reflections across
hyperplanes of Rn which contain the origin."

For some background, see William Kantor's 1981 paper "Generation of Linear Groups"
(quoted at the finitegeometry.org page on the simple order-168 counterexample).
Kantor discusses Mitchell's work in some detail, but does not mention the
simple order-168 group explicitly.

Monday, November 26, 2012

“The Eight”…

Filed under: General — Tags: , — m759 @ 2:18 pm

Meets "The Master"—

IMAGE- Joaquin Phoenix, corridor scene in 'The Master'

Today's midday NY Lottery: 333 and 5885.

"Continue a search for thirty-three and three." — The Eight  (1988)

"Make me young." — Kilgore Trout in
Breakfast of Champions . Trout was modeled after
author Theodore Sturgeon who died on 5/8/85.

(An example of Sturgeon's work: The Dreaming Jewels  (1950).)

Related illustrations from the eighth day of 2012—

See also "I'm sorry to be catechizing you like this."

Sunday, November 25, 2012

By the Numbers

Filed under: General — m759 @ 9:18 pm

The New York Lottery:

CATCH OUR LIVE DRAWINGS:
NUMBERS and WIN 4
Draw Day: Twice Daily
Draw Time: Midday: 12:20 p.m. – 12:30 p.m.
Evening: 7:30 p.m. – 7:40 p.m. 

NY Lottery this evening: 674 and 1252 —

.

Contrapuntal themes:

Related Log24 posts today—
at 11:30 AM ET  (see post 674 ) and
at 7 PM ET (see post 1252).

The Devil at Midday:

Interpreting the midday numbers,
172 and 7817, is more difficult. Perhaps 172
refers to a Zen page number in a post from 
the Feast of Saint Louis in 2003, and perhaps,
in a less saintly manner, 7817 refers to
two posts in which these four digits appear
in product numbers within links— namely,
the Garden Party  "Background" link and 
the Seven Bridges  "wild" link.

Then again, perhaps not.

Grim Joke

Filed under: General,Geometry — m759 @ 7:00 pm

"It's a grim joke." — Amy Adams in "The Master"

When Irish Eyes Are Smiling

Geometry lesson

Click diagram for some background from 3/17.
See, too, some background on Amy Adams and on Leap Day.

For related Harvard humor, see Venn Diagram.

Darstellung…

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

… For the Boston Church of the Advent coffee hour:

Suggested topic: 

The Klee picture on the above cup— a graphic rendition of the poem
Once Emerged from the Gray of Night — as presented on the cover
and discussed in the text of Martha B. Helfer's The Word Unheard .

Talk amongst yourselves.

Will*

Filed under: General — m759 @ 11:00 am

Today's sermon is for Martha B. Helfer, author of
the treatise on Darstellung  in today's previous post
and of the following—

(Click for clearer image.)

Helfer's The Word Unheard  was published by Northwestern University Press
on St. Andrew's Day, 2011. Log24 posts on that day—

Lines, Grids, and Fatuity for St. Andrew's Day.

The last of these warned of an upcoming Jewish Book Week event
on February 22, 2012.

That date turned out to be Ash Wednesday. See a Log24 post on that topic
that quotes a poet, T.S. Eliot, with anti-Semitic proclivities—

"And the light shone in darkness and
Against the Word the unstilled world still whirled
About the centre of the silent Word."

— T. S. Eliot, "Ash Wednesday"

This is perhaps not entirely irrelevant to Helfer's title, The Word Unheard .

* A concept of Schopenhauer and Hitler, and the first name of
   a fictional Boston mathematician.

Representation

Filed under: General — m759 @ 10:31 am

The title of yesterday's post Will and Representation is of course
a reference to Schopenhauer's philosophical work of that name.

As the post itself indicates, the title is also a punning reference to
mathematical representation theory . 

To avoid confusion, it should be noted that Schopenhauer's
representation , in the original German, was Vorstellung .

The German for mathematical  representation theory is,
on the other hand, Darstellungstheorie . (The mathematical
use of Vorstellung  is non-technical, referring to concepts
of pedagogy. (A group presentation  is a Präsentation .))

For a discussion of the Vorstellung-Darstellung  distinction
in philosophy, not mathematics, see… 

The Retreat of Representation: The Concept of  Darstellung
in German Critical Discourse , by Martha B. Helfer,
State University of New York Press, 1996, esp. pp. 24-26.

Saturday, November 24, 2012

Will and Representation*

Filed under: General,Geometry — Tags: — m759 @ 2:56 pm

Robert A. Wilson, in an inaugural lecture in April 2008—

Representation theory

A group always arises in nature as the symmetry group of some object, and group
theory in large part consists of studying in detail the symmetry group of some
object, in order to throw light on the structure of the object itself (which in some
sense is the “real” object of study).

But if you look carefully at how groups are used in other areas such as physics
and chemistry, you will see that the real power of the method comes from turning
the whole procedure round: instead of starting from an object and abstracting
its group of symmetries, we start from a group and ask for all possible objects
that it can be the symmetry group of 
.

This is essentially what we call Representation theory . We think of it as taking a
group, and representing it concretely in terms of a symmetrical object.

Now imagine what you can do if you combine the two processes: we start with a
symmetrical object, and find its group of symmetries. We now look this group up
in a work of reference, such as our big red book (The ATLAS of Finite Groups),
and find out about all (well, perhaps not all) other objects that have the same
group as their group of symmetries.

We now have lots of objects all looking completely different, but all with the same
symmetry group. By translating from the first object to the group, and then to
the second object, we can use everything we know about the first object to tell
us things about the second, and vice versa.

As Poincaré said,

Mathematicians do not study objects, but relations between objects.
Thus they are free to replace some objects by others, so long as the
relations remain unchanged.

Par exemple

Fano plane transformed to eightfold cube,
and partitions of the latter as points of the former:

IMAGE- Fano plane transformed to eightfold cube, and partitions of the latter as points of the former

* For the "Will" part, see the PyrE link at Talk Amongst Yourselves.

Reappearing All Over Again

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

For the title, see the phrase "reappearing number" in this journal.

Some related mathematics—

the Greek labyrinth of Borges, as well as…

IMAGE- Robert Wilson on the projective line with 24 points and its image in the MOG.

Note that "0" here stands for "23," while corresponds to today's date.

Deep Agents

Filed under: General — m759 @ 6:00 am

New today
John Markoff in this morning's New York Times

"…what is new in recent months is the growing speed and accuracy
of deep-learning programs, often called artificial neural networks
or just 'neural nets' for their resemblance to the neural connections
in the brain."

Not so new
From the early days of Mike Lynch's Autonomy Inc.

"Autonomy 's intelligent agents use neural networking
to search for patterns of information, rather than
specific words or phrases, thereby distinguishing relevant
from irrelevant information." (Business Wire , October 8, 1996)

And from 1999

IMAGE- Agent Smith from 'The Matrix,' 1999

Who Shot J. R.?

Filed under: General — m759 @ 4:24 am

For the answer, click here.

Connoisseurs of synchronicity may note two posts
from the date the above photo was taken:

First Draft of History and The Swedish Solution.

(The late Larry Hagman was, according to NBC News, "a longtime member 
of the Peace and Freedom Party, a minor leftist organization in California.")

Thursday, November 22, 2012

Finite Relativity

Filed under: General,Geometry — Tags: , — m759 @ 10:48 pm

(Continued from 1986)

S. H. Cullinane
The relativity problem in finite geometry.
Feb. 20, 1986.

This is the relativity problem: to fix objectively a class of equivalent coordinatizations and to ascertain the group of transformations S mediating between them.

— H. Weyl, The Classical Groups ,
Princeton Univ. Pr., 1946, p. 16

In finite geometry "points" are often defined as ordered n-tuples of a finite (i.e., Galois) field GF(q). What geometric structures ("frames of reference," in Weyl's terms) are coordinatized by such n-tuples? Weyl's use of "objectively" seems to mean that such structures should have certain objective— i.e., purely geometric— properties invariant under each S.

This note suggests such a frame of reference for the affine 4-space over GF(2), and a class of 322,560 equivalent coordinatizations of the frame.

The frame: A 4×4 array.

The invariant structure:

The following set of 15 partitions of the frame into two 8-sets.

Fifteen partitions of a 4x4 array into two 8-sets
 

A representative coordinatization:

 

0000  0001  0010  0011
0100  0101  0110  0111
1000  1001  1010  1011
1100  1101  1110  1111

 

The group: The group AGL(4,2) of 322,560 regular affine transformations of the ordered 4-tuples over GF(2).

S. H. Cullinane
The relativity problem in finite geometry.
Nov. 22, 2012.

This is the relativity problem: to fix objectively a class of equivalent coordinatizations and to ascertain the group of transformations S mediating between them.

— H. Weyl, The Classical Groups ,
Princeton Univ. Pr., 1946, p. 16

In finite geometry "points" are often defined as ordered n-tuples of a finite (i.e., Galois) field GF(q). What geometric structures ("frames of reference," in Weyl's terms) are coordinatized by such n-tuples? Weyl's use of "objectively" seems to mean that such structures should have certain objective— i.e., purely geometric— properties invariant under each S.

This note suggests such a frame of reference for the affine 4-space over GF(2), and a class of 322,560 equivalent coordinatizations of the frame.

The frame: An array of 16 congruent equilateral subtriangles that make up a larger equilateral triangle.

The invariant structure:

The following set of 15 partitions of the frame into two 8-sets.


Fifteen partitions of an array of 16 triangles into two 8-sets


A representative coordinatization:

 

Coordinates for a triangular finite geometry

The group: The group AGL(4,2) of 322,560 regular affine transformations of the ordered 4-tuples over GF(2).

For some background on the triangular version,
see the Square-Triangle Theorem,
noting particularly the linked-to coordinatization picture.

Putting the “I” in “IT”

Filed under: General — Tags: — m759 @ 12:00 pm

Jennifer Scott at IT Pro , Feb. 16, 2012, on Autonomy

Mike Lynch, founder of Autonomy  and vice president
of information management at HP, took to the stage
at his new parent company’s global partner conference
to impart his philosophy to the 3,000 partners gathered.

‘It is no longer about the data but about the meaning
of that data,’ he said. ‘There is a fundamental revolution
going on in information and the industry is now about
the “I” not the “T” in IT.'”

Click on the logo below for the source.

Putting the I in IT

See also today’s previous post and…

Madeleine L’Engle in
The Irrational Season
(1977), Chapter 9:

“After A Wrinkle in Time  was finally published,
it was pointed out to me that the villain,
a naked disembodied brain, was called ‘It’
because It stands for Intellectual truth
as opposed to a truth which involves the whole of us,
heart as well as mind.  That acronym had never
occurred to me.  I chose the name It intuitively,
because an IT does not have a heart or soul.
And I did not understand consciously
at the time of writing that the intellect,
when it is not informed by the heart, is evil.”

The Red Line vs. the Red Eye

Filed under: General — m759 @ 11:07 am

Arthur C. Clarke

"Any sufficiently advanced technology is indistinguishable from magic."

"The HP/Autonomy  Debacle," by John C. Dvorak at pcmag.com on Tuesday, Nov. 20, 2012—

"The whole Autonomy  thing was weird since the company seemed to be performing magic. On co-founder Michael Richard Lynch's Wikipedia page, the company is described as 'a leader in the area of computer understanding of unstructured information, an area which is becoming known as meaning-based computing .'

I do not know how gullible HP's board of directors is, but when I see the sudden emergence of something called 'meaning-based computing,' the alarms sound and the bullcrap meter begins to tag the red line."

A story by Terence K. Huwe in Online  magazine, Sept.-Oct. 2011, defines meaning-based computing (MBC), discusses Autonomy , and llnks to…

John Markoff in The New York Times , March 4, 2011— 

"Engineers and linguists at Cataphora, an information-sifting company based in Silicon Valley, have their software mine documents for the activities and interactions of people— who did what when, and who talks to whom. The software seeks to visualize chains of events. It identifies discussions that might have taken place across e-mail, instant messages and telephone calls.

Then the computer pounces, so to speak, capturing 'digital anomalies' that white-collar criminals often create in trying to hide their activities.

For example, it finds 'call me' moments— those incidents when an employee decides to hide a particular action by having a private conversation. This usually involves switching media, perhaps from an e-mail conversation to instant messaging, telephone or even a face-to-face encounter."

For example

IMAGE- HAL reading lips in '2001: A Space Odyssey'

Wednesday, November 21, 2012

Hunting Goodwill

Filed under: General — m759 @ 1:37 pm

Jonathan Weil at Bloomberg.com yesterday
on the HP-Autonomy  story—

"The goodwill figure is especially telling."

Tuesday, November 20, 2012

Resisting the Bogus

Filed under: General — m759 @ 12:00 pm

From remarks by Wallace Stevens featured in recent Log24 posts:

"The poet finds that as between these two sources: the imagination and reality, the imagination is false, whatever else may be said of it, and reality is true; and being concerned that poetry should be a thing of vital and virile importance, he commits himself to reality, which then becomes his inescapable and ever-present difficulty and innamorata. In any event, he has lost nothing; for the imagination, while it might have led him to purities beyond definition, never yet progressed except by particulars. Having gained the world, the imaginative remains available to him in respect to all the particulars of the world. Instead of having lost anything, he has gained a sense of direction and a certainty of understanding. He has strengthened himself to resist the bogus."

— Bard College speech of 1951

Related material:

With Autonomy , H-P Bought An Old-Fashioned
Accounting Scandal. Here's How It Worked.

(Forbes , Nov. 20, 2012)

Hewlett-Packard is losing a star in Mike Lynch
(The Guardian , May 25, 2012)

The Quest for Meaning: The world's smartest search engine
took 250 years to build. Autonomy  is here.
 
(Wired , Feb. 2000)

The Particulars of Language

Filed under: General — Tags: , — m759 @ 11:01 am

This post is in memory of an English church musician whose
death was noted here yesterday evening in a post titled
"The Particulars of Rapture," a phrase from Wallace Stevens.

Sir Philip Ledger, who died on Sunday, was a
"church musician who produced magical settings
of carols," according to The Telegraph  RSS feed.

It is not clear what the Telegraph  meant by "magical settings."

Perhaps the phrase "his settings of carols" in his obituary refers
to the annual service of Nine Lessons and Carols at Cambridge,
where he was for a time director of music at King's College.

If so, the settings would be the Lessons, readings from the Bible
(a "ledger," in the sense defined below).  Such readings should
not be confused with notions from the world of Harry Potter. 

Examples: The Lessons from last Christmas in Cambridge.

IMAGE- Meanings of the word 'ledger'

Monday, November 19, 2012

The Particulars of Rapture

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

"And forth the particulars of rapture come."

— Wallace Stevens, "Notes Toward a Supreme Fiction,"
     Canto IV of "It Must Change," quoted here yesterday.

A death yesterday: Sir Philip Ledger.

Poetry and Truth

From today's noon post

"In all his poems with all their enchantments
for the poet himself, there is the final enchantment
that they are true. The significance of the poetic act
then is that it is evidence. It is instance and illustration.
It is an illumination of a surface,
the movement of a self in the rock.
Above all it is a new engagement with life.
It is that miracle to which the true faith of the poet
attaches itself."

— Wallace Stevens at Bard College, March 30, 1951

Stevens also said at Bard that

"When Joan of Arc said: 

Have no fear: what I do, I do by command.
My brothers of Paradise tell me what I have to do.

these words were the words of an hallucination.
No matter what her brothers of Paradise drove her to do,
what she did was never a poetic act of faith in reality
because it could not be."

There are those who would dispute this.

Some related material:

"Ageometretos me eisito."—
"Let no one ignorant of geometry enter."—
Said to be a saying of Plato, part of the
seal of the American Mathematical Society—

A poetic approach to geometry—

"A surface" and "the rock," from All Saints' Day, 2012

Spaces as Hypercubes

— and from 1981—

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

Some mathematical background for poets in Purgatory—

"… the Klein correspondence underlies Conwell's discussion 
of eight heptads. These play an important role in another
correspondence, illustrated in the Miracle Octad Generator
of R. T. Curtis, that may be used to picture actions
of the large Mathieu group M24."

Speech

Filed under: General — Tags: , — m759 @ 12:00 pm

Speech by Wallace Stevens upon accepting
an honorary degree from Bard College in 1951

(Click to enlarge.)

Transcription of conclusion:

"In all his poems with all their enchantments
for the poet himself, there is the final enchantment
that they are true. The significance of the poetic act
then is that it is evidence. It is instance and illustration.
It is an illumination of a surface,
the movement of a self in the rock.
Above all it is a new engagement with life.
It is that miracle to which the true faith of the poet
attaches itself."

— Wallace Stevens at Bard College, March 30, 1951

Sunday, November 18, 2012

Sermon

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

Happy birthday to

IMAGE- Margaret Atwood, Kim Wilde, Peta Wilson

Today's sermon, by Marie-Louise von Franz

Number and Time, by Marie-Louise von Franz

For more on the modern physicist analyzed by von Franz,
see The Innermost Kernel , by Suzanne Gieser.

Another modern physicist, Niels Bohr, died
on this date in 1962

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

The circle above is marked with a version
of the classic Chinese symbol
adopted as a personal emblem
by Danish physicist Niels Bohr,
leader of the Copenhagen School.

For the square, see the diamond theorem.

"Two things of opposite natures seem to depend
On one another, as a man depends
On a woman, day on night, the imagined
On the real. This is the origin of change.
Winter and spring, cold copulars, embrace
And forth the particulars of rapture come."

— Wallace Stevens,
  "Notes Toward a Supreme Fiction,"
  Canto IV of "It Must Change"

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