Log24

Friday, June 30, 2006

Friday June 30, 2006

Filed under: General — m759 @ 6:23 pm
Summers Revels Ended

IMAGE- 'Wind over Water,' i.e. 'Feng Shui'

“Wind over Water” in the I Ching,
the Classic of Transformations,
signifies huan, “dissolving.”

Dissolving:

Our revels now are ended.
These our actors,
as I foretold you,
were all spirits… 

Friday June 30, 2006

Filed under: General,Geometry — m759 @ 2:20 pm
  Independence Day Cover

Chinese Chess

    Click on picture for further details.

Thursday, June 29, 2006

Thursday June 29, 2006

Filed under: General — m759 @ 11:11 am
For the Feast of
St. Peter:

“The rock cannot be broken.
It is the truth.”

— Wallace Stevens,
“Credences of Summer,”

Spellbound, and

Quotes on Mathematics,
collected by
Peter Cameron.

Wednesday, June 28, 2006

Wednesday June 28, 2006

Filed under: General — m759 @ 12:00 pm
Today’s birthdays:

John Cusack is 40,
Mel Brooks is 80.

(See midnight on
Midsummer’s Eve
.)

“Like Gone with the Wind
on mescaline”
a description of Savannah

Noon
in the Garden of
Good and Evil:

The image “http://www.log24.com/log/pix06A/060628-Gump1.jpg” cannot be displayed, because it contains errors.

Related material
from December 2005:

Intelligence/Counterintelligence,

Prequel on St. Cecilia’s Day,

Intelligence/Counterintelligence
Continued

Tuesday, June 27, 2006

Tuesday June 27, 2006

Filed under: General,Geometry — m759 @ 10:31 am
Chinese Jar
Revisited

In memory of
Irving Kaplansky,
who died on
Sunday, June 25, 2006

“Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness.”

T. S. Eliot


Kaplansky received his doctorate in mathematics at Harvard in 1941 as the first Ph.D. student of Saunders Mac Lane.

From the April 25, 2005, Harvard Crimson:

Ex-Math Prof Mac Lane, 95, Dies

Gade University Professor of Mathematics Barry Mazur, a friend of the late Mac Lane, recalled that [a Mac Lane paper of 1945] had at first been rejected from a lower-caliber mathematical journal because the editor thought that it was “more devoid of content” than any other he had read.

“Saunders wrote back and said, ‘That’s the point,'” Mazur said. “And in some ways that’s the genius of it. It’s the barest, most Beckett-like vocabulary that incorporates the theory and nothing else.”

He likened it to a sparse grammar of nouns and verbs and a limited vocabulary that is presented “in such a deft way that it will help you understand any language you wish to understand and any language will fit into it.”

A sparse grammar of lines from Charles Sanders Peirce (Harvard College, class of 1859):

The image “http://www.log24.com/theory/images/PeirceBox.bmp” cannot be displayed, because it contains errors.

The image “http://www.log24.com/theory/images/PeirceSymbols1.jpg” cannot be displayed, because it contains errors.

It is true of this set of binary connectives, as it is true of logic generally, that (as alleged above of Mac Lane’s category theory) “it will help you understand any language you wish to understand and any language will fit into it.” Of course, a great deal of questionable material has been written about these connectives. (See, for instance, Piaget and De Giacomo.) For remarks on the connectives that are not questionable, see Wittgenstein’s Tractatus Logico-Philosophicus (English version, 1922), section 5.101, and Knuth’s “Boolean Basics” (draft, 2006).

Related entry: Binary Geometry.

Monday, June 26, 2006

Monday June 26, 2006

Filed under: General — m759 @ 11:07 am
D-Day Notes
continued:

Lyle Stuart, publisher of The Anarchist Cookbook and The Turner Diaries, died at 83 on Saturday, June 24, 2006.

“Mr. Stuart was named Lionel Simon when he was born in Manhattan, the son of a salesman and a secretary.  His father committed suicide when the boy was 6.”

Anthony Ramirez in
this morning’s New York Times

Related material:

The previous entry,

Plato, Pegasus, and
the Evening Star,
and

Architecture of Eternity

See also two varieties of Hell,
from the New York Times on
Nov. 25, 2005, and yesterday.

Monday June 26, 2006

Filed under: General — Tags: — m759 @ 9:29 am

A Little Extra Reading

In memory of
Mary Martin McLaughlin,
a scholar of Heloise and Abelard.
McLaughlin died on June 8, 2006.

"Following the parade, a speech is given by Charles Williams, based on his book The Place of the Lion. Williams explains the true meaning of the word 'realism' in both philosophy and theology. His guard of honor, bayonets gleaming, is led by William of Ockham."

Midsummer Eve's Dream

A review by John D. Burlinson of Charles Williams's novel The Place of the Lion:

"… a little extra reading regarding Abelard's take on 'universals' might add a little extra spice– since Abelard is the subject of the heroine's … doctoral dissertation. I'd suggest the article 'The Medieval Problem of Universals' in the online Stanford Encyclopedia of Philosophy."

Michael L. Czapkay, a student of philosophical theology at Oxford:

"The development of logic in the schools and universities of western Europe between the eleventh and fifteenth centuries constituted a significant contribution to the history of philosophy. But no less significant was the influence of this development of logic on medieval theology. It provided the necessary conceptual apparatus for the systematization of theology. Abelard, Ockham, and Thomas Aquinas are paradigm cases of the extent to which logic played an active role in the systematic formulation of Christian theology. In fact, at certain points, for instance in modal logic, logical concepts were intimately related to theological problems, such as God's knowledge of future contingent truths."

The Medieval Problem of Universals, by Fordham's Gyula Klima, 2004:

"… for Abelard, a status is an object of the divine mind, whereby God preconceives the state of his creation from eternity."

Status Symbol

(based on Weyl's Symmetry):

The image “http://www.log24.com/log/pix06A/060604-Roots.jpg” cannot be displayed, because it contains errors.

"… for then we would know

the mind of God"
Stephen Hawking, 1988

For further details,
click on the picture.

Sunday, June 25, 2006

Sunday June 25, 2006

Filed under: General — m759 @ 7:00 pm

Language Games:

Chess and Bingo

Chess: See Log24, Midsummer Day, 2003. Happy mate change, Nicole.

Bingo: See a journal entry from seven years ago, On Linguistic Creation. Happy birthday, Willard Van Orman Quine.

Sunday June 25, 2006

Filed under: General — m759 @ 11:00 am
Today’s Sermon:

Carly Simon is 61.

Sunday June 25, 2006

Filed under: General — m759 @ 7:59 am
The image “http://www.log24.com/log/pix06A/060625-History.gif” cannot be displayed, because it contains errors.

Related material:
June 20, 2006

Saturday, June 24, 2006

Saturday June 24, 2006

Filed under: General — m759 @ 4:17 pm

In memory of
Hunter S. Thompson

On Midsummer Day:

Big Time
Parts I, II, III

Part I:
April 17, 2003: Holiday Affair

Saturday June 24, 2006

Filed under: General — m759 @ 4:16 pm

Big Time, Part II:

April 16, 2003: Keeping Time

Saturday June 24, 2006

Filed under: General — m759 @ 4:15 pm

Big Time, Part III:

April 15, 2003: Green and Burning

Saturday June 24, 2006

Filed under: General — Tags: — m759 @ 7:59 am
Zen and the Art

"Man stands in his own shadow and wonders why it is dark."

— "Ancient Zen saying," according to "Today in History," June 24, by the Associated Press

"A man may be free to travel where he likes, but there is no place on earth where he can escape from his own Karma, and whether he lives on a mountain or in a city he may still be the victim of an uncontrolled mind. For man's Karma travels with him, like his shadow. Indeed, it is his shadow, for it has been said, 'Man stands in his own shadow and wonders why it is dark.'"

— Alan W. Watts, The Spirit of Zen, third edition, Grove Press, 1958, page 97

Robert Pirsig, Zen and the Art of Motorcycle Maintenance, 1974:

"But what's happening is that each year our old flat earth of conventional reason becomes less and less adequate to handle the experiences we have and this is creating widespread feelings of topsy-turviness. As a result we're getting more and more people in irrational areas of thought… occultism, mysticism, drug changes and the like… because they feel the inadequacy of classical reason to handle what they know are real experiences."

"I'm not sure what you mean by classical reason."

"Analytic reason, dialectic reason. Reason which at the University is sometimes considered to be the whole of understanding. You've never had to understand it really. It's always been completely bankrupt with regard to abstract art. Nonrepresentative art is one of the root experiences I'm talking about. Some people still condemn it because it doesn’t make 'sense.' But what's really wrong is not the art but the 'sense,' the classical reason, which can't grasp it. People keep looking for branch extensions of reason that will cover art's more recent occurrences, but the answers aren't in the branches, they're at the roots."
 

The image “http://www.log24.com/log/pix06A/060604-Roots.jpg” cannot be displayed, because it contains errors.

Related material:

D-Day Morning,
Figures of Speech,
Ursprache Revisited.

See also
the previous entry.

Saturday June 24, 2006

Filed under: General — Tags: — m759 @ 12:00 am
In memory of
Aaron Spelling

"Let the midnight special
shine her light on me."

For more on the
eight-point star of Venus,
see Bright Star.

Related material:
April 21-22, 2003.

Friday, June 23, 2006

Friday June 23, 2006

Filed under: General — Tags: — m759 @ 9:00 pm
Go with the Flow
continued

Review of a
Feb. 15, 2006, entry:

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The image ?http://www.log24.com/images/IChing/WilhelmHellmut.gif? cannot be displayed, because it contains errors.

Friday June 23, 2006

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

Binary Geometry

There is currently no area of mathematics named “binary geometry.” This is, therefore, a possible name for the geometry of sets with 2n elements (i.e., a sub-topic of Galois geometry and of algebraic geometry over finite fields– part of Weil’s “Rosetta stone” (pdf)).

Examples:

Wednesday, June 21, 2006

Wednesday June 21, 2006

Filed under: General,Geometry — Tags: , — m759 @ 10:00 am

Go with the Flow

The previous entry links to a document that discusses the mathematical concept of "Ricci flow (pdf)."

Though the concept was not named for him, this seems as good a time as any to recall the virtues of St. Matteo Ricci, a Jesuit who died in Beijing on May 11, 1610. (The Church does not yet recognize him as a saint; so much the worse for the Church.)

There was no Log24 entry on Ricci's saint's day, May 11, this year, but an entry for 4:29 PM May 10, 2006, seems relevant, since Beijing is 12 hours ahead of my local (Eastern US) time.

Ricci is famous for constructing
a "memory palace."
Here is my equivalent,
from the May 10 entry:
 
The image ?http://www.log24.com/theory/images/MySpace.jpg? cannot be displayed, because it contains errors.

The relevance of this structure
to memory and to Chinese culture
is given in Dragon School and in
Geometry of the 4x4x4 Cube.

For some related remarks on
the colloquial, rather than the
mathematical, concept of flow,
see
Philosophy, Religion, and Science
as well as Crystal and Dragon.

Yesterday's entry on the 1865
remarks on aesthetics of
Gerard Manley Hopkins,
who later became a Jesuit,
may also have some relevance.

Wednesday June 21, 2006

Filed under: General — m759 @ 9:00 am

Beijing String continued…

A comment left at Peter Woit’s weblog:

Xinhua has a story from June 20 on Yau showing a video in Beijing of a talk by Hamilton on the Poincare conjecture. This Xinhua story is rather Sinocentric, but it is balanced nicely by a document from China’s Morningside Center of Mathematics that gives a more complete record of Hamilton’s talk.

Tuesday, June 20, 2006

Tuesday June 20, 2006

Filed under: General,Geometry — m759 @ 10:26 pm

Hopkins on Parallelism

“The structure of poetry is that of continuous parallelism, ranging from the technical so-called Parallelism of Hebrew Poetry and the antiphons of Church music up to the intricacy of Greek or Italian or English verse. But parallelism is of two kinds necessarily – where the opposition is clearly marked, and where it is transitional rather or chromatic. Only the first kind, that of marked parallelism is concerned with the structure of verse — in rhythm, the recurrence of a certain sequence of rhythm, in alliteration, in assonance and in rhyme. Now the force of this recurrence is to beget a recurrence or parallelism answering to it in the words or thought and, speaking roughly and rather for the tendency than the invariable result, the more marked parallelism in structure whether of elaboration or of emphasis begets more marked parallelism in the words and sense. And moreover parallelism in expression tends to beget or passes into parallelism in thought. This point reached we shall be able to see and account for the peculiarities of poetic diction. To the marked or abrupt kind of parallelism belong metaphor, simile, parable, and so on, where the effect is sought in likeness of things, and antithesis, contrast, and so on, where it is sought in unlikeness. To the chromatic parallelism belong gradation, intensity, climax, tone, expression (as the word is used in music), chiaroscuro, perhaps emphasis: while the faculties of Fancy and Imagination might range widely over both kinds, Fancy belonging more especially to the abrupt than to the transitional class.”

— From Gerard Manley Hopkins, “Poetic Diction,” 1865

For an application to Hopkins’s poetry, see an excerpt from Stephen Prickett, Words and the Word: Language, Poetics and Biblical Interpretation (Cambridge: Cambridge University Press, 1986).

See also the publisher’s description of Maria R. Lichtmann’s The Contemplative Poetry of Gerard Manley Hopkins, Princeton University Press, 1989.

Tuesday June 20, 2006

Filed under: General — m759 @ 1:23 pm
Cat’s Yarn


The Poincare Conjecture:
  Its Past, Present, and Future

“The history of topology dates back at least to the middle of the 18th century. One of its first major boosts came at the end of the 19th century, when Poincare was trying to understand the set of solutions to a general algebraic equation….”

“The end is where
   we start from.”

T. S. Eliot

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plus.maths.org
and
Garfield 2003-06-24

Related material:

Zen Koan
and
Blue Dream

Tuesday June 20, 2006

Filed under: General — m759 @ 7:59 am
Beijing String

Oh, do not ask, “What is it?
Let us go and make our visit.

On Tuesday evening, the schedule says “Prof. Yau present his new research result,” which presumably will be about the proof of the Poincare conjecture.

Would it have been worth while,
To have bitten off the matter
   with a smile,
To have squeezed the universe
   into a ball
To roll it toward some
   overwhelming question….

Yau rated the conjecture as one of  the major mathematical puzzles of the 20th Century. 
    “The conjecture is that if in a closed  three-dimensional space, any closed  curves can shrink to a point continuously, this space can be deformed to a sphere,” he said.

Monday, June 19, 2006

Monday June 19, 2006

Filed under: General — m759 @ 4:00 pm

Snippets:
A Reply to John Updike

See Updike on digitized snippets.

The following four snippets were pirated from the end of MathPages Quotations, compiled by Kevin Brown.

They are of synchronistic interest in view of the previous two Log24 entries, which referred (implicitly) to a Poe story and (explicitly) to Pascal.

"That is another of your odd notions,"
said the Prefect, who had the fashion
of calling everything 'odd' that was
beyond his comprehension, and thus
lived amid an absolute legion of 'oddities.'
Edgar Allan Poe

I knew when seven justices could not
take up a quarrel, but when the parties
were met themselves, one of them
thought but of an If, as, 'If you said so,
then I said so'; and they shook hands
and swore brothers. Your If is the only
peacemaker; much virtue in If.
Shakespeare

I have made this letter longer than usual
because I lack the time to make it shorter.
Blaise Pascal

S'io credessi che mia risposta fosse
a persona che mai tornasse al mondo,
questa fiamma staria senza piu scosse.
Ma per cio che giammai di questo fondo
non torno vivo alcun, s'i'odo il vero,
senza tema d'infamia ti rispondo.
Dante, 1302

For translations of the Dante (including one by Dorothy Sayers), see everything2.com.

An anonymous author there notes that Dante describes a flame in which is encased a damned soul. The flame vibrates as the soul speaks:

If I thought that I were making
Answer to one that might return to view
The world, this flame should evermore
cease shaking.

But since from this abyss, if I hear true,
None ever came alive, I have no fear
Of infamy, but give thee answer due.

-- Dante, Inferno, Canto 27, lines 61-66,
translated by Dorothy Sayers

Updike says,

“Yes, there is a ton of information on the web but much of it is grievously inaccurate, unedited, unattributed and juvenile. The electronic marvels that abound around us serve, I have the impression, to inflame what is most informally and non-critically human about us. Our computer screens stare back at us with a kind of giant, instant aw-shucks, disarming in its modesty.”

Note Updike’s use of “inflame.”

For an aw-shucks version of “what is most informally and non-critically human about us,” as well as a theological flame, see both the previous entry and the above report from Hell.

Note that the web serves also to correct material that is inaccurate, unedited, unattributed, and juvenile. For examples, see Mathematics and Narrative. The combination of today’s entry for Pascal’s birthday with that web page serves both to light one candle and to curse the darkness.

Monday June 19, 2006

Filed under: General — m759 @ 7:59 am
For Blaise Pascal
on His Birthday

The Pascal Candle

“A Pascal Candle can be found
in most churches, and it is easy
to identify. It could well be taller
and fatter than any other candle
   in the church….”

The image “http://www.log24.com/log/pix06A/060619-Candle1.gif” cannot be displayed, because it contains errors.

Sunday, June 18, 2006

Sunday June 18, 2006

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

Gold Bug
Variations

The personae of summer
    play the characters
Of an inhuman author,
    who meditates
With the gold bugs,
    in blue meadows,
    late at night.

— Wallace Stevens,
“Credences of Summer,”
Canto X, Collected Poetry
and Prose
, 322-326

Sunday June 18, 2006

Filed under: General — m759 @ 7:59 am
Father’s Day

For Mel Gibson,
who may or may not
see a parallel here.

IMDb Trivia for Music Box (1989)

  • After the movie was released, screenwriter Joe Eszterhas‘s own father Istvan Eszterhas was accused of war crimes in Hungary by printing anti-Semitic editorials and even organizing a book burning.
  • Both Kirk Douglas and Walter Matthau wanted to play the father….
Once a son,
now a father:

The image “http://www.log24.com/log/pix06A/060618-Eszterhas.gif” cannot be displayed, because it contains errors.

“He spent his earliest years in post WWII–refugee camps. He came to America and grew up in Cleveland–stealing cars, rolling drunks, battling priests, nearly going to jail. He became the screenwriter of the worldwide hits Basic Instinct, Jagged Edge, and Flashdance. He also wrote the legendary disasters Showgirls and Jade. The rebellion never ended, even as his films went on to gross more than a billion dollars at the box office and he became the most famous–or infamous–screenwriter in Hollywood. Joe Eszterhas is a complex and paradoxical figure: part outlaw and outsider combined with equal parts romantic and moralist. More than one person has called him ‘the devil.’ He has been referred to as ‘the most reviled man in America.’ But Time asked, ‘If Shakespeare were alive today, would his name be Joe Eszterhas?'”

Random House promotional material

And eventually to become
a holy ghost…

“Yea, though I walk
through the valley of death
I will fear no evil,
for I am the meanest
son of a bitch
in the valley.”

Karl Cullinane

in The Silver Crown,
by Joel Rosenberg

Saturday, June 17, 2006

Saturday June 17, 2006

Filed under: General,Geometry — Tags: , , — m759 @ 7:59 am
In memory of
Barbara Epstein:
 

Spellbound

“Breaking the spell of religion is a
 game that many people can play.”
— Freeman Dyson in the current
   New York Review of Books

Part I:
The Game

The image “http://www.log24.com/log/pix06A/060617-Boggle.jpg” cannot be displayed, because it contains errors.

Part II:
Many People

The image “http://www.log24.com/log/pix06A/060617-Spellbound.jpg” cannot be displayed, because it contains errors.

For further details,
see Solomon’s Cube
and myspace.com/affine.

“The rock cannot be broken.
It is the truth.”
— Wallace Stevens     

Friday, June 16, 2006

Friday June 16, 2006

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

For Bloomsday 2006:

Hero of His Own Story

"The philosophic college should spare a detective for me."

Stephen Hero.  Epigraph to Chapter 2, "Dedalus and the
Beauty Maze," in Joyce and Aquinas, by William T. Noon, S. J.,
Yale University Press, 1957 (in the Yale paperback edition of
1963, page 18)

"Dorothy Sayers makes a great deal of sense when she points out
in her highly instructive and readable book The Mind of the Maker
that 'to complain that man measures God by his own measure is
a waste of time; man measures everything by his own experience;
he has no other yardstick.'"

— William T. Noon, S. J., Joyce and Aquinas (in the Yale paperback
edition of 1963, page 106)

Related material:

  • Dorothy Sayers and Jill Paton Walsh
  • Jill Paton Walsh's detective novel A Piece of Justice (1995):
    "The mathematics of tilings and quilting play background
    roles in this mystery in which a graduate student attempts
    to write a biography of the (fictitious) mathematician
    Gideon Summerfield. Summerfield is about to posthumously
    receive the prestigious (and, I should point out, also fictitious)
    Waymark Prize in mathematics…but it soon becomes clear
    that someone with evil intentions does not want the student's
    book to be published!
    By all accounts this is a well written mystery…
    the second by the author with college nurse Imogen Quy playing
    the role of the detective."
    Mathematical Fiction by Alex Kasman,
    College of Charleston

AD PULCHRITUDINEM TRIA REQUIRUNTUR:
INTEGRITAS, CONSONANTIA, CLARITAS.

St. Thomas Aquinas

Thursday, June 15, 2006

Thursday June 15, 2006

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

Baez Link

John Baez’s latest This Week’s Finds
(Week 234, June 12, 2006) has a link
to my “Geometry of the 4×4 Square” at
http://finitegeometry.org/sc/16/geometry.html.

Wednesday, June 14, 2006

Wednesday June 14, 2006

Filed under: General — m759 @ 5:00 pm

On the Brighter Side…

At 8 EDT tonight on CBS:
The American Film Institute’s
100 most inspiring American films.

For the list of 300 films on
the AFI ballot sent to voters,
click here (pdf, 772k).

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