Wednesday, February 28, 2007

Wednesday February 28, 2007

Filed under: General,Geometry — Tags: , — m759 @ 7:59 AM

of Geometry

The title of Euclid’s Elements is, in Greek, Stoicheia.

From Lectures on the Science of Language,
by Max Muller, fellow of All Souls College, Oxford.
New York: Charles Scribner’s Sons, 1890, pp. 88-90 –


“The question is, why were the elements, or the component primary parts of things, called stoicheia by the Greeks? It is a word which has had a long history, and has passed from Greece to almost every part of the civilized world, and deserves, therefore, some attention at the hand of the etymological genealogist.

Stoichos, from which stoicheion, means a row or file, like stix and stiches in Homer. The suffix eios is the same as the Latin eius, and expresses what belongs to or has the quality of something. Therefore, as stoichos means a row, stoicheion would be what belongs to or constitutes a row….

Hence stoichos presupposes a root stich, and this root would account in Greek for the following derivations:–

  1. stix, gen. stichos, a row, a line of soldiers
  2. stichos, a row, a line; distich, a couplet
  3. steichoestichon, to march in order, step by step; to mount
  4. stoichos, a row, a file; stoichein, to march in a line

In German, the same root yields steigen, to step, to mount, and in Sanskrit we find stigh, to mount….

Stoicheia are the degrees or steps from one end to the other, the constituent parts of a whole, forming a complete series, whether as hours, or letters, or numbers, or parts of speech, or physical elements, provided always that such elements are held together by a systematic order.”

Tuesday, February 27, 2007

Tuesday February 27, 2007

Filed under: General,Geometry — m759 @ 9:25 PM
Suggested by today’s 
New York Times story
on a Harvard student’s
research on pattern in
Islamic art —

and in memory of
George Sadek

From Log24 in July 2005:


A Trinity Sunday sermon
quotes T. S. Eliot:

“… to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint.”

See also The Diamond Project.

Related material:

                                  ” … an alphabet
By which to spell out holy doom and end,
A bee for the remembering of happiness.”

— Wallace Stevens,
“The Owl in the Sarcophagus”

The image “http://www.log24.com/theory/images/HeathI47A-Illustrations.jpg” cannot be displayed, because it contains errors.

Some context for these figures:
The Diamond Theory of Truth

Tuesday February 27, 2007

Filed under: General,Geometry — m759 @ 7:59 AM
Continued from 2/06:

The Poetics of Space

Log24 yesterday:

+John Cardinal Farley,
Archbishop of New York”

Tom Hanks as Robert Langdon in The Da Vinci Code

Tom Hanks as Robert Langdon
in “The Da Vinci Code”

“… and by ‘+’ I mean
artistic vision.”

New York State Lottery
yesterday, Feb. 26, 2007:

Mid-day 206
Evening 888

For more on the artistic
significance of 206,
see 2/06.

For more on the artistic
significance of 888, see
St. Bonaventure on the
Trinity at math16.com.

A trinity:

Click on picture for further details.

Monday, February 26, 2007

Monday February 26, 2007

Filed under: General — m759 @ 9:29 AM

The image “http://www.log24.com/log/pix07/070226-Scorsese.jpg” cannot be displayed, because it contains errors.
Monica Almeida/The New York Times
Martin Scorsese won the best-director
Oscar last night for “The Departed.”
From left, Francis Ford Coppola, Scorsese,
George Lucas and Steven Spielberg.

“Synaxis (synaxis from synago) means gathering, assembly, reunion. It is exactly equivalent to the Latin collecta (from colligere), and corresponds to synagogue (synagoge), the place of reunion.”

The Catholic Encyclopedia, Volume XIV. Published 1912. New York: Robert Appleton Company. Nihil Obstat, July 1, 1912. Remy Lafort, S.T.D., Censor. Imprimatur. +John Cardinal Farley, Archbishop of New York

Related material:
Yesterday’s entries.

Sunday, February 25, 2007

Sunday February 25, 2007

Filed under: General — Tags: — m759 @ 10:31 AM

Between Two Worlds

Nicolas Cage as Ghost Rider

Nicolas Cage as Ghost Rider

"I'm the only one who can
walk in both worlds.
I'm T. S. Eliot."
Four Quartets:

I caught the sudden look of some dead master
Whom I had known, forgotten, half recalled
     Both one and many; in the brown baked features
     The eyes of a familiar compound ghost
Both intimate and unidentifiable.
     So I assumed a double part, and cried
     And heard another's voice cry: 'What! are you here?'
Although we were not. I was still the same,
     Knowing myself yet being someone other—
     And he a face still forming; yet the words sufficed
To compel the recognition they preceded.
     And so, compliant to the common wind,
     Too strange to each other for misunderstanding,
In concord at this intersection time
     Of meeting nowhere, no before and after,
     We trod the pavement in a dead patrol.
I said: 'The wonder that I feel is easy,
     Yet ease is cause of wonder. Therefore speak:
     I may not comprehend, may not remember.'
And he: 'I am not eager to rehearse
     My thoughts and theory which you have forgotten.
     These things have served their purpose: let them be.
So with your own, and pray they be forgiven
     By others, as I pray you to forgive
     Both bad and good. Last season's fruit is eaten
And the fullfed beast shall kick the empty pail.
     For last year's words belong to last year's language
     And next year's words await another voice.
But, as the passage now presents no hindrance
     To the spirit unappeased and peregrine
     Between two worlds become much like each other,
So I find words I never thought to speak
     In streets I never thought I should revisit
     When I left my body on a distant shore.
Since our concern was speech, and speech impelled us
     To purify the dialect of the tribe
     And urge the mind to aftersight and foresight,
Let me disclose the gifts reserved for age
     To set a crown upon your lifetime's effort.
     First, the cold friction of expiring sense
Without enchantment, offering no promise
     But bitter tastelessness of shadow fruit
     As body and soul begin to fall asunder.
Second, the conscious impotence of rage
     At human folly, and the laceration
     Of laughter at what ceases to amuse.
And last, the rending pain of re-enactment
     Of all that you have done, and been; the shame
     Of motives late revealed, and the awareness
Of things ill done and done to others' harm
     Which once you took for exercise of virtue.
     Then fools' approval stings, and honour stains.
From wrong to wrong the exasperated spirit
     Proceeds, unless restored by that refining fire
     Where you must move in measure, like a dancer.'

Sunday February 25, 2007

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

Devil's Night in Hollywood

On the night of October 30-31, 1993, also known as Devil's Night, there was a full Hunter's Moon and the Pennsylvania Lottery number was 666.
— Steven H. Cullinane, 03/20/01

"Mystery surrounds the death of young actor River Phoenix…. The actor… was declared dead at 1:51 a.m. PT Sunday [Oct. 31, 1993]. Phoenix died about 50 minutes after collapsing in front of the Viper Room, a new club on the Sunset Strip…."
— Karen Thomas, USA Today, Monday, November 1, 1993

Related material:

The five Log24 entries
ending on Yom Kippur, 2006.

Tuesday, February 20, 2007

Tuesday February 20, 2007

Filed under: General — m759 @ 10:15 AM

On this, the second anniversary of Hunter Thompson’s death, two Xanga footprints from Texas furnish appropriate links:

Texas /514659186/item.html 2/20/2007 7:47 AM

Texas /534740724/item.html 2/20/2007 9:39 AM.

The first link is to Highway 1 Revisited (8/1/06).

The second link is to Serious (10/3/06).
(See also today’s previous entry.)

Related material:

The Crimson Passion: A Drama at Mardi Gras.

Tuesday February 20, 2007

Filed under: General,Geometry — m759 @ 7:09 AM

Today is the 21st birthday of my note “The Relativity Problem in Finite Geometry.”

Some relevant quotations:

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

— Hermann Weyl, The Classical Groups, Princeton University Press, 1946, p. 16

Describing the branch of mathematics known as Galois theory, Weyl says that it

“… is nothing else but the relativity theory for the set Sigma, a set which, by its discrete and finite character, is conceptually so much simpler than the infinite set of points in space or space-time dealt with by ordinary relativity theory.”

— Weyl, Symmetry, Princeton University Press, 1952, p. 138

Weyl’s set Sigma is a finite set of complex numbers.   Some other sets with “discrete and finite character” are those of 4, 8, 16, or 64 points, arranged in squares and cubes.  For illustrations, see Finite Geometry of the Square and Cube.  What Weyl calls “the relativity problem” for these sets involves fixing “objectively” a class of equivalent coordinatizations.  For what Weyl’s “objectively” means, see the article “Symmetry and Symmetry  Breaking,” by Katherine Brading and Elena Castellani, in the Stanford Encyclopedia of Philosophy:

“The old and natural idea that what is objective should not depend upon the particular perspective under which it is taken into consideration is thus reformulated in the following group-theoretical terms: what is objective is what is invariant with respect to the transformation group of reference frames, or, quoting Hermann Weyl (1952, p. 132), ‘objectivity means invariance with respect to the group of automorphisms [of space-time].‘[22]

22. The significance of the notion of invariance and its group-theoretic treatment for the issue of objectivity is explored in Born (1953), for example. For more recent discussions see Kosso (2003) and Earman (2002, Sections 6 and 7).


Born, M., 1953, “Physical Reality,” Philosophical Quarterly, 3, 139-149. Reprinted in E. Castellani (ed.), Interpreting Bodies: Classical and Quantum Objects in Modern Physics, Princeton, NJ: Princeton University Press, 1998, pp. 155-167.

Earman, J., 2002, “Laws, Symmetry, and Symmetry Breaking; Invariance, Conservation Principles, and Objectivity,’ PSA 2002, Proceedings of the Biennial Meeting of the Philosophy of Science Association 2002, forthcoming [Abstract/Preprint available online]

Kosso, P., 2003, “Symmetry, objectivity, and design,” in K. Brading and E. Castellani (eds.), Symmetries in Physics: Philosophical Reflections, Cambridge: Cambridge University Press, pp. 410-421.

Weyl, H., 1952, Symmetry, Princeton, NJ: Princeton University Press.

See also

Archives Henri Poincaré (research unit UMR 7117, at Université Nancy 2, of the CNRS)–

Minkowski, Mathematicians, and the Mathematical Theory of Relativity,” by Scott Walter, in The Expanding Worlds of General Relativity (Einstein Studies, volume 7), H. Goenner, J. Renn, J. Ritter and T. Sauer, editors, Boston/Basel: Birkhäuser, 1999, pp. 45-86–

“Developing his ideas before Göttingen mathematicians in April 1909, Klein pointed out that the new theory based on the Lorentz group (which he preferred to call ‘Invariantentheorie’) could have come from pure mathematics (1910: 19). He felt that the new theory was anticipated by the ideas on geometry and groups that he had introduced in 1872, otherwise known as the Erlangen program (see Gray 1989: 229).”


Gray, Jeremy J. (1989). Ideas of Space. 2d ed. Oxford: Oxford University Press.

Klein, Felix. (1910). “Über die geometrischen Grundlagen der Lorentzgruppe.” Jahresbericht der deutschen Mathematiker-Vereinigung 19: 281-300. [Reprinted: Physikalische Zeitschrift 12 (1911): 17-27].

Related material: A pathetically garbled version of the above concepts was published in 2001 by Harvard University Press.  See Invariances: The Structure of the Objective World, by Robert Nozick.

Sunday, February 18, 2007

Sunday February 18, 2007

Filed under: General — m759 @ 10:30 AM
Further Adventures
in Harvard Iconology

The image “http://www.log24.com/log/pix06A/061001-Langdon2.jpg” cannot be displayed, because it contains errors.

The next novel starring
Robert Langdon, Harvard author
of "the renowned collegiate
texbook Religious Iconology"
is said to be titled
The Solomon Key.

Related material–

The Harvard Crimson online:

Fishburne To Receive Honors at Cultural Rhythms
Acclaimed actor and humanitarian chosen as the Harvard Foundation's Artist of the Year

Friday, February 16, 2007
9:37 PM

Tony and Emmy Award-winning actor Laurence Fishburne will take the stage later this month as the 2007 Artist of the Year during the 22nd annual Cultural Rhythms festival, the Harvard Foundation for Intercultural and Race Relations announced Friday afternoon.

The image “http://www.log24.com/log/pix07/070218-Morpheus.jpg” cannot be displayed, because it contains errors.
as Morpheus

"Metaphor for Morphean morphosis,
Dreams that wake, transform, and die,
Calm and lucid this psychosis,
Joyce's nightmare in Escher's eye….

Dabo claves regni caelorum.  By silent shore
Ripples spread from castle rock.  The metaphor
For metamorphosis no keys unlock."

— Steven H. Cullinane,
  November 7, 1986,

More on metamorphosis–

Cat's Yarn
(Log24, June 20, 2006):

"The end is where
   we start from."

T. S. Eliot

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Garfield 2003-06-24

See also:

Zen Koan
  Blue Dream.

Update of 5:24 PM
Feb. 18, 2007:

A Xanga footprint from France
this afternoon (3:47 PM EST)
indicates that someone there
may be interested in the above
poem's "claves regni caelorum."

The visitor from France viewed
"Windmills" (Nov. 15, 2005).
Material related to that entry
may be found in various places
at Log24.com.  See particularly
"Shine On, Hermann Weyl," and
entries for Women's History
last year that include
"Christ at the Lapin Agile."

Sunday February 18, 2007

Filed under: General — m759 @ 2:00 AM
Lady of Situations

The image “http://www.log24.com/log/pix07/070216-Eyes2.jpg” cannot be displayed, because it contains errors.

“Many dreams have been brought to your doorstep
They just lie there and they die there
Are you warm, are you real, Mona Lisa?
Or just a cold and lonely lovely work of art?”

Ray Evans, who died at 92
   on Thursday, Feb. 15, 2007

For the source of the above illustration, see “Dear Dan Brown, All Eyes Are on You,” a New York Times piece linked to in a Log24 entry from the day after Evans died. That entry concludes as follows:

“And what the dead had no speech for, when living, they can tell you, being dead: the communication of the dead is tongued with fire beyond the language of the living.”

— T. S. Eliot, Four Quartets

Saturday, February 17, 2007

Saturday February 17, 2007

Filed under: General — m759 @ 9:00 AM

Zen Mind, Empty Mind


A mathematician hopes for more exciting vulgarizations of his subject–

“I would hope that clever writers might point out how mathematics is altering our lifestyles and do it in a manner that would not lead Garfield the Cat to say ‘ho hum.'”

— Philip J. Davis, “The Media and Mathematics Look at Each Other” (pdf), Notices of the American Mathematical Society, March 2006

Part I:

“Our mathematical skills are assumed to derive from a special ‘mental vacuum state,’ whose origin is explained on the basis of anthropic and biological arguments, taking into account the need for the informational processes associated with such a state to be of a life-supporting character.  ESP is then explained in terms of shared ‘thought bubbles’ generated by the participants out of the mental vacuum state.”

— Nobel laureate Brian D. Josephson, Department of Physics, University of Cambridge, “String Theory, Universal Mind, and the Paranormal” (Dec. 2003)

Part II:

The image “http://www.log24.com/log/pix07/070217-Garfield2.jpg” cannot be displayed, because it contains errors.

Thanks to “Q” at Peter Woit’s weblog
for the link to Josephson.

Friday, February 16, 2007

Friday February 16, 2007

Filed under: General — Tags: — m759 @ 6:16 AM

The Judas Seat

Janet Maslin in today’s New York Times:

“The much-borrowed Brown formula involves some very specific things. The name of a great artist, artifact or historical figure must be in the book’s story, not to mention on its cover. The narrative must start in the present day with a bizarre killing, then use that killing as a reason to investigate the past. And the past must yield a secret so big, so stunning, so saber-rattling that all of civilization may be changed by it. Probably not for the better.

This formula is neatly summarized….”

Cover illustration
The Judas Seat:
The Narrative:

The Secret:

Part I

“Little ‘Jack’ Horner was actually Thomas Horner, steward to the Abbot of Glastonbury during the reign of King Henry VIII…. Always keen to raise fresh funds, Henry had shown a interest in Glastonbury (and other abbeys). Hoping to appease the royal appetite, the nervous Abbot, Richard Whiting, allegedly sent Thomas Horner to the King with a special gift. This was a pie containing the title deeds to twelve manor houses in the hope that these would deflect the King from acquiring Glastonbury Abbey. On his way to London, the not so loyal courier Horner apparently stuck his thumb into the pie and extracted the deeds for Mells Manor, a plum piece of real estate. The attempted bribe failed and the dissolution of the monasteries (including Glastonbury) went ahead from 1536 to 1540. Richard Whiting was subsequently executed, but the Horner family kept the house, so the moral of this one is: treachery and greed pay off, but bribery is a bad idea.” –Chris Roberts, Heavy Words Lightly Thrown: The Reason Behind the Rhyme

Part II

“The Grail Table has thirteen seats, one of which is kept vacant in memory of Judas Iscariot who betrayed Christ.” —Symbolism of King Arthur’s Round Table

“In medieval romance, the grail was said to have been brought to Glastonbury in Britain by Joseph of Arimathea and his followers. In the time of Arthur, the quest for the Grail was the highest spiritual pursuit.” —The Camelot Project

Part III

The Log24 entry
for the date–
February 13, 2007–
of the above Bible scholar’s death,

and the three entries preceding it:

“And what the dead had no speech for, when living,
they can tell you, being dead:
the communication of the dead is tongued with fire
beyond the language of the living.”

— T. S. Eliot, Four Quartets

Thursday, February 15, 2007

Thursday February 15, 2007

Filed under: General — m759 @ 6:25 AM

From “Music and Lyrics” (2007)

Yesterday, Valentine’s Day, Hollywood released a romantic comedy, “Music and Lyrics,” based on a fictional reality-TV show called “Battle of the 80’s Has-Beens.”

This, along with the Feb. 13 Log24 entry touching on both pop science and pop music, and the fact that today is the anniversary of the 1988 death of physicist Richard Feynman, suggests the following exercise:

Compare and contrast the lives and works of Feynman (May 11, 1918 – Feb. 15, 1988) and the late Carl Sagan (Nov. 9, 1934 – Dec. 20, 1996).

(Being dead, both are, in a sense, has-beens, and both were popular in the 1980’s.)

I personally regard Feynman as one of science’s saints, and Sagan as, shall we say, a non-saint.  For some related reflections on pop science and pop music, see the five Log24 entries ending on Michaelmas 2002.  And then there is popcorn–

A 1980’s Hollywood ending
that Feynman may have liked:

The image “http://www.log24.com/log/pix07/070215-Popcorn.jpg” cannot be displayed, because it contains errors.

Click on picture for details.

 “… slow-motion romp
   through the popcorn…
Tears for Fears’
‘Everybody Wants to
Rule the World’ ramps up
on the soundtrack….”

Tuesday, February 13, 2007

Tuesday February 13, 2007

Filed under: General — Tags: — m759 @ 5:24 AM
Modern Times
vs. City Lights

Bob Dylan Wins a Folk Grammy

"Modern Times, his first album since Love and Theft, debuted at No. 1
on the US pop charts last September. At 65, Dylan became the oldest
living person to achieve this feat."  –New Zealand Herald, Feb. 12

From an entry of 
October 29, 2004:

"Each epoch has its singer."
Jack London,
    Oakland, California, 1901

"Anything but the void. And so we keep hoping to luck into a winning combination, to tap into a subtle harmony, trying like lock pickers to negotiate a compromise with the 'mystery tramp,' as Bob Dylan put it…."
— Dennis Overbye,
   Quantum Baseball,
   New York Times,
   Oct.  26, 2004

"You said you'd never compromise
With the mystery tramp,
    but now you realize
He's not selling any alibis
As you stare into
    the vacuum of his eyes
And ask him do you want to
    make a deal?"
— Bob Dylan,
    Like a Rolling Stone

"Climbing up on 
Solsbury Hill"

In today's meditation for
the Church of Peter Gabriel,
Dennis Overbye plays
the role of Jack Horner.

Jack Horner with Christmas pie

(See Overbye on Sagan in today's
New York Times, Sagan on Pi,
and Pi Day at Harvard.)

For more on Jack Horner, see
The Rise and Fall
of Popular Music
by Donald Clarke,
Chapter One.

For two contrasting approaches
to popular music, see two artists
whose birthdays are today:

Peter Hook and Peter Gabriel

In other Grammy news–
At the end of Sunday's awards,

"Scarlett Johansson and Don Henley
 put themselves in the pole position
to star in a remake of 'Adam's Rib'
with the following exchange:

Henley: So you're recording
your first album?

Johansson: Yeah. Do you
have any advice for me?

Henley: No."

David Marchese, Salon.com

"Her wall is filled with pictures,
she gets 'em one by one….

Monday, February 12, 2007

Monday February 12, 2007

Filed under: General — m759 @ 5:24 AM
Tongued with Fire

“The communication
of the dead is tongued with fire
   beyond the language of the living.”

— T. S. Eliot, Four Quartets

Christina Aguilera singing James Brown song at Grammys, 2007
Photo by Mark J. Terrill / AP

Above: Christina Aguilera performs “It’s a Man’s Man’s Man’s World” in tribute to the late James Brown during the Grammy Awards in Los Angeles on Sunday, February 11, 2007.

This morning’s New York Times:

Woman in the News

Drew Gilpin Faust:
Coming of Age in a Changed World

Published: February 12, 2007

CAMBRIDGE, Mass., Feb. 11– Recalling her coming of age as the only girl in a privileged, tradition-bound family in Virginia horse country, Drew Gilpin Faust, 59, has often spoken of her “continued confrontations” with her mother “about the requirements of what she usually called femininity.” Her mother, Catharine, she has said, told her repeatedly, “It’s a man’s world, sweetie, and the sooner you learn that the better off you’ll be.”….

… Asked Sunday whether her appointment signified the end of sex inequities at the university, Dr. Faust said: “Of course not. There is a lot of work still to be done, especially in the sciences.”

What would her mother, who never went to college and died in 1966, have to say about her appointment? “I’ve often thought about that,” she said. “I’ve had dialogues with my dead mother over the 40 years since she died.”

Then she added with a rueful smile, “I think in many ways that comment– ‘It’s a man’s world, sweetie’– was a bitter comment from a woman of a generation who didn’t have the kind of choices my generation of women had.”

“But it wouldn’t mean  
nothin’ … nothin’ …
without a woman or a girl.”

James Brown,
who died last year
on Christmas Day

James Brown

Sunday, February 11, 2007

Sunday February 11, 2007

Filed under: General — m759 @ 11:00 AM

“And what the dead had
   no speech for, when living,
They can tell you, being dead:
   the communication
Of the dead is tongued with fire
   beyond the language of the living.”

— T. S. Eliot, Four Quartets

Sunday February 11, 2007

Filed under: General,Geometry — m759 @ 2:56 AM
George Sadek, 78,
Graphic Design Educator,

The image “http://www.log24.com/log/pix07/070211-GeorgeSadek.jpg” cannot be displayed, because it contains errors.

Sadek died on Feb. 5.

Related material:

“Harvard Design” (Feb. 6),

“Geometry and Death”
(entries of December 2006)

“Release Date”
in “Immortal Diamond”
(Feb. 5 four years ago).

The design over Sadek’s
head is a St. Bridget’s cross.

(See the “Release Date”
link above.)

Saturday, February 10, 2007

Saturday February 10, 2007

Filed under: General — m759 @ 10:00 AM

Willard Van Orman Quine on the title of his book From A Logical Point of View (Harvard University Press): “Henry Aiken and I were with our wives in a Greenwich Village nightspot when I told him of the plan, and Harry Belafonte had just sung the calypso ‘From a logical point of view.’ Henry noted that this would do nicely as a title for the volume, and so it did.”

Come, Mister Tally Man…

Catherine O'Hara in Beetlejuice

From this morning,
eight consecutive Xanga
footprints from Great Britain:

/524459252/item.html newsdor.com 8:25 AM
/490604390/item.html newsdor.com 8:25 AM
/426273644/item.html newsdor.com 8:25 AM
/569157082/annals-… newsdor.com 8:25 AM
/524081776/item.html newsdor.com 8:25 AM
/446066083/item.html newsdor.com 8:24 AM
/522299668/item.html newsdor.com 8:24 AM
/447354678/item.html newsdor.com 8:24 AM

Saturday February 10, 2007

Filed under: General — m759 @ 2:00 AM
The Graduate

From this morning’s
New York Times:

Classmates: Actor Ian Richardson and writer Art Buchwald

The actor Ian Richardson

Richardson died yesterday,
Friday, Feb. 9, 2007.

He seems well qualified
to be patron saint of
  the “icily sardonic.”

“… it was his portrayal of the alluringly evil Francis Urquhart, a scheming, icily sardonic Tory member of Parliament, that finally made him a household name in Britain and a celebrity abroad.”

Campbell Robertson in today’s New York Times

Related material: Log24 yesterday, the date of Richardson’s death.

Friday, February 9, 2007

Friday February 9, 2007

Filed under: General,Geometry — m759 @ 3:24 PM
The Romance
of Mathematics

The image “http://www.log24.com/log/pix07/070209-Cupid2.gif” cannot be displayed, because it contains errors.

On teachers of “core mathematics classes for non-majors, mathematics appreciation courses, and other lower level courses”:

“We are accustomed to being marginalized by society, our political leaders, and even our college and university administrations who often fail to see the scholarship involved in teaching. But how dare the Notices ignore us?”

— Complaint in the March 2007 Notices of the American Mathematical Society by “Julian F. Fleron, Ph.D., Professor of Mathematics, Westfield State College”

Let us examine Fleron’s alleged scholarship:

“Before each of my classes I put a quote on the board. The quote is either related to the mathematics we are studying, related to mathematics more generally, or related to learning and education. Student response has been tremendous, and I have found it to be very beneficial.” —Julian Fleron

Fleron offers us, without specifying an exact source, the following quotation:

“Mighty is geometry; joined with art, resistless. Euripides.

A search for the source leads us to a quotation from 1914, a time when teaching did sometimes involve scholarship:

“1568. Mighty are numbers, joined with art resistless. EURIPIDES. Hecuba, Line 884.”

Memorabilia Mathematica, by Robert Edouard Moritz, The Macmillan Company, 1914

But even in 1914, the scholarship, if one can call it that, was misleading. The 1914 quotation (which at least refers accurately to numbers, not geometry) is blatantly taken out of context to imply a connection with the mathematical art of number theory (as practiced by, say, G. H. Hardy) that is certainly not found in Euripides. The details:

HECUBA Sheltered beneath these tents is a host of Trojan women.

AGAMEMNON Dost mean the captives, the booty of the Hellenes?

HECUBA With their help will I punish my murderous foe.

AGAMEMNON How are women to master men?

HECUBA Numbers are a fearful thing, and joined to craft a desperate foe.

AGAMEMNON True; still I have a mean opinion of the female race.

This dialogue may have some relevance to today’s rumored selection at Harvard of a woman (Drew Gilpin Faust as Hecuba) to replace a man (Larry Summers as Agamemnon) in the president’s office. The dialogue’s only relevance to mathematics is in its reference to the perennial conflict between the sexes. Perhaps that conflict will serve to illustrate the title given by the Notices to Fleron’s complaint: “Teaching the Romance of Mathematics.”

Wednesday, February 7, 2007

Wednesday February 7, 2007

Filed under: General — m759 @ 3:00 AM

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“Times when I know you’ll be lonesome,
   times when I know you’ll be sad
Don’t let temptation surround you,
   don’t let the blues make you bad”

— “We’ll Be Together Again,”
    Frankie Laine,
    March 30, 1913 —
    February 6, 2007

Tuesday, February 6, 2007

Tuesday February 6, 2007

Filed under: General,Geometry — Tags: — m759 @ 8:00 AM
The Poetics of Space

The title is from Bachelard.
I prefer Stevens:

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.
It is the rock where tranquil must adduce
Its tranquil self, the main of things, the mind,

The starting point of the human and the end,
That in which space itself is contained, the gate
To the enclosure, day, the things illumined

By day, night and that which night illumines,
Night and its midnight-minting fragrances,
Night's hymn of the rock, as in a vivid sleep.

— Wallace Stevens,
   "The Rock," 1954

Joan Ockman in Harvard Design Magazine (Fall 1998):

"'We are far removed from any reference to simple geometrical forms,' Bachelard wrote…."

No, we are not. See Log24, Christmas 2005: 

Compare and contrast:

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


(Click on pictures for details.)

More on Bachelard from Harvard Design Magazine:

"The project of discerning a loi des quatre éléments would preoccupy him until his death…."

For such a loi, see Theme and Variations and…

The image “http://www.log24.com/log/pix07/070206-Elements.gif” cannot be displayed, because it contains errors.

(Click on design for details.)

Thought for Today:
"If you can talk brilliantly
about a problem, it can create
the consoling illusion that
it has been mastered."
— Stanley Kubrick, American
movie director (1928-1999).

(AP, "Today in History,"
February 6, 2007)

Sunday, February 4, 2007

Sunday February 4, 2007

Filed under: General — m759 @ 9:00 AM

Seven consecutive Xanga footprints
this morning:

United States Weblog 2/4/2007 4:31 AM
United States Weblog  2/4/2007 4:32 AM
United States Weblog 2/4/2007 4:32 AM
United States Weblog  2/4/2007 4:32 AM
United States Weblog  2/4/2007 4:32 AM
United States Weblog  2/4/2007 4:32 AM
United States Weblog  2/4/2007 4:32 AM

Related material:
Footprints of Dec. 13, 2006

Saturday, February 3, 2007

Saturday February 3, 2007

Filed under: General — m759 @ 11:07 PM
Catholic Schools Week,

Jan. 28 – Feb. 3, 2007,

 PA Lottery 2/3/07: Day 373, Evening 401

For 373, see

For 401, see 4/01:
April 1 at Noon.

“Feel lucky? 
Well, do you?”

Saturday February 3, 2007

Filed under: General — m759 @ 1:00 PM
The church bells
all were broken.

— Don McLean 

“Emergentism claims that a whole is ‘something more than the sum of its parts,’ or has properties that cannot be understood in terms of the properties of the parts.”

— Michael Silberstein, “Reduction, Emergence and Explanation” (pdf), Chapter Five in The Blackwell Guide to the Philosophy of Science

“The whole is greater than the sum of its parts, no matter what you name it.”

— Alfred Bester, Chapter Eight, “The Search,” in The Deceivers

Saturday February 3, 2007

Filed under: General — m759 @ 2:45 AM


Friday, February 2, 2007

Friday February 2, 2007

Filed under: General — m759 @ 7:59 AM

Friday February 2, 2007

Filed under: General — m759 @ 7:11 AM

The Night Watch

For Catholic Schools Week
(continued from last year)–

Last night’s Log24 Xanga
footprints from Poland:

Poland 2/2/07 1:29 AM
2/20/06: The Past Revisited
(with link to online text of
Many Dimensions, by Charles Williams)

Poland 2/2/07 2:38 AM
1/15/06 Inscape
(the mathematical concept, with
square and “star” diagrams)

Poland 2/2/07 3:30 AM
2/8/05 The Equation
(Russell Crowe as John Nash
with “star” diagram from a
Princeton lecture by Langlands)

Poland 2/2/07 4:31 AM
8/29/06 Hollywood Birthday
(with link to online text of
Plato on the Human Paradox,
by a Fordham Jesuit)

Poland 2/2/07 4:43 AM
8/30/06 Seven
(Harvard, the etymology of the
word “experience,” and the
Catholic funeral of a professor’s
23-year-old daughter)

Poland 2/2/07 4:56 AM
12/19/05 Quarter to Three (cont.)

(remarks on permutation groups
for the birthday of Helmut Wielandt)

Poland 2/2/07 5:03 AM
5/29/06 For JFK’s Birthday
(The Call Girls revisited)

Poland 2/2/07 5:32 AM
8/24/06 Beginnings
(Nasar in The New Yorker and
T. S. Eliot in Log24, both on the 2006
Beijing String Theory conference)

Poland 2/2/07 5:46 AM
2/22/06 In the Details
(Harvard’s president resigns,
with accompanying “rosebud”)

Friday February 2, 2007

Filed under: General — m759 @ 6:00 AM

Then put your little hand in mine….

Friday February 2, 2007

Filed under: General — m759 @ 5:00 AM

A way a lone a last a loved a long the

Thursday, February 1, 2007

Thursday February 1, 2007

Filed under: General — Tags: — m759 @ 7:59 AM

The image “http://www.log24.com/theory/images/GF64-63cycleA495.gif” cannot be displayed, because it contains errors.

The above is from
Feb. 15, 2006.

"I don't believe in an afterlife, so I think this is it, and I'm trying to spend my time as best I can, and I'm trying to spend my time so I'm proud of what I've done, and I try not to do any things that I'm not proud of."

Jim Gray, 2002 interview (pdf)

Commencement Address (doc)
to Computer Science Division,
College of Letters and Science,
University of California, Berkeley,
by Jim Gray,
May 25, 2003:

"I was part of Berkeley's class of 1965. Things have changed a lot since then….

So, what's that got to do with you? Well, there is going to be MORE change…. Indeed, change is accelerating– Vernor Vinge suggests we are approaching singularities when social, scientific and economic change are so rapid that we cannot imagine what will happen next.  These futurists predict humanity will become post-human. Now, THAT! is change– a lot more than I have seen.

If it happens, the singularity will happen in your lifetime– and indeed, you are likely to make it happen."


I Ching, Hexagram 39

For other singular
sci-fi tales, click on
the above hexagram.

More from Gray's speech:

"I am an optimist. Science is a Faustian bargain– and I am betting on mankind muddling through. I grew up under the threat of atomic war; we've avoided that so far. Information Technology is a Faustian bargain. I am optimistic that we can have the good parts and protect ourselves from the worst part– but I am counting on your help in that."

"Not fare well,
But fare forward, voyagers."

— T. S. Eliot,
"The Dry Salvages"

Thursday February 1, 2007

Filed under: General — m759 @ 2:00 AM
Turing Award
for Jim Gray

The image “http://www.log24.com/log/pix07/070201-JimGray.jpg” cannot be displayed, because it contains errors.


Vast search off coast
for data wizard

Gray was last heard from on
  Sunday, Jan. 28, at about 10 AM.
His sailboat was reported missing
on Sunday evening.

He is known for, among other things,
work on the SkyServer program
and on the data cube operator.

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