Monday, November 20, 2006

Monday November 20, 2006

Filed under: General — Tags: — m759 @ 7:20 PM


Yesterday's link to a Log24 entry for the Feast of the Triumph of the Cross led to the following figure:

Primitive roots modulo 17
(Based on Weyl's Symmetry)

Today, an entry in the The New Criterion's weblog tells of Hilton Kramer's new collection of essays on art, The Triumph of Modernism.

From a Booklist review:

Kramer "celebrates the revelations of modern art, defining modernism as nothing less than 'the discipline of truthfulness, the rigor of honesty.'"

Further background: Kramer opposes

"willed frivolity and politicized vulgarization as fashionable enemies of high culture as represented in the recent past by the integrity of modernism."


— "25 Years of The New Criterion"

Perhaps Kramer would agree that such integrity is exemplified by "Two Giants" of modernism described by Roberta Smith in The New York Times recently (Nov. 3– birthdate of A. B. Coble, an artist of a different kind). She is reviewing an exhibit, ''Albers and Moholy-Nagy: From the Bauhaus to the New World,'' that continues through Jan. 21 at the Whitney Museum of American Art,

945 Madison Avenue: '945' as an 'artist's signature'

Madison Avenue.

This instance of the number 945 as an "artists' signature" is perhaps more impressive than the instances cited in yesterday's Log24 entry, Signature.

Sunday, November 19, 2006

Sunday November 19, 2006

Filed under: General — m759 @ 2:02 PM


From AP’s “Today in History,” Nov. 19, 2006:

Today’s birthdays: … Actress-director Jodie Foster is 44….

Thought for Today: “My theology, briefly, is that the universe was dictated but not signed.” –[Attributed to] Christopher Morley, American author and journalist (1890-1957).

A different story: Carl Sagan, Contact, Chapter 24– “The Artist’s Signature.”

Yet another story:  The Pennsylvania lottery yesterday, November 18, 2006– mid-day 914, evening 945. For interpretations, see 9/14 (Feast of the Triumph of the Cross) and also the following “signature” (i.e., “denominator”):

The image “http://www.log24.com/log/pix06B/061119-Zeta6.jpg” cannot be displayed, because it contains errors.

Number theorists may prefer to
think of 945 as the smallest
odd abundant number
(Al-Baghdadi, ca. 980-1037).

Neither of these occurrences
 of 945 in mathematics seems
 particularly divine; perhaps there
are some other properties of
 this number that make it more
credible as a divine signature–
other, that is, than its occurrence
in a lottery just in time for
Jodie Foster’s birthday.

Thursday, March 10, 2005

Thursday March 10, 2005

Filed under: General — Tags: — m759 @ 5:31 PM
Final Arrangements

The image “http://www.log24.com/log/pix05/050310-Final3.jpg” cannot be displayed, because it contains errors.

Macalester College on Don Celender:
“An Art History prize fund
has been established in his name.
Contributions can be sent to
the Macalester Art Department.”

In today’s Art History competition,
Glenn Davis is, of course,
the first runner-up,
and is represented below
by the X.
(Hexagram 34,
The Power of the Great)

Art itself is represented
by the box.
(Hexagram 20,
Contemplation, View)

  Women’s History Month
is represented by
the X in a box.
(Hexagram 2,
  The Receptive)
The image “http://www.log24.com/log/pix05/050310-hex.jpg” cannot be displayed, because it contains errors.

The winner of the
Art History competition
is Jodie Foster, for
combining astrophysics
with interpretive dancing.

The image “http://www.log24.com/log/pix05/050310-Nell2.jpg” cannot be displayed, because it contains errors.

“… as in a great work of art, there is,
written small, the artist’s signature….
 Standing over humans, gods, and demons…
there is an intelligence that
antedates the universe.”

— Carl Sagan,  

“Dr. Kinsey, Dr. Arroway;
  Dr. Arroway, Dr. Kinsey.”

Tuesday, November 26, 2002

Tuesday November 26, 2002

Filed under: General — Tags: — m759 @ 10:23 AM

Dancing about Architecture

The title’s origin is obscure, but its immediate source is a weblog entry and ensuing comments: “Writing about music is like dancing about architecture.”

A related quote:

“At the still point, there the dance is.”

— T. S. Eliot, “Burnt Norton” in Four Quartets

“Eliot by his own admission took ‘the still point of the turning world’ in ‘Burnt Norton’ from the Fool in Williams’s The Greater Trumps.”

— Humphrey Carpenter, The Inklings (1978), Ballantine Books, 1981, page 106. Carpenter cites an “unpublished journal of Mary Trevelyan (in possession of the author).”

The following was written this morning as a comment on a weblog entry, but may stand on its own as a partial description of Eliot’s and Williams’s “dance.”

Three sermons on the Fool card, each related to Charles Williams’s novel The Greater Trumps:

To Play the Fool,
Games “Not Unlike Chesse,” and
Charles Williams and Inklings Links.

“Here is the Church,
Here is the steeple,
Open the door and see all the People.”

For some architecture that may or may not be worth dancing about, see the illustrations to Simone Weil’s remarks in my note of November 25, 2002, “The Artist’s Signature.”

Monday, November 25, 2002

Monday November 25, 2002

Filed under: General,Geometry — m759 @ 1:00 PM

Swashbucklers and Misfits

There are two theories of truth, according to a a book on the history of geometry —

The “Story Theory” and the “Diamond Theory.” 

For those who prefer the story theory…

From a review by Brian Hayes of A Beautiful Mind:

“Mathematical genius is rare enough. Cloaked in madness, or wrapped in serious eccentricity, it’s the stuff legends are made of.

There are brilliant and productive mathematicians who go to the office from nine to five, play tennis on the weekend, and worry about fixing the gearbox in the Volvo. Not many of them become the subjects of popular biographies. Instead we read about the great swashbucklers and misfits of mathematics, whose stories combine genius with high romance or eccentricity.”

Russell Crowe,


Hollywood has recently given us a mathematical Russell Crowe.  For a somewhat tougher sell, Marilyn Monroe as a mathematician, see “Insignificance,” 1985: “Marilyn Monroe on her hands and knees explains the theory of relativity to Albert Einstein.”  

For a combination of misfit and swashbuckler in one Holy Name, see today’s earlier note, “The Artist’s Signature.”

See also my note of October 4, 2002, on Michelangelo, and the description of “the face of God” in this review.

Monday November 25, 2002

Filed under: General — m759 @ 11:32 AM

The Artist’s Signature

This title is taken from the final chapter of Carl Sagan’s novel Contact.

“There might be a game in which paper figures were put together to form a story, or at any rate were somehow assembled. The materials might be collected and stored in a scrap-book, full of pictures and anecdotes. The child might then take various bits from the scrap-book to put into the construction; and he might take a considerable picture because it had something in it which he wanted and he might just include the rest because it was there.”

— Ludwig Wittgenstein, Lectures and Conversations on Aesthetics, Psychology and Religious Belief

“Not games. Puzzles. Big difference. That’s a whole other matter. All art — symphonies, architecture, novels — it’s all puzzles. The fitting together of notes, the fitting together of words have by their very nature a puzzle aspect. It’s the creation of form out of chaos. And I believe in form.”

— Stephen Sondheim, in Stephen Schiff, Deconstructing Sondheim,” The New Yorker, March 8, 1993, p. 76

Vesica Piscis

Arch at
Glastonbury Tor

“All goods in this world, all beauties, all truths, are diverse and partial aspects of one unique good. Therefore they are goods which need to be ranged in order. Puzzle games are an image of this operation. Taken all together, viewed from the right point and rightly related, they make an architecture. Through this architecture the unique good, which cannot be grasped, becomes apprehensible. All architecture is a symbol of this, an image of this. The entire universe is nothing but a great metaphor.”

Simone Weil, sister of Princeton mathematician André Weil, First and Last Notebooks, p. 98

This passage from Weil is quoted in
Gateway to God,
p. 42, paperback, fourth impression,
printed in Glasgow in 1982 by
Fontana Books

“He would leave enigmatic messages on blackboards,
signed Ya Ya Fontana.”

Brian Hayes on John Nash,
The Sciences magazine, Sept.-Oct., 1998

“I have a friend who is a Chief of the Aniunkwia (Cherokee) people and I asked him the name of the Creator in which
he replied… Ya Ho Wah. This is also how it is spoken in Hebrew. In my native language it is spoken
Ya Ya*,
which is also what Moses was told
at the ‘Burning Bush’ incident.”

“Tank” (of Taino ancestry), Bronx, NY, Wednesday, April 17, 2002

From a website reviewing books published by

Master and Commander (Patrick O’Brian)”

1/17/02: NEW YORK (Variety) – Russell Crowe is negotiating to star in 20th Century Fox’s “Master and Commander,” the Peter Weir-directed adaptation of the Patrick O’Brian book series.


*For another religious interpretation of this phrase, see my note of October 4, 2002, “The Agony and the Ya-Ya.”

Sunday, September 29, 2002

Sunday September 29, 2002

Filed under: General — m759 @ 10:18 PM

New from Miracle Pictures

Pi in the Sky
for Michaelmas 2002

“Fear not, maiden, your prayer is heard.
Michael am I, guardian of the highest Word.”

A Michaelmas Play

Contact, by Carl Sagan:

Chapter 1 – Transcendental Numbers

  In the seventh grade they were studying “pi.” It was a Greek letter that looked like the architecture at Stonehenge, in England: two vertical pillars with a crossbar at the top. If you measured the circumference of a circle and then divided it by the diameter of the circle, that was pi. At home, Ellie took the top of a mayonnaise jar, wrapped a string around it, straightened the string out, and with a ruler measured the circle’s circumference. She did the same with the diameter, and by long division divided the one number by the other. She got 3.21. That seemed simple enough.

  The next day the teacher, Mr. Weisbrod, said that pi was about 22/7, about 3.1416. But actually, if you wanted to be exact, it was a decimal that went on and on forever without repeating the pattern of numbers. Forever, Ellie thought. She raised her hand. It was the beginning of the school year and she had not asked any questions in this class.
  “How could anybody know that the decimals go on and on forever?”
  “That’s just the way it is,” said the teacher with some asperity.
  “But why? How do you know? How can you count decimals forever?”
  “Miss Arroway” – he was consulting his class list – “this is a stupid question. You’re wasting the class’s time.”

  No one had ever called Ellie stupid before and she found herself bursting into tears….

  After school she bicycled to the library at the nearby college to look through books on mathematics. As nearly as she could figure out from what she read, her question wasn’t all that stupid. According to the Bible, the ancient Hebrews had apparently thought that pi was exactly equal to three. The Greeks and Romans, who knew lots of things about mathematics, had no idea that the digits in pi went on forever without repeating. It was a fact that had been discovered only about 250 years ago. How was she expected to know if she couldn’t ask questions? But Mr. Weisbrod had been right about the first few digits. Pi wasn’t 3.21. Maybe the mayonnaise lid had been a little squashed, not a perfect circle. Or maybe she’d been sloppy in measuring the string. Even if she’d been much more careful, though, they couldn’t expect her to measure an infinite number of decimals.

  There was another possibility, though. You could calculate pi as accurately as you wanted. If you knew something called calculus, you could prove formulas for pi that would let you calculate it to as many decimals as you had time for. The book listed formulas for pi divided by four. Some of them she couldn’t understand at all. But there were some that dazzled her: pi/4, the book said, was the same as 1 – 1/3 + 1/5 – 1/7 + …, with the fractions continuing on forever. Quickly she tried to work it out, adding and subtracting the fractions alternately. The sum would bounce from being bigger than pi/4 to being smaller than pi/4, but after a while you could see that this series of numbers was on a beeline for the right answer. You could never get there exactly, but you could get as close as you wanted if you were very patient. It seemed to her

a miracle

 Cartoon by S.Harris

that the shape of every circle in the world was connected with this series of fractions. How could circles know about fractions? She was determined to learn


  The book said something else: pi was called a “transcendental” number. There was no equation with ordinary numbers in it that could give you pi unless it was infinitely long. She had already taught herself a little algebra and understood what this meant. And pi wasn’t the only transcendental number. In fact there was an infinity of transcendental numbers. More than that, there were infinitely more transcendental numbers that ordinary numbers, even though pi was the only one of them she had ever heard of. In more ways than one, pi was tied to infinity.

  She had caught a glimpse of something majestic.

Chapter 24 – The Artist’s Signature

  The anomaly showed up most starkly in Base 2 arithmetic, where it could be written out entirely as zeros and ones. Her program reassembled the digits into a square raster, an equal number across and down. Hiding in the alternating patterns of digits, deep inside the transcendental number, was a perfect circle, its form traced out by unities in a field of noughts.

  The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover

a miracle

— another circle, drawn kilometers downstream of the decimal point. There would be richer messages farther in. It doesn’t matter what you look like, or what you’re made of, or where you come from. As long as you live in this universe, and have a modest talent for mathematics, sooner or later you’ll find it. It’s already here. It’s inside everything. You don’t have to leave your planet to find it. In the fabric of space and in the nature of matter, as in a great work of art, there is, written small, the artist’s signature. Standing over humans, gods, and demons… there is an intelligence that antedates the universe. The circle had closed. She found what she had been searching for.

Song lyric not in Sagan’s book:

Will the circle be unbroken
by and by, Lord, by and by?
Is a better home a-waitin’
in the sky, Lord, in the sky?

“Contact,” the film: 


Columbia 37669

Date Issued:





Can The Circle Be Unbroken


Carter Family

Recording Date:

May 6, 1935



Music courtesy of honkingduck.com.
For bluegrass midi version, click here.

The above conclusion to Sagan’s book is perhaps the stupidest thing by an alleged scientist that I have ever read.  As a partial antidote, I offer the following.

Today’s birthday: Stanley Kramer, director of “On the Beach.”

From an introduction to a recording of the famous Joe Hill song about Pie in the Sky:

“They used a shill to build a crowd… You know, a carny shill.”


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