Log24

Tuesday, April 14, 2020

Confluence, or:

Filed under: General — Tags: — m759 @ 7:21 pm

Church Diamond   Continued

The above article leads to remarks by Stephen Wolfram published today :

See also “Invariance” as the title of the previous post  here.

Wednesday, September 18, 2019

The Siegfried Line

Filed under: General — m759 @ 9:01 pm

See also this  journal on the above date (Jan. 27, 2012).

Backstory:  Search this journal for sciencenews.

Saturday, February 28, 2015

Recycled Religion

Filed under: General — Tags: , — m759 @ 3:16 pm

The previous post's Kirkridge link leads to
a mention of religious philosopher Parker J. Palmer.

From an Utne Reader  page on Palmer:

See also Theodore Sturgeon's 1949 story "What Dead Men Tell"—

"… He’d read about it in a magazine or somewhere.
He took a strip of scrap film about eighteen
inches long and put the ends together. He turned
one end over and spliced ’em. Now, if you trace
that strip, or mark it with a grease pencil, right up
the center, you find that the doggone thing only
has one side!”
The doctor nodded, and the girl said:
“A Möbius strip.”
“That what they call it?” said Hulon. “Well, I figured
this corridor must be something like that. On that
strip, a single continuous line touched both sides.
All I had to do was figure out an object built so that
a continuous line would cover all three of three sides,
and I’d have it. So I sat down and thought it out…."

— and the following mathematical illustration —

Sunday, July 23, 2006

Sunday July 23, 2006

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

Dance of the Numbers, continued:

Partitions

Freeman Dyson on the role of the “crank” in the theory of partitions:

“‘Each step in the story is a work of art,’ Dyson says, ‘and the story as a whole is a sequence of episodes of rare beauty, a drama built out of nothing but numbers and imagination.'”

Erica Klarreich in
    Science News Online, week of
    June 18, 2005, quoted in
   “In Honor of Freeman Dyson’s Birthday:
    Dance of the Numbers
    (Log24, Dec. 15, 2005)

Paraphrase of Freeman Dyson’s remarks in The New York Review of Books, issue dated May 28, 1998:

“Theology is about words; science is about things.

“What is 256 about?”
Reply to Freeman Dyson,
    (May 15, 1998)

A partial answer to that rhetorical question: 256 is the cardinality of the power set of an 8-set.

For the role played by 8-sets and by 23 (today’s date) in partitions of a different sort, see Geometry of the 4×4 Square.

Thursday, December 15, 2005

Thursday December 15, 2005

Filed under: General — m759 @ 3:48 pm
In honor of Freeman Dyson’s birthday:

Dance of the Numbers

“Mahlburg likens his approach to an analogous one for deciding whether a dance party has an even or odd number of attendees. Instead of counting all the participants, a quicker method is to see whether everyone has a partner—in effect making groups that are divisible by 2.

In Mahlburg’s work, the partition numbers play the role of the dance participants, and the crank splits them not into couples but into groups of a size divisible by the prime number in question. The total number of partitions is, therefore, also divisible by that prime.

Mahlburg’s work ‘has effectively written the final chapter on Ramanujan congruences,’ Ono says.

‘Each step in the story is a work of art,’ Dyson says, ‘and the story as a whole is a sequence of episodes of rare beauty, a drama built out of nothing but numbers and imagination.'”

Erica Klarreich in Science News Online, week of June 18, 2005

This would seem to meet the criteria set by Fritz Leiber for “a story that works.” (See previous entry.)  Whether the muse of dance (played in “Xanadu” by a granddaughter of physicist Max Born– see recent entries) has a role in the Dyson story is debatable.

Born Dec. 11, 1882, Breslau, Germany.

Died Jan. 5, 1970, Göttingen,
West Germany.

The image “http://www.log24.com/log/pix05B/051215-Born.jpg” cannot be displayed, because it contains errors.
Max Born

Those who prefer less abstract stories may enjoy a mythic tale by Robert Graves, Watch the North Wind Rise, or a Christian tale by George MacDonald, At the Back of the North Wind.

Related material:

“The valley spirit never dies. It’s named the mystic woman.”

Tao Te Ching

For an image of a particular
incarnation of the mystic woman
(whether as muse, as goddess,
or as the White Witch of Narnia,
I do not know) see Julie Taymor.

“Down in the valley,
 valley so low,
 hang your head over,
 hear the wind blow.”

Folk song

“Which is the sound of the land
Full of the same wind
That is blowing in
    the same bare place

For the listener,
    who listens in the snow,
And, nothing himself, beholds
Nothing that is not there
    and the nothing that is.”

Wallace Stevens

Monday, December 22, 2003

Monday December 22, 2003

Filed under: General — m759 @ 7:59 pm

California Earthquake
Rang Planet ‘Like a Bell’

By Peter Henderson

December 22, 2003 07:06 PM ET

LOS ANGELES (Reuters) – California’s largest earthquake in four years struck on Monday, causing Planet Earth to ring “like a bell” and mountains to grow a foot (30 cm) taller, geologists said on Monday.

The magnitude 6.5 quake hit near the coastal city of San Simeon….

“Rosebud.”

Thursday, March 6, 2003

Thursday March 6, 2003

Filed under: General,Geometry — Tags: , — m759 @ 2:35 am

ART WARS:

Geometry for Jews

Today is Michelangelo's birthday.

Those who prefer the Sistine Chapel to the Rothko Chapel may invite their Jewish friends to answer the following essay question:

Discuss the geometry underlying the above picture.  How is this geometry related to the work of Jewish artist Sol LeWitt? How is it related to the work of Aryan artist Ernst Witt?  How is it related to the Griess "Monster" sporadic simple group whose elements number 

808 017 424 794 512 875 886 459 904 961 710 757 005 754 368 000 000 000?

Some background:

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