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.
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.
See also this journal on the above date (Jan. 27, 2012).
Backstory: Search this journal for sciencenews.
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 —
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.
“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, |
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.”
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.”“Which is the sound of the land
Full of the same wind
That is blowing in
the same bare placeFor the listener,
who listens in the snow,
And, nothing himself, beholds
Nothing that is not there
and the nothing that is.”
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.”
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:
From Nobel Prize Women in Science, by Sharon Bertsch McGrayne, Second Edition (2001), Joseph Henry Press:
"Storm trooper Ernst Witt, resplendent in the Brownshirt uniform of Hitler's paramilitary, knocked on a Jew's apartment door in 1934. A short, rotund woman opened the door. Emmy Noether smiled, welcomed the young Nazi into her home, and started her underground math class. The Brownshirt was one of her favorite pupils."
On this date in 1962, Frank Sinatra recorded "I Gotta Right To Sing The Blues" for Capitol Records. This was his last recording for Capitol. He had already started recording for Reprise Records.
Related reading:
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