This afternoon I added a new page to finitegeometry.org and updated the Geometry of Logic page. These changes are due to my coming across the Usenet postings of Carol von der Lin.
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The Magic of Numbers
“Emphasis will be placed on discovery through conjecture and experimentation.”
— Elena Mantovan, pre-2007 undated Harvard syllabus for Quantitative Reasoning 28, “The Magic of Numbers”
“The lunatic, the lover, and the poet, said Shakespeare, are of imagination all compact. He forgot the mathematician…. Those who win through to the end of The Magic of Numbers will be for the rest of their lives in touch with the accessible mystery of things.”
— Review, Harvard Magazine, Jan/Feb 2004
“Lear becomes almost lyrical. ‘When thou dost ask me blessing, I’ll kneel down/ And pray, and sing, and tell old tales, and laugh/ At gilded butterflies, and hear poor rogues/ Talk of court news; and we’ll talk with them too/ Who loses and who wins; who’s in, who’s out– And take upon’s the mystery of things/ As if we were God’s spies.’ That is a remarkable, haunting passage.”
— Father James V. Schall, Society of Jesus, Georgetown Hoya, undated column (perhaps, the URL indicates, from All Hallows’ Eve, 2006)
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Lease Renewed
The New York Times,
Thursday, September 13, 2007–
Burt Hasen, Artist Inspired
by Maps, Dies at 85
Burt Hasen, a New York painter who drew inspiration from his experience working with maps as a military technician during World War II, died on Friday [September 7, 2007] in Manhattan. He was 85 and lived in Lower Manhattan….
During the war he served in the Air Force in the Pacific, where his duties involved close study of aerial maps, an activity that lastingly influenced his work. His densely worked canvases often had an overhead perspective….Toward the end of his life, many of his seemingly abstract paintings were based directly, and in detail, on maps….
In 2006 Mr. Hasen, his wife and the other tenants of a five-story building at 7 Dutch Street near the South Street Seaport made news when they organized against their landlord’s attempt to evict them from the rent-regulated lofts they had occupied for more than 30 years. They subsequently had their leases renewed.
“For every kind of vampire,
there is a kind of cross.”
— Gravity’s Rainbow
Battlefield Geometry
“The general, who wrote the Army’s book on counterinsurgency, said he and his staff were ‘trying to do the battlefield geometry right now’ as he prepared his troop-level recommendations.”
— Steven R. Hurst, The Associated Press, Wednesday, Aug. 15, 2007
“‘… we are in the process of doing the battlefield geometry to determine the way ahead.’”
— Charles M. Sennott, Boston Globe, Friday, Sept. 7, 2007
“Based on these considerations, and having worked the battlefield geometry … I have recommended a drawdown of the surge forces from Iraq.”
— United States Army, Monday, Sept. 10, 2007
Related material:
Log24 entries of
June 11 and 12, 2005:
“In the desert you can
remember your name
‘Cause there ain’t no one
for to give you no pain.”
May 25, 2007:
“Let’s give ‘em somethin’ to talk about,
A little mystery to figure out”
– Scarlett Johansson singing on
Saturday Night Live, April 21, 2007
Related material:
Today’s previous entry
and the following:
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This place was reserved at 9:29 PM Sept. 7, 2007.
The place now seems suitable to note a memorial to Burt Hasen, an artist who died on Sept. 7, 2007. For the memorial itself, see Sept. 13, 2007, 2:02 AM.
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The New York Times online,
Friday, Sept. 7, 2007:
Madeleine L’Engle,
Children’s Writer,
Is Dead
“Madeleine L’Engle, who in writing more than 60 books, including childhood fables, religious meditations and science fiction, weaved emotional tapestries transcending genre and generation, died Thursday [Sept. 6, 2007] in Connecticut. She was 88.
Her death, of natural causes, was announced today by her publisher, Farrar, Straus and Giroux.”
More >>
Related material:
Log24 entries of
August 31–
“That is how we travel.”
— A Wrinkle in Time,
Chapter 5,
“The Tesseract”
– and of
September 2
(with update of
September 5)–
“There is such a thing
as a tesseract.”
— A Wrinkle in Time
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Re: This Week’s Finds in Mathematical Physics (Week 251)
On Spekkens’ toy system and finite geometry
Background–
- In “Week 251” (May 5, 2007), John wrote:
“Since Spekkens’ toy system resembles a qubit, he calls it a “toy bit”. He goes on to study systems of several toy bits – and the charming combinatorial geometry I just described gets even more interesting. Alas, I don’t really understand it well: I feel there must be some mathematically elegant way to describe it all, but I don’t know what it is…. All this is fascinating. It would be nice to find the mathematical structure that underlies this toy theory, much as the category of Hilbert spaces underlies honest quantum mechanics.”
- In the n-Category Cafe ( May 12, 2007, 12:26 AM, ) Matt Leifer wrote:
“It’s crucial to Spekkens’ constructions, and particularly to the analog of superposition, that the state-space is discrete. Finding a good mathematical formalism for his theory (I suspect finite fields may be the way to go) and placing it within a comprehensive framework for generalized theories would be very interesting.”
- In the n-category Cafe ( May 12, 2007, 6:25 AM) John Baez wrote:
“Spekkens and I spent an afternoon trying to think about his theory as quantum mechanics over some finite field, but failed — we almost came close to proving it couldnt’ work.”
On finite geometry:
The actions of permutations on a 4 × 4 square in Spekkens’ paper (quant-ph/0401052), and Leifer’s suggestion of the need for a “generalized framework,” suggest that finite geometry might supply such a framework. The geometry in the webpage John cited is that of the affine 4-space over the two-element field.
Related material:
Update of
Sept. 5, 2007
See also arXiv:0707.0074v1 [quant-ph], June 30, 2007:
A fully epistemic model for a local hidden variable emulation of quantum dynamics,
by Michael Skotiniotis, Aidan Roy, and Barry C. Sanders, Institute for Quantum Information Science, University of Calgary. Abstract: “In this article we consider an augmentation of Spekkens’ toy model for the epistemic view of quantum states [1]….”
Hypercube from the Skotiniotis paper:
Reference:
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