Log24

Sunday, April 24, 2011

Romancing the Metaphor

Filed under: General — Tags: — m759 @ 2:24 PM

Background —

From a 1990 novel —
http://www.log24.com/log/pix11A/110424-StoneJunction.jpg

Friday, April 22, 2011

Romancing the Hyperspace

Filed under: General,Geometry — m759 @ 7:59 PM

For the title, see Palm Sunday.

"There is a pleasantly discursive treatment of
Pontius Pilate's unanswered question 'What is truth?'" — H. S. M. Coxeter, 1987

From this date (April 22) last year—

Image-- examples from Galois affine geometry

Richard J. Trudeau in The Non-Euclidean Revolution , chapter on "Geometry and the Diamond Theory of Truth"–

"… Plato and Kant, and most of the philosophers and scientists in the 2200-year interval between them, did share the following general presumptions:

(1) Diamonds– informative, certain truths about the world– exist.
(2) The theorems of Euclidean geometry are diamonds.

Presumption (1) is what I referred to earlier as the 'Diamond Theory' of truth. It is far, far older than deductive geometry."

Trudeau's book was published in 1987. The non-Euclidean* figures above illustrate concepts from a 1976 monograph, also called "Diamond Theory."

Although non-Euclidean,* the theorems of the 1976 "Diamond Theory" are also, in Trudeau's terminology, diamonds.

* "Non-Euclidean" here means merely "other than  Euclidean." No violation of Euclid's parallel postulate is implied.

Trudeau comes to reject what he calls the "Diamond Theory" of truth. The trouble with his argument is the phrase "about the world."

Geometry, a part of pure mathematics, is not  about the world. See G. H. Hardy, A Mathematician's Apology .

Romancing the Symmetry

Filed under: General,Geometry — Tags: — m759 @ 2:29 PM

From a story about mathematician Emmy Noether and 1882, the year she was born—

"People were then slowly becoming 'modern'— fortunately they had finally discovered not just that there are no Easter bunnies and Santa Claus, but also that there probably never were women who were led to evil ways by their curiosity and ended up, depending on their level of education, as common witches, as 'wiccans,' or as those particularly mysterious 'benandanti.'"

"… in the Balkans people believe that the souls of the dead rise to heaven in the guise of butterflies."

— "The Fairytale of the Totally Symmetrical Butterfly," by Dietmar Dath, in Intoxicating Heights  (Eichborn AG, Frankfurt 2003)

An insect perhaps more appropriate for the afternoon of Good Friday— the fly in the logo of Dath's publisher

http://www.log24.com/log/pix11/110422-EichbornLogo.jpg

Related material— Holy Saturday of 2004 and Wittgenstein and the Fly Bottle.

(After clicking, scroll down to get past current post.)

http://www.log24.com/log/pix11/110422-WittgensteinFly.jpg http://www.log24.com/log/pix11/110422-DTfly.gif

Wednesday, April 20, 2011

Romancing the Cube

Filed under: General,Geometry — Tags: — m759 @ 1:00 AM

It was a dark and stormy night…

http://www.log24.com/log/pix11/110420-DarkAndStormy-Logicomix.jpg

— Page 180, Logicomix

“… the class of reflections is larger in some sense over an arbitrary field than over a characteristic zero field.”

– Julia Hartmann and Anne V. Shepler, “Jacobians of Reflection Groups

For some context, see the small cube in “A Simple Reflection Group of Order 168.”

See also the larger cube in “Many Dimensions” + Whitehead in this journal (scroll down to get past the current post).

That search refers to a work by Whitehead published in 1906, the year at the top of the Logicomix  page above—

http://www.log24.com/log/pix11/110420-Whitehead1906Axioms.jpg

A related remark on axiomatics that has metaphysical overtones suitable for a dark and stormy night

“An adequate understanding of mathematical identity requires a missing theory that will account for the relationships between formal systems that describe the same items. At present, such relationships can at best be heuristically described in terms that invoke some notion of an ‘intelligent user standing outside the system.'”

— Gian-Carlo Rota, “Syntax, Semantics, and…” in Indiscrete Thoughts . See also the original 1988 article.

Tuesday, April 19, 2011

Romancing the Omega

Filed under: General,Geometry — m759 @ 12:25 PM

Today's news from Oslo suggests a review—

Image- Josefine Lyche work (with 1986 figures by Cullinane) in a 2009 exhibition in Oslo

Click for further details.

The circular sculpture in the foreground
is called by the artist "The Omega Point."
This has been described as
"a portal that leads in or out of time and space."

Some related philosophical remarks—

Oslo Connection and some notes on Galois connections.

Monday, April 18, 2011

Romancing the Junction

Filed under: General — m759 @ 1:06 PM

http://www.log24.com/log/pix11/110418-StoneJunction.jpg

From Thomas Pynchon's 1997 Introduction to Stone Junction

"He takes the Diamond, and then the Diamond takes him. For it turns out to be a gateway to elsewhere, and Daniel's life's tale an account of the incarnation of a god, not the usual sort that ends up bringing aid and comfort to earthly powers, but that favorite of writers, the incorruptible wiseguy known to anthropologists as the Trickster, to working alchemists as Hermes, to card-players everywhere as the Joker. We don't learn this till the end of the story, by which point, knowing Daniel as we've come to, we are free to take it literally as a real transfiguration, or as a metaphor of spiritual enlightenment, or as a description of Daniel's unusually exalted state of mind as he prepares to cross, forever, the stone junction between Above and Below— by this point, all of these possibilities have become equally true, for we have been along on one of those indispensable literary journeys, taken nearly as far as Daniel— though it is for him to slip along across the last borderline, into what Wittgenstein once supposed cannot be spoken of, and upon which, as Eliphaz Levi advised us— after 'To know, to will, to dare' as the last and greatest of the rules of Magic— we must keep silent."

"The devil likes metamorphoses." —The Club Dumas

Tuesday, April 19, 2011

Catechisms

Filed under: General — m759 @ 2:01 AM

Q— Why is this night different from all other nights?

A—

http://www.log24.com/log/pix11/110419-Shachath.jpg

Click on Hebrew for commentary.

See also a simpler Christian midrash—

"Who Was the Mysterious Death Angel?"

Q— Why is Leaving Las Vegas  different from all other movies?

A—

http://www.log24.com/log/pix11/110419-Cage.jpg

Hotel bedroom in Leaving Las Vegas  (1995)

Midrash— Romancing the Junction and Damnation Morning

"… this woman with the sigil on her forehead looked in on me from the open doorway of the hotel bedroom where I'd hidden myself and the bottles and asked me, 'Look, Buster, do you want to live?'"

Sunday, April 17, 2011

Annals of Search

Filed under: General,Geometry — m759 @ 6:29 PM

The following has rather mysteriously appeared in a search at Google Scholar for "Steven H. Cullinane."

[HTML] Romancing the Non-Euclidean Hyperspace
AB Story – Annals of Pure and Applied Logic, 2002 – m759.net

This turns out to be a link to a search within this weblog. I do not know why Google Scholar attributes the resulting web page to a journal article by "AB Story" or why it drew the title from a post within the search and applied it to the entire list of posts found. I am, however, happy with the result— a Palm Sunday surprise with an eclectic mixture of styles that might please the late Robert de Marrais.

I hope the late George Temple would also be pleased. He appears in "Romancing" as a resident of Quarr Abbey, a Benedictine monastery.

The remarks by Martin Hyland quoted in connection with Temple's work are of particular interest in light of the Pope's Christmas remark on mathematics quoted here yesterday.

Powered by WordPress