Tuesday, October 24, 2006

Tuesday October 24, 2006

Filed under: General — Tags: — m759 @ 9:00 PM

Another illustration
of the previous entry's concept of
a "critical mass" of weblog entries,
a concept reflected in
the saying
"You can't win the lottery
    if you don't buy a ticket." 

Mathematics and Narrative:
A Two-Part Invention

Here are today's
numbers from the
Keystone State:

The image “http://www.log24.com/log/pix06A/061024-PAlottery.jpg” cannot be displayed, because it contains errors.

Here is an interpretation
of those numbers:
8/21 — Mathematics:

The Wikipedia article on
the Geometrization Conjecture

revision of 13:22 UTC, 21 August 2006:

"The geometrization conjecture, also known as Thurston's geometrization conjecture, concerns the geometric structure of compact 3-manifolds. The geometrization conjecture can be considered an analogue for 3-manifolds of the uniformization theorem for surfaces. It was proposed by William Thurston in the late 1970s. It 'includes' other conjectures, such as the Poincaré conjecture and the Thurston elliptization conjecture."

The second sentence, in bold type, was added on 8/21 by yours truly. No deep learning or original thought was required to make this important improvement in the article; the sentence was simply copied from the then-current version of the article on Grigori Perelman (who has, it seems, proved the geometrization conjecture).

This may serve as an example of the "mathematics" part of the above phrase "Mathematics and Narrative" — a phrase which served, with associated links, as the Log24 entry for 8/21.

7/23 — Narrative:

"Each step in the story is a work of art, and the story as a whole is a sequence of episodes of rare beauty, a drama built out of nothing but numbers and imagination." –Freeman Dyson

This quotation appeared in the Log24 entry for 7/23, "Dance of the Numbers."  What Dyson calls a "story" or "drama" is in fact mathematics. (Dyson calls the "steps" in the story "works of art," so  it is clear that Dyson (a former student of G. H. Hardy) is discussing mathematical steps, not paragraphs in someone's account– perhaps a work of art, perhaps not– of mathematical history.)  I personally regard the rhetorical trick of calling the steps leading to a mathematical result a "story" as contemptible vulgarization, but Dyson, as someone whose work (pdf) led to the particular result he is discussing, is entitled to dramatize it as he pleases.

For related material on mathematics, narrative, and vulgarization, click here.

The art of interpretation (applied above to a lottery) is relevant to narrative and perhaps also, in some sense, to the arts of mathematical research and exposition (if not to mathematics itself).  This art is called hermeneutics.

For more on the subject, see the Stanford Encyclopedia of Philosophy article on Hans-Georg Gadamer, "the decisive figure in the development of twentieth-century hermeneutics."

See also the work of Msgr. Robert Sokolowski of the Catholic University of America, which includes

"Foreword" in Gian-Carlo Rota,
 Indiscrete Thoughts,
 Boston: Birkhäuser Verlag,
 1996, xiii-xvii, and

"Gadamer's Theory of Hermeneutics" in
 The Philosophy of Hans-Georg Gadamer,
 edited by Lewis E. Hahn,
 The Library of Living Philosophers, Vol. 24,
 Chicago: Open Court Publishers,
 1997, 223-34.

Tuesday October 24, 2006

Filed under: General — Tags: — m759 @ 2:56 PM

Critical Mass

The image “http://www.log24.com/log/pix06A/061024-Christmas.jpg” cannot be displayed, because it contains errors.
Thanks to University Diaries for
yesterday's entry on Harvard:

"I wonder if there's just been a critical mass of creepy stories about Harvard in the last couple of years… A kind of piling on of nastiness and creepiness…"

See also the previous Log24 entry, on yesterday's Pennsylvania lottery, and this description of an experiment I remember fondly from my youth:

"The floor in a large room was covered with mouse traps that were 'cocked' and on each was placed a ping pong ball. At the key moment an additional ping pong ball was tossed out and triggered a single mouse trap to go off. The net result after the balls started bouncing was a classic chain reaction."

"I thought Christmas
comes but once a year."
James Bond

Tuesday October 24, 2006

Filed under: General — Tags: — m759 @ 2:02 AM

Robbing Peter
to Pay Paul

Serious Numbers:

PA lottery Oct. 23, 2006

"Paul must not have been
talking about time
in a linear way."

— Sermon at Nassau Church,
Princeton, New Jersey,
Christmas Eve, 2004

Related material:


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