Plato's From The Unknowable (1999), by Gregory J.
Chaitin, who has written extensively about his constant, which he calls
Omega: "What is Omega? It's just the diamond-hard distilled and
crystallized essence of mathematical truth! It's what you get when you
compress tremendously the coal of redundant mathematical
truth..." Charles H. Bennett has written about Omega as a
cabalistic number. Here is another result with religious associations which,
historically, has perhaps more claim to be called the "diamond-hard
essence" of mathematical truth: The demonstration in Plato's Meno
that a diamond inscribed in a square has half the area of the square (or
that, vice-versa, the square has twice the area of the diamond). From Ivars Peterson's discussion of Plato's diamond and the
Pythagorean theorem: "In his textbook The History of Mathematics, Roger Cooke of
the University of Vermont describes how the Babylonians might have
discovered the Pythagorean theorem more than 1,000 years before
Pythagoras. Basing his account on a passage in Plato's dialogue Meno,
Cooke suggests that the discovery arose when someone, either for a
practical purpose or perhaps just for fun, found it necessary to
construct a square twice as large as a given square...." From "Halving a Square," a presentation of Plato's diamond by
Alexander Bogomolny, the moral of the story: SOCRATES: And if the truth about reality is always in our soul, the
soul must be immortal.... From "Renaissance Metaphysics and the History of Science," at The John Dee Society
website: Galileo on Plato's diamond: "Cassirer, drawing attention to Galileo's frequent use of the Meno,
particularly the incident of the slave's solving without instruction a
problem in geometry by 'natural' reason stimulated by questioning,
remarks, 'Galileo seems to accept all the consequences drawn by Plato
from this fact.....'" Roger Bacon on Plato's diamond: "Fastening on the incident of the slave in the Meno, which he had
found reproduced in Cicero, Bacon argued from it 'wherefore since this
knowledge (of mathematics) is almost innate and as it were precedes
discovery and learning or at least is less in need of them than other
sciences, it will be first among sciences and will precede others
disposing us towards them.'" It is perhaps appropriate to close this entry, made on All
Hallows' Eve, with a link to a page on Dr. John Dee
himself.
Diamond
|
And God said, "I am the Alpha and the cabalistic
number." | |
| Posted 11/3/2002 at 5:59 pm by oOMisfitOo |
dolph Green, the playwright, performer and lyricist who in a
six-decade collaboration with Betty Comden was co-author of such hit
Broadway musicals as "On the Town," "Wonderful Town" and "Bells Are
Ringing" and the screenplays for "Singin' in the Rain" and "The Band
Wagon," died today at his home in Manhattan. He was 87.
