Log24

Tuesday, November 22, 2011

Serious

Filed under: General — m759 @ 10:18 PM

Today's New York Lottery numbers:

231, 4403, 550, 0764.

Continuing the Serious Hardy Apology sequence,
here is a reference to volume number 231 in the
Springer Graduate Texts in Mathematics series—

IMAGE- 'Serious work on groups generated by reflections,' Springer GTM 231

For some less  serious work, see posts on 4403 (4/4/03)
as well as posts numbered 550 and 764.

Saturday, June 2, 2007

Saturday June 2, 2007

Filed under: General,Geometry — m759 @ 8:00 AM
The Diamond Theorem
 
Four diamonds in a square
 

“I don’t think the ‘diamond theorem’ is anything serious, so I started with blitzing that.”

— Charles Matthews at Wikipedia, Oct. 2, 2006

“The ‘seriousness’ of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects. We may say, roughly, that a mathematical idea is ‘significant’ if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas.”

— G. H. Hardy, A Mathematician’s Apology

Tuesday, October 3, 2006

Tuesday October 3, 2006

Filed under: General,Geometry — m759 @ 9:26 AM

Serious

"I don't think the 'diamond theorem' is anything serious, so I started with blitzing that."

Charles Matthews at Wikipedia, Oct. 2, 2006

"The 'seriousness' of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects. We may say, roughly, that a mathematical idea is 'significant' if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas."

— G. H. Hardy, A Mathematician's Apology

Matthews yesterday deleted references to the diamond theorem and related material in the following Wikipedia articles:

Affine group‎
Reflection group‎
Symmetry in mathematics‎
Incidence structure‎
Invariant (mathematics)‎
Symmetry‎
Finite geometry‎
Group action‎
History of geometry‎

This would appear to be a fairly large complex of mathematical ideas.

See also the following "large complex" cited, following the above words of Hardy, in Diamond Theory:

Affine geometry, affine planes, affine spaces, automorphisms, binary codes, block designs, classical groups, codes, coding theory, collineations, combinatorial, combinatorics, conjugacy classes, the Conwell correspondence, correlations, design theory, duads, duality, error correcting codes, exceptional groups, finite fields, finite geometry, finite groups, finite rings, Galois fields, generalized quadrangles, generators, geometry, GF(2), GF(4), the (24,12) Golay code, group actions, group theory, Hadamard matrices, hypercube, hyperplanes, hyperspace, incidence structures, invariance, Karnaugh maps, Kirkman's schoolgirl problem, Latin squares, Leech lattice, linear groups, linear spaces, linear transformations, Mathieu groups, matrix theory, Meno, Miracle Octad Generator, MOG, multiply transitive groups, octads, the octahedral group, orthogonal arrays, outer automorphisms, parallelisms, partial geometries, permutation groups, PG(3,2), polarities, Polya-Burnside theorem, projective geometry, projective planes, projective spaces, projectivities, Reed-Muller codes, the relativity problem, Singer cycle, skew lines,  sporadic simple groups, Steiner systems, symmetric, symmetry, symplectic, synthemes, synthematic, tesseract, transvections, Walsh functions, Witt designs.

Monday, September 18, 2006

Monday September 18, 2006

Filed under: General — Tags: — m759 @ 9:14 AM
Apology

 

Excerpts from
Log 24, January 18, 2004:

 
A Living Church

"Plato has told you a truth; but Plato is dead. Shakespeare has startled you with an image; but Shakespeare will not startle you with any more. But imagine what it would be to live with such men still living. To know that Plato might break out with an original lecture to-morrow, or that at any moment Shakespeare might shatter everything with a single song. The man who lives in contact with what he believes to be a living Church is a man always expecting to meet Plato and Shakespeare to-morrow at breakfast. He is always expecting to see some truth that he has never seen before."

— G. K. Chesterton, Orthodoxy

C. P. Snow on G. H. Hardy in the foreword to A Mathematician's Apology:

"… he had another favourite entertainment…."

… If, as Chesterton might surmise, he… met Plato and Shakespeare in Heaven, the former might discuss with him the eternal Platonic form of the number 17*, while the latter might offer….

* Footnote of 9/18/06: For the Platonic form of 17, see Feast of the Triumph of the Cross (9/14/06) and Medal (9/15/06).

A Living Church,
continued…

Apology:
An Exercise in Rhetoric

Related material:


MOVIE RELEASED
ON 6-6-6 —


"Seamus Davey-Fitzpatrick stars in a scene from the R-rated movie 'The Omen.' An official of the Australian bishops conference took on the superstition surrounding the movie's release date of June 6, 2006, noting that 'I take evil far too seriously to think "The Omen" is telling me anything realistic or important.'" (CNS/20th Century Fox)

and

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Thursday, May 22, 2003

Thursday May 22, 2003

Filed under: General — m759 @ 7:29 PM

Seek and Ye Shall Find:

On the Mystical Properties
of the Number 162

On this date in history:

May 22, 1942:  Unabomber Theodore John Kaczynski is born in the Chicago suburb of Evergreen Park, Ill., to Wanda Kaczynski and her husband Theodore R. Kaczynski, a sausage maker. His mother brings him up reading Scientific American.

From the June 2003 Scientific American:

“Seek and ye shall find.” – Michael Shermer

From my note Mark of April 25, 2003:

“Tell me of runes to grave
 That hold the bursting wave,
 Or bastions to design
 For longer date than mine.”

— A. E. Housman, quoted by G. H. Hardy in A Mathematician’s Apology

“Here, as examples, are one rune and one bastion…. (illustrations: the Dagaz rune and the Nike bastion of the Acropolis)…. Neither the rune nor the bastion discussed has any apparent connection with the number 162… But seek and ye shall find.”

Here is a connection to runes:

Mayer, R.M., “Runenstudien,” Beiträge zur Geschichte der deutschen Sprache und Literatur 21 (1896): pp. 162 – 184.

Here is a connection to Athenian bastions from a UN article on Communist educational theorist Dimitri Glinos:

“Educational problems cannot be scientifically solved by theory and reason alone….” (D. Glinos (1882-1943), Dead but not Buried, Athens, Athina, 1925, p. 162)

“Schools are…. not the first but the last bastion to be taken by… reform….”

“…the University of Athens, a bastion of conservatism and counter-reform….”

I offer the above with tongue in cheek as a demonstration that mystical numerology may have a certain heuristic value overlooked by fanatics of the religion of Scientism such as Shermer.

For a more serious discussion of runes at the Acropolis, see the photo on page 16 of the May 15, 2003, New York Review of Books, illustrating the article “Athens in Wartime,” by Brady Kiesling.

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