For the birthday of the late C. P. Snow

Saturday, October 14, 2006  7:00 PM

Pirsig and the Master Diamond Cutter

Saturday, October 14, 2006  10:31 AM

Nobel Prize in Literature, continued

Miniature
Prize

Related material:

Miniature

(Thursday, Oct. 12, 2006)

and a novel by
the author of the
above review,
Margaret Atwood:



Click on pictures for details.

Friday, October 13, 2006  12:00 AM

Gee, Saint Peter, that's an old one....

Thursday, October 12, 2006  10:31 AM

Nobel Prize in Literature, 2006

Miniature

This year's winner of the
Nobel Prize in Literature
has written a novel that
  "uses the art of
miniature illumination,
much as Mann's
Doctor Faustus
did music, to explore
a nation's soul"
(John Updike in
The New Yorker).

For the explorer,
here is a
miniature story:

 
 
This story was published on
September 29, 2006,
the Feast of St. Michael
and All Angels.

For illumination of the story,
see Log24, Sept. 30, 2006.

The author is unknown.

Wednesday, October 11, 2006  11:07 AM

Halmos Tombstone, continued:

Tuesday, October 10, 2006  8:00 PM

Mate in
Two Seconds

From Oct. 14 last year:

From Oct. 13 last year
(Yom Kippur):

A Poem for Pinter Oct. 13, 2005 The Guardian on Harold Pinter, winner of this year's Nobel Prize for Literature: "Earlier this year, he announced his decision to retire from playwriting in favour of poetry," Michael Muskal in today's Los Angeles Times: "Pinter, 75, is known for his sparse and thin style as well as his etched characters whose crystal patter cuts through the mood like diamond drill bits." Robert Stone, A Flag for Sunrise (See Jan. 25): "'That old Jew gave me this here.'  Egan looked at the diamond....  'It's worth a whole lot of money-- you can tell that just by looking-- but it means something, I think.  It's got a meaning, like.' 'Let's see,' Egan said, 'what would it mean?'  He took hold of Pablo's hand cupping the stone and held his own hand under it.  '"The jewel is in the lotus," perhaps that's what it means.  The eternal in the temporal....'" Notes on Modal Logic: "Modal logic was originally developed to investigate logic under the modes of necessary and possible truth.  The words 'necessary' and 'possible' are called modal connectives, or modalities.  A modality is a word that when applied to a statement indicates when, where, how, or under what circumstances the statement may be true.  In terms of notation, it is common to use a box [] for the modality 'necessary' and a diamond <> for the modality 'possible.'" A Poem for Pinter Waka waka bang splat tick tick hash Commentary: "Waka" also means Japanese poem or Maori canoe.  (For instance, this Japanese poem and this Maori canoe.) For a meditation on "bang splat," see Sept. 25-29. For the meaning of "tick tick," see Emily Dickinson on "degreeless noon." "Hash," of course, signifies "checkmate."  (See previous three entries.)

For language more suited to
the year's most holy day, see
this year's Yom Kippur entry,
from October 2.

That was also the day of the
Amish school killings in
Pennsylvania and the day that
mathematician Paul Halmos died.

For more on the former, see
Death in Two Seconds.

For more on the latter, see
The Halmos Tombstone.

Tuesday, October 10, 2006  12:00 PM

Mate

Orson Welles Welles died on this date in 1985, the same day as Yul Brynner.

"The crème de la crème of the chess world in a show with everything  but Yul Brynner" -- One Night in Bangkok

New York Lottery,
mid-day on Yom Kippur,
October 2, 2006:

256.

Pennsylvania Lottery,
mid-day on the same day:

723.

For more on 256,
see Symmetries
and 7/23.

"It is a very difficult
philosophical question,
 the question of
  what 'random' is."

-- Herbert Robbins, co-author
   of What is Mathematics?

Monday, October 9, 2006  9:00 AM

ART WARS:
To Apollo



"This is the garden of Apollo,
the field of Reason...."
John Outram, architect

To Apollo (10/09/02)

Art Wars: Apollo and Dionysus (10/09/02)

Balanchine's Birthday (01/09/03)

Art Theory for Yom Kippur (10/05/03)

A Form (05/22/04)

Ineluctable (05/27/04)

A Form, continued (06/05/04)

Parallelisms (06/06/04)

Ado (06/25/04)

Deep Game (06/26/04)

Gameplayers of Zen (06/27/04)

And So To Bed (06/29/04)

Translation Plane for Rosh Hashanah (09/15/04)

Derrida Dead (10/09/04)

The Nine (11/09/04)

From Tate to Plato (11/19/04)

Art History (05/11/05)

A Miniature Rosetta Stone (08/06/05)

High Concept (8/23/05)

High Concept, Continued (8/24/05)

Analogical Train of Thought (8/25/05)

Today's Sermon: Magical Thinking (10/09/05)

Balance (10/31/05)

Matrix (11/01/05)

Seven is Heaven, Eight is a Gate (11/12/05)

Nine is a Vine (11/12/05)

Apollo and Christ (12/02/05)

Hamilton's Whirligig (01/05/06)

Cross (01/06/06)

On Beauty (01/26/06)

Sunday Morning (01/29/06)

Centre (01/29/06)

New Haven (01/29/06)

Washington Ballet (02/05/06)

Catholic Schools Sermon (02/05/06)

The Logic of Apollo (02/05/06)

Game Boy (08/06/06)

Art Wars Continued: The Krauss Cross (09/13/06)

Art Wars Continued: Pandora's Box (09/16/06)

The Pope in Plato's Cave (09/16/06)

Today's Birthdays (09/26/06)

Symbology 101 (09/26/06)

Sunday, October 8, 2006  12:00 AM

Enlarge this image



"Cubistic"

-- New York Times review
of Scorsese's The Departed

Related material:

Log24, May 26, 2006 --

"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."

Platonic solid	Natasha Wescoat, 2004 Shakespearean Fool
Not to mention Euclid and Picasso (Log24, Oct. 6, 2006) --
(Click on pictures for details. Euclid is represented by Alexander Bogomolny, Picasso by Robert Foote.)

See also works by the late Arthur Loeb of Harvard's Department of Visual and Environmental Studies.

"I don't want to be a product of my environment.  I want my environment to be a product of me." -- Frank Costello in The Departed

For more on the Harvard environment,
see today's online Crimson:

The Harvard Crimson, Online Edition

Sunday, Oct. 8, 2006

POMP AND CIRCUS-STANCE CRIMSON/ MEGHAN T. PURDY Friday, Oct. 6: The Ringling Bros. Barnum & Bailey Circus has come to town, and yesterday the animals were disembarked near MIT and paraded to their temporary home at the Banknorth Garden.

OPINION At Last, a Guiding Philosophy The General Education report is a strong cornerstone, though further scrutiny is required. By THE CRIMSON STAFF After four long years, the Curricular Review has finally found its heart. The Trouble With the Germans The College is a little under-educated these days. By SAHIL K. MAHTANI Harvard College-- in the best formulation I’ve heard-- promulgates a Japanese-style education, where the professoriate pretend to teach, the students pretend to learn, and everyone is happy.

Saturday, October 7, 2006  10:31 PM

Today's birthday:
Yo-Yo Ma
 


Here is an excerpt from the sarabande
of Bach's Cello Suite 6 in D Major,
which Ma apparently played at the
77th annual Academy Awards as a
tribute to the departed.

Also departed, perhaps on this date:

Cristobal de Morales,
"generally regarded as the leading
Spanish composer during the
so-called Golden Age of Spain."

Those who find the Bach
too frivolous may enjoy
an excerpt from Morales's work
Missa pro Defunctis (1544),
Introitus: "Requiem aeternam."

Today, incidentally, is the date
of the 1571 Battle of Lepanto.

Friday, October 6, 2006  5:00 PM

Friday, October 6, 2006  12:00 PM

A Visual Proof

The great mathematician
Robert P. Langlands
is 70 today.

In honor of his expository work--
notably, lectures at
The Institute for Advanced Study
on "The Practice of Mathematics"
and a very acerbic review (pdf) of
a book called Euclid's Window--
here is a "Behold!" proof of
the Pythagorean theorem:



The picture above is adapted from
 a sketch by Eves of a "dynamical"
proof suitable for animation.

The proof has been
 described by Alexander Bogomolny
as "a variation on" Euclid I.47.
Bogomolny says it is a proof
by "shearing and translation."

It has, in fact, been animated.
The following version is
by Robert Foote:

Thursday, October 5, 2006  9:11 AM

In Touch with God

(Title of an interview with
the late Paul Halmos, mathematician)

Since Halmos died on Yom Kippur, his thoughts on God may be of interest to some.

From a 1990 interview:

"What's the best part of being a mathematician? I'm not a religious man, but it's almost like being in touch with God when you're thinking about mathematics. God is keeping secrets from us, and it's fun to try to learn some of the secrets."

I personally prefer Annie Dillard on God:

"... if Holy the Firm is matter at its dullest, Aristotle's materia prima, absolute zero, and since Holy the Firm is in touch with the Absolute at base, then the circle is unbroken.  And it is.... Holy the Firm is in short the philosopher's stone."

Some other versions of
the philosopher's stone:

Nov. 9, 2005:

Escher's Verbum



Solomon's Cube

Sept. 3, 2003:

March 11, 2006:

And, more simply,
April 28, 2004:



This last has the virtue of
being connected with Halmos
via his remarks during the
"In Touch with God" interview:

"... at the root of all deep mathematics there is a combinatorial insight... the really original, really deep insights are always combinatorial...."

"Combinatorics, the finite case, is where the genuine, deep insight is."

See also the remark of Halmos that serves as an epigraph to Theme and Variations.

Finally, it should be noted that
the 4x9 black rectangle



has also served
at least one interpreter
as a philosopher's stone,
and is also the original
"Halmos tombstone."

(See previous entry.)

Wednesday, October 4, 2006  6:15 AM

"Prof. Paul Halmos died of pneumonia early in the morning of October 2, 2006. He was 90 years old. He is survived by his wife, Virginia Halmos. An obituary may be found at the website of the Mathematical Association of America...."

-- Halmos's home page
at Santa Clara University

For a memorial of sorts, see
Lovely, Dark and Deep. 

Update of 8 PM Oct. 4 --

From Google Book Search:
 

This is the source of the
"Halmos tombstone" symbol,
which has been described in a
different form at Wikipedia:

"The tombstone, or halmos--
symbol ∎ (Unicode U+220E)--
is used in mathematics to denote
the end of a proof." 

This Unicode character is rendered
as an empty square in Explorer
and as a black square in Firefox.

Related material:

The Unity of Mathematics
and
Monolith

Tuesday, October 3, 2006  12:00 PM

"Hard lessons lately."
 
-- Bruce Springsteen

A belated meditation for Yom Kippur, which ended at sundown yesterday:

"Whatever the shatterings Hopkins felt threatened his and other sacred selves, perhaps precisely because of that threat, he composed the greatest passage on the God-relation of identity since Galatians 2:20....

The aesthetics of truth form alliances, profoundly elective affinities, that the intellect stripped of feeling inclines to reject.... Intellection must address the matter of its feeling."

-- Philip Rieff,
    Sacred Order/Social Order, Vol. 1:
    My Life among the Deathworks:
    Illustrations of the
    Aesthetics of Authority,
    University of Virginia Press, 2006.
    256 pages.

Tuesday, October 3, 2006  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.

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 schoolgirls 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, October 2, 2006  8:00 AM

From Wallace Stevens
On His Birthday

"Logos and logic, crystal hypothesis,
Incipit and a form to speak the word
And every latent double in the word...."

-- Notes Toward a Supreme Fiction

Sunday, October 1, 2006  6:00 PM

The Joy of Six

Yom Kippur begins on the East Coast
at about 6:38 PM today.

Recommended holiday reading list
from Robert Langdon, Harvard author
of "the renowned collegiate texbook
Religious Iconology" --

Elegance

Gerard Manley Hopkins on parallelism

Figures of Speech

Hamlet's Transformation and the four
Log24 entries that preceded it

Finite Geometry of the Hexahedron
(Alternate title for the Christmas, 2005, entry)

Happy Six

Sunday, October 1, 2006  8:00 AM

Recipe for Disaster
 
according to Jerome Kagan,
Harvard psychologist emeritus 

From Log24 --
The Line	The Cube
From Harvard's Jerome Kagan --
"'Humans demand that there be a clear right and wrong,' he said. 'You've got to believe that the track you've taken is the right track. You get depressed if you're not certain as to what it is you're supposed to be doing or what's right and wrong in the world.'"	"People need to divide the world into good and evil, us and them, Kagan continued. To do otherwise-- to entertain the possibility that life is not black and white, but variously shaded in gray-- is perhaps more honest, rational and decent. But it's also, psychically, a recipe for disaster."
Black and White: Log24 in May 2005	Shades of Gray: An affine space and  Harvard's Jerome Kagan

The above Kagan quotes are taken
from a New York Times essay by
Judith Warner as transcribed by
Mark Finkelstein on Sept. 29.

See also Log24 on
Sept. 29 and 30.

Related material:

Kagan's book

Surprise, Uncertainty,
and Mental Structures

(Harvard U. Press, April 2002)

and Werner Heisenberg--
discoverer of the
uncertainty principle--
as Anakin Skywalker
being tempted by
the Dark Side: