To Announce a Faith From 7/07, an art review from The New York Times: Endgame Art? It's Borrow, Sample and Multiply in an Exhibition at Bard College "The show has an endgame, end-time mood.... I would call all these strategies fear of form.... the dismissal of originality is perhaps the oldest ploy in the postmodern playbook. To call yourself an artist at all is by definition to announce a faith, however unacknowledged, in some form of originality, first for yourself, second, perhaps, for the rest of us. Fear of form above
all means fear of compression-- of an artistic focus that condenses
experiences, ideas and feelings into something whole, committed and
visually comprehensible." It is doubtful that Smith would consider the following "found" art an example of originality. It nevertheless does "announce a faith." "First for yourself" Today's mid-day Pennsylvania number: 707 See Log24 on 7/07 and the above review. "Second, perhaps, for the rest of us" Today's evening Pennsylvania number: 384 This number is an example of what the reviewer calls "compression"-- "an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible." "Experiences" See (for instance) Joan Didion's writings (1160 pages, 2.35 pounds) on "the shifting phantasmagoria which is our actual experience." "Ideas" See Plato. "Feelings" See A Wrinkle in Time. "Whole" The automorphisms of the tesseract form a group of order 384. "Committed" See the discussions of groups of degree 16 in R. D. Carmichael's classic Introduction to the Theory of Groups of Finite Order. "Visually comprehensible" See "Diamond Theory in 1937," an excerpt from which is shown below. The "faith" announced by the above lottery numbers on All Hallows' Eve is perhaps that of the artist Madeleine L'Engle: "There is such a thing as a tesseract." Posted 10/31/2006 at 11:00 PM |
Trick "Card tricks can be used to liven up many classes for mathematics students." ... or Treat? Related material: yesterday's entry. Posted 10/31/2006 at 9:00 AM |
Religion at Harvard From The Harvard Crimson, Monday, October 30, 2006 6:09 AM "Why is the Task Force on General Education afraid of teaching religion? True, their report did recommend a reason and faith requirement, but the committee has clearly shied away from teaching religious principles and has treated the study of religion itself with contempt.... In the general education report... there is no mention of the fundamental principles of religious thought, even though the general education report stresses that students are affected by religion and should think critically about it." Here is one approach to religious thought-- Scientism-- exemplified by Harvard's Emperor of Math. Screenshot of doctoryau.com Here is a rather different approach to religious thought--
For more on Harvard's real religion, Scientism, and the political background in which it thrives, click on the picture below. . Posted 10/30/2006 at 11:30 AM |
Decrease
(Readings for the
Halloween season) In 1692 on July 31, at the time of the Salem witchcraft trials, Increase Mather reportedly "delivered a sermon... in Boston in which he posed the question... 'O what makes the difference between the devils in hell and the angels of heaven?'" Increase, the father of Cotton Mather, was president of Harvard from June 27, 1692, to Sept. 6, 1701. His name is memorialized by Harvard's Mather House. From Log24 on Jan. 15, 2003:
To honor Harvard's Oct. 28 founding, here are yesterday's numbers from the state of Grace (Kelly, of Philadelphia): Related material: Log24 on 1/16, and Hexagram 41, Decrease The ImageAt the foot of the mountain, the lake:The image of Decrease. Thus the superior man controls his anger And restrains his instincts. This suggests thoughts of the novel Cold Mountain (see yesterday morning) and the following from Log24 on St. Luke's Day this year:
From Nell: "The valley spirit never dies..." See also St. Luke's Day, 2004, as well as a journal entry prompted by both the ignorant religion of Harvard's past and the ignorant scientism of Harvard's present-- Hitler's Still Point: A Hate Speech for Harvard. This last may, of course, not quite fit the description of the superior man controlling his anger so wisely provided by yesterday's lottery and Hexagram 41. Nobody's perfect. Posted 10/29/2006 at 1:00 AM |
Recommended. Posted 10/28/2006 at 12:00 PM |
Recommended. Posted 10/28/2006 at 8:00 AM |
Shem the Penman Related material: The Crimson Passion, the previous entry, Hall of Shem, and the link, in the Ash Wednesday, 2006, entry, Deaconess, to The House of God, a novel by Samuel Shem. Shem is the pen-name of Stephen J. Bergman, Clinical Instructor in Psychiatry at Harvard Medical School. Posted 10/27/2006 at 12:31 PM |
Hardy & Wright "When he was taken to church he amused himself by factorizing the numbers of the hymns." -- C. P. Snow, foreword to A Mathematician's Apology, by G. H. Hardy An application of lottery hermeneutics: 420 --> 4/20 --> Hall of Shame, Easter Sunday, April 20, 2003; 145 --> 5*29 --> 5/29 --> The Shining of May 29. The Rev. Wright may also be interested in the following Related material: "Shem was a sham...." (FW I.7, 170 and Log24 Oct. 13), and The Hebrew Word Shem:
"When I teach introductory Hebrew, the first word I typically teach is the
common noun
This word occurs, notably, in Psalm (or "hymn") 145. See http://scripturetext.com/psalms/145-1.htm: thy name shem (shame) an appellation, as a mark or memorial of individuality; by implication honor, authority, character -- + base, (in-)fame(-ous), named(-d), renown, report. Update of 12:25 PM 10/26
from the online Crimson: Posted 10/26/2006 at 12:00 PM |
Conceit
at Harvard
"... there is some virtue in tracking cultural trends in terms of their relation to the classic Trinitarian framework of Christian thought." -- Description of lectures to be given Monday, Tuesday, and Wednesday of this week (on Father, Son, and Holy Spirit, respectively, and their relationship to "cultural trends") at Harvard's Memorial Church I prefer more-classic trinitarian frameworks-- for example, and the structural trinity underlying classic quilt patterns: Click on pictures for further details. These mathematical trinities are conceits in the sense of concepts or notions; examples of the third kind of conceit are easily found, especially at Harvard. For a possible corrective to examples of the third kind, see To Measure the Changes. Posted 10/25/2006 at 9:00 AM |
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: 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."
Posted 10/24/2006 at 9:00 PM |
Critical Mass 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." Posted 10/24/2006 at 2:56 PM |
Robbing Peter to Pay Paul Serious Numbers: "Paul must not have been talking about time in a linear way." -- Sermon at Nassau Church, Princeton, New Jersey, Christmas Eve, 2004 Related material: 1/19, 4/29. Posted 10/24/2006 at 2:02 AM |
Posted 10/23/2006 at 12:00 AM |
Jane Wyatt turns into
Posted 10/22/2006 at 11:59 PM |
Posted 10/22/2006 at 7:45 PM |
Go Tigers! On this date: "In 1746, -- Today in History "The charter... authorized Posted 10/22/2006 at 5:01 PM |
Ad for "The Prestige": "Every great magic trick consists of three acts. The first act is called 'The Pledge.' The magician shows you something ordinary, but of course... it probably isn't. The second act is called 'The Turn.' The magician makes his ordinary 'some thing' do something extraordinary. Now if you're looking for the secret... you won't find it. That's why there's a third act, called 'The Prestige.' This is the part with the twists and turns, where lives hang in the balance, and you see something shocking you've never seen before." The Associated Press Thought for Today, Oct. 22, 2006: "You can fool too many of the people too much of the time." -- James Thurber, American humorist (1894-1961) click on the above Posted 10/22/2006 at 9:00 AM |
"A World of His Own" Twilight Zone Season 1, Episode 36 First aired: July 1, 1960 "The best Twilight Zone twist ending ever?" -- Amazon.com reviewer "Alexiel" Here are the lottery numbers in Pennsylvania (state of Grace) on Thursday, Oct. 19, the day that Phyllis Kirk died: "I've got a little story* you oughta know..." -- Sinatra * 3/23, 37: Posted 10/22/2006 at 2:45 AM |
An application of the finite geometry underlying the diamond theorem: "Qubits in phase space: Wigner function approach to quantum error correction and the mean king problem," by Juan Pablo Paz, Augusto Jose Roncaglia, and Marcos Saraceno (arXiv:quant-ph/0410117 v2 4 Nov 2004) (pdf) Posted 10/21/2006 at 8:23 AM |
"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 in Indiscrete Thoughts, p. 152 Related Material The Devil's Bible and Nothing Nothings (Again). The Context One context for the Rota quote is Paul Halmos's remark, quoted in today's New York Times, that mathematics is "almost like being in touch with God." Another context is Log24 on Aug. 29, 2005. Here is the original context: Posted 10/20/2006 at 12:00 PM |
"Halmos" For one definition, see Tombstone (typography) at Wikipedia. A halmos, according to the Wikipedia definition: Click on the halmos for further details from today's New York Times. Posted 10/20/2006 at 2:00 AM |
Posted 10/19/2006 at 10:31 PM |
King of Infinite Space (continued from Sept. 5): Thanks to Peter Woit's weblog for a link to the above illustration. This picture of "Coxeter Exhuming Geometry" suggests the following comparison: For the second tombstone, see this morning's entry, Birth, Death, and Symmetry. Further details on the geometry underlying the second tombstone: The above is from Variable Resolution 4–k Meshes: Concepts and Applications (pdf), by Luiz Velho and Jonas Gomes. See also Symmetry Framed and The Garden of Cyrus.
Posted 10/19/2006 at 7:59 PM |
For Sir Thomas Browne (Born Oct. 19, 1605, died Oct. 19, 1682) Browne is noted for Hydriotaphia (Urne-Buriall) and The Garden of Cyrus. Related material: Tombstone and Symmetry Framed Posted 10/19/2006 at 7:59 AM |
Flashback Log24, May 11, 2005:
From Nell: Posted 10/18/2006 at 5:11 PM |
To Measure the Changes (continued from midnight)
The Emperor of Math and Harvard philosopher Illustrations -- To measure the changes: The smartest are nothing: Posted 10/17/2006 at 2:00 PM |
To Measure the Changes (continued from "The Legacy Codes," Nov. 5-6, 2003) From this morning's New York Times: The Emperor of Math Rick Friedman for "The much-honoredThe New York Times mathematician Shing-Tung Yau" Numbers from the Keystone State on October 16: For interpretations of 621, see 6/21's Beijing String and Go with the Flow. For an interpretation of 596, see Wikipedia, 596 (nuclear test): "596 is the codename of the People's Republic of China's first nuclear weapons test, detonated on October 16, 1964." Related material: "'In China he is a movie star,' said Ronnie Chan, a Hong Kong real estate developer and an old friend.... And last summer Dr. Yau played the part.... He ushered Stephen Hawking into the Great Hall of the People in Tiananmen Square to kick off a meeting of some of the world's leading physicists on string theory, and beamed as a poem he had written was performed by a music professor on the conference stage. It reads in part:
Posted 10/17/2006 at 12:00 AM |
Characters Two items from a Wikipedia watchlist today: 1. User Loyola added a list of central characters to the article on The Glass Bead Game. 2. A dialogue between the Wikipedia characters Prof02 and Charles Matthews continues. Item 2 seems almost to echo item 1. The Bead Game, a classic novel by Hermann Hesse, is, in part, a commentary on German cultural history, and the Prof02-Matthews dialogue concerns the Wikipedia article on Erich Heller, a noted scholar of German cultural history. Matthews is an expert on the game of Go. The Bead Game article says that "The Game derives its name from the fact that it was originally played with tokens, perhaps analogous to those of an abacus or the game Go.... Although invented after Hesse's death, Conway's Game of Life can be seen as an example of a Go-like glass bead game with surprisingly deep properties; since it can encode Turing machines, it contains in some sense everything." For some related thoughts on cellular automata (i.e., Conway's game) and Go, see The Field of Reason with its links Deep Game, And So To Bed. For some related thoughts on Turing, see the November 2006 Notices of the American Mathematical Society (special issue on Turing). For some related religious reflections, see Wolfram's Theory of Everything and the Gameplayers of Zan, as well as the Log24 entries of last Halloween. Posted 10/16/2006 at 11:00 AM |
Cleavage Term Snow is mainly remembered as the author of The Two Cultures and the Scientific Revolution (1959). According to Orrin Judd, we can now see "how profoundly wrong Snow was in everything except for his initial metaphor, of a divide between science and the rest of the culture." For more on that metaphor, see the previous entry, "The Line." I prefer a lesser-known work of Snow-- his long biographical foreword to G. H. Hardy's A Mathematician's Apology. The foreword, like the book itself, is an example of what Robert M. Pirsig calls "Quality." It begins with these words: "It was a perfectly ordinary night at Christ's high table, except that Hardy was dining as a guest." Related material: Wallace Stevens, "The Sail of Ulysses," Canto V Posted 10/15/2006 at 2:00 PM |
The Line Continued from Aug. 15, 2004: Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance, Part III: "The wave of crystallization rolled ahead. He was seeing two worlds, simultaneously. On the intellectual side, the square side, he saw now that Quality was a cleavage term. What every intellectual analyst looks for. You take your analytic knife, put the point directly on the term Quality and just tap, not hard, gently, and the whole world splits, cleaves, right in two... hip
and square, classic and romantic, technological and humanistic...and
the split is clean. There's no mess. No slop. No little items that
could be one way or the other. Not just a skilled break but a very
lucky break. Sometimes the best analysts, working with the most obvious
lines of cleavage, can tap and get nothing but a pile of trash. And yet
here was Quality; a tiny, almost unnoticeable fault line; a line of
illogic in our concept of the universe; and you tapped it, and the
whole universe came apart, so neatly it was almost unbelievable. He
wished Kant were alive. Kant would have appreciated it. That master
diamond cutter. He would see. Hold Quality undefined. That was the
secret." See also the discussion of "Probably quite a way yet," "Will we see a lot?" "I think so. Look for blue sky Related material: The Boys from Uruguay, The philosophy of Heidegger See also Posted 10/14/2006 at 7:00 PM |
On a novel by this year's winner of the Nobel Prize in Literature: "In Snow, translated by Maureen Freely, the line between playful farce and gruesome tragedy is very fine. For instance, the town's newspaper publisher, Serdar Bey, prints an article describing Ka's public performance of his poem 'Snow.' When Ka protests that he hasn't written a poem called 'Snow' and is not going to perform it in the theater, Serdar Bey replies: 'Don't be so sure. There are those who despise us for writing the news before it happens.... Quite a few things do happen only because we've written them up first. This is what modern journalism is all about.' And sure enough...." -- Margaret Atwood in the New York Times Book Review of Aug. 15, 2004 Related material: Miniature (Thursday, Oct. 12, 2006) and a novel by the author of the above review, Margaret Atwood: Click on pictures for details. Posted 10/14/2006 at 10:31 AM |
To a Dark Lady* "Something inside is telling me that I've got your secret. Are you still listening? Fear is the lock, and laughter the key to your heart.... ... you are what you are. And you make it hard, and you make it hard...." -- Stephen Stills Songbook * Suggested by... (1) A Harvard Crimson opinion piece of Oct. 12, "A Psychosexual Sham" (2) Remarks on the sin of masturbation (Ask Father Hardon) (3) Shem was a sham.... (FW I.7, 170). See also the Crimson on Jack Nicholson and Log24 on a food joke. "Ours is a very gutsy religion, Cullinane." -- The Source, by James A. Michener Tell it to James Joyce. Posted 10/13/2006 at 12:00 AM |
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. Posted 10/12/2006 at 10:31 AM |
Ticket Home Yesterday's Pennsylvania Lottery numbers: Mid-day 266 Evening 529 Related material: The 266-Day Method and
Posted 10/11/2006 at 11:07 AM |
Mate in Two Seconds From Oct. 14 last year: From Oct. 13 last year (Yom Kippur):
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. Posted 10/10/2006 at 8:00 PM |
Mate
256. Pennsylvania Lottery, 723. 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? Posted 10/10/2006 at 12:00 PM |
Today's Birthday: Matt Damon 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." -- G. K. Chesterton
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,
Posted 10/8/2006 at 12:00 AM |
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. Posted 10/7/2006 at 10:31 AM |
Incipit For the Amish Schoolchildren "Philosophers
ponder the idea of identity: what it is to give something a name on
Monday and have it respond to that name on Friday...." -- Bernard Holland in The New York Times Monday, May 20, 1996 From Log24 on Monday, Oct. 2, 2006: "Logos and logic, crystal hypothesis, -- Wallace Stevens, Pennsylvania lottery, "331" Related material: Log24, 3/31, 2006. Posted 10/6/2006 at 5:00 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: Posted 10/6/2006 at 12:00 PM |
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 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.) Posted 10/5/2006 at 9:11 AM |
Paul R. Halmos died on Yom Kippur, 2006 "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 For a memorial of sorts, see Update of 8 PM Oct. 4 -- This is the source of the "The tombstone, or halmos-- This Unicode character is rendered Related material: The Unity of Mathematics Posted 10/4/2006 at 6:15 AM |
"Hard lessons lately." 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, Posted 10/3/2006 at 12:00 PM |
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 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
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. Posted 10/3/2006 at 9:26 AM |
From Wallace Stevens "Logos and logic, crystal hypothesis, -- Notes Toward a Supreme Fiction Posted 10/2/2006 at 8:00 AM |
The Joy of Six Yom Kippur begins on the East Coast Recommended holiday reading list Gerard Manley Hopkins on parallelism Hamlet's Transformation and the four Finite Geometry of the Hexahedron Posted 10/1/2006 at 6:00 PM |
Tales of Philosophy: Recipe for Disaster
The above Kagan quotes are taken See also Log24 on Related material: Kagan's book Surprise, Uncertainty, (Harvard U. Press, April 2002) and Werner Heisenberg-- George Lucas, who has profited enormously from public depictions of the clash between good and evil, light and dark, may in private life be inclined to agree with Hercule Poirot: "It is the brain, the little gray cells on which one must rely. One must seek the truth within-- not without." (This is another version of the "Descartes before dehors" principle-- See "A Table," Sept. 28.) Posted 10/1/2006 at 8:00 AM |