New Haven The eye's plain version is a thing apart, The vulgate of experience. Of this, A few words, an and yet, and yet, and yet-- As part of the never-ending meditation, Part of the question that is a giant himself: Of what is this house composed if not of the sun, These houses, these difficult objects, dilapidate Appearances of what appearances, Words, lines, not meanings, not communications, Dark things without a double, after all, Unless a second giant kills the first-- A recent imagining of reality, Much like a new resemblance of the sun, Down-pouring, up-springing and inevitable, A larger poem for a larger audience, As if the crude collops came together as one, A mythological form, a festival sphere, A great bosom, beard and being, alive with age. -- Wallace Stevens, opening lines of "An Ordinary Evening in New Haven" Posted 1/29/2006 at 10:00 AM |
Centre In the punctual centre of all circles white Stands truly.... ... and Bloom with his vast accumulation Stands and regards and repeats the primitive lines. -- Wallace Stevens, "From the Packet of Anacharsis" Related material: Balanchine's Birthday. Posted 1/29/2006 at 9:00 AM |
Sunday Morning Today is the Chinese New Year, 4074. Posted 1/29/2006 at 8:00 AM |
Memorial of St. Thomas Aquinas: Joyce and Aquinas, by William T. Noon, S. J. St. Thomas Aquinas, by G. K. Chesterton Log24, Epiphany 2006 Posted 1/28/2006 at 12:48 PM |
Mozart, 2006 Mozart, 1935 Poet, be seated at the piano. Play the present, its hoo-hoo-hoo, Its shoo-shoo-shoo, its ric-a-nic, Its envious cachinnation. If they throw stones upon the roof While you practice arpeggios, It is because they carry down the stairs A body in rags. Be seated at the piano. That lucid souvenir of the past, The divertimento; That airy dream of the future, The unclouded concerto . . . The snow is falling. Strike the piercing chord. Be thou the voice, Not you. Be thou, be thou The voice of angry fear, The voice of this besieging pain. Be thou that wintry sound As of the great wind howling, By which sorrow is released, Dismissed, absolved In a starry placating. We may return to Mozart. He was young, and we, we are old. The snow is falling And the streets are full of cries. Be seated, thou. -- Wallace Stevens, Ideas of Order (1936) From the center: "'Mozart, 1935' immediately discloses a will to counter complaints of pure poetry, to refute that charge heard regularly from Stevens's critics, to find 'his particular celebration out of tune today' on his own if necessary; and, in short, to meet the communist [poet and critic Willard] Maas's 'respect for his magnificent rhetoric' at least halfway across from right to left." -- Alan Filreis, Modernism from Right to Left: Wallace Stevens, the Thirties, and Literary Radicalism (Cambridge: Cambridge University Press, 1994), p. 211 From the left: Norman Lebrecht on this year's celebration of the 250th anniversary of Mozart's birth (January 27, 1756): "... Mozart, it is safe to say, failed to take music one step forward.... ... Mozart merely filled the space between staves with chords that he knew would gratify a pampered audience. He was a provider of easy listening, a progenitor of Muzak.... ... He lacked the rage of justice that pushed Beethoven into isolation, or any urge to change the world. Mozart wrote a little night music for the ancien regime. He was not so much reactionary as regressive.... ... Little in such a mediocre life gives cause for celebration.... ... The bandwaggon of Mozart commemorations was invented by the Nazis in 1941.... ... In this orgy of simple-mindedness, the concurrent centenary of Dmitri Shostakovich-- a composer of true courage and historical significance-- is being shunted to the sidelines, celebrated by the few. Mozart is a menace to musical progress, a relic of rituals that were losing relevance in his own time and are meaningless to ours. Beyond a superficial beauty and structural certainty, Mozart has nothing to give to mind or spirit in the 21st century. Let him rest. Ignore the commercial onslaught. Play the Leningrad Symphony. Listen to music that matters." The left seems little changed since 1935. Posted 1/27/2006 at 8:25 AM |
In honor of Paul Newman's age today, 81: On Beauty Elaine Scarry, On Beauty (pdf), page 21:
"Something beautiful fills the mind yet invites the search for something beyond itself, something larger or something of the same scale with which it needs to be brought into relation. Beauty, according to its critics, causes us to gape and suspend all thought. This complaint is manifestly true: Odysseus does stand marveling before the palm; Odysseus is similarly incapacitated in front of Nausicaa; and Odysseus will soon, in Book 7, stand 'gazing,' in much the same way, at the season-immune orchards of King Alcinous, the pears, apples, and figs that bud on one branch while ripening on another, so that never during the cycling year do they cease to be in flower and in fruit. But simultaneously what is beautiful prompts the mind to move chronologically back in the search for precedents and parallels, to move forward into new acts of creation, to move conceptually over, to bring things into relation, and does all this with a kind of urgency as though one's life depended on it." The above symbol of Apollo suggests, in accordance with Scarry's remarks, larger structures. Two obvious structures are the affine 4-space over GF(3), with 81 points, and the affine plane over GF(32), also with 81 points. Less obvious are some related projective structures. Joseph Malkevitch has discussed the standard method of constructing GF(32) and the affine plane over that field, with 81 points, then constructing the related Desarguesian projective plane of order 9, with See also Miniquaternion Geometry: The Four Projective Planes of Order 9 (pdf), by Katie Gorder (Dec. 5, 2003), and a book she cites:
Miniquaternion geometry: An introduction to the study of projective planes, by T. G. Room and P. B. Kirkpatrick. Cambridge Tracts in Mathematics and Mathematical Physics, No. 60. Cambridge University Press, London, 1971. viii+176 pp.For "miniquaternions" of a different sort, see my entry on Visible Mathematics for Hamilton's birthday last year: Posted 1/26/2006 at 9:00 AM |
Born Today and playing with a full deck: Alicia Keys "... it's going to be accomplished in steps, this establishment of the Talented in the scheme of things." -- Anne McCaffrey, Radcliffe '47, To Ride Pegasus (And born yesterday... Neil "I am, I cried" Diamond) Posted 1/25/2006 at 4:00 PM |
ART WARS for Michael Harris (See previous entry.) Related material: A classic book in a postmodern ("free-floating signs") cover -- This is my Princeton Companion to Mathematics, from the days when Princeton University Press had higher scholarly standards. Posted 1/24/2006 at 7:00 AM |
In Defense of Hilbert (On His Birthday) Michael Harris (Log24, July 25 and 26, 2003) in a recent essay, Why Mathematics? You Might Ask (pdf), to appear in the forthcoming Princeton Companion to Mathematics: "Mathematicians can... claim to be the first postmodernists: compare an art critic's definition of postmodernism-- 'meaning is suspended in favor of a game involving free-floating signs'-- with Hilbert's definition of mathematics as 'a game played according to certain simple rules with meaningless marks on paper.'" Harris adds in a footnote: "... the Hilbert quotation is easy to find but is probably apocryphal, which doesn't make it any less significant." If the quotation is probably apocryphal, Harris should not have called it "Hilbert's definition." For a much more scholarly approach to the concepts behind the alleged quotation, see Richard Zach, Hilbert's Program Then and Now (pdf): [Weyl, 1925] described Hilbert's project as replacing meaningful mathematics by a meaningless game of formulas. He noted that Hilbert wanted to 'secure not truth, but the consistency of analysis' and suggested a criticism that echoes an earlier one by Frege: Why should we take consistency of a formal system of mathematics as a reason to believe in the truth of the pre-formal mathematics it codifies? Is Hilbert's meaningless inventory of formulas not just 'the bloodless ghost of analysis'?" Some of Zach's references: [Ramsey, 1990] Frank P. Ramsey. Philosophical Papers, D. H. Mellor, editor. Cambridge University Press, Cambridge, 1990 [Weyl, 1925] Hermann Weyl. Die heutige Erkenntnislage in der Mathematik. Symposion, 1:1-23, 1925. Reprinted in: [Weyl, 1968, 511-42]. English translation in: [Mancosu, 1998a, 123-42].... [Weyl, 1968] Hermann Weyl. Gesammelte Abhandlungen, volume 1, K. Chandrasekharan, editor. Springer Verlag, Berlin, 1968. [Mancosu, 1998a] Paolo Mancosu, editor. From Brouwer to Hilbert. The Debate on the Foundations of Mathematics in the 1920s. Oxford University Press, Oxford, 1998. Constance Reid says it was not Hilbert himself, but his critics, who
described Hilbert's formalism as reducing mathematics to "a meaningless
game," and quotes the Platonist Hardy as saying that Hilbert was
ultimately concerned not with meaningless marks on paper, but with ideas:
Harris concludes his essay with a footnote giving an unsourced Weyl quotation he found on a web page of David Corfield:
One source for the Weyl quotation is the above-cited book edited by Mancosu, page 136. The quotation in the English translation given there: "Mathematics is not the rigid and petrifying schema, as the layman so much likes to view it; with it, we rather stand precisely at the point of intersection of restraint and freedom that makes up the essence of man itself." Corfield says of this quotation that he'd love to be told the original German. He should consult the above references cited by Richard Zach.
For more on the intersection of restraint and freedom and the essence
of man's nature, see the Kierkegaard chapter cited in the previous
entry. Posted 1/23/2006 at 6:00 PM |
The Case An entry suggested by today's New York Times story by Tom Zeller Jr., A Million Little Skeptics: From The Hustler, by Walter Tevis: The only light in the room was from the lamp over the couch where she was reading. He looked at her face. She was very drunk. Her eyes were swollen, pink at the corners. "What's the book?" he said, trying to make his voice conversational. But it sounded loud in the room, and hard. She blinked up at him, smiled sleepily, and said nothing. "What's the book?" His voice had an edge now. "Oh," she said. "It's Kierkegaard. Soren Kierkegaard." She pushed her legs out straight on the couch, stretching her feet. Her skirt fell back a few inches from her knees. He looked away. "What's that?" he said. "Well, I don't exactly know, myself." Her voice was soft and thick. He turned his face away from her again, not knowing what he was angry with. "What does that mean, you don't know, yourself?" She blinked at him. "It means, Eddie, that I don't exactly know what the book is about. Somebody told me to read it, once, and that's what I'm doing. Reading it." He looked at her, tried to grin at her-- the old, meaningless, automatic grin, the grin that made everybody like him-- but he could not. "That's great," he said, and it came out with more irritation than he had intended. She closed the book, tucked it beside her on the couch. "I guess this isn't your night, Eddie. Why don't we have a drink?" "No." He did not like that, did not want her being nice to him, forgiving. Nor did he want a drink. Her smile, her drunk, amused smile, did not change. "Then let's talk about something else," she said. "What about that case you have? What's in it?" Her voice was not prying, only friendly. "Pencils?" "That's it," he said. "Pencils." She raised her eyebrows slightly. Her voice seemed thick. "What's in it, Eddie?" "Figure it out yourself." He tossed the case on the couch. Soren Kierkegaard on necessity and possibility in The Sickness Unto Death, Chapter 3, The Diamond of Possibility, the Baseball Almanac,
and this morning's entry, "Natural Hustler." Posted 1/23/2006 at 12:00 PM |
Natural Hustler (jpg, 283 KB) Posted 1/23/2006 at 3:57 AM |
Play
On this date in 1938, Thornton Wilder's "Our Town" premiered at the McCarter Theatre, Princeton University. Related material: St. Patrick's Day, 2005, St. Patrick's Day, 2003, and, for Piper Laurie's birthday (today) in 2003, Through a Soda-Fountain Mirror, Darkly. Posted 1/22/2006 at 2:08 PM |
Fourstone Parable (continued) Alms for Oblivion: In memory of Akkadian scholar Erica Reiner, who died at 81 on December 31, 2005. "Erica combined a tough-minded commitment to intellectual
excellence with a dry wit, charm, and a deep love of art, music,
and literature. Erica's passion for her work was legendary.
She was someone who expected the very highest standards of scholarly
rigor both in her own work, and in the efforts of others." -- Gil Stein, director of the Oriental Institute at the University of Chicago
A Mass for Dr. Reiner was scheduled for Friday the 13th at the church of "doubting Thomas"-- St. Thomas the Apostle in Chicago. Posted 1/22/2006 at 7:00 AM |
Posted 1/22/2006 at 4:07 AM |
Jews on Fiction See Tony Kushner and E.L. Doctorow in today's New York Times, Rebecca Goldstein's talk from last summer's Mykonos conference on mathematics and narrative, and Martin Buber on the Bible. Posted 1/21/2006 at 7:48 AM |
Fourstone Parable
"Wherefore let it hardly... be... thought that the prisoner... was at his best a onestone parable... for... pathetically few... cared... to doubt... the canonicity of his existence as a tesseract." -- Finnegans Wake, page 100, abridged "... we have forgotten that we were angels and painted ourselves into a corner of resource extraction and commodification of ourselves." -- A discussion, in a draft of a paper (rtf) attributed to Josh Schultz, of the poem "Diamond" by Attila Jozsef Commodification of See the logos at
To adapt a phrase from Fourstone Parable: (See also yesterday's "Logos." For a more elegant Posted 1/20/2006 at 12:00 PM |
VERA JOHNSON Posted 1/19/2006 at 8:00 PM |
Logos
Posted 1/19/2006 at 9:00 AM |
"Wallace Stevens's remarkable oeuvre is a quasi-spiritual quest for the supreme fiction, for a poetry that 'must take the place / Of empty heaven and its hymns' and thus help modern man find meaning in a godless world. The poet's role, for Stevens, is that of high priest of the imagination: it is the poet who 'gives to life the supreme fictions without which we are unable to conceive of it.' .... ... Stevens's hallmark 'imagination-reality' complex... is pursued almost obsessively in his poetry and prose of the 1940s. Parts of a World, published in 1942, and the poem-sequence of the same year, 'Notes toward a Supreme Fiction' ('Notes' was subsequently collected in Transport to Summer in 1947), comprise a prolonged meditation in a time of war on poetry and the poet's role, in the face of what Stevens, in his essay 'The Noble Rider and the Sound of Words,' terms 'the pressure of reality.' Parts of a World is riven by its competing vocabularies. A discourse of desire, of process, of the poet's contemplation of the mind in the act of finding what will suffice, is elaborated in 'the never-resting mind' of 'The Poems of Our Climate' and in 'The Well Dressed Man with a Beard,' in which 'It can never be satisfied, the mind, never' [occurs]. A very different idiom, that of the 'hero' or 'major man,' the figure of capable imagination, dominates and directs such poems as 'Mrs Alfred Uruguay,' 'Asides on the Oboe' and 'Examination of the Hero in a Time of War,' where Summer, jangling the savagest diamonds and Dressed in its azure-doubled crimsons, May truly bear its heroic fortunes For the large, the solitary figure." -- Lee M. Jenkins, University College Cork, "Wallace Stevens," The Literary Encyclopedia, 9 Dec., 2004. For some related serious, but less solemn, remarks, click on the above date. Posted 1/19/2006 at 7:48 AM |
Plato and Shakespeare at Breakfast "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 For Plato:
Inscapes. For Shakespeare: Hopkins on Inscape. For both: Click on the picture for related remarks. Posted 1/19/2006 at 6:23 AM |
Bang Splat (review) School Book Depository "Many people look at the Kennedy assassination as a turning point, when people started realizing and thinking and believing their government would lie to them and lie to them repeatedly," said Gary Mack, curator of the Sixth Floor Museum at Dealey Plaza in Dallas. Better late than never.Posted 1/17/2006 at 11:00 PM |
BBC News Jan. 17 Related material: Log24 Sept. 27 and Sept. 28, 2005, as well as The Harvard Crimson, Jan. 13, 2006: "President was resolute-- 'This is bullshit'" Posted 1/17/2006 at 12:00 PM |
Mathematics and Narrative Rebecca Goldstein, Mathematics and the Character of Tragedy: "It was Plato who best expressed-- who veritably embodied-- the tension between the narrative arts and mathematics." Veritably. Posted 1/16/2006 at 4:00 AM |
Inscape My entry for New Year's Day links to a paper by Robert T. Curtis* from The Arabian Journal for Science and Engineering (King Fahd University, Dhahran, Saudi Arabia), Volume 27, Number 1A, January 2002. From that paper: "Combinatorially, an outer automorphism [of S6] can exist because the number of unordered pairs of 6 letters is
equal to the number of ways in which 6 letters can be partitioned into three pairs. Which is to say that the
two conjugacy classes of odd permutations of order 2 in S6
contain the same number of elements, namely 15. Sylvester... refers to
the unordered pairs as duads and the partitions as synthemes. Certain
collections of five synthemes... he refers to as synthematic totals or simply totals; each total is stabilized within S6 by a subgroup acting triply transitively on the 6 letters as PGL2(5)
acts on the projective line. If we draw a bipartite graph on (15+15)
vertices by joining each syntheme to the three duads it contains, we
obtain the famous 8-cage (a graph of valence 3 with minimal cycles of
length 8)...." Here is a way of picturing the 8-cage and a related configuration of points and lines:
Diamond Theory shows that this structure
The illustration below shows how the
* "A fresh approach to the exceptional automorphism and covers of the symmetric groups"
Posted 1/15/2006 at 7:59 AM |
Diamond Jubilance
(See previous entry.)
"A (very brief!) lit search reveals very little on the intersection
between probability theory and modal logic.... probability and modality
are such big topics one would think there'd be something on their intersection, and I don't think the way I've framed the problem is entirely idiosyncratic."
-- Brian Weatherson, Associate Professor of Philosophy, Cornell University, May 11, 2004 Here, on the other hand, is a way of framing the problem that is entirely idiosyncratic: On this date: Probability: In 1970, William Feller died. Modality: In 1978, Kurt Gödel died. Intersection: In 1898, the Rev. Deacon Charles Lutwidge Dodgson died. Posted 1/14/2006 at 4:07 AM |
Beyond the Fire "Who Needs a White Cube These Days?" -- Headline in today's New York Times "That Nature is a Heraclitean Fire..." -- Poem title, Gerard Manley Hopkins "... Sleep realized Was the whiteness that is the ultimate intellect, A diamond jubilance beyond the fire, That gives its power to the wild-ringed eye." -- Wallace Stevens, "The Owl in the Sarcophagus" III 13-16, from The Auroras of Autumn, 1950 Related material: The five entries ending on Christmas, 2005. Posted 1/13/2006 at 12:00 PM |
Time in the Rock "a world of selves trying to remember the self before the idea of self is lost-- Walk with me world, upon my right hand walk, speak to me Babel, that I may strive to assemble of all these syllables a single word before the purpose of speech is gone." -- Conrad Aiken, "Prelude" (1932), later part of "Time in the Rock, or Preludes to Definition, XIX" (1936), in Selected Poems, Oxford U. Press paperback, 2003, page 156 "The rock is the habitation of the whole, Its strength and measure, that which is near, point A In a perspective that begins again At B: the origin of the mango's rind. It is the rock where tranquil must adduce Its tranquil self, the main of things, the mind, The starting point of the human and the end, That in which space itself is contained, the gate To the enclosure, day, the things illumined By day, night and that which night illumines, Night and its midnight-minting fragrances, Night's hymn of the rock, as in a vivid sleep." -- Wallace Stevens in The Rock (1954) "Poetry is an illumination of a surface, the movement of a self in the rock." -- Wallace Stevens, introduction to The Necessary Angel, 1951 Related material: Jung's Imago and Solomon's Cube. The following may help illuminate the previous entry: "I want, as a man of the imagination, to write poetry with all the power of a monster equal in strength to that of the monster about whom I write. I want man's imagination to be completely adequate in the face of reality." -- Wallace Stevens, 1953 (Letters 790) The "monster" of the previous entry is of course not Reese Witherspoon, but rather Vox Populi itself. Posted 1/11/2006 at 10:30 PM |
Monster
BBC News today: Reese Witherspoon was the winner of the leading lady award at the People's Choice ceremony in Los Angeles. "Walk the Line could turn out
to be a monster chick flick, because its design is almost mythic...." -- Entertainment Weekly Almost? See the two previous entries. Related material: Election, All About Eve. Posted 1/11/2006 at 11:07 AM |
Chick Flicks
From NT Gateway Weblog,
Sunday, Nov. 6, 2005: Question: What does Chicken Little have in common with The Passion of the Christ? An anonymous commenter's answer: "The title character announces the coming of the end, suffers mockery and condemnation, and ends up saving the world through his actions." (The "real" answer: "The music for each was composed by John Debney.") Related sermon: Click on the chicken. Related hymn: "Till Armageddon, no Shalam, no Shalom. Then the father hen will call his chickens home." -- Johnny Cash Posted 1/11/2006 at 4:09 AM |
Ten is a Hen
(continued) From Nov. 12, 2005: "Follow the spiritual journey that is BEE SEASON." "'Tikkun Olam, the fixing of the world,' she whispers. 'I've been gathering up the broken vessels to make things whole again.'" From Nov. 14, 2005:
Today's vocabulary lesson: Click on the word for the definition. A search on the related adjective "hendiadic" leads to an insightful discussion of religion and law in contemporary Latin America by Antônio Flávio Pierucci. For other material on Latin America and religion from Robert Stone and Nythamar Fernandes de Oliveira, see the Jan. 25, 2005, entry Diamonds Are Forever. Related material: Yesterday's link for Nixon's birthday led to an obituary of a Marxist writer that concluded as follows: "In 2004, Mr. Magdoff wrote about his friendship with Che Guevara,
one of his revolutionary heroes. At what proved to be their final
meeting before Mr. Guevara's death in 1967, Mr. Magdoff asked what he
could do to help Cuba. 'Keep on educating me,' was the response." For the education of Latin America
I recommend the writings of Pierucci, Stone, and Oliveira, but not those of Magdoff. Posted 1/10/2006 at 5:01 AM |
Posted 1/9/2006 at 6:01 AM |
Cornerstone "In 1782, the Swiss mathematician Leonhard Euler posed a problem
whose mathematical content at the time seemed about as much as that of
a parlor puzzle. 178 years passed before a complete solution was found;
not only did it inspire a wealth of mathematics, it is now a cornerstone
of modern design theory."
-- Dean G. Hoffman, Auburn U., July 2001 Rutgers talk Diagrams from Dieter Betten's 1983 proof of the nonexistence of two orthogonal 6x6 Latin squares (i.e., a proof of Tarry's 1900 theorem solving Euler's 1782 problem of the 36 officers): Compare with the partitions into two 8-sets of the 4x4 Latin squares discussed in my 1978 note (pdf). Posted 1/9/2006 at 5:01 AM |
For Stephen Hawking's Birthday Epigraphs to the classic novel Cosmic Banditos:
Today's Pennsylvania Lottery numbers:
Posted 1/8/2006 at 8:00 PM |
Strange Attractor (See also the star as a For Heinrich Harrer,
Harrer was one of the 1938 team that first climbed the north face (the Nordwand, also called the Mordwand, or "death" face) of the Eiger.
Wikipedia on the north face of the Eiger: "Connoisseur of Chaos,"
After all the pretty contrast of life and death
The pensive man . . . He sees that eagle float Related material:
Posted 1/7/2006 at 11:09 PM |
Cross
Today's birthday: E. L. Doctorow, author of City of God "In the Garden of Adding live Even and Odd." -- City of God Adapted from Ad Reinhardt "... I don't write exclusively on Jewish
themes or about Jewish characters. My collection of short stories, Strange
Attractors, contained nine pieces, five of which were, to some degree, Jewish,
and this ratio has provided me with a precise mathematical answer (for me, still
the best kind of answer) to the question of whether I am a Jewish writer. I am
five-ninths a Jewish writer."
Posted 1/6/2006 at 8:23 AM |
Posted 1/5/2006 at 6:15 PM |
Hamilton's Whirligig For details, see Visualizing GL(2,p). "Mathematical relationships were enough to satisfy him, mere
formal relationships which existed at all times, everywhere, at once.
It was a thin nectar, but he was convinced it was the nectar of the
gods...."
-- Paul Preuss, Broken Symmetries
Posted 1/5/2006 at 9:00 AM |
Dark City
I stood in the cold on the porch -- Richard Eberhart, Posted 1/5/2006 at 12:00 AM |
Dragon School
In memory of Humphrey Carpenter, author of The Inklings, who attended The Dragon School. Carpenter died a year ago today.
From Log24 on Nov. 16, 2005:
Images
"Lewis began with a number of haunted images...." "The best of the books are the ones... where the allegory is at a minimum and the images just flow." "'Everything began with images,' Lewis wrote...." From Paul Preuss, Broken Symmetries (see previous entry): "Mathematical relationships were enough to satisfy him, mere
formal relationships which existed at all times, everywhere, at once.
It was a thin nectar, but he was convinced it was the nectar of the
gods...."
From Verbum Sat Sapienti? Escher's Verbum Solomon's Cube Geometry of the I Ching Posted 1/4/2006 at 4:04 AM |
"The Transfiguration of Christ is the culminating point of His public life.... Jesus took with him Peter and James and John and led them to a high mountain apart, where He was transfigured before their ravished eyes. St. Matthew and St. Mark express this phenomenon by the word metemorphothe, which the Vulgate renders transfiguratus est. The Synoptics explain the true meaning of the word by adding 'his face did shine as the sun: and his garments became white as snow,' according to the Vulgate, or 'as light,' according to the Greek text. This dazzling brightness which emanated from His whole Body was produced by an interior shining of His Divinity." -- The Catholic Encyclopedia of 1912 The Shining according to
Paul Preuss: From Broken Symmetries, 1983, Chapter 16: "He'd toyed with 'psi' himself.... The reason he and so many other theoretical physicists were suckers for the stuff was easy to understand-- for two-thirds of a century an enigma had rested at the heart of theoretical physics, a contradiction, a hard kernel of paradox.... Peter [Slater] had never thirsted after 'hidden variables' to explain what could not be pictured. Mathematical relationships were enough to satisfy him, mere formal relationships which existed at all times, everywhere, at once. It was a thin nectar, but he was convinced it was the nectar of the gods.... Those so-called crazy psychics were too sane, that was their problem-- they were too stubborn to admit that the universe was already more bizarre than anything they could imagine in their wildest dreams of wizardry." Posted 1/4/2006 at 2:00 AM |
See also Step One -- "Happy Six,"* and Step Two -- "Then a Miracle Occurs."** The miracle occurred on the Feast of the Transfiguration, August 6, 1945, at 8:15 AM in Hiroshima, Japan. * This Jan. 1 entry links to a paper by Robert T. Curtis from The Arabian Journal for Science and Engineering (King Fahd University, Dhahran, Saudi Arabia), Volume 27, Number 1A, January 2002.
** This Jan. 2 entry discusses Einstein as, according to the New York Times, "a moral and even spiritual sage." Posted 1/3/2006 at 8:06 PM |
Then a Miracle Occurs The New York Times on Sunday, New Year's Day, 2006, by John Horgan-- "Einstein Has Left the Building"-- "Down the hall from my office, Albert Einstein's electric-haired visage beams from a poster for the 'World Year of Physics 2005.' The poster celebrates the centennial of the 'miraculous year' when a young patent clerk in Bern, Switzerland, revolutionized physics with five papers on relativity, quantum mechanics and thermodynamics. 'Help make 2005 another Miraculous Year!' the poster exclaims.... As 2005 wound down with no miracles in sight, the poster took on an increasingly poignant cast, like a Kerry/Edwards bumper sticker...."From a debate:
Click on "religion" in this quote to find out what Einstein really meant. Here's a bumper sticker for Horgan: More from Horgan's New Year's Day sermon: "We revere [Einstein] not only as a scientific genius but also as a moral and even spiritual sage....""What you mean 'we,' blue man?" -- The Red States Posted 1/2/2006 at 12:25 PM |
Posted 1/1/2006 at 6:00 AM |