Monday, September 8, 2025
For My Dear Watson —
Elementary Deep Blue Magic
Elementary Deep Blue Magic
Saturday, July 20, 2024
Annals of Western Philosophy:
Blue Opera Meets Blue Magic
For the "Blue Opera" part, see other posts so tagged.
The above may, if one likes, be regarded as ekphrasis for . . .
(For the part played by "six" and "nine" above, see Lo Shu.)
Blue Opera Meets Blue Magic
Sunday, March 31, 2024
Blue
From this journal on October 15, 2023 —
|
"Can you make it any more complicated?" |
One approach . . .
Friday, September 29, 2023
36 Shades of Blue: Namespace Mastery and Subjection
Tom McCarthy today on a new novel about von Neumann at Los Alamos:
|
"Beyond its mid-20th-century viewfinder, though, it quickly becomes clear that what The Maniac is really trying to get a lock on is our current age of digital-informational mastery and subjection." "Amid — or, more aptly, beneath — the panoply of brilliant men in The Maniac , women function as bit players. At Los Alamos they’re even called 'computers,' since they carry out the secondary, workaday calculations that are then fed upward for male geniuses to work their magic on. But does von Neumann really deserve the title 'Father of Computers,' granted him here by his first wife, Mariette Kovesi? Doesn’t Ada Lovelace have a prior claim as their mother?" |

Tuesday, July 23, 2019
Word Magic
"Business-wise, Magic is working—Bloomberg reported
that the game brought in $500 million in revenue last year.
Hasbro owns Monopoly and Scrabble, but Magic is its top
game brand. . . .
The idea of using a card mechanic to generate story has
precedent—the Italian postmodern writer Italo Calvino
generated an entire novel based on drawing from a
tarot card deck. Games provide frameworks that miniaturize
and represent idealized realities; so do narratives."
— Adam Rogers, Sunday, July 21, 2019, at Wired
"The Esper party began . . ." —
|
Life of the Party From Stephen King's Dreamcatcher :
From Alfred Bester's The Demolished Man :
From Anne McCaffrey's To Ride Pegasus :
"… it's going to be accomplished in steps, this |
Adam Rogers at Wired as quoted above —
"The idea of using a card mechanic to generate story
has precedent. . . ."
See The Greater Trumps .
Monday, April 14, 2025
Märchen — A Bella Vista Song
♪ "So you wanna play with magic?" ♪ — Katy Perry

Wednesday, December 4, 2024
Tuesday, November 12, 2024
Poster Art
Friday, April 14, 2023
Saturday, September 10, 2022
Solomon’s Mental Health Month
May 2003 was "Solomon's Mental Health Month" in this journal.
An essay linked to on the 9th of May in that month —
|
"Taking the Veil," by Jessica Kardon
https://web.archive.org/web/20021102182519/ James Hillman, writing in The Soul's Code, argues for his "acorn theory" of human individual identity, and suggests that "each person bears a uniqueness that asks to be lived and that is already present before it can be lived." He insists we are born with a given character, a daimon, the carrier of destiny. This theory is closely linked to the beautiful myth described by Plato in his Republic, when the soul stands before Lachesis and receives his specific soul guardian. Hillman maintains that the daimon will always emerge somehow, even if thwarted or unrecognized. I never had ambitions that reached fruition in the adult world. I have had only two career interests in my life – both formed precognitively. I wanted to be a mermaid or a nun. By the time I learned – shockingly late – that I could not be a mermaid, I had realized I would not be a nun. I concur with Hillman's emphasis on the persistence of early disposition, and I like to imagine that my dreamy, watery, Victorian and self-righteous psyche has held aspects of both of these early interests, throughout my life. I was adopted one month after my birth. I was tended by nuns during the first four weeks of my life. Thereafter, I spent my whole educational life in convent schools. It was the sisters of Saint Vincent de Paul that gave me my favorite musical and my early distortions about romantic love and the gender plans of Our Lord. My misconceptions about love and marriage were culled from the Lerner Loewe musical Gigi, a wonderful film based loosely on a Colette novel. I was summoned along with my whole class to the gymnasium to view the movie under the edgy eye of Sister Bernadette. Sister Bernadette was a large, mesomorphic nun famed for the beatings she gave to boys and girls alike, and feared for the mean zest with which she bestowed her favors upon many of us. I was not beaten – but once, believing I was wearing lipstick, she held my head in a sink and scrubbed my lips until they bled, then slapped me. I recall this with a mild, rueful whimsy. We were all manhandled. In memory, Bernadette seems more like an angry and troubled older sibling than a true figure of authority. Anyway, I loved Gigi. It fed directly into my Francophilia. I was convinced that at some future date, I, like Gigi, would be trained as a courtesan. I, too, would cause some hard case, experienced roué to abandon his chill and irony. I saw myself strolling down the Champs Elysee with Louis Jordan in rapt attendance, pushing a baby carriage, wearing a hat the size of a manhole cover, hoisting a parasol above that to assure the longevity of my adorable pallor. The gender plans of Our Lord had recently been revealed to me too. Sister B. had drawn a ladder on the blackboard, a ladder with three rungs. At the top, she explained, were the priests, the nuns, and the monks. These souls had surrendered their lives to God. All would be taken directly to heaven upon their passing from this vale of tears, as we all referred to the world in those lean emotional times. On the middle rung stood the married. If you married and kept the law – which meant leaving every act of marital congress open to the reception of a child, you would be eligible for heaven. If you were foul in marriage, seeking your pleasure, you were going to be damned. On the bottom rung were those selfish souls who had remained single and had imagined their lives their own. This group had never given themselves to Our Lord. They were headed to hell in a sort of preternatural laundry chute. So we little ladies had two viable options: marry and breed without ceasing – or take the veil. Despite my hat and perambulator fantasies, once given the sorry news of the ladder, the veil became the clear romantic favorite. Therefore I began my research. I obtained a catalogue of nunnery. It offered photographs of each order, describing the duties of the specific order, and displaying the garb of that order. I was looking for two things – a great looking veil and gown, and a contemplative order. I had no desire to sully my glorious vision of myself with a life in the outer world. It was apparent to me that the teaching of children was going to involve a whole range of miseries – making them cry, telling them the bad news about the ladder, and so forth. This was not for me. I saw myself kneeling on the floor of my pristine little cell, serene and untouched by human hands. Teaching would be certain to interfere with the proper lighting. Yoked to a bunch of messy children, I could not possibly have the opalescent illumination of heaven falling reliably on my upturned visage. What divided me from my dream of rebirth as a mermaid was the force of what was real: I could not morph. What divided me from my dream of life as a nun was the force of the erotic: I would not abstain. Now, long years later, I am still underwater, and I am still bending the knee. I live in the blue shadows of hidden grottoes, and I am swimming, too, in the gold of my drifting prayers. September 7th, this dream. I am standing in a dimly lit room, gazing at a group of heavy, antique silk burqas that look weirdly like Fortuny gowns. A holy woman approaches me, and tells me that my soul will leave my body, and enter these garments. She turns and points at a young girl standing nearby, a child with close-cropped hair and a solemn look. My heart knows her, but my eyes don't. For a moment I am thinking, exactly as I did in the seventies when holding a joint: "This isn't working." Suddenly, these things: I feel the shape of flame, then I am the shape. I am released into the air, and as pure essence I enter other forms, dissolving in them, gathering my energy back into myself, and flying out again. This was a sensation so exquisite that my dreaming brain woke up and announced to me: "This is a dream about death." I saw that child again as I flew. This time my eyes knew her. I flew to her, but the flame of my soul would not cohere with hers, this child who was, of course, my own self. In the shadows alone, I heard myself whisper: "I'm in the wind. I'm in the water." This lovely dream, which gave me the sublime gift of a little visceral preview of the soul in the death process, also showed me my guardian spirit; divided, but viable. I pass through my life swimming in one self, kneeling in the other. I thought of Rilke's 29th Sonnet to Orpheus and realized this was what I had been dreaming about all my life, moving between them.
by jessica kardon |
See as well yesterday's post "At a Still Point."
Sunday, March 6, 2022
Overarching Symmetries
By the Daniel J. Peterson whose Swarthmore honors thesis was quoted
here last night —
"What, then, is the relationship between theory-relative symmetries
(physical symmetries) and theory-independent symmetries
(overarching symmetries)? My statement of this problem is
a bit abstract, so let’s look at an example: classical Newtonian gravity
and classical electromagnetism . . . ."
— Prospects for a New Account of Time Reversal
by Daniel J. Peterson, Ph.D. dissertation, U. Mich., 2013, p. 16.
Another 2013 approach to the word "overarching" and sytmmetries —
Other terms of interest: Tenet , Nolanism , and Magic for Liars .
Tuesday, December 28, 2021
The Redgrave Pill
"Redgrave proceeded to focus on the end of Blue Nights ,
and Didion’s determination to maintain momentum after
the death of Quintana, when she and Redgrave mounted
their production of The Year of Magical Thinking . Here,
St John the Divine became a setting in the narrative of
Blue Nights yet again – this time, as Quintana’s final resting
place in St Ansgar’s Chapel within the cathedral."
The feast of St. Ansgar is Feb. 3. See that date this year.
Related song lyric from "Finian's Rainbow" —
Necessity,
That's the maximum that a minimum thing could be,
There's nothing lower than less unless it's Necessity.
Tuesday, April 3, 2018
The Cage Country
Saturday, August 26, 2017
The Seventh Door Meets the Seventh Function
|
The Seventh Function
The New York Times
"What if . . . Barthes was murdered? . . . in order to |
Schorske mentioned hopefully "the fresh light of
the present" in 1971.
Some later light from Brian Aldiss in his novel
Frankenstein Unbound , first published in 1973 —
Friday, December 2, 2016
Smoke from the Sacred Wood
The beginning of an essay by Emily Witt that is to appear on Sunday,
Dec. 4, 2016, in the T Magazine of The New York Times —
| "Palo santo, which means 'holy stick' in Spanish, is a tree indigenous to the Caribbean and South America. When burned, it emits a fragrance of pine and citrus. Lighting a stick of palo santo, like burning a bundle of sage or sweetgrass, is believed to chase away misfortune. Amazonian shamans use it in ayahuasca ceremonies to cleanse a ceremonial space of bad spirits. Given its mystical connotations, it’s not a scent associated with the secular world, but lately I have noticed its distinctive smoke wafting over more earthly settings, from Brooklyn dive bars to blue-chip art openings." |
The ending of an essay by T. S. Eliot that appeared in his 1921 book
titled The Sacred Wood —
Those who prefer ayahuasca ceremonies may consult
a Sept. 10 post, Cocktail of the Damned.
Thursday, November 17, 2011
Void
From "Elegy to the Void," by Cathleen Schine, New York Review of Books , issue dated Nov. 24, 2011—
“We tell ourselves stories in order to live,” Didion famously wrote in The White Album . Blue Nights is about what happens when there are no more stories we can tell ourselves, no narrative to guide us and make sense out of the chaos, no order, no meaning, no conclusion to the tale. The book has, instead, an incantatory quality: it is a beautiful, soaring, polyphonic eulogy, a beseeching prayer that is sung even as one knows the answer to one’s plea, and that answer is: No.
Blue Nights is a sequel of sorts to The Year of Magical Thinking , Didion's story of the year following the death on December 30th, 2003, of her husband, fellow writer John Gregory Dunne.
Related material:



For some context, see
- Cosmic Banditos in this journal,
- the Fall 1997 newsletter of the Institute for Advanced Study,
- and Oppenheimer's Aria.
For a different link to that aria, see a journal entry dated December 28, 2003.
(Click link, scroll down.)
Sunday, May 25, 2008
Sunday May 25, 2008
— Song lyric, Cyndi Lauper
Magister Ludi
Hermann Hesse's 1943 The Glass Bead Game (Picador paperback, Dec. 6, 2002, pp. 139-140)–
"For the present, the Master showed him a bulky memorandum, a proposal he had received from an organist– one of the innumerable proposals which the directorate of the Game regularly had to examine. Usually these were suggestions for the admission of new material to the Archives. One man, for example, had made a meticulous study of the history of the madrigal and discovered in the development of the style a curved that he had expressed both musically and mathematically, so that it could be included in the vocabulary of the Game. Another had examined the rhythmic structure of Julius Caesar's Latin and discovered the most striking congruences with the results of well-known studies of the intervals in Byzantine hymns. Or again some fanatic had once more unearthed some new cabala hidden in the musical notation of the fifteenth century. Then there were the tempestuous letters from abstruse experimenters who could arrive at the most astounding conclusions from, say, a comparison of the horoscopes of Goethe and Spinoza; such letters often included pretty and seemingly enlightening geometric drawings in several colors."
A Bulky Memorandum
From Siri Hustvedt, author of Mysteries of the Rectangle: Essays on Painting (Princeton Architectural Press, 2005)– What I Loved: A Novel (Picador paperback, March 1, 2004, page 168)–
A description of the work of Bill Wechsler, a fictional artist:
"Bill worked long hours on a series of autonomous pieces about numbers. Like O's Journey, the works took place inside glass cubes, but these were twice as large– about two feet square. He drew his inspiration from sources as varied as the Cabbala, physics, baseball box scores, and stock market reports. He painted, cut, sculpted, distorted, and broke the numerical signs in each work until they became unrecognizable. He included figures, objects, books, windows, and always the written word for the number. It was rambunctious art, thick with allusion– to voids, blanks, holes, to monotheism and the individual, the the dialectic and yin-yang, to the Trinity, the three fates, and three wishes, to the golden rectangle, to seven heavens, the seven lower orders of the sephiroth, the nine Muses, the nine circles of Hell, the nine worlds of Norse mythology, but also to popular references like A Better Marriage in Five Easy Lessons and Thinner Thighs in Seven Days. Twelve-step programs were referred to in both cube one and cube two. A miniature copy of a book called The Six Mistakes Parents Make Most Often lay at the bottom of cube six. Puns appeared, usually well disguised– one, won; two, too, and Tuesday; four, for, forth; ate, eight. Bill was partial to rhymes as well, both in images and words. In cube nine, the geometric figure for a line had been painted on one glass wall. In cube three, a tiny man wearing the black-and-white prison garb of cartoons and dragging a leg iron has
— End of page 168 —
opened the door to his cell. The hidden rhyme is "free." Looking closely through the walls of the cube, one can see the parallel rhyme in another language: the German word drei is scratched into one glass wall. Lying at the bottom of the same box is a tiny black-and-white photograph cut from a book that shows the entrance to Auschwitz: ARBEIT MACHT FREI. With every number, the arbitrary dance of associations worked togethere to create a tiny mental landscape that ranged in tone from wish-fulfillment dream to nightmare. Although dense, the effect of the cubes wasn't visually disorienting. Each object, painting, drawing, bit of text, or sculpted figure found its rightful place under the glass according to the necessary, if mad, logic of numerical, pictorial, and verbal connection– and the colors of each were startling. Every number had been given a thematic hue. Bill had been interested in Goethe's color wheel and in Alfred Jensen's use of it in his thick, hallucinatory paintings of numbers. He had assigned each number a color. Like Goethe, he included black and white, although he didn't bother with the poet's meanings. Zero and one were white. Two was blue. Three was red, four was yellow, and he mixed colors: pale blue for five, purples in six, oranges in seven, greens in eight, and blacks and grays in nine. Although other colors and omnipresent newsprint always intruded on the basic scheme, the myriad shades of a single color dominated each cube.
The number pieces were the work of a man at the top of his form. An organic extension of everything Bill had done before, these knots of symbols had an explosive effect. The longer I looked at them, the more the miniature constructions seemed on the brink of bursting from internal pressure. They were tightly orchestrated semantic bombs through which Bill laid bare the arbitrary roots of meaning itself– that peculiar social contract generated by little squiggles, dashes, lines, and loops on a page."
(named not for
Bill Wechsler, the
fictional artist above,
but for the non-fictional
David Wechsler) –
|
From 2002:
Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale "block design" subtest. |
A Magic Gallery
|
ZZ
Figures from the
Poem by Eugen Jost:
Mit Zeichen und Zahlen
Numbers and Names,
With numbers and names
English translation A related poem:
Alphabets
From time to time
But if a savage
— Hermann Hesse (1943), |
Sunday, March 2, 2008
Sunday March 2, 2008
what it is to be awake,
To be living
on several planes at once
Though one cannot speak
with several voices at once.”
— T. S. Eliot,
The Family Reunion

Several voices:
Margaret Wertheim in today’s
Los Angeles Times and at
The Pearly Gates of Cyberspace,
Linda Dalrymple Henderson, and
Madeleine L’Engle and husband.
From Wertheim’s Pearly Gates:

“There is such a thing
as a tesseract.”
Friday, May 25, 2007
Friday May 25, 2007
From Log24 on
this date last year:
"May there be an ennui
of the first idea?
What else,
prodigious scholar,
should there be?"
— Wallace Stevens,
"Notes Toward a
Supreme Fiction"
The Associated Press,
May 25, 2007–
Thought for Today:
"I hate quotations.
Tell me what you know."
— Ralph Waldo Emerson

This "telling of what
I know" will of course
mean little to those
who, like Emerson,
have refused to learn
through quotations.
For those less obdurate
than Emerson —Harold Bloom
on Wallace Stevens
and Paul Valery's
"Dance and the Soul"–
"Stevens may be playful, yet seriously so, in describing desire, at winter's end, observing not only the emergence of the blue woman of early spring, but seeing also the myosotis, whose other name is 'forget-me-not.' Desire, hearing the calendar hymn, repudiates the negativity of the mind of winter, unable to bear what Valery's Eryximachus had called 'this cold, exact, reasonable, and moderate consideration of human life as it is.' The final form of this realization in Stevens comes in 1950, in The Course of a Particular, in the great monosyllabic line 'One feels the life of that which gives life as it is.' But even Stevens cannot bear that feeling for long. As Eryximachus goes on to say in Dance and the Soul:
A cold and perfect clarity is a poison impossible to combat. The real, in its pure state, stops the heart instantaneously….[…] To a handful of ashes is the past reduced, and the future to a tiny icicle. The soul appears to itself as an empty and measurable form. –Here, then, things as they are come together, limit one another, and are thus chained together in the most rigorous and mortal* fashion….
O Socrates, the universe cannot for one instant endure to be only what it is.
Valery's formula for reimagining the First Idea is, 'The idea introduces into what is, the leaven of what is not.' This 'murderous lucidity' can be cured only by what Valery's Socrates calls 'the intoxication due to act,' particularly Nietzschean or Dionysiac dance, for this will rescue us from the state of the Snow Man, 'the motionless and lucid observer.'" —Wallace Stevens: The Poems of Our Climate
* "la sorte… la plus mortelle":
mortal in the sense
"deadly, lethal"
Other quotations
(from March 28,
the birthday of
Reba McEntire):
Logical Songs

Logical Song I
(Supertramp)
"When I was young, it seemed that
Life was so wonderful, a miracle,
Oh it was beautiful, magical
And all the birds in the trees,
Well they'd be singing so happily,
Joyfully, playfully watching me"
Logical Song II
(Sinatra)
"You make me feel so young,
You make me feel like
Spring has sprung
And every time I see you grin
I'm such a happy in-
dividual….
You and I are
Just like a couple of tots
Running across the meadow
Picking up lots
Of forget-me-nots"
Tuesday, July 11, 2006
Tuesday July 11, 2006
It's like tryin' to
tell a stranger 'bout
Rock 'n' Roll
— Terry Kirby, Syd Barrett: The Crazy Diamond, in The Independent of July 12
Keynote
"Each scene is punctuated with a rock track from such acts as the Velvet Underground, the Doors, the Rolling Stones, Bob Dylan and Pink Floyd. Songs by Floyd's lost founder, Syd Barrett, are the keynote for Stoppard's theme that rock music sounded the death knell for repression but also heralded a freedom filled with its own perils."
— Ray Bennett, today's review of a new play, "Rock 'n' Roll," by Tom Stoppard
Dance of the Numbers,
for Tom Stoppard
on his birthday,
July 3, 2006,
and
Knock, Knock, Knockin',
from yesterday.
Sunday, October 9, 2005
Sunday October 9, 2005
Magical Thinking
the first generator at Boulder
(later Hoover) Dam began
transmitting electricity to Los Angeles."
— Today in History, Associated Press
generates radiance."
— Hexagram 30
"I know what nothing means."
— Maria Wyeth in Play It As It Lays
"Nothing is random."
— Mark Helprin in Winter's Tale
"… She thought about nothing. Her mind was a blank tape, imprinted daily with snatches of things overheard, fragments of dealers' patter, the beginnings of jokes and odd lines of song lyrics. When she finally lay down nights in the purple room she would play back the day's tape, a girl singing into a microphone and a fat man dropping a glass, cards fanned on a table and a dealer's rake in closeup and a woman in slacks crying and the opaque blue eyes of the guard at some baccarat table. A child in the harsh light of a crosswalk on the Strip. A sign on Fremont Street. A light blinking. In her half sleep the point was ten, the jackpot was on eighteen, the only man that could ever reach her was the son of a preacher man, someone was down sixty, someone was up, Daddy wants a popper and she rode a painted pony let the spinning wheel spin.
By the end of a week she was thinking constantly about where her body stopped and the air began, about the exact point in space and time that was the difference between Maria and other. She had the sense that if she could get that in her mind and hold it for even one micro-second she would have what she had come to get. As if she had fever, her skin burned and crackled with a pinpoint sensitivity. She could feel smoke against her skin. She could feel voice waves. She was beginning to feel color, light intensities, and she imagined that she could be put blindfolded in front of the signs at the Thunderbird and the Flamingo and know which was which. 'Maria,' she felt someone whisper one night, but when she turned there was nobody.
She began to feel the pressure of Hoover Dam, there on the desert, began to feel the pressure and pull of the water. When the pressure got great enough she drove out there. All that day she felt the power surging through her own body. All day she was faint with vertigo, sunk in a world where great power grids converged, throbbing lines plunged finally into the shallow canyon below the dam's face, elevators like coffins dropped into the bowels of the earth itself. With a guide and a handful of children Maria walked through the chambers, stared at the turbines in the vast glittering gallery, at the deep still water with the hidden intakes sucking all the while, even as she watched, clung to the railings, leaned out, stood finally on a platform over the pipe that carried the river beneath the dam. The platform quivered. Her ears roared. She wanted to stay in the dam, lie on the great pipe itself, but reticence saved her from asking.
'Just how long have you been here now,' Freddy Chaikin asked when she ran into him in Caesar's. 'You planning on making a year of it? Or what?'"
Related material
The front page of today's
New York Times Book Review
and Log24, July 15, 2004:
|
A quotation that somehow
seems relevant:
O the mind, mind has mountains, |
Thursday, June 23, 2005
Thursday June 23, 2005
Mathematics and Metaphor
The current (June/July) issue of the Notices of the American Mathematical Society has two feature articles. The first, on the vulgarizer Martin Gardner, was dealt with here in a June 19 entry, Darkness Visible. The second is related to a letter of André Weil (pdf) that is in turn related to mathematician Barry Mazur’s attempt to rewrite mathematical history and to vulgarize other people’s research by using metaphors drawn, it would seem, from the Weil letter.
A Mathematical Lie conjectures that Mazur’s revising of history was motivated by a desire to dramatize some arcane mathematics, the Taniyama conjecture, that deals with elliptic curves and modular forms, two areas of mathematics that have been known since the nineteenth century to be closely related.
Mazur led author Simon Singh to believe that these two areas of mathematics were, before Taniyama’s conjecture of 1955, completely unrelated —
“Modular forms and elliptic equations live in completely different regions of the mathematical cosmos, and nobody would ever have believed that there was the remotest link between the two subjects.” — Simon Singh, Fermat’s Enigma, 1998 paperback, p. 182
This is false. See Robert P. Langlands, review of Elliptic Curves, by Anthony W. Knapp, Bulletin of the American Mathematical Society, January 1994.
It now appears that Mazur’s claim was in part motivated by a desire to emulate the great mathematician André Weil’s manner of speaking; Mazur parrots Weil’s “bridge” and “Rosetta stone” metaphors —
From Peter Woit’s weblog, Feb. 10, 2005:
“The focus of Weil’s letter is the analogy between number fields and the field of algebraic functions of a complex variable. He describes his ideas about studying this analogy using a third, intermediate subject, that of function fields over a finite field, which he thinks of as a ‘bridge‘ or ‘Rosetta stone.'”
In “A 1940 Letter of André Weil on Analogy in Mathematics,” (pdf), translated by Martin H. Krieger, Notices of the A.M.S., March 2005, Weil writes that
“The purely algebraic theory of algebraic functions in any arbitrary field of constants is not rich enough so that one might draw useful lessons from it. The ‘classical’ theory (that is, Riemannian) of algebraic functions over the field of constants of the complex numbers is infinitely richer; but on the one hand it is too much so, and in the mass of facts some real analogies become lost; and above all, it is too far from the theory of numbers. One would be totally obstructed if there were not a bridge between the two. And just as God defeats the devil: this bridge exists; it is the theory of the field of algebraic functions over a finite field of constants….
On the other hand, between the function fields and the ‘Riemannian’ fields, the distance is not so large that a patient study would not teach us the art of passing from one to the other, and to profit in the study of the first from knowledge acquired about the second, and of the extremely powerful means offered to us, in the study of the latter, from the integral calculus and the theory of analytic functions. That is not to say that at best all will be easy; but one ends up by learning to see something there, although it is still somewhat confused. Intuition makes much of it; I mean by this the faculty of seeing a connection between things that in appearance are completely different; it does not fail to lead us astray quite often. Be that as it may, my work consists in deciphering a trilingual text {[cf. the Rosetta Stone]}; of each of the three columns I have only disparate fragments; I have some ideas about each of the three languages: but I know as well there are great differences in meaning from one column to another, for which nothing has prepared me in advance. In the several years I have worked at it, I have found little pieces of the dictionary. Sometimes I worked on one column, sometimes under another.”
Here is another statement of the Rosetta-stone metaphor, from Weil’s translator, Martin H. Krieger, in the A.M.S. Notices of November 2004, “Some of What Mathematicians Do” (pdf):
“Weil refers to three columns, in analogy with the Rosetta Stone’s three languages and their arrangement, and the task is to ‘learn to read Riemannian.’ Given an ability to read one column, can you find its translation in the other columns? In the first column are Riemann’s transcendental results and, more generally, work in analysis and geometry. In the second column is algebra, say polynomials with coefficients in the complex numbers or in a finite field. And in the third column is arithmetic or number theory and combinatorial properties.”
For greater clarity, see Armand Borel (pdf) on Weil’s Rosetta stone, where the three columns are referred to as Riemannian (transcendental), Italian (“algebraico-geometric,” over finite fields), and arithmetic (i.e., number-theoretic).
From Fermat’s Enigma, by Simon Singh, Anchor paperback, Sept. 1998, pp. 190-191:
Barry Mazur: “On the one hand you have the elliptic world, and on the other you have the modular world. Both these branches of mathematics had been studied intensively but separately…. Than along comes the Taniyama-Shimura conjecture, which is the grand surmise that there’s a bridge between these two completely different worlds. Mathematicians love to build bridges.”
Simon Singh: “The value of mathematical bridges is enormous. They enable communities of mathematicians who have been living on separate islands to exchange ideas and explore each other’s creations…. The great potential of the Taniyama-Shimura conjecture was that it would connect two islands and allow them to speak to each other for the first time. Barry Mazur thinks of the Taniyama-Shimura conjecture as a translating device similar to the Rosetta stone…. ‘It’s as if you know one language and this Rosetta stone is going to give you an intense understanding of the other language,’ says Mazur. ‘But the Taniyama-Shimura conjecture is a Rosetta stone with a certain magical power.'”
If Mazur, who is scheduled to speak at a conference on Mathematics and Narrative this July, wants more material on stones with magical powers, he might consult The Blue Matrix and The Diamond Archetype.
Wednesday, September 22, 2004
Wednesday September 22, 2004
Tribute
In memory of Russ Meyer, who "made industrial films for Standard Oil and lumber companies before making his own films," a picture that might aptly (see Pi continued) be titled
By the same designer:
Click on picture for details.
Object of game:
Connect the devils
with their tail ends.
Manufacturer:
Click on logo for details.
Related material:
The Crimson Passion
Tuesday, June 29, 2004
Tuesday June 29, 2004
|
When? Going to dark bed there was a square round Sinbad the Sailor roc's auk's egg in the night of the bed of all the auks of the rocs of Darkinbad the Brightdayler. Where?
— Ulysses, conclusion of Ch. 17 |
A Visual Meditation for
the Feast of St. Peter
For further details on this structure, see
Magic Squares, Finite Planes,
and Points of Inflection
on Elliptic Curves,
by Ezra Brown, and
Visualizing GL(2, p)
by Steven H. Cullinane.
For a more literary approach
to this structure, see
Balanchine's Birthday (Jan. 9, 2003),
Art Theory for Yom Kippur (Oct. 5, 2003),
A Form (May 22, 2004),
Ineluctable (May 27, 2004),
A Form, continued (June 5, 2004),
Parallelisms (June 6, 2004),
Deep Game (June 26, 2004), and
Gameplayers of Zen (June 27, 2004).
To appreciate fully this last entry
on Gameplayers,
one must understand
the concept of "suicide"
in the game of Go
and be reminded
by the fatuous phrase of the
Institute of Contemporary Art
quoted in Gameplayers —
"encompassed by 'nothing' " —
of John 1:5.





















