From the website Scotland: St. Andrew —

Saint Andrew is the Patron Saint of Scotland, and St. Andrew's Day is celebrated by Scots around the world on the 30th November.
	The flag of Scotland is the Cross of St. Andrew, and this is widely displayed as a symbol of national identity.

Xangans without Scots ancestry may still celebrate by displaying the following symbol:

My previous note includes the following:

"For a... literary antidote to postmodernist nihilism, see Archetypal Theory and Criticism, by Glen R. Gill."

Carl Gustav Jung, from a strongly Protestant background, has been vilified as an "Aryan Christ" by Catholics and Jews. 

To counteract this vilification, here are two links:

Today we examine the relativist, nominalist, leftist, nihilist, despairing, depressing, absurd, and abominable work of Samuel Beckett, darling of the postmodernists.

One lens through which to view Beckett is an essay by Jennifer Martin, "Beckettian Drama as Protest: A Postmodern Examination of the 'Delogocentering' of Language." Martin begins her essay with two quotations: one from the contemptible French twerp Jacques Derrida, and one from Beckett's masterpiece of stupidity, Molloy. For a logocentric deconstruction of Derrida, see my note, "The Shining of May 29," which demonstrates how Derrida attempts to convert a rather important mathematical result to his brand of nauseating and pretentious nonsense, and of course gets it wrong. For a logocentric deconstruction of Molloy, consider the following passage:

"I took advantage of being at the seaside to lay in a store of sucking-stones. They were pebbles but I call them stones.... I distributed them equally among my four pockets, and sucked them turn and turn about. This raised a problem which I first solved in the following way. I had say sixteen stones, four in each of my four pockets these being the two pockets of my trousers and the two pockets of my greatcoat. Taking a stone from the right pocket of my greatcoat, and putting it in my mouth, I replaced it in the right pocket of my greatcoat by a stone from the right pocket of my trousers, which I replaced by a stone from the left pocket of my trousers, which I replaced by a stone from the left pocket of my greatcoat, which I replaced by the stone which was in my mouth, as soon as I had finished sucking it. Thus there were still four stones in each of my four pockets, but not quite the same stones....But this solution did not satisfy me fully. For it did not escape me that, by an extraordinary hazard, the four stones circulating thus might always be the same four."

Beckett is describing, in great detail, how a damned moron might approach the extraordinarily beautiful mathematical discipline known as group theory, founded by the French anticleric and leftist Evariste Galois. Disciples of Derrida may play at mimicking the politics of Galois, but will never come close to imitating his genius. For a worthwhile discussion of permutation groups acting on a set of 16 elements, see R. D. Carmichael's masterly work, Introduction to the Theory of Groups of Finite Order, Ginn, Boston, 1937, reprinted by Dover, New York, 1956.

There are at least two ways of approaching permutations on 16 elements in what Pascal calls "l'esprit géométrique." My website Diamond Theory discusses the action of the affine group in a four-dimensional finite geometry of 16 points. For a four-dimensional euclidean hypercube, or tesseract, with 16 vertices, see the highly logocentric movable illustration by Harry J. Smith. The concept of a tesseract was made famous, though seen through a glass darkly, by the Christian writer Madeleine L'Engle in her novel for children and young adults, A Wrinkle in Tme.

This tesseract may serve as an archetype for what Pascal, Simone Weil (see my earlier notes), Harry J. Smith, and Madeleine L'Engle might, borrowing their enemies' language, call their "logocentric" philosophy.

For a more literary antidote to postmodernist nihilism, see Archetypal Theory and Criticism, by Glen R. Gill.

For a discussion of the full range of meaning of the word "logos," which has rational as well as religious connotations, click here.

There is such a thing as a tesseract.

Searching for background on the phrase "logos and logic" in yesterday's "Notes toward a Supreme Fact," I found this passage:

"...a theory of psychology based on the idea of the soul as the dialectical, self-contradictory syzygy of a) soul as anima and b) soul as animus. Jungian and archetypal psychology appear to have taken heed more or less of only one half of the whole syzygy, predominantly serving an anima cut loose from her own Other, the animus as logos and logic (whose first and most extreme phenomenological image is the killer of the anima, Bluebeard). Thus psychology tends to defend the virginal innocence of the anima and her imagination..."

-- Wolfgang Giegerich, "Once More the Reality/Irreality Issue: A Reply to Hillman's Reply," website 

The anima and other Jungian concepts are used to analyze Wallace Stevens in an excellent essay by Michael Bryson, "The Quest for the Fiction of an Absolute." Part of Bryson's motivation in this essay is the conflict between the trendy leftist nominalism of postmodern critics and the conservative realism of more traditional critics:

"David Jarraway, in his Stevens and the Question of Belief, writes about a Stevens figured as a proto-deconstructionist, insisting on 'Steven's insistence on dismantling the logocentric models of belief' (311) in 'An Ordinary Evening in New Haven.' In opposition to these readings comes a work like Janet McCann's Wallace Stevens Revisited: 'The Celestial Possible', in which the claim is made (speaking of the post-1940 period of Stevens' life) that 'God preoccupied him for the rest of his career.'"

Here "logocentric" is a buzz word for "Christian." Stevens, unlike the postmodernists, was not anti-Christian. He did, however, see that the old structures of belief could not be maintained indefinitely, and pondered what could be found to replace them. "Notes toward a Supreme Fiction" deals with this problem. In his essay on Stevens' "Notes," Bryson emphasizes the "negative capability" of Keats as a contemplative technique:

"The willingness to exist in a state of negative capability, to accept that sometimes what we are seeking is not that which reason can impose...."

For some related material, see Simone Weil's remarks on Electra waiting for her brother Orestes. Simone Weil's brother was one of the greatest mathematicians of the past century, André Weil.

"Electra did not seek Orestes, she waited for him..."

-- Simone Weil

"...at the end, she pulls it all together brilliantly in the story of Electra and Orestes, where the importance of waiting on God rather than seeking is brought home forcefully."

-- Tom Hinkle, review of Waiting for God 

Compare her remarks on waiting for Orestes with the following passage from Waiting for God:

"We do not obtain the most precious gifts by going in search of them but by waiting for them. Man cannot discover them by his own powers, and if he sets out to seek for them he will find in their place counterfeits of which he will be unable to discern falsity.

The solution of a geometry problem does not in itself constitute a precious gift, but the same law applies to it because it is the image of something precious. Being a little fragment of particular truth, it is a pure image of the unique, eternal, and living Truth, the very Truth that once in a human voice declared: "I am the Truth."

Every school exercise, thought of in this way, is like a sacrament.

In every school exercise there is a special way of waiting upon truth, setting our hearts upon it, yet not allowing ourselves to go out in search of it. There is a way of giving our attention to the data of a problem in geometry without trying to find the solution...."

-- Simone Weil, "Reflections on the Right Use of School Studies with a View to the Love of  God"

Weil concludes the preceding essay with the following passage:

"Academic work is one of those fields containing a pearl so precious that it is worth while to sell all of our possessions, keeping nothing for ourselves, in order to be able to acquire it."

This biblical metaphor is also echoed in the work of Pascal, who combined in one person the theological talent of Simone Weil and the mathematical talent of her brother. After discussing how proofs should be written, Pascal says

"The method of not erring is sought by all the world. The logicians profess to guide to it, the geometricians alone attain it, and apart from their science, and the imitations of it, there are no true demonstrations. The whole art is included in the simple precepts that we have given; they alone are sufficient, they alone afford proofs; all other rules are useless or injurious. This I know by long experience of all kinds of books and persons.

And on this point I pass the same judgment as those who say that geometricians give them nothing new by these rules, because they possessed them in reality, but confounded with a multitude of others, either useless or false, from which they could not discriminate them, as those who, seeking a diamond of great price amidst a number of false ones, but from which they know not how to distinguish it, should boast, in holding them all together, of possessing the true one equally with him who without pausing at this mass of rubbish lays his hand upon the costly stone which they are seeking and for which they do not throw away the rest."

-- Blaise Pascal, The Art of Persuasion

As we prepare to see publicity for Russell Crowe in a new role, that of Captain Jack Aubrey in "The Far Side of the World," based on Master and Commander by Patrick O'Brian, we bid farewell to Patti LaBelle and her Ya-Ya, and say hello to a piece more attuned to Aubrey's tastes.  This site's background music is now Mozart's Duo for Violin and Viola in Bb, K.424, 2, andante cantabile. 

In "Notes toward a Supreme Fiction," Wallace Stevens lists criteria for a work of the imagination:

• It Must Be Abstract
• It Must Change
• It Must Give Pleasure.

For a work that seems to satisfy these criteria, see the movable images at my diamond theory website. Central to these images is the interplay of rational sides and irrational diagonals in square subimages.

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

-- "Notes toward a Supreme Fiction," Section 1, Canto VIII

Recall that "logos" in Greek means "ratio," as well as (human or divine) "word." Thus when I read the following words of Simone Weil today, I thought of Stevens.

"The beautiful in mathematics resides in contradiction.   Incommensurability, logoi alogoi, was the first splendor in mathematics."

-- Simone Weil, Oeuvres Choisies, éd. Quarto, Gallimard, 1999, p. 100

In the conclusion of Section 3, Canto X, of "Notes," Stevens says

"They will get it straight one day at the Sorbonne.
 We shall return at twilight from the lecture
 Pleased that the irrational is rational...."

This is the logoi alogoi of Simone Weil.

The title's origin is obscure, but its immediate source is a weblog entry and ensuing comments: "Writing about music is like dancing about architecture.''

A related quote:

"At the still point, there the dance is."

-- T. S. Eliot, "Burnt Norton" in Four Quartets

"Eliot by his own admission took 'the still point of the turning world' in 'Burnt Norton' from the Fool in Williams's The Greater Trumps."

-- Humphrey Carpenter, The Inklings (1978), Ballantine Books, 1981, page 106. Carpenter cites an "unpublished journal of Mary Trevelyan (in possession of the author)."

The following was written this morning as a comment on a weblog entry, but may stand on its own as a partial description of Eliot's and Williams's "dance."

Three sermons on the Fool card, each related to Charles Williams's novel The Greater Trumps:

To Play the Fool,
Games "Not Unlike Chesse," and
Charles Williams and Inklings Links.

"Here is the Church,
Here is the steeple,
Open the door and see all the People."

For some architecture that may or may not be worth dancing about, see the illustrations to Simone Weil's remarks in my note of November 25, 2002, "The Artist's Signature."

From

SUSAN WEIL

EAR'S EYE FOR JAMES JOYCE:

From Finnegans Wake,
by James Joyce, p. 293:

The Vesica Piscis,
also known as
The Ya-Ya:

See also the
Geometries of Creation
art exhibit at the University of Waterloo.

There are two theories of truth, according to a a book on the history of geometry —

The "Story Theory" and the "Diamond Theory." 

For those who prefer the story theory...

From a review by Brian Hayes of A Beautiful Mind:

"Mathematical genius is rare enough. Cloaked in madness, or wrapped in serious eccentricity, it's the stuff legends are made of.

There are brilliant and productive mathematicians who go to the office from nine to five, play tennis on the weekend, and worry about fixing the gearbox in the Volvo. Not many of them become the subjects of popular biographies. Instead we read about the great swashbucklers and misfits of mathematics, whose stories combine genius with high romance or eccentricity."

Russell Crowe, swashbuckler

Marilyn Monroe, misfit

Hollywood has recently given us a mathematical Russell Crowe.  For a somewhat tougher sell, Marilyn Monroe as a mathematician, see "Insignificance," 1985: "Marilyn Monroe on her hands and knees explains the theory of relativity to Albert Einstein."  

For a combination of misfit and swashbuckler in one Holy Name, see today's earlier note, "The Artist's Signature."

See also my note of October 4, 2002, on Michelangelo, and the description of "the face of God" in this review.

This title is taken from the final chapter of Carl Sagan's novel Contact.

"There might be a game in which paper figures were put together to form a story, or at any rate were somehow assembled. The materials might be collected and stored in a scrap-book, full of pictures and anecdotes. The child might then take various bits from the scrap-book to put into the construction; and he might take a considerable picture because it had something in it which he wanted and he might just include the rest because it was there.”

— Ludwig Wittgenstein, Lectures and Conversations on Aesthetics, Psychology and Religious Belief

“Not games. Puzzles. Big difference. That’s a whole other matter. All art — symphonies, architecture, novels — it’s all puzzles. The fitting together of notes, the fitting together of words have by their very nature a puzzle aspect. It’s the creation of form out of chaos. And I believe in form.”

— Stephen Sondheim, in Stephen Schiff, Deconstructing Sondheim,” The New Yorker, March 8, 1993, p. 76

Architectural Vesica Piscis Arch at Glastonbury Tor "All goods in this world, all beauties, all truths, are diverse and partial aspects of one unique good. Therefore they are goods which need to be ranged in order. Puzzle games are an image of this operation. Taken all together, viewed from the right point and rightly related, they make an architecture. Through this architecture the unique good, which cannot be grasped, becomes apprehensible. All architecture is a symbol of this, an image of this. The entire universe is nothing but a great metaphor." — Simone Weil, sister of Princeton mathematician André Weil, First and Last Notebooks, p. 98

This passage from Weil is quoted in
Gateway to God,
p. 42, paperback, fourth impression,
printed in Glasgow in 1982 by
Fontana Books

"He would leave enigmatic messages on blackboards,
signed Ya Ya Fontana."

— Brian Hayes on John Nash,
The Sciences magazine, Sept.-Oct., 1998

"I have a friend who is a Chief of the Aniunkwia (Cherokee) people and I asked him the name of the Creator in which
he replied... Ya Ho Wah. This is also how it is spoken in Hebrew. In my native language it is spoken
Ya Ya*,
which is also what Moses was told
at the 'Burning Bush' incident."

— "Tank" (of Taino ancestry), Bronx, NY, Wednesday, April 17, 2002

From a website reviewing books published by
 Fontana:

1/17/02: NEW YORK (Variety) - Russell Crowe is negotiating to star in 20th Century Fox's "Master and Commander,'' the Peter Weir-directed adaptation of the Patrick O'Brian book series.

Hmmm.

*For another religious interpretation of this phrase, see my note of October 4, 2002, "The Agony and the Ya-Ya."

Results of a Google search -

Searched the web for "Joyce and Aquinas" "William T. Noon".  Results 1-5 of about 15:

Dogma
... Dogma, theological" -- entry in the index (paper, not marble) to Joyce and Aquinas,
by William T. Noon, SJ, Yale U. Press 1957, 2nd printing 1963, page 162. ...
m759.freeservers.com/2001-03-20-dogma.html - 9k - Nov. 23, 2002 - Cached - Similar pages

The Matthias Defense
... Contemplatio: aesthetic joy of, 54-5" -- index to Joyce and Aquinas, by William
T. Noon, SJ, Yale University Press, second printing, 1963, page 162. ...
m759.freeservers.com/2001-03-22-matthias.html - 6k - Nov. 23, 2002 - Cached - Similar pages

Wag the Dogma
... One economy would be to teach the trivium using only one book -- Joyce and Aquinas,
by William T. Noon (Yale, 1957), which ties together philology, logic, and ...
m759.freeservers.com/2001-04-06-wag.html - 6k - Nov. 23, 2002 - Cached - Similar pages

Shining Forth
... Please go away, Paz begged silently.... "De veras! It's so romantic!". -- Let Noon
Be Fair William T. Noon, SJ, Chapter 4 of Joyce and Aquinas, Yale University ...
m759.freeservers.com/2001-03-15-shining.html - 10k - Nov. 23, 2002 - Cached - Similar pages

Midsummer Eve's Dream
... notions... The quidditas or essence of an angel is the same as its
form. (See William T. Noon, SJ, Joyce and Aquinas, Yale, 1957). ...
m759.freeservers.com/1995-06-23-midsummer.html - 12k - Nov. 23, 2002 - Cached - Similar pages

Carl Sagan in Contact:

"According to the Bible, the ancient Hebrews had apparently thought that pi was exactly equal to three."

Don McLean, song lyric: 

"The three men I admire the most,
The Father, Son, and Holy Ghost,
They caught the last train for the coast
The day the music died.*"

Those days are not entirely forgotten in Texas.

*November 22 is the feast day of Saint Cecelia,
celebrated by Chaucer in the Second Nun's Tale. 

Trivia quiz: What is the world's most popular
 piece of music? 

On this date in 1963...

1. Father:  C. S. Lewis (The Abolition of Man), 
2. Son:  John F. Kennedy ("Grace under Pressure" -- displayed, not written), and 
3. Holy Spirit:  Aldous Huxley (The Perennial Philosophy)

all died.

On the bright side:

On this date, Tarzan (John Clayton III, the future Lord Greystoke) was born and Ravel's "Bolero" was first performed.

Jack London died on this date.  On the other hand, Hoagy Carmichael, Jamie Lee Curtis, and Mariel Hemingway were born.

Professor Arthur T. Winfree died on November 5, 2002. 
He was the author of "The Geometry of Biological Time."

• Charles Small (see the earlier entry "Hope of Heaven," November 21):

"I've always been enthralled by the notion that Time is an illusion, a trick our minds play in an attempt to keep things separate, without any reality of its own. My experience suggests that this is literally true...."

• Kylie Minogue in my November 5 entry:

"Time disappears with Tequila.
It goes elastic, then vanishes."

• Octavio Paz on his childhood in Mexico

(Nobel Prize lecture):

"All time, past or future, real or imaginary, was pure presence."

• A colleague on Professor Winfree:

"He just wanted to get to the truth."

• Octavio Paz, condensed and translated 
  
  Nobel Prize lecture:

"Gracias."

This brief heading echoes the title of the latest novel by Michael Crichton, perhaps the best-known member of the Harvard College class of 1964. In honor of that class and of Q (see the preceding entry), here is a condensed excerpt from a passage of Plato quoted by Q:  

Socrates. 'Should we not, before going, offer up a prayer to these local deities?’

'By all means,’ Phaedrus agrees.

Socrates (praying): ‘Beloved Pan, and all ye other gods who haunt this place, grant me beauty in the inward soul, and that the outward and inward may be at one!....

That prayer, I think, is enough for me.’

Phaedrus. ‘Ask the same for me, Socrates. Friends, methinks, should have all things in common.’

Socrates. ‘So be it…. Let us go.’

In accordance with this prayer, and with the coming of summer to Australia, that land beloved of Pan, this site's music now returns to the theme introduced in my note of September 10, 2002, "The Sound of Hanging Rock."

This title is taken from a John O'Hara novel I like very much. It seems appropriate because today is the birthday of three admirable public figures:

• Eleanor Powell, dancer,
• Coleman Hawkins, saxophonist, and
• Sir Arthur Quiller-Couch (Q), teacher.

"No one can top Eleanor Powell - not even Fred Astaire." -- A fellow professional.  Reportedly, "Astaire himself said she was better than him." 

That's as good as it gets.

Let us hope that Powell, Hawkins, and Q are enjoying a place that Q, quoting Plato's Phaedrus, described as follows:

"a fair resting-place, full of summer sounds and scents!"

This is a rather different, and more pleasant, approach to the Phaedrus than the one most familiar to later generations -- that of Pirsig in Zen and the Art of Motorcyle Maintenance.  Both approaches, however, display what Pirsig calls "Quality."

One of my own generation's closest approaches to Quality is found in the 25th Anniversary Report of the Harvard Class of 1964.  Charles Small remarks,

"A lot of other stuff has gone down the drain since 1964, of course, besides my giving up being a mathematician and settling into my first retirement.  My love-hate relationship with the language has intensified, and my despair with words as instruments of communion is often near total.  I read a little, but not systematically. I've always been enthralled by the notion that Time is an illusion, a trick our minds play in an attempt to keep things separate, without any reality of its own. My experience suggests that this is literally true, but not the kind of truth that can be acted upon....

I'm always sad and always happy. As someone says in Diane Keaton's film 'Heaven,' 'It's kind of a lost cause, but it's a great experience.'"

I agree.  Here are two links to some work of what is apparently this same Charles Small:

• Arithmetic of Finite Fields and
• Manontroppo Music -- Arrangements, especially for string quartet

Sorry for the hiatus in weblog entries since November 9.  There were two reasons for this...

• The five entries ending Nov. 9 formed a sort of story, taken as a whole, and I didn't want to break up the set.  But now I have archived this set of five entries. See my Diamond 16 Puzzle notes.
• A very nasty entry in my Diamond Theory Forum site shook me up, and I haven't felt like blogging until now.

Result of a Google search Nov. 9, 2002...

Searched the web for weyl symmetry.
Result 1 of about 15,400... 

Category:  Science > Math > Algebra > Group Theory 

Weyl, H.: Symmetry. Description of the book Symmetry by Weyl, H., published by Princeton University Press. ... pup.princeton.edu/titles/ 865.html - 7k - Nov. 8, 2002

Sponsored Link Symmetry Puzzle New free online puzzle illustrates the mathematics of symmetry. m759.freeservers.com/puzzle. html

Quotation from Weyl's Symmetry:

"Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect."

In honor of Princeton University, of Sylvia Nasar (see entries of Nov, 6), of the Presbyterian Church (see entry of Nov. 8), and of Professor Weyl (whose work partly inspired the website Diamond Theory), this site's background music is now Pink Floyd's

"Shine On,     You Crazy Diamond."

Updates of Friday, November 15, 2002:

In order to clarify the meaning of "Shine" and "Crazy" in the above, consult the following --

• "Shine" ... The Shining, by Stephen King
• "Crazy" ... The Hollow Man, by Dan Simmons 

To accompany this detailed exegesis of Pink Floyd, click here for a reading by Marlon Brando.

For a related educational experience, see pages 126-127 of The Book of Sequels, by Henry Beard, Christopher Cerf, Sarah Durkee, and Sean Kelly (Random House paperback, 1990).

Speaking of sequels, be on the lookout for Annie Dillard's sequel to Teaching a Stone to Talk, titled Teaching a Brick to Sing. 

In memory of Steve McQueen ("The Great Escape" and "The Thomas Crown Affair"... see preceding entry) and of Rudolf Augstein (publisher of Der Spiegel), both of whom died on November 7 (in 1980 and 2002, respectively), in memory of the following residents of

The Princeton Cemetery
of the Nassau Presbyterian Church
Established 1757

and of the long and powerful association of Princeton University with the Presbyterian Church, as well as the theological perspective of Carl Jung in Man and His Symbols, I offer the following "windmill," taken from the Presbyterian Creedal Standards website, as a memorial:

The background music Les Moulins de Mon Coeur, selected yesterday morning in memory of Steve McQueen, continues to be appropriate.

"A is for Anna."
-- James Joyce

Endgame

Metaphor for Morphean morphosis,
Dreams that wake, transform, and die,
Calm and lucid this psychosis,
Joyce's nightmare in Escher's eye.

At the end there is a city
With cathedral bright and sane
Facing inward from the pity
On the endgame's wavy plane.

Black the knight upon that ocean,
Bright the sun upon the king.
Dark the queen that stands beside him,
White his castle, threatening.

In the shadows' see a bishop
Guards his queen of love and hate.
Another move, the game will be up;
Take the queen, her knight will mate.

The knight said "Move, be done.  It's over."
"Love and resign," the bishop cried.
"When it's done you'll stand forever
By the darkest beauty's side."

Dabo claves regni caelorum.  By silent shore
Ripples spread from castle rock.  The metaphor
For metamorphosis no keys unlock.

-- Steven H. Cullinane, November 7, 1986

Accompaniment from "The Thomas Crown Affair":
Michel Legrand, "Les Moulins de Mon Coeur"

Lyrics by Eddy Marnay:

Comme une pierre que l'on jette
Dans l'eau vive d'un ruisseau
Et qui laisse derrière elle
Des milliers de ronds dans l'eau....

Trivia quiz on tonight's "West Wing" --

What do you feed a stolen goat?

Prologue

Where the statue stood
Of Newton with his prism and silent face,
The marble index of a mind for ever
Voyaging through strange seas of Thought, alone.
-- WILLIAM WORDSWORTH

John Forbes Nash, Jr. -- mathematical genius, inventor of a theory of rational behavior, visionary of the thinking machine -- had been sitting with his visitor, also a mathematician, for nearly half an hour. It was late on a weekday afternoon in the spring of 1959, and, though it was only May, uncomfortably warm. Nash was slumped in an armchair in one corner of the hospital lounge, carelessly dressed in a nylon shirt that hung limply over his unbelted trousers. His powerful frame was slack as a rag doll's, his finely molded features expressionless. He had been staring dully at a spot immediately in front of the left foot of Harvard professor George Mackey, hardly moving except to brush his long dark hair away from his forehead in a fitful, repetitive motion. His visitor sat upright, oppressed by the silence, acutely conscious that the doors to the room were locked. Mackey finally could contain himself no longer. His voice was slightly querulous, but he strained to be gentle. "How could you," began Mackey, "how could you, a mathematician, a man devoted to reason and logical proof...how could you believe that extraterrestrials are sending you messages? How could you believe that you are being recruited by aliens from outer space to save the world? How could you...?"

Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispassionate as that of any bird or snake. "Because," Nash said slowly in his soft, reasonable southern drawl, as if talking to himself, "the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously."

What I take seriously:

Introduction to Topology and Modern Analysis, by George F. Simmons, McGraw-Hill, New York, 1963 

An Introduction to Abstract Harmonic Analysis, by Lynn H. Loomis, Van Nostrand, Princeton, 1953

"Harmonic Analysis as the Exploitation of Symmetry -- A Historical Survey," by George W. Mackey, pp. 543-698, Bulletin of the American Mathematical Society, July 1980

Walsh Functions and Their Applications, by K. G. Beauchamp, Academic Press, New York, 1975

Walsh Series: An Introduction to Dyadic Harmonic Analysis, by F. Schipp, P. Simon, W. R. Wade, and J. Pal, Adam Hilger Ltd., 1990

The review, by W. R. Wade, of Walsh Series and Transforms (Golubov, Efimov, and Skvortsov, publ. by Kluwer, Netherlands, 1991) in the Bulletin of the American Mathematical Society, April 1992, pp. 348-359

Music courtesy of Franz Schubert.

From a web page on Kylie Minogue:

Turns out she's a party girl who loves Tequila:
"Time disappears with Tequila.
It goes elastic, then vanishes."

From a web page on Malcolm Lowry's classic novel
Under the Volcano: 

The day begins with Yvonne’s arrival at the Bella Vista bar in Quauhnahuac. From outside she hears Geoffrey’s familiar voice shouting a drunken lecture this time on the topic of the rule of the Mexican railway that requires that  "A corpse will be transported by express!" (Lowry, Volcano, p. 43).

From the 440 International Archives:

1988 - And speaking of music trivia (thanks to http://www.rockdate.co.uk Rockdate Diary): "The Loco-Motion", by Kylie Minogue hit #4 on the "Billboard Hot 100" this day, the song became the first to reach the top-5 in the U.S. for three different artists (Little Eva in 1962, Grand Funk in 1974).

Click here for a nicely done vibraphone-midi version of "Locomotion."  To honor Kylie's unforgettable video of that classic, this site's music is now one of my childhood favorites.

Kylie, 1988

Down by the Station

Down by the station early in the morning,
See the little puffer bellies all in a row.
See the engine driver pull the little throttle:
Puff, puff, Toot! Toot! Off we go!

As Sinatra said,
"Whatever gets you through the night, baby."

In honor of Roger Cooke's review of Helson's Harmonic Analysis, 2nd Edition, today's site music is "Moonlight in Vermont."

Today is All Souls' Day, the Day of the Dead in Mexico. This site's music for today, in honor of Rufino Tamayo, is "Luna y Sol."

Art Director of "Harvey" Dies at 95

In memory of Ellis Larkins and other departed souls, this site's music, taken from the website of Wesley Dick, is now the music of All Saints' Day.