Today's birthdays: Mike Nichols and Sally Field.

From A Beautiful Mind, by Sylvia Nasar:

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.

Kylie on Tequila

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).

Back to You, Kylie

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."

Music to Read By

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

Día de los Muertos

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 WARS:

Art Director of "Harvey" Dies at 95

All Saints' Day

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.

From The Unknowable (1999), by Gregory J. Chaitin, who has written extensively about his constant, which he calls Omega:

"What is Omega? It's just the diamond-hard distilled and crystallized essence of mathematical truth! It's what you get when you compress tremendously the coal of redundant mathematical truth..." 

Charles H. Bennett has written about Omega as a cabalistic number.

Here is another result with religious associations which, historically, has perhaps more claim to be called the "diamond-hard essence" of mathematical truth: The demonstration in Plato's Meno that a diamond inscribed in a square has half the area of the square (or that, vice-versa, the square has twice the area of the diamond).

From Ivars Peterson's discussion of Plato's diamond and the Pythagorean theorem:

"In his textbook The History of Mathematics, Roger Cooke of the University of Vermont describes how the Babylonians might have discovered the Pythagorean theorem more than 1,000 years before Pythagoras.

Basing his account on a passage in Plato's dialogue Meno, Cooke suggests that the discovery arose when someone, either for a practical purpose or perhaps just for fun, found it necessary to construct a square twice as large as a given square...."

From "Halving a Square," a presentation of Plato's diamond by Alexander Bogomolny, the moral of the story:

SOCRATES: And if the truth about reality is always in our soul, the soul must be immortal....

From "Renaissance Metaphysics and the History of Science," at The John Dee Society website:

Galileo on Plato's diamond:

"Cassirer, drawing attention to Galileo's frequent use of the Meno, particularly the incident of the slave's solving without instruction a problem in geometry by 'natural' reason stimulated by questioning, remarks, 'Galileo seems to accept all the consequences drawn by Plato from this fact.....'"

Roger Bacon on Plato's diamond:

"Fastening on the incident of the slave in the Meno, which he had found reproduced in Cicero, Bacon argued from it 'wherefore since this knowledge (of mathematics) is almost innate and as it were precedes discovery and learning or at least is less in need of them than other sciences, it will be first among sciences and will precede others disposing us towards them.'"

It is perhaps appropriate to close this entry, made on All Hallows' Eve, with a link to a page on Dr. John Dee himself.

Our Judeo-Christian Heritage:

Two Sides of the Same Coin

From On All Hallows' Eve, by Grace Chetwin:

"Please continue your account of Morgan le Fay."

"People think of her as bad. They say that she tried to murder her brother, King Arthur of the Round Table.... But she did good things too. She gave Arthur his sword, Excalibur, and, well, when he lay dying, she and two other queens took him onto their barge and bore him from the world to heal his wounds and make him whole again. It was '... a dusky barge, Dark as a funeral scarf from stem to stern,' and the three queens wore 'crowns of gold'...."

Greylen smiled. "Very good. You like this Morgan le Fay very much, it is clear."....

"I know more than that," Meg went on quickly. "She is also called Nimue and Vivian, but those names are wrong, too.  Her true name goes right back to the Mabinogion -- that's a really old collection of Welsh bardic tales.  Her real name is Rhiannon...."

In honor of Grace Chetwin, this site's music is now a theme more suitable for All Hallows' Eve.