Midnight in the Garden

From a Nina Simone Lyrics site:

Pack up all my cares and woe,
here I go, singing low,
Bye-bye Blackbird.
Where somebody waits for me,
sugar's sweet, so is she,
Bye-bye Blackbird.
No one here can love and understand me.
Oh, what hard-luck stories they all hand me.
Make my bed and light the light,
I'll arrive late tonight,
Blackbird, Bye-bye.

Nina Simone

For more on the eight-point star of Venus,
see "Bright Star," my note of October 23.

Wrestling Pablo Picasso

The old men know when an old man dies.
-- Ogden Nash

ART WARS:
Picasso's Birthday

From an art quotes website:

Dore Ashton's Picasso on Art --

"We all know that Art is not truth.
Art is a lie that makes us realize truth,
at least the truth that is given us
to understand." -- Pablo Picasso

From "Xanadu" --

"You have to believe we are magic."
-- Olivia Newton-John

Trinity

The last two days were eventful on the obituary front.  See below for a reasonably holy trinity of lives: 

• Richard Helms as the Father,
  
• Derek Bell as the Son, and
  
• Adolph Green as the Holy Spirit. 

See also Bonaventure's
Itinerarium Mentis in Deum and

the graves list for Bonaventure Cemetery in Savannah,
final resting place for Johnny Mercer and plot key
to Midnight in the Garden of Good and Evil.

Green Music

From the online New York Times, Oct. 24, 2002:

Adolph Green, Broadway
Playwright, Dies at 87

By RICHARD SEVERO

dolph Green, the playwright, performer and lyricist who in a six-decade collaboration with Betty Comden was co-author of such hit Broadway musicals as "On the Town," "Wonderful Town" and "Bells Are Ringing" and the screenplays for "Singin' in the Rain" and "The Band Wagon," died today at his home in Manhattan. He was 87.

"On the Town" Opens in New York, 1944

Adolph Green, Betty Comden, Leonard Bernstein

---

In honor of Green, of the music of New York City, and of Mrs. Adolph Green, this site's music is now a piano rendition by Doug McKenzie of "Some Other Time." 

Death of a Chieftain

New York Times, Oct. 24:

Derek Bell, Harpist of the Chieftains, 66, Is Dead

Derek Bell rehearsing for a 1998 St. Patrick’s Day concert in New York.

"Derek Bell, the versatile harpist with The Chieftains, one of the most celebrated Irish traditional bands, died on Oct. 15 in his hotel in Phoenix. He was 66 and lived in Belfast."

In honor of Bell, this site's music is,

for the time being,

the following classic tune by Turlough O'Carolan,

A (Very Brief) Course of
Modern Analysis 

In honor of today's anniversary of the 1873 birth of Edmund Taylor Whittaker, here are some references to a topic that still interests some mathematicians of today.

From A Course of Modern Analysis, by E. T. Whittaker and G. N. Watson, Fourth Edition, Cambridge University Press, 1927, reprinted 1969:

Section 20.7  "...the fact, that x and y can be expressed as one-valued functions of the variable z, makes this variable z of considerable importance... z is called the uniformizing variable of the equation.... When the genus of the algebraic curve f(x,y) = 0 is greater than unity, the uniformisation can be effected by means of what are known as automorphic functions. Two classes of such functions of genus greater than unity have been constructed, the first by Weber...(1886), the second by Whittaker...(1898)...."

The topic of uniformisation of algebraic curves has appeared frequently lately in connection with Wiles's attack on Fermat's Last Theorem. See, for instance, Lang's 1995 AMS Notices article

"Shimura's... insight was that the ordinary modular functions for a congruence subgroup of SL₂(Z) suffice to uniformize elliptic curves defined over the rationals."

and Charles Daney's notes

"The property of an elliptic curve [over Q] of being parameterized by modular functions is one way of defining a modular elliptic curve, and the Taniyama-Shimura conjecture asserts that every elliptic curve is modular."

For a deeper discussion of uniformisation in the context of Wiles's efforts, see "Elliptic curves and p-adic uniformisation," by H. Darmon, 1999.

For a more traditional approach to uniformisation, see "On the uniformisation of algebraic curves," by Yu. V. Brezhnev (24 May, 2002), which cites two of Whittaker's papers on automorphic functions (from 1898 and 1929) and a 1930 paper, "The uniformisation of algebraic curves," by J. M. Whittaker, apparently E. T. Whittaker's son.  

Bright Star

From the website of Karey Lea Perkins:

"The truth is that man's capacity for symbol-mongering
in general and language in particular is…intimately part and parcel of
his being human, of his perceiving and knowing, of his very
consciousness…"

-- Walker Percy, The Message in the Bottle, Farrar, Strauss, and Giroux, 1975

Today's New York Times story
on Richard Helms, together with my reminiscences in the entry that
follows it below, suggest the following possibility for
symbol-mongering:

Compare the 16-point star of the C.I.A.
with the classic 8-point star of Venus:

This comparison is suggested by the Spanish word "Lucero" (the name, which means "Bright Star," of the girl in Cuernavaca mentioned two entries down) and by the following passage from Robert A. Heinlein's classic novel, Glory Road:

"I have many names. What would you like to call me?"     "Is one of them 'Helen'?"     She smiled like sunshine and I learned that she had dimples. She looked sixteen and in her first party dress. "You are very gracious. No, she's not even a relative. That was many, many years ago." Her face turned thoughtful. "Would you like to call me 'Ettarre'?"     "Is that one of your names?"     "It is much like one of them, allowing for different spelling and accent. Or it could be 'Esther' just as closely. Or 'Aster.' Or even 'Estrellita.' "     " 'Aster,' " I repeated. "Star. Lucky Star!"

The C.I.A. star above is from that organization's own site.  The star of Venus (alias Aster, alias Ishtar) is from Symbols.com, an excellent site that has the following variations on the Bright Star theme:

Ideogram for light	Alchemical sign
Greek "Aster"	Babylonian Ishtar
Phoenician Astarte	Octagram of Venus
Phaistos Symbol	Fortress Octagram

See also my notes The Still Point and the Wheel and Midsummer Eve's Dream.  Both notes quote Robinson Jeffers:

"For the essence and the end
Of his labor is beauty...
one beauty, the rhythm of that Wheel,
and who can behold it is happy
and will praise it to the people."

-- Robinson Jeffers, "Point Pinos and Point Lobos,"
quoted at the end of The Cosmic Code,
by Heinz Pagels, Simon & Schuster, 1982

Place the eightfold star in a circle, and you have the Buddhist Wheel of Life:

In Memoriam

From the New York Times of Oct. 23, 2002:

Richard M. Helms Dies at 89;
Dashing Ex-Chief of the C.I.A.

Associated Press Richard M. Helms, a former C.I.A. director, died today.

By CHRISTOPHER MARQUIS WASHINGTON Oct. 23 — "Richard Helms, a former director of central intelligence who defiantly guarded some of the darkest secrets of the cold war, died today of multiple myeloma. He was 89. An urbane and dashing spymaster, Mr. Helms began his career with a reputation as a truthteller...."

Needless to say, that didn't last.  I encountered this story this afternoon, after writing the entry below this morning.  The site I described there,

http://www.geocities.com/Athens/2740/,

reads as though it were compiled by an intelligence officer, and may serve as a small memorial to Helms.  

Eleven Years Ago Today...

On October 23, 1991, I placed in my (paper) journal various entries that would remind me of the past... of Cuernavaca, Mexico, and a girl I knew there in 1962. One of the entries dealt with a book by Arthur Koestler, The Challenge of Chance. A search for links related to that book led to the following site, which I find very interesting:

http://www.geocities.com/Athens/2740/.

This is a commonplace-book site, apparently a collection of readings for the end of the century and millennium. No site title or owner is indicated, but the readings are excellent. Accepting the challenge of chance, I reproduce one of the readings... The author was not writing about Cuernavaca, but may as well have been.

From Winter's Tale, Harcourt Brace (1983):

Four Gates to the City By MARK HELPRIN Every city has its gates, which need not be of stone. Nor need soldiers be upon them or watchers before them. At first, when cities were jewels in a dark and mysterious world, they tended to be round and they had protective walls. To enter, one had to pass through gates, the reward for which was shelter from the overwhelming forests and seas, the merciless and taxing expanse of greens, whites, and blues--wild and free--that stopped at the city walls. In time the ramparts became higher and the gates more massive, until they simply disappeared and were replaced by barriers, subtler than stone, that girded every city like a crown and held in its spirit. Some claim that the barriers do not exist, and disparage them. Although they themselves can penetrate the new walls with no effort, their spirits (which, also, they claim do not exist) cannot, and are left like orphans around the periphery. To enter a city intact it is necessary to pass through one of the new gates. They are far more difficult to find than their solid predecessors, for they are tests, mechanisms, devices, and implementations of justice. There once was a map, now long gone, one of the ancient charts upon which colorful animals sleep or rage. Those who saw it said that in its illuminations were figures and symbols of the gates. The east gate was that of acceptance of responsibility, the south gate that of the desire to explore, the west gate that of devotion to beauty, and the north gate that of selfless love. But they were not believed. It was said that a city with entryways like these could not exist, because it would be too wonderful. Those who decide such things decided that whoever had seen the map had only imagined it, and the entire matter was forgotten, treated as if it were a dream, and ignored. This, of course, freed it to live forever.