Saturday, June 20, 2015

Conceptual Art for Basel

Filed under: General,Geometry — Tags: — m759 @ 7:59 PM

The previous post's link to The Lindbergh Manifesto
and Thursday's post on Basel-born artist Wolf Barth 
suggest the following —

See as well a June 14 New York Times
piece on Art Basel.

The logo of the University of Basel 

suggests a review of The Holy Field —


Monday, March 16, 2020

The Lindbergh Plot

Filed under: General — m759 @ 9:30 AM

Philip Roth's 2004 paranoid classic premieres on TV tonight.

I prefer an alternative Lindbergh plot. See Peter  Lindbergh in this  journal.

At right below, a work of art that the fashion photographer  Lindbergh
made when he was young and known as "Sultan."

Tuesday, July 16, 2019

Morf Vandewalt, Social Prism

Filed under: General — Tags: , — m759 @ 8:38 AM

From the 2019 film "Velvet Buzzsaw" —

What is going on in this picture?

Wednesday, April 3, 2019

Nocturnal Object of Beauty

Filed under: General — Tags: — m759 @ 2:41 AM



What is going on in this picture?

Sunday, July 1, 2018

Springtime for Wagner

Filed under: General — m759 @ 2:47 PM

Tuesday, June 12, 2018

Like Decorations in a Cartoon Graveyard

Filed under: General — m759 @ 11:00 PM


Two visions of happy neurons:

This post was suggested by a link in today's New York Times

"Simon Denny, the New Zealand artist whose work incorporates
board games, intervenes by introducing his own pieces into an attic of
the late-18th-century Haus zum Kirschgarten, already filled with
'old historical dollhouses, board games, chess games' and the like …."

Sunday, May 7, 2017

Art Space

Filed under: General,Geometry — Tags: — m759 @ 1:00 PM

Detail of an image in the previous post

This suggests a review of a post on a work of art by fashion photographer
Peter Lindbergh, made when he was younger and known as "Sultan."

The balls in the foreground relate Sultan's work to my own.

Linguistic backstory —

The art space where the pieces by Talman and by Lindbergh
were displayed is Museum Tinguely in Basel.

As the previous post notes, the etymology of "glamour" (as in
fashion photography) has been linked to "grammar" (as in 
George Steiner's Grammars of Creation ). A sculpture by 
Tinguely (fancifully representing Heidegger) adorns one edition
of Grammars .

Yale University Press, 2001:

Tinguely, "Martin Heidegger,
Philosopher," sculpture, 1988

Monday, October 10, 2016

Mono Type 1, by Sultan (1966)

Filed under: General,Geometry — m759 @ 12:06 PM

"Sultan" was a pseudonym of Peter Lindbergh, now a 
well-known fashion photographer. Click image for the source.

Related art — Diamond Theory Roullete, by Radames Ajna,
2013 (Processing  code at ReCode Project based on
"Diamond Theory" by Steven H. Cullinane, 1977).

Sunday, May 22, 2016


Filed under: General — m759 @ 7:30 PM

"(CBS News) Two decades after Morley Safer took
a critical look at contemporary art in his 60 Minutes
story  'Yes…But is it Art?'  he has found the definitive
answer to his snide question . . . ."

— March 30, 2012, introduction to a "60 Minutes" piece 
dated April 1, 2012

Sunday, August 23, 2015


Filed under: General — Tags: — m759 @ 9:00 AM

"William Tell’s weapon of choice has become
the symbol of Switzerland, a sign of sovereignty
and a guarantee of Swiss quality. On the eve of
the Second World War, these values seemed
especially important and necessary to the Swiss.
This five-centime green stamp was issued for
the 1939 national exhibition."

Related material in this journal:  Basel.

See also Jung + Imago.

Tuesday, May 19, 2015

The Lindbergh Manifesto

Filed under: General,Geometry — Tags: , — m759 @ 3:24 AM

"Creation is the birth of something, and
something cannot come from nothing."

— Photographer Peter Lindbergh at his website

From a biography of Lindbergh —

" it took Lindbergh awhile to find his true métier.
Born in Krefeld, Germany, in 1944….
Barely out of his teens, he became a painter who
embraced conceptual art and — for reasons he
has since forgotten — adopted the professional
name « Sultan. »   Lindbergh was a few years
short of his 30th birthday when he turned to

— "The Man Who Loves Women," by Pamela Young,
Toronto Globe & Mail , September 19, 1996

A Lindbergh work (at right below) from his conceptual-art days —

For a connection between the above work by Paul Talman and the
above "Mono Type 1" of Lindbergh, see…

Wednesday, February 25, 2015

AI News

Filed under: General — m759 @ 4:00 PM

The New Yorker —
Artificial Intelligence Goes to the Arcade

Sunday, May 30, 2010

A Post for Galois

Filed under: General,Geometry — m759 @ 2:00 PM

Evariste Galois, 1811-1832 (Vita Mathematica, V. 11)

  • Paperback: 168 pages
  • Publisher: Birkhäuser Basel; 1 edition (December 6, 1996)
  • Language: English
  • ISBN-10: 3764354100
  • ISBN-13: 978-3764354107
  • Product Dimensions: 9.1 x 6 x 0.4 inches
  • Shipping Weight: 9.1 ounces
  • Average Customer Review: 5.0 out of 5 stars  (1 customer review)
  • Amazon Bestsellers Rank: #933,939 in Books

Awarded 5 stars by Christopher G. Robinson (Cambridge, MA USA).
See also other reviews by Robinson.

Galois was shot in a duel on today's date, May 30, in 1832. Related material for those who prefer entertainment to scholarship—

"It is a melancholy pleasure that what may be [Martin] Gardner’s last published piece, a review of Amir Alexander’s Duel at Dawn: Heroes, Martyrs & the Rise of Modern Mathematics, will appear next week in our June issue." —Roger Kimball of The New Criterion, May 23, 2010.

Today is, incidentally, the feast day of St. Joan of Arc, Die Jungfrau von Orleans. (See "against stupidity" in this journal.)

Wednesday, April 30, 2008

Wednesday April 30, 2008

Filed under: General — Tags: — m759 @ 10:30 AM

Lucy in the Sky
with Diamonds
and Sacred Heart

PARIS — Albert Hofmann, the mystical Swiss chemist who gave the world LSD, the most powerful psychotropic substance known, died Tuesday at his hilltop home near Basel, Switzerland. He was 102.

Related material:

Star and Diamond: A Tombstone for Plato

a film by Julie Taymor,
Across the Universe:

Across the Universe DVD

Detail of the
Strawberry Fields Forever
Sacred Heart:

Strawberry Fields Sacred Heart from 'Across the Universe'

A song:

Julie Taymor

Julie Taymor

Shinin’ like a diamond,
she had tombstones
in her eyes.

Album “The Dark,”
by Guy Clark

For related tombstones,
see May 16-19, 2006,
and April 19, 2008.

Further background:
Art Wars for
Red October.

Thursday, June 28, 2007

Thursday June 28, 2007

Filed under: General — m759 @ 12:06 PM
Cornelius Uhlenbeck

Oct. 18, 1866 – Aug. 12, 1951

“… born at Voorburg near The Hague in Holland, and studied philology at the University of Leiden…. Though he would actually have preferred to graduate in Basque, Uhlenbeck in 1888, when only 22 years old, took his doctor’s degree in Dutch.  It must be here noted that for this degree the requirements in comparative philology were very considerable….” —International Journal of American Linguistics, Jan. 1953

From Uhlenbeck’s A Manual of Sanskrit Phonetics (1898):

The Indogermanic family of languages. The great family of languages, in which Sanskrit belongs, is called the Indogermanic, Indoceltic or Aryan…. The word Indogermanic dates from a time, when it was not yet proved, that the Celtic dialects also make part of our family of languages, and indicates by the combined name of the utmost branches, Indian and Germanic, the whole territory of speech, to which they belong. Now that it is certain, that Celtic also is a member of our family, it would be accurate to replace the word Indogermanic by Indoceltic, because not Germanic, but Celtic is the utmost branch in the Occident. The name Indogermanic however is generally adopted and it would be impossible to supplant it by another. By the word Aryan is generally understood a certain subdivision of the Indogermanic family, viz. the Indo-Iranian, and therefore it would seem unsuitable to use this name also for the whole Indogermanic family.”

An unsuitable Santa:

The image “http://www.log24.com/log/pix07/070628-Santa.jpg” cannot be displayed, because it contains errors.

A Santa understudy:

The image “http://www.log24.com/log/pix07/070628-christianus_cornelius_uhlenbeck.jpg” cannot be displayed, because it contains errors.

Transcript of
“Miracle on 34th Street”

KRIS: Bye. Merry Christmas!   

Well, young lady,
what's your name?

MOTHER: I'm sorry.
She doesn't speak English.

She's Dutch. She just came over.

She's been living
in an orphans home...

in Rotterdam ever since...

We've adopted her.

I told her you wouldn't
be able to speak to her...

but when she saw you
in the parade yesterday...

she said you were
"Sinter Claes"...

and you could talk to her.

I didn't know what to do.

KRIS: Hello. [Speaking Dutch]

[Speaking Dutch]

[Singing in Dutch]

DORIS: Now do you understand?

Related material:

Pope Approves Wider
Use of Latin Mass

The image “http://www.log24.com/log/pix07/070628-Sanctus.jpg” cannot be displayed, because it contains errors.

(Click on image for details),


Seminar für Klassische Philologie
 der Universität Basel

The image “http://www.log24.com/log/pix07/070628-UnivBasel.gif” cannot be displayed, because it contains errors.

Indogermanistische Bibliothek

Tuesday, February 20, 2007

Tuesday February 20, 2007

Filed under: General,Geometry — m759 @ 7:09 AM

Today is the 21st birthday of my note “The Relativity Problem in Finite Geometry.”

Some relevant quotations:

“This is the relativity problem: to fix objectively a class of equivalent coordinatizations and to ascertain the group of transformations S mediating between them.”

— Hermann Weyl, The Classical Groups, Princeton University Press, 1946, p. 16

Describing the branch of mathematics known as Galois theory, Weyl says that it

“… is nothing else but the relativity theory for the set Sigma, a set which, by its discrete and finite character, is conceptually so much simpler than the infinite set of points in space or space-time dealt with by ordinary relativity theory.”

— Weyl, Symmetry, Princeton University Press, 1952, p. 138

Weyl’s set Sigma is a finite set of complex numbers.   Some other sets with “discrete and finite character” are those of 4, 8, 16, or 64 points, arranged in squares and cubes.  For illustrations, see Finite Geometry of the Square and Cube.  What Weyl calls “the relativity problem” for these sets involves fixing “objectively” a class of equivalent coordinatizations.  For what Weyl’s “objectively” means, see the article “Symmetry and Symmetry  Breaking,” by Katherine Brading and Elena Castellani, in the Stanford Encyclopedia of Philosophy:

“The old and natural idea that what is objective should not depend upon the particular perspective under which it is taken into consideration is thus reformulated in the following group-theoretical terms: what is objective is what is invariant with respect to the transformation group of reference frames, or, quoting Hermann Weyl (1952, p. 132), ‘objectivity means invariance with respect to the group of automorphisms [of space-time].‘[22]

22. The significance of the notion of invariance and its group-theoretic treatment for the issue of objectivity is explored in Born (1953), for example. For more recent discussions see Kosso (2003) and Earman (2002, Sections 6 and 7).


Born, M., 1953, “Physical Reality,” Philosophical Quarterly, 3, 139-149. Reprinted in E. Castellani (ed.), Interpreting Bodies: Classical and Quantum Objects in Modern Physics, Princeton, NJ: Princeton University Press, 1998, pp. 155-167.

Earman, J., 2002, “Laws, Symmetry, and Symmetry Breaking; Invariance, Conservation Principles, and Objectivity,’ PSA 2002, Proceedings of the Biennial Meeting of the Philosophy of Science Association 2002, forthcoming [Abstract/Preprint available online]

Kosso, P., 2003, “Symmetry, objectivity, and design,” in K. Brading and E. Castellani (eds.), Symmetries in Physics: Philosophical Reflections, Cambridge: Cambridge University Press, pp. 410-421.

Weyl, H., 1952, Symmetry, Princeton, NJ: Princeton University Press.

See also

Archives Henri Poincaré (research unit UMR 7117, at Université Nancy 2, of the CNRS)–

Minkowski, Mathematicians, and the Mathematical Theory of Relativity,” by Scott Walter, in The Expanding Worlds of General Relativity (Einstein Studies, volume 7), H. Goenner, J. Renn, J. Ritter and T. Sauer, editors, Boston/Basel: Birkhäuser, 1999, pp. 45-86–

“Developing his ideas before Göttingen mathematicians in April 1909, Klein pointed out that the new theory based on the Lorentz group (which he preferred to call ‘Invariantentheorie’) could have come from pure mathematics (1910: 19). He felt that the new theory was anticipated by the ideas on geometry and groups that he had introduced in 1872, otherwise known as the Erlangen program (see Gray 1989: 229).”


Gray, Jeremy J. (1989). Ideas of Space. 2d ed. Oxford: Oxford University Press.

Klein, Felix. (1910). “Über die geometrischen Grundlagen der Lorentzgruppe.” Jahresbericht der deutschen Mathematiker-Vereinigung 19: 281-300. [Reprinted: Physikalische Zeitschrift 12 (1911): 17-27].

Related material: A pathetically garbled version of the above concepts was published in 2001 by Harvard University Press.  See Invariances: The Structure of the Objective World, by Robert Nozick.

Saturday, September 6, 2003

Saturday September 6, 2003

Filed under: General — Tags: — m759 @ 12:00 AM

The Tempest

IMAGE- 'Wind over Water,' i.e. 'Feng Shui'

A tropical storm over Florida (lower left)
and a hurricane at Bermuda (upper right)
at 3:15 p.m. EDT on Friday, Sept. 5, 2003:

Wind over Water

as described by William Shakespeare in 1611.

“Wind over Water” in the I Ching,
the Classic of Transformations,
signifies huan, “dissolving.”


Our revels now are ended. These our actors, as I foretold you, were all spirits and are melted into air, into thin air: and, like the baseless fabric of this vision, the cloud-capp’d towers, the gorgeous palaces, the solemn temples, the great globe itself, yea, all which it inherit, shall dissolve and, like this insubstantial pageant faded, leave not a rack behind. We are such stuff as dreams are made on, and our little life is rounded with a sleep. (Prospero, IV.i)

Monday, September 1, 2003

Monday September 1, 2003

Filed under: General — m759 @ 3:33 PM

The Unity of Mathematics,

or “Shema, Israel”

A conference to honor the 90th birthday (Sept. 2) of Israel Gelfand is currently underway in Cambridge, Massachusetts.

The following note from 2001 gives one view of the conference’s title topic, “The Unity of Mathematics.”

Reciprocity in 2001

by Steven H. Cullinane
(May 30, 2001)

From 2001: A Space Odyssey, by Arthur C. Clarke, New American Library, 1968:

The glimmering rectangular shape that had once seemed no more than a slab of crystal still floated before him….  It encapsulated yet unfathomed secrets of space and time, but some at least he now understood and was able to command.

How obvious — how necessary — was that mathematical ratio of its sides, the quadratic sequence 1: 4: 9!  And how naive to have imagined that the series ended at this point, in only three dimensions!

— Chapter 46, “Transformation”

From a review of Himmelfarb, by Michael Krüger, New York, George Braziller, 1994:

As a diffident, unsure young man, an inexperienced ethnologist, Richard was unable to travel through the Amazonian jungles unaided. His professor at Leipzig, a Nazi Party member (a bigot and a fool), suggested he recruit an experienced guide and companion, but warned him against collaborating with any Communists or Jews, since the objectivity of research would inevitably be tainted by such contact. Unfortunately, the only potential associate Richard can find in Sao Paulo is a man called Leo Himmelfarb, both a Communist (who fought in the Spanish Civil War) and a self-exiled Jew from Galicia, but someone who knows the forests intimately and can speak several of the native dialects.

“… Leo followed the principle of taking and giving, of learning and teaching, of listening and storytelling, in a word: of reciprocity, which I could not even imitate.”

… E. M. Forster famously advised his readers, “Only connect.” “Reciprocity” would be Michael Kruger’s succinct philosophy, with all that the word implies.

— William Boyd, New York Times Book Review, October 30, 1994

Reciprocity and Euler

Applying the above philosophy of reciprocity to the Arthur C. Clarke sequence

1, 4, 9, ….

we obtain the rather more interesting sequence
1/1, 1/4, 1/9, …..

This leads to the following problem (adapted from the St. Andrews biography of Euler):

Perhaps the result that brought Euler the most fame in his young days was his solution of what had become known as the Basel problem. This was to find a closed form for the sum of the infinite series

1/1 + 1/4 + 1/9 + 1/16 + 1/25 + …

— a problem which had defeated many of the top mathematicians including Jacob Bernoulli, Johann Bernoulli and Daniel Bernoulli. The problem had also been studied unsuccessfully by Leibniz, Stirling, de Moivre and others. Euler showed in 1735 that the series sums to (pi squared)/6. He generalized this series, now called zeta(2), to zeta functions of even numbers larger than two.

Related Reading

For four different proofs of Euler’s result, see the inexpensive paperback classic by Konrad Knopp, Theory and Application of Infinite Series (Dover Publications).

Related Websites

Evaluating Zeta(2), by Robin Chapman (PDF article) Fourteen proofs!

Zeta Functions for Undergraduates

The Riemann Zeta Function

Reciprocity Laws
Reciprocity Laws II

The Langlands Program

Recent Progress on the Langlands Conjectures

For more on
the theme of unity,

Monolithic Form

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