Log24

Monday, May 28, 2018

Figaro (by Cartier)

Filed under: General — m759 @ 7:17 PM

Related material from Log24 —

Posts tagged Cartier's Groundhog Day.

Thursday, July 2, 2015

Shema Cartier*

Filed under: General — m759 @ 1:00 PM

Woody as Figaro

* For the title, see a search for Inside Man .


Related material: The co-editor of The Architecture of Modern Mathematics

"I love those Bavarians."

Sunday, February 3, 2013

The Gospel According to Cartier

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

Yesterday's 11 AM post Mad Day concluded
with a link to a 2001 American Mathematical Society
article by Pierre Cartier that sums up the religion and
politics of many mathematicians

"Here ends the infancy narrative of the gospel…."

"… while Simone Weil's Catholicism was violently
anti-Semitic (in 1942!), Grothendieck's Buddhism
bears a strong resemblance to the practices of
his Hasidic ancestors."

See also Simone Weil in this journal.

Note esp. a post of April 6, 2004 that provides
a different way of viewing Derrida's notion of
inscription .

Friday, December 9, 2016

Snow Dance

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

See Ballet Blanc  in this journal.

For a darker perspective, click on the image below.

IMAGE- Detail of large 'Search for the Lost Tesseract' image with Amy Adams, Richard Zanuck, 'snowflake' structure, and white gloves

See also Cartier in The Hexagon of Opposition.

Happy birthday to Kirk Douglas.

Kirk Douglas in 'Diamonds'

Thursday, July 21, 2016

A Mad Day’s Preprint*

Filed under: General — m759 @ 2:02 PM

Pierre Cartier, 'How to take advantage of the blur between the finite and the infinite,' preprint of May 3,2011

See also, from that same day, "24-Part Invention."

* The title is a reference to a 2001 article by Cartier on
   "the evolution of concepts of space and symmetry" —

Thursday, February 12, 2015

Dead Reckoning

Filed under: General,Geometry — Tags: — m759 @ 12:48 PM

Continued from yesterday.

The passage on Claude Chevalley quoted here
yesterday in the post Dead Reckoning was, it turns out,
also quoted by Peter Galison in his essay "Structure of Crystal,
Bucket of Dust" in Circles Disturbed: The Interplay of 
Mathematics and Narrative  
(Princeton University Press, 2012,
ed. by Apostolos Doxiadis and Barry Mazur).

Galison gives a reference to his source:

"From 'Claude Chevalley Described by His Daughter (1988),' 
in Michèle Chouchan, Nicolas Bourbaki: Faits et légendes
(Paris: Éditions du Choix, 1995), 36–40, translated and cited
in Marjorie Senechal, 'The Continuing Silence of Bourbaki:
An Interview with Pierre Cartier, June 18, 1997,' 
Mathematical Intelligencer  1 (1998): 22–28."

Galison's essay compares Chevalley with the physicist
John Archibald Wheeler. His final paragraph —

"Perhaps, then, it should not surprise us too much if,
as Wheeler approaches the beginning-end of all things,
there is a bucket of Borelian dust. Out of this filth,
through the proposition machine of quantum mechanics
comes pregeometry; pregeometry makes geometry;
geometry gives rise to matter and the physical laws
and constants of the universe. At once close to and far
from the crystalline story that Bourbaki invoked,
Wheeler’s genesis puts one in mind of Genesis 3:19:
'In the sweat of thy face shalt thou eat bread, till thou
return unto the ground; for out of it wast thou taken:
for dust thou art, and unto dust shalt thou return.'"

See also posts tagged Wheeler.

Monday, March 10, 2014

God’s Architecture

Filed under: General — m759 @ 1:19 PM

Part I:

The sermon, “God’s Architecture,” at Nassau Presbyterian
Church in Princeton on Sunday, Feb. 23, 2014.  (This is the
“sermon” link in last Sunday’s 11 AM ET Log24 post.)

An excerpt:

“I wonder what God sees when God looks at our church.
Bear with me here because I’d like to do a little architectural
redesign. I look up at our sanctuary ceiling and I see buttons.
In those large round lights, I see buttons. I wonder what would
happen if we unbutton the ceiling, Then I wonder if we were to
unzip the ceiling, pull back the rooftop, and God were to look in
from above – What does God see? What pattern, what design,
what shape takes place?” — Rev. Lauren J. McFeaters

Related material —  All About Eve: 

A. The Adam and Eve sketch from the March 8 “Saturday Night Live”

B. “Katniss, get away from that tree!” —

C. Deconstructing God in last evening’s online New York Times .

Part II:

Heavensbee!” in the above video, as well as Cartier’s Groundhog Day
and Say It With Flowers.

Part III:

Humans’  architecture, as described (for instance) by architecture
theorist Anne Tyng, who reportedly died at 91 on Dec. 27, 2011.
See as well Past Tense and a post from the date of Tyng’s death.

Monday, February 3, 2014

Designs

Filed under: General — Tags: — m759 @ 7:00 AM

This journal a year ago yesterday

“Some designs work subtly.
Others are successful through sheer force.”

Penelope Green

Subtly:

Sheer force:

IMAGE- The Cartier diamond ring from 'Inside Man'

Saturday, February 2, 2013

Mad Day

Filed under: General — Tags: , , — m759 @ 11:00 AM

A perceptive review of Missing Out: In Praise of the Unlived Life

IMAGE- The perception of doors

"Page 185: 'Whatever else we are, we are also mad.' "

Related material— last night's Outside the Box and, from Oct. 22 last year

"Some designs work subtly.
Others are successful through sheer force."

Par exemple—

IMAGE- The Cartier diamond ring from 'Inside Man'

See also Cartier in this journal.

The Cartier link leads to, among other things

A Mad Day’s Work: From Grothendieck to Connes and Kontsevich.
The Evolution of Concepts of Space and Symmetry
,”
by Pierre Cartier, Bulletin of the American Mathematical Society ,
Vol. 38 (2001) No. 4, pages 389-408

Monday, October 22, 2012

Follow the Ring

Filed under: General — m759 @ 2:00 AM

(Continued)

From Penelope Green's New York Times  story on Wednesday night's Cooper-Hewitt design awards gala (links added)—

"Then Mr. Wurman went into full curmudgeon mode, fiddling with the two mikes on the podium and questioning the format of the night.

'We should have talked to each other longer,' he said. 'This is the least interesting part.'

When he was done, Gloria Nagy, his wife, recalled how he had critiqued Mrs. Obama’s speech during the awards luncheon in July. (The Huffington Post reported Mrs. Obama as saying Mr. Wurman was 'quite dashing and sassy.') Ms. Nagy said Mrs. Obama had teased her by offering condolences and asking how she put up with her husband. In answer, Ms. Nagy said, she flashed what she called her Hazardous Duty Prize, a blindingly huge diamond ring.

Some designs work subtly. Others are successful through sheer force."

Par exemple—

IMAGE- The Cartier diamond ring from 'Inside Man'

See also Cartier in this journal.

Wednesday, June 13, 2012

State of the Art

Filed under: General,Geometry — m759 @ 9:48 PM

The new June/July issue of the AMS Notices
on a recent Paris exhibit of art and mathematics—

Mathématiques, un dépaysement soudain
Exhibit at the Fondation Cartier, Paris
October 21, 2011–March 18, 2012

                                            … maybe walking
into the room was supposed to evoke the kind of
dépaysement  for which the exhibition is named
(the word dépaysement  refers to the sometimes
disturbing feeling one gets when stepping outside
of one’s usual reference points). I was with
my six-year-old daughter, who quickly gravitated
toward the colorful magnetic tiles on the wall that
visitors could try to fit together. She spent a good
half hour there, eventually joining forces with a
couple of young university students. I would come
and check on her every once in a while and heard
some interesting discussions about whether or not
it was worth looking for patterns to help guide the
placing of the tiles. The fifteen-year age difference
didn’t seem to bother anyone.
     The tiles display was one of the two installations
here that offered the visitor a genuine chance to
engage in mathematical activity, to think about
pattern and structure while satisfying an aesthetic
urge to make things fit and grow….

Nathalie Sinclair

The Notices  included no pictures with this review.
A search to find out what sort of tiles were meant
led, quite indirectly, to the following—

IMAGE- French weblog post on Truchet tiles dated May 1st, 2011

The search indicated it is unlikely that these Truchet  tiles
were the ones on exhibit.

Nevertheless, the date  of the above French weblog post,
1 May 2011, is not without interest in the context of 
today's previous post. (That post was written well before
I had seen the new AMS Notices  issue online.)

Tuesday, June 22, 2010

Hermeneutics for Bernstein

Filed under: General — m759 @ 8:28 PM

J. M. Bernstein (previous post) has written of moving toward "a Marxist hermeneutic."

I prefer lottery hermeneutics.

Some background from Bernstein—

http://www.log24.com/log/pix10A/100622-StoryStatements.gif

I would argue that at least sometimes, lottery numbers may be regarded, according to Bernstein's definition, as story statements. For instance—

Today's New York State Lottery— Midday 389, Evening 828.

For the significance of 389, see

A Mad Day’s Work: From Grothendieck to Connes and Kontsevich.
 The Evolution of Concepts of Space and Symmetry
,”
 by Pierre Cartier, Bulletin of the American Mathematical Society,
 Vol. 38 (2001) No. 4, beginning on page 389.

The philosophical import of page 389 is perhaps merely in Cartier's title (see previous post).

For the significance of 828, see 8/28, the feast of St. Augustine, in 2006.

See also Halloween 2007. (Happy birthday, Dan Brown.)

Friday, March 2, 2007

Friday March 2, 2007

Filed under: General — m759 @ 6:00 PM
"I was reading Durant's section on Plato, struggling to understand his theory of the ideal Forms that lay in inviolable perfection out beyond the phantasmagoria. (That was the first, and I think the last, time that I encountered that word.)"

Part I: Phantasmagoria
 
Enlarge this image
Father and daughter in Bee Season
Photo by Phil Bray

Transcendence through spelling:
Richard Gere and Flora Cross
as father and daughter
in the film of Bee Season.

"Every aspect of the alef's
construction has been
Divinely designed
to teach us something."

Alef– The Difference Between
Exile And Redemption,
by Rabbi Aaron L. Raskin

Related material–

Art Theory for Yom Kippur
and
Log24 entries, Nov. 2005.


Part II: Hunt for the Real

The Alphabet Versus the Goddess:
The Conflict Between Word and Image
.

See also the references
to Zelazny's Eye of Cat
in the Nov. 2005 entries
as well as
today's previous entry
with the Norton Simon motto
"Hunt for the best"– and…

The image “http://www.log24.com/log/pix07/070302-EyeOfCat.jpg” cannot be displayed, because it contains errors.
Click for details.

"Photography has always involved waiting…. the photographer is understood to be waiting for the right convergence of subject, lighting and frame before clicking the shutter– waiting for what a master of the genre, Henri Cartier-Bresson, famously called 'the decisive moment.' Lee Friedlander, another great street photographer, compared this anticipatory state to the hunting alertness of a 'one-eyed cat.' The metaphor of the hunt has seeped into the essential language of photography."

Arthur Lubow in The New York Times, Feb. 25, 2007

Tuesday, September 2, 2003

Tuesday September 2, 2003

Filed under: General,Geometry — m759 @ 1:11 PM

One Ring to Rule Them All

In memory of J. R. R. Tolkien, who died on this date, and in honor of Israel Gelfand, who was born on this date.

Leonard Gillman on his collaboration with Meyer Jerison and Melvin Henriksen in studying rings of continuous functions:

“The triple papers that Mel and I wrote deserve comment. Jerry had conjectured a characterization of beta X (the Stone-Cech compactification of X) and the three of us had proved that it was true. Then he dug up a 1939 paper by Gelfand and Kolmogoroff that Hewitt, in his big paper, had referred to but apparently not appreciated, and there we found Jerry’s characterization. The three of us sat around to decide what to do; we called it the ‘wake.’  Since the authors had not furnished a proof, we decided to publish ours. When the referee expressed himself strongly that a title should be informative, we came up with On a theorem of Gelfand and Kolmogoroff concerning maximal ideals in rings of continuous functions. (This proved to be my second-longest title, and a nuisance to refer to.) Kolmogoroff died many years ago, but Gelfand is still living, a vigorous octogenarian now at Rutgers. A year or so ago, I met him at a dinner party in Austin and mentioned the 1939 paper. He remembered it very well and proceeded to complain that the only contribution Kolmogoroff had made was to point out that a certain result was valid for the complex case as well. I was intrigued to see how the giants grouse about each other just as we do.”

Leonard Gillman: An Interview

This clears up a question I asked earlier in this journal….

Wednesday, May 14, 2003

Common Sense

On the mathematician Kolmogorov:

“It turns out that he DID prove one basic theorem that I take for granted, that a compact hausdorff space is determined by its ring of continuous functions (this ring being considered without any topology) — basic discoveries like this are the ones most likely to have their origins obscured, for they eventually come to be seen as mere common sense, and not even a theorem.”

Richard Cudney, Harvard ’03, writing at Xanga.com as rcudney on May 14, 2003

That this theorem is Kolmogorov’s is news to me.

See

The above references establish that Gelfand is usually cited as the source of the theorem Cudney discusses.  Gelfand was a student of Kolmogorov’s in the 1930’s, so who discovered what when may be a touchy question in this case.  A reference that seems relevant: I. M. Gelfand and A. Kolmogoroff, “On rings of continuous functions on topological spaces,” Doklady Akad. Nauk SSSR 22 (1939), 11-15.  This is cited by Gillman and Jerison in the classic Rings of Continuous Functions.

There ARE some references that indicate Kolmogorov may have done some work of his own in this area.  See here (“quite a few duality theorems… including those of Banaschewski, Morita, Gel’fand-Kolmogorov and Gel’fand-Naimark”) and here  (“the classical theorems of M. H. Stone, Gelfand & Kolmogorov”).

Any other references to Kolmogorov’s work in this area would be of interest.

Naturally, any discussion of this area should include a reference to the pioneering work of M. H. Stone.  I recommend the autobiographical article on Stone in McGraw-Hill Modern Men of Science, Volume II, 1968.

A response by Richard Cudney:

“In regard to your entry, it is largely correct.  The paper by Kolmogorov and Gelfand that you refer to is the one that I just read in his collected works.  So, I suppose my entry was unfair to Gelfand.  You’re right, the issue of credit is a bit touchy since Gelfand was his student.  In a somewhat recent essay, Arnol’d makes the claim that this whole thread of early work by Gelfand may have been properly due to Kolmogorov, however he has no concrete proof, having been but a child at the time, and makes this inference based only on his own later experience as Kolmogorov’s student.  At any rate, I had known about Gelfand’s representation theorem, but had not known that Kolmogorov had done any work of this sort, or that this theorem in particular was due to either of them. 

And to clarify-where I speak of the credit for this theorem being obscured, I speak of my own experience as an algebraic geometer and not a functional analyst.  In the textbooks on algebraic geometry, one sees no explanation of why we use Spec A to denote the scheme corresponding to a ring A.  That question was answered when I took functional analysis and learned about Gelfand’s theorem, but even there, Kolmogorov’s name did not come up.

This result is different from the Gelfand representation theorem that you mention-this result concerns algebras considered without any topology(or norm)-whereas his representation theorem is a result on Banach algebras.  In historical terms, this result precedes Gelfand’s theorem and is the foundation for it-he starts with a general commutative Banach algebra and reconstructs a space from it-thus establishing in what sense that the space to algebra correspondence is surjective, and hence by the aforementioned theorem, bi-unique.  That is to say, this whole vein of Gelfand’s work started in this joint paper.

Of course, to be even more fair, I should say that Stone was the very first to prove a theorem like this, a debt which Kolmogorov and Gelfand acknowledge.  Stone’s paper is the true starting point of these ideas, but this paper of Kolmogorov and Gelfand is the second landmark on the path that led to Grothendieck’s concept of a scheme(with Gelfand’s representation theorem probably as the third).

As an aside, this paper was not Kolmogorov’s first foray into topological algebra-earlier he conjectured the possibility of a classification of locally compact fields, a problem which was solved by Pontryagin.  The point of all this is that I had been making use of ideas due to Kolmogorov for many years without having had any inkling of it.”

Posted 5/14/2003 at 8:44 PM by rcudney

Wednesday, May 14, 2003

Wednesday May 14, 2003

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

Common Sense

On the mathematician Kolmogorov:

“It turns out that he DID prove one basic theorem that I take for granted, that a compact hausdorff space is determined by its ring of continuous functions (this ring being considered without any topology) — basic discoveries like this are the ones most likely to have their origins obscured, for they eventually come to be seen as mere common sense, and not even a theorem.”

Richard Cudney, Harvard ’03, writing at Xanga.com as rcudney on May 14, 2003

That this theorem is Kolmogorov’s is news to me.

See

The above references establish that Gelfand is usually cited as the source of the theorem Cudney discusses.  Gelfand was a student of Kolmogorov’s in the 1930’s, so who discovered what when may be a touchy question in this case.  A reference that seems relevant: I. M. Gelfand and A. Kolmogoroff, “On rings of continuous functions on topological spaces,” Doklady Akad. Nauk SSSR 22 (1939), 11-15.  This is cited by Gillman and Jerison in the classic Rings of Continuous Functions.

There ARE some references that indicate Kolmogorov may have done some work of his own in this area.  See here (“quite a few duality theorems… including those of Banaschewski, Morita, Gel’fand-Kolmogorov and Gel’fand-Naimark”) and here  (“the classical theorems of M. H. Stone, Gelfand & Kolmogorov”).

Any other references to Kolmogorov’s work in this area would be of interest.

Naturally, any discussion of this area should include a reference to the pioneering work of M. H. Stone.  I recommend the autobiographical article on Stone in McGraw-Hill Modern Men of Science, Volume II, 1968.

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