A review. See also previous posts on this topic.
Wednesday, October 11, 2017
Monday, October 2, 2017
Advanced Study
"Mathematical research currently relies on
a complex system of mutual trust
based on reputations."
— The late Vladimir Voevodsky,
Institute for Advanced Study, Princeton,
The Institute Letter , Summer 2014, p. 8
Voevodsky reportedly died unexpectedly at 51
on the morning of Saturday, Sept. 30, 2017.
Yom Kippur began on Friday evening, Sept. 29, 2017.
Related material —
Comments Off on Advanced Study
Wednesday, November 25, 2020
Requiem for a Jewel
See this evening’s New York Times obituary for the figure below,
who reportedly died today.
IAS is the Institute for Advanced Study at Princeton, NJ.
For more IAS rhetoric, see yesterday evening’s post on
The Building-Block Metaphor.
Comments Off on Requiem for a Jewel
Tuesday, November 24, 2020
Tuesday, April 7, 2020
Eichler’s Amazing Bridge
The following historical remarks are quoted here because
of the above Quanta Magazine article from yesterday.
From Richard Taylor, “Modular arithmetic: driven by
inherent beauty and human curiosity,” The Letter of the
Institute for Advanced Study [IAS], Summer 2012,
pp. 6– 8 (link added) :
“Stunningly, in 1954, Martin Eichler (former IAS Member)
found a totally new reciprocity law . . . .” See as well —
Comments Off on Eichler’s Amazing Bridge
Monday, May 6, 2019
In Memoriam Goro Shimura (d. May 3, 2019)
From Richard Taylor, "Modular arithmetic: driven by inherent beauty
and human curiosity," The Letter of the Institute for Advanced Study [IAS],
Summer 2012, pp. 6– 8 (links added) :
"Stunningly, in 1954, Martin Eichler (former IAS Member)
found a totally new reciprocity law . . . .
Within less than three years, Yutaka Taniyama and Goro Shimura
(former IAS Member) proposed a daring generalization of Eichler’s
reciprocity law to all cubic equations in two variables. A decade later,
André Weil (former IAS Professor) added precision to this conjecture,
and found strong heuristic evidence supporting the Shimura-Taniyama
reciprocity law. This conjecture completely changed the development of
number theory."
Comments Off on In Memoriam Goro Shimura (d. May 3, 2019)
Tuesday, June 19, 2018
Death on Father’s Day
From the University of Notre Dame in an obituary dated June 17 —
|
Timothy O’Meara, provost emeritus, Kenna Professor of Mathematics Emeritus and Trustee Emeritus at the University of Notre Dame, died June 17. He was 90.
A member of the Notre Dame faculty since 1962, O’Meara twice served as chairman of the University’s mathematics department and served as its first lay provost from 1978 to 1996.
He was graduated from the University of Cape Town in 1947 and earned a master’s degree in mathematics there the following year. Earning his doctoral degree from Princeton University in 1953, he taught at the University of Otago in New Zealand from 1954 to 1956 before returning to Princeton where he served on the mathematics faculty and as a member of the Institute for Advanced Study for the next six years.
In addition to his mathematical teaching and scholarship, he published magisterial works, including “Introduction to Quadratic Forms,” “Lectures on Linear Groups,” “Symplectic Groups” and “The Classical Groups and K-Theory,” co-authored with Alexander J. Hahn, professor of mathematics emeritus at Notre Dame and a former O’Meara doctoral student. |
Related material (update of 9:20 PM ET on June 19) —
Comments Off on Death on Father’s Day
Friday, February 16, 2018
Two Kinds of Symmetry
The Institute for Advanced Study (IAS) at Princeton in its Fall 2015 Letter
revived "Beautiful Mathematics" as a title:
This ugly phrase was earlier used by Truman State University
professor Martin Erickson as a book title. See below.
In the same IAS Fall 2015 Letter appear the following remarks
by Freeman Dyson —
". . . a special case of a much deeper connection that Ian Macdonald
discovered between two kinds of symmetry which we call modular and affine.
The two kinds of symmetry were originally found in separate parts of science,
modular in pure mathematics and affine in physics. Modular symmetry is
displayed for everyone to see in the drawings of flying angels and devils
by the artist Maurits Escher. Escher understood the mathematics and got the
details right. Affine symmetry is displayed in the peculiar groupings of particles
created by physicists with high-energy accelerators. The mathematician
Robert Langlands was the first to conjecture a connection between these and
other kinds of symmetry. . . ." (Wikipedia link added.)
The adjective "modular" might aptly be applied to . . .
The adjective "affine" might aptly be applied to . . .
The geometry of the 4×4 square combines modular symmetry
(i.e., related to theta functions) with the affine symmetry above.
Hudson's 1905 discussion of modular symmetry (that of Rosenhain
tetrads and Göpel tetrads) in the 4×4 square used a parametrization
of that square by the digit 0 and the fifteen 2-subsets of a 6-set, but
did not discuss the 4×4 square as an affine space.
For the connection of the 15 Kummer modular 2-subsets with the 16-
element affine space over the two-element Galois field GF(2), see my note
of May 26, 1986, "The 2-subsets of a 6-set are the points of a PG(3,2)" —
— and the affine structure in the 1979 AMS abstract
"Symmetry invariance in a diamond ring" —
For some historical background on the symmetry investigations by
Dyson and Macdonald, see Dyson's 1972 article "MIssed Opportunities."
For Macdonald's own use of the words "modular" and "affine," see
Macdonald, I. G., "Affine Lie algebras and modular forms,"
Séminaire N. Bourbaki , Vol. 23 (1980-1981), Talk no. 577, pp. 258-276.
Comments Off on Two Kinds of Symmetry
Tuesday, October 3, 2017
Show Us Your Wall
From Monday morning's post Advanced Study —
"Mathematical research currently relies on
a complex system of mutual trust
based on reputations."
— The late Vladimir Voevodsky,
Institute for Advanced Study, Princeton,
The Institute Letter , Summer 2014, p. 8
Related news from today's online New York Times —
A heading from the above screenshot: "SHOW US YOUR WALL."
This suggests a review of a concept from Galois geometry —
(On the wall — a Galois-geometry inscape .)
Comments Off on Show Us Your Wall
Monday, March 6, 2017
Bullshit Studies
From The Chronicle of Higher Education on March 2, 2017 —
|
These days, in a world totally dependent on microprocessors, lasers, and nanotechnology, it has been estimated that 30 percent of the U.S. gross national product is based on inventions made possible by quantum mechanics. With the booming high-tech industry and the expected advent of quantum computers, this percentage will only grow. Within a hundred years, an esoteric theory of young physicists became a mainstay of the modern economy. It took nearly as long for Einstein’s own theory of relativity, first published in 1905, to be used in everyday life in an entirely unexpected way. The accuracy of the global positioning system, the space-based navigation system that provides location and time information in today’s mobile society, depends on reading time signals of orbiting satellites. The presence of Earth’s gravitational field and the movement of these satellites cause clocks to speed up and slow down, shifting them by 38 milliseconds a day. In one day, without Einstein’s theory, our GPS tracking devices would be inaccurate by about seven miles. — Robbert Dijkgraaf, Director, Institute for Advanced Study, Princeton |
The above paragraphs are clearly propaganda, not physics.
For "It has been estimated," see …
The "without Einstein 's theory" statement may or may not be correct.
See the lengthy discussion at …
http://physics.stackexchange.com/questions/1061/
why-does-gps-depend-on-relativity .
Comments Off on Bullshit Studies
Thursday, December 22, 2016
Constructivist Witness
The title refers to a philosophy of mathematics.
For those who prefer metaphor… Folk Etymology.
See also Stages of Math at Princeton's
Institute for Advanced Study in March 2013 —
— and in this journal starting in August 2014.
Comments Off on Constructivist Witness
Thursday, April 7, 2016
Plan 9 Continues (Very Slowly)
From the American Mathematical Society today —
|
Verena Huber-Dyson (1923-2016) Huber-Dyson, who worked in group theory and logic, died March 12 at the age of 92. She was born to Swiss parents in Naples and grew up in Athens but moved with her family to Switzerland in 1940 because of the war. Huber-Dyson received her PhD from the University of Zurich in 1947 and moved to the U.S. in 1948 for a post-doctoral fellowship at the Institute for Advanced Study. She held positions at many universities around the world and taught courses on the foundation of mathematics as a philosophy professor at the University of Calgary from 1973 to 1988. Her son, George Dyson, said that her last words were, "This will all go smoothly. Let's get going." She was an AMS member since 1949. Read more about her life. |
See also Huber-Dyson in this journal.
Comments Off on Plan 9 Continues (Very Slowly)
Tuesday, February 18, 2014
Eichler’s Reciprocity Law
Edward Frenkel on Eichler's reciprocity law
(Love and Math , Kindle edition of 2013-10-01,
page 88, location 1812)—
"It seems nearly unbelievable that there
would be a rule generating these numbers.
And yet, German mathematician Martin
Eichler discovered one in 1954.11 "
"11. I follow the presentation of this result
given in Richard Taylor, Modular arithmetic:
driven by inherent beauty and human
curiosity , The Letter of the Institute for
Advanced Study [IAS], Summer 2012,
pp. 6– 8. I thank Ken Ribet for useful
comments. According to André Weil’s book
Dirichlet Series and Automorphic Forms ,
Springer-Verlag, 1971 [pp. 143-144], the
cubic equation we are discussing in this
chapter was introduced by John Tate,
following Robert Fricke."
|
Update of Feb. 19:
Actually, the cubic equation discussed Y 2 + Y = X 3 – X 2
whereas the equation given by Weil, Y 2 – Y = X 3 – X 2 .
Whether this is a misprint in Weil's book,
At any rate, the cubic equation discussed by
For further background, see (for instance) |
Richard Taylor, op. cit. —
|
One could ask for a similar method that given any number of polynomials in any number of variables helps one to determine the number of solutions to those equations in arithmetic modulo a variable prime number p . Such results are referred to as “reciprocity laws.” In the 1920s, Emil Artin gave what was then thought to be the most general reciprocity law possible—his abelian reciprocity law. However, Artin’s reciprocity still only applied to very special equations—equations with only one variable that have “abelian Galois group.” Stunningly, in 1954, Martin Eichler (former IAS Member) found a totally new reciprocity law, not included in Artin’s theorem. (Such reciprocity laws are often referred to as non-abelian.) More specifically, he found a reciprocality [sic ] law for the two variable equation Y 2 + Y = X 3 – X 2. He showed that the number of solutions to this equation in arithmetic modulo a prime number p differs from p [in the negative direction] by the coefficient of q p in the formal (infinite) product
q (1 – q 2 )(1 – q 11) 2 (1 – q 2)2 For example, you see that the coefficient of q5 is 1, so Eichler’s theorem tells us that Y 2 + Y = X 3 − X 2 should have 5 − 1 = 4 solutions in arithmetic modulo 5. You can check this by checking the twenty-five possibilities for (X,Y) modulo 5, and indeed you will find exactly four solutions: (X,Y) ≡ (0,0), (0,4), (1,0), (1,4) mod 5. Within less than three years, Yutaka Taniyama and Goro Shimura (former IAS Member) proposed a daring generalization of Eichler’s reciprocity law to all cubic equations in two variables. A decade later, André Weil (former IAS Professor) added precision to this conjecture, and found strong heuristic evidence supporting the Shimura-Taniyama reciprocity law. This conjecture completely changed the development of number theory. |
With this account and its context, Taylor has
perhaps atoned for his ridiculous remarks
quoted at Log24 in The Proof and the Lie.
Comments Off on Eichler’s Reciprocity Law
Wednesday, November 13, 2013
X-Code
From the obituary of a Bletchley Park
codebreaker who reportedly died on
Armistice Day (Monday, Nov. 11)—
"The main flaw of the Enigma machine,
seen by the inventors as a security-enhancing
measure, was that it would never encipher
a letter as itself…."
Update of 9 PM ET Nov. 13—
"The rogue’s yarn that will run through much of
the material is the algebraic symmetry to which
the name of Galois is attached…."
— Robert P. Langlands,
Institute for Advanced Study, Princeton
"All the turmoil, all the emotions of the scenes
have been digested by the mind into
a grave intellectual whole. It is as though
Bach had written the 1812 Overture."
— Aldous Huxley, "The Best Picture," 1925
Comments Off on X-Code
Sunday, February 10, 2013
The Cleaning
"In 2005 Arthur Jaffe succeeded Sir Michael Atiyah as
Chair of the Board of the Dublin Institute for Advanced Study,
School of Theoretical Physics."
Related material:
Biddies in this journal and…
Detail:
An early version of quaternions.
Comments Off on The Cleaning
Tuesday, November 29, 2011
The Flight from Ennui
Post 2310 in yesterday evening’s Short Story links to two posts
from 2006 inspired by Oxford mathematician Marcus du Sautoy—
|
Thursday, May 25, 2006
|
The first paragraph of
“Zeta Functions of Groups: The Quest for Order
Versus the Flight from Ennui,” by Marcus du Sautoy,
Mathematical Institute, University of Oxford—
“Mathematics is about the search for patterns,
to see order where others see chaos. We are very lucky
to find ourselves studying a subject which is neither so rigid
that the patterns are easy, yet not too complicated
lest our brains fail to master its complexities.
John Cawelti sums up this interplay perfectly in a book*
not about mathematics but about mystery and romance:
‘if we seek order and security, the result is likely to be
boredom and sameness. But rejecting order for the sake
of change and novelty brings danger and uncertainty…
the history of culture can be interpreted as a dynamic
tension between these two basic impulses…
between the quest for order and the flight from ennui.”’
* John G. Cawelti, Adventure, Mystery, and Romance:
Formula Stories as Art and Popular Culture ,
University of Chicago Press, 1976.
[Cawelti cites as his souce on interpreting “the history
of culture” Harry Berger, Jr., “Naive Consciousness and
Culture Change: An Essay in Historical Structuralism,”
Bulletin of the Midwest Modern Language Association ,
Vol. 6, No. 1 (Spring 1973): page 35.]
Here du Sautoy paints mathematicians as seekers of order,
apparently not realizing that the author he approvingly quotes
states that seekers of order face the danger of boredom.
Another danger to seekers
of order is, of course, seeing
order where there is none.
Comments Off on The Flight from Ennui
Thursday, November 17, 2011
Void
From "Elegy to the Void," by Cathleen Schine, New York Review of Books , issue dated Nov. 24, 2011—
“We tell ourselves stories in order to live,” Didion famously wrote in The White Album . Blue Nights is about what happens when there are no more stories we can tell ourselves, no narrative to guide us and make sense out of the chaos, no order, no meaning, no conclusion to the tale. The book has, instead, an incantatory quality: it is a beautiful, soaring, polyphonic eulogy, a beseeching prayer that is sung even as one knows the answer to one’s plea, and that answer is: No.
Blue Nights is a sequel of sorts to The Year of Magical Thinking , Didion's story of the year following the death on December 30th, 2003, of her husband, fellow writer John Gregory Dunne.
Related material:
For some context, see
- Cosmic Banditos in this journal,
- the Fall 1997 newsletter of the Institute for Advanced Study,
- and Oppenheimer's Aria.
For a different link to that aria, see a journal entry dated December 28, 2003.
(Click link, scroll down.)
Comments Off on Void
Thursday, February 25, 2010
Through the Blackboard
Or: "Gopnik Meets Oppenheimer in Heaven"
(Or, for those less philosophically minded, "Raiders of the Lost Pussy")
|
Midrash on "A Serious Man" "A Serious Man kicks off with a Yiddish-language frame story that takes place in a 19th-century Eastern European shtetl, where a married couple has an enigmatic encounter with an old acquaintance who may be a dybbuk," recounts Dana Stevens . "The import of this parable is cryptic to the point of inscrutability." It seems to me that the Coen Brothers’ dybbuk is the Jewish folkloric equivalent of Schrodinger’s Cat . When we first meet the main character, a physics professor named Larry Gopnik, he’s writing equations on the board: "So if that’s that, then we can do this, right? Is that right? Isn’t that right? And that’s Schrodinger’s paradox, right? Is the cat dead or is the cat not dead?" Likewise, we can’t know whether Fyvush Finkel [the aforementioned old acquaintance] is alive or a dybbuk. We can only evaluate probabilities. When a Korean student named Clive Park complains to Larry that he shouldn’t have failed the Physics midterm because "I understand the physics. I understand the dead cat," Larry says: You can’t really understand the physics without understanding the math. The math tells how it really works. That’s the real thing; the stories I give you in class are just illustrative; they’re like, fables, say, to help give you a picture. An imperfect model. I mean— even I don’t understand the dead cat. The math is how it really works. But the fable actually tells us that the math doesn’t capture reality. |
The story in images below summarizes a meditation suggested by this parable and by
- Tuesday's post "Fish Story"
- Today's AP thought:
"Open-mindedness is not the same as empty-mindedness." –John Dewey
- "Zen mind, empty mind."
- Today's NY Times obituary for Selma G. Hirsh,
author of The Fears Men Live By (Harper, 1955).
Hirsh died on St. Bridget's Day.
- A search for the Hirsh book that led to a web page
with a 1955 review of J. Robert Oppenheimer's book The Open Mind
- A search for the Oppenheimer book that led to
LIFE magazine's issue of Oct. 10, 1949
- "Satori means 'awakening.'" — TIME magazine, Nov. 21, 1960
Blackboard in "A Serious Man"–
Blackboard at the Institute for Advanced Study–
"Daddy's home! Daddy's home!"
Related material–
A Zen meditation from Robert Pirsig
is suggested by the time on the above
alarm clock– 8:20– interpreted,
surrealistically, as a date — 8/20.
Comments Off on Through the Blackboard
Wednesday, April 23, 2008
Wednesday April 23, 2008
Upscale Realism
or, "Have some more
wine and cheese, Barack."
Allyn Jackson on Rebecca Goldstein
in the April 2006 AMS Notices (pdf)
|
"Rebecca Goldstein’s 1983 novel The Mind-Body Problem has been widely admired among mathematicians for its authentic depiction of academic life, as well as for its exploration of how philosophical issues impinge on everyday life. Her new book, Incompleteness: The Proof and Paradox of Kurt Gödel, is a volume in the 'Great Discoveries' series published by W. W. Norton….
In March 2005 the Mathematical Sciences Research Institute (MSRI) in Berkeley held a public event in which its special projects director, Robert Osserman, talked with Goldstein about her work. The conversation, which took place before an audience of about fifty people at the Commonwealth Club in San Francisco, was taped…. A member of the audience posed a question that has been on the minds of many of Goldstein’s readers: Is The Mind-Body Problem based on her own life? She did indeed study philosophy at Princeton, finishing her Ph.D. in 1976 with a thesis titled 'Reduction, Realism, and the Mind.' She said that while there are correlations between her life and the novel, the book is not autobiographical…. She… talked about the relationship between Gödel and his colleague at the Institute for Advanced Study, Albert Einstein. The two were very different: As Goldstein put it, 'Einstein was a real mensch, and Gödel was very neurotic.' Nevertheless, a friendship sprang up between the two. It was based in part, Goldstein speculated, on their both being exiles– exiles from Europe and intellectual exiles. Gödel's work was sometimes taken to mean that even mathematical truth is uncertain, she noted, while Einstein's theories of relativity were seen as implying the sweeping view that 'everything is relative.' These misinterpretations irked both men, said Goldstein. 'Einstein and Gödel were realists and did not like it when their work was put to the opposite purpose.'" |
Related material:
From Log24 on
March 22 (Tuesday of
Passion Week), 2005:
|
"'What is this Stone?' Chloe asked…. 'It is told that, when the Merciful One made the worlds, first of all He created that Stone and gave it to the Divine One whom the Jews call Shekinah, and as she gazed upon it the universes arose and had being.'"
— Many Dimensions,
For more on this theme
appropriate to Passion Week — Jews playing God — see
Rebecca Goldstein
Wine and cheese |
From
UPSCALE,
a website of the
physics department at
the University of Toronto:
|
Mirror Symmetry
"The image [above]
The caption of the
'That most divine and beautiful
The caption of the
'A shadow, likeness, or * Sic. The original is incomprehensibilis, a technical theological term. See Dorothy Sayers on the Athanasian Creed and John 1:5. |
For further iconology of the
above equilateral triangles,
see Star Wars (May 25, 2003),
Mani Padme (March 10, 2008),
Rite of Sping (March 14, 2008),
and
Art History: The Pope of Hope
(In honor of John Paul II
three days after his death
in April 2005).
Happy Shakespeare's Birthday.
Comments Off on Wednesday April 23, 2008
Monday, April 14, 2008
Monday April 14, 2008
Classical Quantum
From this morning's
New York Times:
"John A. Wheeler, a visionary physicist… died Sunday morning [April 13, 2008]….
… Dr. Wheeler set the agenda for generations of theoretical physicists, using metaphor as effectively as calculus to capture the imaginations of his students and colleagues and to pose questions that would send them, minds blazing, to the barricades to confront nature….
'He rejuvenated general relativity; he made it an experimental subject and took it away from the mathematicians,' said Freeman Dyson, a theorist at the Institute for Advanced Study….
… he [Wheeler] sailed to Copenhagen to work with Bohr, the godfather of the quantum revolution, which had shaken modern science with paradoxical statements about the nature of reality.
'You can talk about people like Buddha, Jesus, Moses, Confucius, but the thing that convinced me that such people existed were the conversations with Bohr,' Dr. Wheeler said….
… Dr. Wheeler was swept up in the Manhattan Project to build an atomic bomb. To his lasting regret, the bomb was not ready in time to change the course of the war in Europe….
Dr. Wheeler continued to do government work after the war, interrupting his research to help develop the hydrogen bomb, promote the building of fallout shelters and support the Vietnam War….
… Dr. Wheeler wondered if this quantum uncertainty somehow applied to the universe and its whole history, whether it was the key to understanding why anything exists at all.
'We are no longer satisfied with insights only into particles, or fields of force, or geometry, or even space and time,' Dr. Wheeler wrote in 1981. 'Today we demand of physics some understanding of existence itself.'
At a 90th birthday celebration in 2003, Dr. Dyson said that Dr. Wheeler was part prosaic calculator, a 'master craftsman,' who decoded nuclear fission, and part poet. 'The poetic Wheeler is a prophet,' he said, 'standing like Moses on the top of Mount Pisgah, looking out over the promised land that his people will one day inherit.'"
— Dennis Overbye, The New York Times,
Monday, April 14, 2008
As prophets go, I prefer
the poet Wallace Stevens:
the poet Wallace Stevens:
"point A / In a perspective
that begins again / At B"
— Wallace Stevens,
"The Rock"
Comments Off on Monday April 14, 2008
Tuesday, October 16, 2007
Tuesday October 16, 2007
In memory of
Harish-Chandra,
who died at 60
on this date in 1983 
Harish-Chandra in 1981
(Photo by Herman Landshof)
Harish-Chandra,
who died at 60
on this date in 1983
Harish-Chandra in 1981
(Photo by Herman Landshof)
Recent Log24 entries have parodied the use of the phrase “deep beauty” as the title of the Oct. 3-4 physics symposium of that name, which was supported by a grant from the John Templeton Foundation and sponsored by the Department of Philosophy at Princeton University.
Such parody was in part suggested by the symposium’s sources of financial and academic support. This support had, in the view of some, the effect of linking the symposium’s topic, the mathematics of quantum theory, with both religion (the Templeton Foundation) and philosophy (a field sometimes associated in popular thought– though not at Princeton— with quantum mysticism.)
As a corrective to the previous parodies here, the following material on the mathematician Harish-Chandra may help to establish that there is, in fact, such a thing as “deep beauty”– if not in physics, religion, or philosophy, at least in pure mathematics.
MacTutor History of Mathematics:
“Harish-Chandra worked at the Institute of Advanced Study at Princeton from 1963. He was appointed IBM-von Neumann Professor in 1968.”
R. P. Langlands (pdf, undated, apparently from a 1983 memorial talk):
“Almost immediately upon his arrival in Princeton he began working at a ferocious pace, setting standards that the rest of us may emulate but never achieve. For us there is a welter of semi-simple groups: orthogonal groups, symplectic groups, unitary groups, exceptional groups; and in our frailty we are often forced to treat them separately. For him, or so it appeared because his methods were always completely general, there was a single group. This was one of the sources of beauty of the subject in his hands, and I once asked him how he achieved it. He replied, honestly I believe, that he could think no other way. It is certainly true that he was driven back upon the simplifying properties of special examples only in desperate need and always temporarily.”
“It is difficult to communicate the grandeur of Harish-Chandra’s achievements and I have not tried to do so. The theory he created still stands– if I may be excused a clumsy simile– like a Gothic cathedral, heavily buttressed below but, in spite of its great weight, light and soaring in its upper reaches, coming as close to heaven as mathematics can. Harish, who was of a spiritual, even religious, cast and who liked to express himself in metaphors, vivid and compelling, did see, I believe, mathematics as mediating between man and what one can only call God. Occasionally, on a stroll after a seminar, usually towards evening, he would express his feelings, his fine hands slightly upraised, his eyes intent on the distant sky; but he saw as his task not to bring men closer to God but God closer to men. For those who can understand his work and who accept that God has a mathematical side, he accomplished it.”
For deeper views of his work, see
- Rebecca A. Herb, “Harish-Chandra and His Work” (pdf), Bulletin of the American Mathematical Society, July 1991, and
- R. P. Langlands, “Harish-Chandra, 1923-1983” (pdf, 28 pp., Royal Society memoir, 1985)
Comments Off on Tuesday October 16, 2007
Friday, October 5, 2007
Friday October 5, 2007
The Sign of
the Hat
A man returns a crucifix
to a Huichol village chapel.
(Schweidewege should be
Scheidewege, “crossroads.”)
Scheidewege, “crossroads.”)
Related material:
and Log24 entries of
Those for whom entertainment,
is God, may also consult
Comments Off on Friday October 5, 2007
Monday, October 1, 2007
Monday October 1, 2007
Bright as Magnesium
"Definitive"
— The New York Times,
Sept. 30, 2007, on
Blade Runner:
The Final Cut
Institute for Advanced Study, Princeton, N.J.—
"The art historian Kirk Varnedoe died on August 14, 2003, after a long and valiant battle with cancer. He was 57. He was a faculty member in the Institute for Advanced Study’s School of Historical Studies, where he was the fourth art historian to hold this prestigious position, first held by the German Renaissance scholar Erwin Panofsky in the 1930s."
"His final lecture was an eloquent, prophetic flight of free association….
Varnedoe chose to introduce his final lecture with the less-quoted last words of the android Roy Batty (Rutger Hauer) in Ridley Scott's film Blade Runner: 'I've seen things you people wouldn't believe– attack ships on fire off the shoulder of Orion, bright as magnesium; I rode on the back decks of a blinker and watched C-beams glitter in the dark near the Tannhauser Gate. All those moments will be lost in time, like tears in the rain. Time to die.'"
Comments Off on Monday October 1, 2007
Wednesday, November 1, 2006
Wednesday November 1, 2006
Professor Emeritus,
Institute for Advanced Study
Savage Logic
"Savage logic works like a kaleidoscope whose chips can fall into a variety of patterns while remaining unchanged in quantity, form, or color. The number of patterns producible in this way may be large if the chips are numerous and varied enough, but it is not infinite. The patterns consist in the disposition of the chips vis-a-vis one another (that is, they are a function of the relationships among the chips rather than their individual properties considered separately). And their range of possible transformations is strictly determined by the construction of the kaleidoscope, the inner law which governs its operation. And so it is too with savage thought. Both anecdotal and geometric, it builds coherent structures out of 'the odds and ends left over from psychological or historical process.'
These odds and ends, the chips of the kaleidoscope, are images drawn from myth, ritual, magic, and empirical lore. (How, precisely, they have come into being in the first place is one of the points on which Levi-Strauss is not too explicit, referring to them vaguely as the 'residue of events… fossil remains of the history of an individual or a society.') Such images are inevitably embodied in larger structures– in myths, ceremonies, folk taxonomies, and so on– for, as in a kaleidoscope, one always sees the chips distributed in some pattern, however ill-formed or irregular. But, as in a kaleidoscope, they are detachable from these structures and arrangeable into different ones of a similar sort. Quoting Franz Boas that 'it would seem that mythological worlds have been built up, only to be shattered again, and that new worlds were built from the fragments,' Levi-Strauss generalizes this permutational view of thinking to savage thought in general."
— Clifford Geertz, "The Cerebral Savage: the Structural Anthropology of Claude Levi-Strauss," in Encounter, Vol. 28 No. 4 (April 1967), pp. 25-32.
Today's New York Times
reports that
Geertz died on Monday,
October 30, 2006.
Related material:
and Up the River:
|
While it's a story that's never been written, a suggested title– Indiana Jones Sails Up The River Of Death–
shows how readily we as individuals or we as a culture can automatically visualize a basic story motif. We may each see the particular elements of the story differently, but almost instantaneously we catch its drift. The hero sails up the river of death to discover what lies within his own heart: i.e., how much moral and physical strength he has. Indiana Jones sails up the River of Death. We are following Indiana Jones up the River of Death. We're going to visit with Colonel Kurtz. (You may not want to get off the boat.) No, I am not mixing up metaphors. These are the Story. |
Amen.
Comments Off on Wednesday November 1, 2006
Friday, October 6, 2006
Friday October 6, 2006
A Visual Proof
The great mathematician
Robert P. Langlands
is 70 today.
In honor of his expository work–
notably, lectures at
The Institute for Advanced Study
on “The Practice of Mathematics“
and a very acerbic review (pdf) of
a book called Euclid’s Window—
here is a “Behold!” proof of
the Pythagorean theorem:
The picture above is adapted from
a sketch by Eves of a “dynamical”
proof suitable for animation.
The proof has been
described by Alexander Bogomolny
as “a variation on” Euclid I.47.
Bogomolny says it is a proof
by “shearing and translation.”
It has, in fact, been animated.
The following version is
by Robert Foote:
Comments Off on Friday October 6, 2006
Thursday, May 25, 2006
Thursday May 25, 2006
Order and Ennui
Meanwhile, back at the Institute for Advanced Study:
May 25, 4:40 PM —
Research Seminar
(Simonyi Hall Seminar Room) —
Pirita Paajanen,
The Hebrew University of Jerusalem:
Zeta functions of
finitely generated infinite groups
Some background cited by Paajanen:
M.P.F. du Sautoy, “Zeta functions of groups: The quest for order versus the fl ight from ennui,” Groups St Andrews 2001 – in Oxford, Volume 1, CUP 2003.
Those who prefer the showbiz approach to mathematics (the flight from ennui?) may enjoy a website giving further background from du Sautoy.
Friday, May 19, 2006
Friday May 19, 2006
Women-Only
Meeting at Princeton
Meeting at Princeton
From May 15 through May 26, there is a women-only meeting on zeta functions at the Institute for Advanced Study in Princeton, New Jersey. Today’s activities:
| Breakfast (Dining Hall) | |
| T-shirt Sale, Harry’s Bar – Dining Hall | |
| Depart for Princeton University (talks, lunch, campus and art museum tour, and dinner) |
No movie?
|
From Log24, July 27, 2003: “…my despair with words as instruments of communion is often near total.” — Charles Small, Harvard ’64 25th Anniversary Report, 1989 (See 11/21/02).
|
|
|
Lucero |
See also |
Related material:
Women’s History Month–
Global and Local: One Small Step
Comments Off on Friday May 19, 2006
Monday, May 15, 2006
Monday May 15, 2006
For the next generation:
“‘Zeta, Zeta, Zeta!‘”
— Robert A. Heinlein,
The Number of the Beast
Some websites on zeta functions (a classic topic of considerable current interest):
- The course descriptions, lecturers, and schedule of the Institute for Advanced Study women’s meeting on zeta functions that begins today and continues through May 26
- Riemann’s zeta function and A directory of known zeta functions by Matthew R. Watkins
Comments Off on Monday May 15, 2006
Friday, March 10, 2006
Friday March 10, 2006
Women’s History Month continues…
Raiders of the Lost
Stone
In honor of the upcoming program
on Women and Mathematics
at the Institute for Advanced Study
and of Sharon Stone’s 2005 lecture
at Harvard’s Memorial Church,
here are links to reviews of
two Sharon Stone classics:
“King Solomon’s Mines” (1985),
said to be inspired by the
1981 box-office success of
“Raiders of the Lost Ark,” and
Stone as a teacher of mathematics
at St. Anselm’s School for Boys.
See also yesterday’s entry
and Log24, Jan. 1-15, 2006.
In honor of the upcoming program
on Women and Mathematics
at the Institute for Advanced Study
and of Sharon Stone’s 2005 lecture
at Harvard’s Memorial Church,
here are links to reviews of
two Sharon Stone classics:
“King Solomon’s Mines” (1985),
said to be inspired by the
1981 box-office success of
“Raiders of the Lost Ark,” and
“Diabolique” (1996), starring
Stone as a teacher of mathematics
at St. Anselm’s School for Boys.
For related material on St. Anselm
and mathematics at Princeton, see
Modal Theology and the
April 2006 AMS Notices
on
See also yesterday’s entry
and Log24, Jan. 1-15, 2006.
Today’s birthdays:
Sharon Stone and
Gregory La Cava.
Comments Off on Friday March 10, 2006
Friday, March 3, 2006
Friday March 3, 2006
Women's History Month continues.
Global and Local:
One Small Step
One Small Step
Audrey Terras, University of Maryland '64:
We cannot discuss the proof here as it requires some knowledge of zeta functions of curves over finite fields.
Charles Small, Harvard '64:
The moral is that the zeta function exhibits a subtle connection between the "global" (topological, characteristic 0) nature of the curve and its "local" (diophantine, characteristic p for all but finitely many "bad" primes p) behaviour. The full extent of this connection only becomes apparent in the context of varieties more general than curves….
"Some friends of mine
are in this band…."
— David Auburn, "Proof"
"Women and Mathematics
is a joint program of
the Institute for Advanced Study
and Princeton University."
— School of Mathematics,
1 Einstein Drive,
Princeton, New Jersey
Comments Off on Friday March 3, 2006
Tuesday, February 8, 2005
Tuesday February 8, 2005
New from the
Oscar-winning producer,
director, and screenwriter
of “A Beautiful Mind” –
Oscar-winning producer,
director, and screenwriter
of “A Beautiful Mind” –
“The Divine Proportion…
is an irrational number and
the positive solution
of the quadratic equation
x2 – x – 1 = 0,
which is (1+Sqrt(5))/2,
about 1.618034.
about 1.618034.
The Greek letter ‘phi’
(see below for the symbol)
is sometimes used
to represent this number.”
For another approach to
the divine proportion, see
“The rogue’s yarn that will run through much of the material is the algebraic symmetry to which the name of Galois is attached and which I wanted to introduce in as concrete and appealing a way as possible….
Apart from its intrinsic appeal, that is the reason for treating the construction of the pentagon, and our task today will be to acquire some feel for this construction. It is not easy.”
— R. P. Langlands, 1999 lecture (pdf) at the Institute for Advanced Study, Princeton, in the spirit of Hermann Weyl
Comments Off on Tuesday February 8, 2005
Friday, September 17, 2004
Friday September 17, 2004
God is in…
The Details
From an entry for Aug. 19, 2003 on
conciseness, simplicity, and objectivity:
Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale "block design" subtest. Another Harvard psychiatrist, Armand Nicholi, is in the news lately with his book The Question of God: C.S. Lewis and Sigmund Freud Debate God, Love, Sex, and the Meaning of Life.
For the meaning of the Old-Testament logos above, see the remarks of Plato on the immortality of the soul at For the meaning of the New-Testament logos above, see the remarks of R. P. Langlands at |
On Harvard and psychiatry: see
The Crimson Passion:
A Drama at Mardi Gras
(February 24, 2004)
This is a reductio ad absurdum of the Harvard philosophy so eloquently described by Alston Chase in his study of Harvard and the making of the Unabomber, Ted Kaczynski. Kaczynski's time at Harvard overlapped slightly with mine, so I may have seen him in Cambridge at some point. Chase writes that at Harvard, the Unabomber "absorbed the message of positivism, which demanded value-neutral reasoning and preached that (as Kaczynski would later express it in his journal) 'there is no logical justification for morality.'" I was less impressed by Harvard positivism, although I did benefit from a course in symbolic logic from Quine. At that time– the early 60's– little remained at Harvard of what Robert Stone has called "our secret culture," that of the founding Puritans– exemplified by Cotton and Increase Mather.
From Robert Stone, A Flag for Sunrise:
"Our secret culture is as frivolous as a willow on a tombstone. It's a wonderful thing– or it was. It was strong and dreadful, it was majestic and ruthless. It was a stranger to pity. And it's not for sale, ladies and gentlemen."
Some traces of that culture:
|
A web page
|
A contemporary
Click on pictures for details. |
A more appealing view of faith was offered by PBS on Wednesday night, the beginning of this year's High Holy Days:
|
Armand Nicholi: But how can you believe something that you don't think is true, I mean, certainly, an intelligent person can't embrace something that they don't think is true — that there's something about us that would object to that.
Jeremy Fraiberg: Well, the answer is, they probably do believe it's true. Armand Nicholi: But how do they get there? See, that's why both Freud and Lewis was very interested in that one basic question. Is there an intelligence beyond the universe? And how do we answer that question? And how do we arrive at the answer of that question? Michael Shermer: Well, in a way this is an empirical question, right? Either there is or there isn't. Armand Nicholi: Exactly. Michael Shermer: And either we can figure it out or we can't, and therefore, you just take the leap of faith or you don't. Armand Nicholi: Yeah, now how can we figure it out? Winifred Gallagher: I think something that was perhaps not as common in their day as is common now — this idea that we're acting as if belief and unbelief were two really radically black and white different things, and I think for most people, there's a very — it's a very fuzzy line, so that — Margaret Klenck: It's always a struggle. Winifred Gallagher: Rather than — I think there's some days I believe, and some days I don't believe so much, or maybe some days I don't believe at all. Doug Holladay: Some hours. Winifred Gallagher: It's a, it's a process. And I think for me the big developmental step in my spiritual life was that — in some way that I can't understand or explain that God is right here right now all the time, everywhere. Armand Nicholi: How do you experience that? Winifred Gallagher: I experience it through a glass darkly, I experience it in little bursts. I think my understanding of it is that it's, it's always true, and sometimes I can see it and sometimes I can't. Or sometimes I remember that it's true, and then everything is in Technicolor. And then most of the time it's not, and I have to go on faith until the next time I can perhaps see it again. I think of a divine reality, an ultimate reality, uh, would be my definition of God. |
|
|
|
Gallagher seemed to be the only participant in the PBS discussion that came close to the Montessori ideals of conciseness, simplicity, and objectivity. Dr. Montessori intended these as ideals for teachers, but they seem also to be excellent religious values. Just as the willow-tombstone seems suited to Geoffrey Hill's style, the Pythagorean sangaku pictured above seems appropriate to the admirable Gallagher.
Tuesday, June 29, 2004
Tuesday June 29, 2004
|
When? Going to dark bed there was a square round Sinbad the Sailor roc's auk's egg in the night of the bed of all the auks of the rocs of Darkinbad the Brightdayler. Where?
— Ulysses, conclusion of Ch. 17 |
Part II: Badcoc
A Visual Meditation for
the Feast of St. Peter
For further details on this structure, see
Magic Squares, Finite Planes,
and Points of Inflection
on Elliptic Curves,
by Ezra Brown, and
Visualizing GL(2, p)
by Steven H. Cullinane.
For a more literary approach
to this structure, see
Balanchine's Birthday (Jan. 9, 2003),
Art Theory for Yom Kippur (Oct. 5, 2003),
A Form (May 22, 2004),
Ineluctable (May 27, 2004),
A Form, continued (June 5, 2004),
Parallelisms (June 6, 2004),
Deep Game (June 26, 2004), and
Gameplayers of Zen (June 27, 2004).
To appreciate fully this last entry
on Gameplayers,
one must understand
the concept of "suicide"
in the game of Go
and be reminded
by the fatuous phrase of the
Institute of Contemporary Art
quoted in Gameplayers —
"encompassed by 'nothing' " —
of John 1:5.
Comments Off on Tuesday June 29, 2004
Saturday, June 26, 2004
Saturday June 26, 2004
Advanced Study
Herman Goldstine (left), shown in 1952
at the Institute for Advanced Study
with J. Robert Oppenheimer (center)
and John von Neumann (right).
Click on the picture above
for an obituary in today's New York Times
of Goldstine, who died on June 16, 2004.
Click on the picture below
for an event appropriate to
the date of Goldstine's death.
The event, a talk on black holes, took place at
the American Philosophical Society in Philadelphia.
Goldstine was executive director of the Society
from 1984 to 1997.
Comments Off on Saturday June 26, 2004
Friday, May 14, 2004
Friday May 14, 2004
Moral Hazard —
The Devil and Wallace Stevens,
continued from May 1-2 entries:
Law Day,
Readings for Law Day,
Fallen from Heaven, and
The Script
University of Southern California, Department of
Professor Jean-Jacques Laffont
(September 4 – October 21):
“The purpose of this course is to introduce the student to modern contract and organization theory. Part 1 of the course focuses upon models with moral hazard and adverse selection.”
From the insurance page at
http://ingrimayne.saintjoe.edu/:
“The size of the insurance industry indicates that people are eager to pay to avoid risk. They pay and get nothing if fortune smiles on them, whereas if misfortune strikes, they break even because the insurance should just pay back the value lost in the misfortune.
Sometimes, however, people do better than break even when misfortune strikes, and this possibility has greatly interested economists. If, for example, the misfortune costs a person $1000, but insurance will pay $2000, the insured person has no incentive to avoid the misfortune and may act to bring it on. This tendency of insurance to change behavior is called moral hazard.
Sometimes moral hazard is dramatic….
People who know that they face large risks are more likely to buy insurance than people who face small risks. Insurance companies try to minimize the problem that only the people with big risks will buy their product, which is the problem of adverse selection ….”
From today’s New York Times:
“Jean-Jacques Laffont, an economist known for developing mathematical models to estimate what something is worth in situations of deep uncertainty, died on May 1 in Toulouse, France. He was 57….
…Jerry R. Green of Harvard said he was ‘an architect of systems’ and ‘a very original figure.’
Eric Maskin, a professor at the Institute for Advanced Study in Princeton, N.J., called Dr. Laffont ‘simply one of the major figures of our time.’
‘Many people would say he was the leading economist in Europe,’ he added, ‘and that wouldn’t be an unfair judgment.’
Although Dr. Laffont’s models were abstruse enough to satisfy the most theoretical economists, Dr. Green said they were adapted for practical purposes by companies, as well as by public television for scheduling programs.”
Wednesday, March 3, 2004
Wednesday March 3, 2004
Deep Play
In the previous entry, there was a reference to Carl Kaysen, former director of the Institute for Advanced Study at Princeton and father of Susanna Kaysen, author of Girl, Interrupted.
A search for further information on Carl Kaysen led to
Mark Turner, Cognitive Dimensions of Social Science: The Way We Think About Politics, Economics, Law, and Society, Oxford University Press, 2001. For a draft of this work, click here.
Turner's book describes thought and culture in terms of what he calls "blends." It includes a meditation on
Clifford Geertz, "Deep Play: Notes on the Balinese Cockfight," in Dædalus, Journal of the American Academy of Arts and Sciences, issue entitled, "Myth, Symbol, and Culture," Winter 1972, volume 101, number 1
That Turner bases weighty ruminations of what he is pleased to call "social science" on the properties of cockfights suggests that the academic world is, in some respects, even more bizarre than the mental hospital described by Kaysen's daughter.
Still, Turner's concept of "blends" is not without interest.
Here is a blend based on a diagram of the fields in which Turner and Kaysen père labor:
"politics, economics,
law, and society" (Turner)
and "economics, sociology,
politics and law" (Kaysen).
In the previous entry we abstracted from the nature of these academic pursuits, representing them simply as sets in a Venn diagram. This led to the following religious icon, an example of a Turner "blend" —
The Jewel
in Venn's Lotus.
Here is another "blend," related both to the religious material in the previous entry and to Geertz's influential essay.
From my entry for
St. Patrick's Day, 2003:
Summa Theologica
How can you tell there's an Irishman
present at a cockfight?
He enters a duck.
How can you tell a Pole is present?
He bets on the duck.
How can you tell an Italian is present?
The duck wins.
(Source: Blanche Knott,
Truly Tasteless Jokes)
Illustration for the entries
of Oct. 27, 2003:
El Pato-lógico and a
"dream of heaven."
Comments Off on Wednesday March 3, 2004
Tuesday, February 3, 2004
Tuesday February 3, 2004
Retiring Faculty
The following is related to
today's previous four log24 entries.
From my paper journal, a Xeroxed note, composed entirely of cut copies
of various documents,
from July 11, 1990….
|
Harvard Alumni Gazette June 1990 Retiring Faculty Continue their Love of Learning, Creativity Thought for today: "He who tells the truth must have one foot in the stirrup." — Armenian Proverb Preserve me from the enemy — T. S. Eliot, Choruses from the Rock — 1934 Pattern in Islamic Art is the most thorough study yet published of the structure of the art.
|
Sources: Harvard Alumni Gazette, local newspaper, a volume of the poems of T. S. Eliot, David Wade's Pattern in Islamic Art, and a paperback novelization of Pale Rider
Wednesday, December 31, 2003
Wednesday December 31, 2003
Personal Jesus
|
Columnist Cal Thomas What exactly does Dean believe about Jesus, and how is it relevant to his presidential candidacy? “Christ was someone who sought out people who were disenfranchised,” he told the Globe, “people who were left behind.” Dean makes it sound as if He might have been a Democrat. “He fought against self-righteousness of people who had everything,” the candidate continued. “He was a person who set an extraordinary example that has lasted 2,000 years, which is pretty inspiring when you think about it.” Not really. If that is all Jesus was (or is), then he is just another entry in Bartlett’s Familiar Quotations, to be read or not, according to one’s inspirational need. C.S. Lewis brilliantly dealt with this watered-down view of Jesus and what He did in the book “Mere Christianity.” Said Lewis, who thought about such things at a far deeper level than Howard Dean, “I’m trying here to prevent anyone from saying the really foolish thing that people often say about Him: ‘I’m ready to accept Jesus as a great moral teacher, but I can’t accept His claim to be God.’ That is the one thing we must not say. A man who was merely a man and said the sort of things Jesus said would not be a great moral teacher. He would either be a lunatic – on a level with the man who says he is a poached egg – or else he would be the Devil of Hell. You must make your choice. Either this man was, and is, the Son of God – or else a madman or something worse.” |
For an excellent dramatic portrayal of C. S. Lewis, see the film “Shadowlands,” starring Sir Anthony Hopkins.
For Sir Anthony Hopkins
on his birthday —
Your Own Personal Jesus:
Mark Vonnegut in
British Columbia, 1970
The Jesus figure above is,
if not the Son of God,
the son of novelist Kurt Vonnegut —
not a bad alternative.
As for “the sort of things Jesus said,”
consider this from a summary of
the younger Vonnegut’s
The Eden Express: A Memoir of Insanity —
“At one point, he decides that
his thoughts are responsible for
an earthquake in California….”
See the rather similar remarks of Jesus
in Mark 11:23.
For further notes on
theology, lunacy, and earthquakes,
see the previous entries, starting with
The Longest Night, Dec. 21, 2003,
and ending with the two Dec. 28 entries
below, both related to the recent Iran
earthquake (and, by implication, to the
quote from Robert Stone in the entries
Stone, not Wood, and Riddle).
Sunday, December 28, 2003 7:29 PM
Season’s Greetings from the
Institute for Advanced Study,
in keeping with the theme of
the previous entry.
“Warren Ellis’ Die Puny Humans….
Worth looking at.”
DPH leads to Sohma G. Dawling
who in turn leads,
via r. sakamoto, to
Oppenheimer’s Aria.
For the aria, after you click on
the above link, click on the
picture at the resulting site
Sunday, December 28, 2003 2:00 PM
Hostages Freed, Iran Says
The Associated Press,
December 28, 2003, 11:46 AM EST
TEHRAN, Iran — Three European hostages seized in southeastern Iran earlier this month have been released, Foreign Minister Kamal Kharrazi said Sunday.
The $6 million ransom demand was not paid, another Iranian official said.
Drug smugglers seized the hostages — two from Germany and one from Ireland — Dec. 2… as they bicycled to the city of Zahedan from
Bam….
 |
Detail:
|
Thank you, Ma’am.
(See The Magdalene Code, 12/26.
For the “Wham,” see Rosebud, 12/22,
and later entries.)
Another entry not without relevance
is that of 3/07.
Comments Off on Wednesday December 31, 2003
Saturday, August 23, 2003
Saturday August 23, 2003
Pictures of Nothing
‘”The artist delights to go back to the first chaos of the world… All is without forms and void. Some one said of his landscapes that they were pictures of nothing, and very like.”
— William Hazlitt, 1816, on J. M. W. Turner
“William Hazlett [sic] once described Turner’s painting as ‘pictures of the elements of air, earth, and water. The artist delights to go back to the first chaos of the world…All is without form and void. Some one said of his landscapes that they were pictures of nothing and very like.‘ This description could equally well be applied to a Pollock, Newman, or Rothko.”
— Sonja J. Klein, thesis, The Nature of the Sublime, September 2000
The fifty-second A. W. Mellon series of Lectures in the Fine Arts was given last spring at the National Gallery in Washington, D.C., by Kirk Varnedoe, art historian at the Institute for Advanced Study, Princeton, New Jersey.
Pictures of Nothing:
The lectures, 2003: Survivals and Fresh Starts … April 6 |
Varnedoe died on Thursday, August 14, 2003,
the day of the Great Blackout.
Pictures of Nothing:
“Record-breaking crowds turned up at the National Gallery for Kirk’s Mellon Lectures….
… the content of Kirk’s talk was miraculously subtle, as he insisted that there could be no single explanation for how abstraction works, that each piece had to be understood on its own terms — how it came to be made, what it meant then and what it has gone on to mean to viewers since.
Dour works like
Frank Stella’s early
gray-on-black canvases …
“Die Fahne Hoch,”
Frank Stella,
1959
“Gray on Black,”
or “Date of Death”
seemed to open up under Kirk’s touch to reveal a delicacy and complexity lost in less textured explanations.”
— Blake Gopnik in the Washington Post,
Aug. 15, 2003
For another memorial to Varnedoe, see
A May 18 Washington Post article skillfully summarized Varnedoe’s Mellon Lectures at the National Gallery:
Closing the Circle on Abstract Art.
For more on art and nihilism, see
Comments Off on Saturday August 23, 2003
Tuesday, August 19, 2003
Tuesday August 19, 2003
Intelligence Test
From my August 31, 2002, entry quoting Dr. Maria Montessori on conciseness, simplicity, and objectivity:
 |
 |
Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale "block design" subtest.
Another Harvard psychiatrist, Armand Nicholi, is in the news lately with his book The Question of God: C.S. Lewis and Sigmund Freud Debate God, Love, Sex, and the Meaning of Life.
|
Pope |
Nicholi |
|
Old |
New |
For the meaning of the Old-Testament logos above, see the remarks of Plato on the immortality of the soul at
For the meaning of the New-Testament logos above, see the remarks of R. P. Langlands at
The Institute for Advanced Study.
For the meaning of life, see
The Gospel According to Jill St. John,
whose birthday is today.
Sunday, March 16, 2003
Sunday March 16, 2003
Letter
On this date in 1850, Nathaniel Hawthorne’s novel
“The Scarlet Letter” was first published.
|
“Ye see how large a letter
Einstein wrote a rather |
Song of God From the Hindu holy scripture Bhagavad Gita (Song of God): “Of orators, I am the speech; of letters the first one, A; I am imperishable time; the Creator whose face is everywhere; death that devours all things.” “… — Suzan-Lori Parks, |
“ 
See also my note of two years ago,
“Random Thoughts for St. Patrick’s Eve.”
For more on Oppenheimer and the Bhagavad Gita, see
Comments Off on Sunday March 16, 2003
Thursday, March 13, 2003
Thursday March 13, 2003
ART WARS:
From The New Yorker, issue of March 17, 2003, Clive James on Aldous Huxley:
“The Perennial Philosophy, his 1945 book compounding all the positive thoughts of West and East into a tutti-frutti of moral uplift, was the equivalent, in its day, of It Takes a Village: there was nothing in it to object to, and that, of course, was the objection.”
For a cultural artifact that is less questionably perennial, see Huxley’s story “Young Archimedes.”
Plato, Pythagoras, and
|
From the New Yorker Contributors page for St. Patrick’s Day, 2003:
“Clive James (Books, p. 143) has a new collection, As of This Writing: The Essential Essays, 1968-2002, which will be published in June.”
See also my entry “The Boys from Uruguay” and the later entry “Lichtung!” on the Deutsche Schule Montevideo in Uruguay.
Comments Off on Thursday March 13, 2003
Friday, November 8, 2002
Friday November 8, 2002
Religious Symbolism
at Princeton
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
|
SYLVIA BEACH (1887-1962), whose father was pastor of the First Presbyterian Church, founded Shakespeare & Company, a Paris bookshop which became a focus for struggling expatriate writers. In 1922 she published James Joyce’s Ulysses when others considered it obscene, and she defiantly closed her shop in 1941 in protest against the Nazi occupation. KURT GÖDEL (1906-1978), a world-class mathematician famous for a vast array of major contributions to logic, was a longtime professor at the Institute for Advanced Study, founded in 1930. He was a corecipient of the Einstein Award in 1951. JOHN (HENRY) O’HARA (1905-1970) was a voluminous and much-honored writer. His novels, Appointment in Samarra (1934) and Ten North Frederick (1955), and his collection of short stories, Pal Joey (1940), are among his best-known works. |
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
Comments Off on Friday November 8, 2002