Thirty-year medallion from
Alcoholics Anonymous —
Error Icon —
Context —
Monday, December 12, 2016
Symbology for Dan Brown and Stephen King
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Friday, December 25, 2015
Wednesday, December 2, 2015
Thursday, May 14, 2015
Imperial Symbology
See Found Symbol in this journal.
See also the Imperial College theorem symbol
and a page from Imperial College about
group actions on a space Ω —
For Han Solo, some less imperial symbology —
Detail of a CKEditor plugin screenshot:
horizontal line, smiley, special characters,
and iframe area.
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Thursday, November 29, 2012
Lines of Symbols
C. P. Snow on G. H. Hardy, in Snow's foreword to A Mathematician's Apology—
"One morning early in 1913, he found, among the letters on his breakfast table, a large untidy envelope decorated with Indian stamps. When he opened it, he found sheets of paper by no means fresh, on which, in a non-English holograph, were line after line of symbols. Hardy glanced at them without enthusiasm. He was by this time, at the age of thirty-six, a world famous mathematician: and world famous mathematicians, he had already discovered, are unusually exposed to cranks. He was accustomed to receiving manuscripts from strangers, proving the prophetic wisdom of the Great Pyramid, the revelations of the Elders of Zion, or the cryptograms that Bacon has inserted in the plays of the so-called Shakespeare."
Some related material (click to enlarge)—
The author links to, but does not name, the source of the above
"line after line of symbols." It is "Visualizing GL(2,p)." See that webpage
for some less esoteric background.
See also the two Wikipedia articles Finite geometry and Hesse configuration
and an image they share—
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Tuesday, January 26, 2010
Symbology
From this journal:
Friday December 5, 2008Mirror-Play of
the Fourfold For an excellent commentary View selected pages Play and the Aesthetic Dimension (Mihai I. Spariosu, Related material: – and Theme and Variations. |
Transition to the
Garden of Forking Paths–
(See For Baron Samedi)–
The Found Symbol
and Dissemination, by Jacques Derrida,
translated by Barbara Johnson,
London, Athlone Press, 1981–
Pages 354-355
On the mirror-play of the fourfold
Pages 356-357
Shaking up a whole culture
Pages 358-359
Cornerstone and crossroads
Pages 360-361
A deep impression embedded in stone
Pages 362-363
A certain Y, a certain V
Pages 364-365
The world is Zeus's play
Page 366
It was necessary to begin again
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Monday, November 30, 2009
Saturday, January 23, 2010
For Baron Samedi
Annals of Deconstruction —
Click on image for background.
Related material
for Baron Samedi —
The Found Symbol
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Wednesday, September 16, 2009
Wednesday, November 22, 2023
For E. Lily Yu* — Devs Setting
Friday, July 11, 2014
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* Author of Jewel Box: Stories ( Erewhon Books, Oct. 24, 2023).
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Thursday, November 24, 2022
The Drum Machine
"A struggling music producer sells his soul to a 1970s drum machine."
— Summary of a short film by Kevin Ignatius, "Hook Man."
The music producer pawns his current drum device
and acquires a demonic 1970s machine.
Artistic symbolism —
The 16-pad device at left may be viewed by enthusiasts of ekphrasis
as a Galois tesseract, and the machine at right as the voice of
Hal Foster, an art theorist who graduated from Princeton in 1977.
For an example of Foster's prose style, see
the current London Review of Books.
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Thursday, November 10, 2022
For Students of the Forked Tongue
The above 1975 book by Robert Greer Cohn, Modes of Art, is
Volume I of a planned three-volume work.
The passage below is from a review of Cohn's Vol. II, Ways of Art —
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Franklin, Ursula (1987) "Book Review: A Critical Work II. . . . . Those not familiar with the author's epistemology should begin with Appendix A of Ways of Art , a schematic demonstration of his tetrapolar-polypolar-dialectic, especially as it concerns the development of the French novel within the European tradition. But this dialectic, which has antecedents in Kierkegaard, Mallarme and Joyce, underlies all art, because: "this dimensional pulsation, or tetrapolar (and polypolar) higher vibrancy is, in short, the stuff of life: life is vibrant in this more complex way as well as in the more bipolar sense" (7). Cohn shows that "far out enough" the male or linear and the female or circular, the male vertical and the female horizontal dimensions "tend to merge as in relativity theory" (19). Ways of Art shows us the way through a historical becoming of art in its complex dialectic in which the metonymic (horizontal) axis constantly interrelates with the metaphoric (vertical). "Life is the mother, art the father" (vii); hence Cohn's quarrel with most contemporary Feminism, which is pronounced throughout the volume. Firmly grounded in its author's tetra-polypolar epistemology, this beautiful book becomes, however, at no point dryly abstract; it is the mature work of a true humanist who stands in clear and open opposition to the dehumanizing trend of "the quasi-scientific reductionism and abstract gimmickry of a great deal of current academic literary study, bellwethered by the structuralists, post-structuralists, and deconstructionists" (vi). Abundant footnotes constitute a substantial part of Ways of Art , on occasion developing insights almost into essays demonstrating crucial points along the general flow of the tradition from "Obscure Beginnings;' the opening chapter, to our "Contemporaries;' the last. Cohn reminds us that "In the Beginning was the Word;' for the Judaeo-Christian tradition at least, which his study fervently embraces; thus, for example, in Appendix 0 on "The Dance of the Sexes;' he censures "those who live by slogans, camps, and peer-opinion, the countless little bastard cults which characterize an era which has massively veered away from our free and beautiful Greco-Judaeo-Christian tradition" (332). Cohn traces man's way and that of his myths and rituals culminating in his art from that beginning along the lines of Freud, Neumann and Cassirer, and many others, always demonstrating the underlying polypolar dialectical rhythm. Thus in "From Barbarism to Young Culture;' we follow the Celts to Druidic ritual, Hebrew beginnings to the Psalms, Dionysian ritual to Greek tragedy, and thence to the beginnings of French dramatic literature originating in the Quem quaeritis sequence of the medieval Mass. Along the way arises artistic symbolism, for Cohn synonymous with "effective poetry;' to finally "ripen in France as never before" (99). Table I (134) graphs this development from the twelfth to the late nineteenth and early twentieth centuries. The author traces the rise of the artistic vocation from its antecedents in the double function of bard and priest, with the figure of Ronsard at the crossroads of that dying institution and the nascent concept of personal glory. "The Enlightenment Vocation" is exemplified in Montaigne, who humanizes the French cultural elite and points the way to French classicism and, farther down the road, after the moral collapse with the outgoing reign of Louis XIV, toward the Age of Reason. Clearly the most significant figure of the French Enlightenment for all of Western civilization is Rousseau, and Cohn beautifully shows us why this is so. Subsequently, "the nineteenth-century stage of the writer's journey will lead, starting from the crossroads of Rousseau, primarily in these two directions: the imperialistic and visionary prose of Balzac, the equally ambitious poetry of Mallarme", brothers under the skin" (199). And these two paths will then be reconciled in Proust's monumental A la recherche du temps perdu . . . . . |
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Friday, May 6, 2022
Use Your Noodle (For Byron Gogol*)
An essay from . . .
The Shape of Things: A Philosophy of Design Wittgenstein’s Architecture The universe of texts can be seen as a landscape. In it one can make out mountains and valleys, rivers and lakes, castles, farmyards and inner-city slums. On the horizon of the scene visualized in this way, the Bible and Homer appear as gigantic ice-covered mountains. The vast, tranquil lake of Aristotle’s texts, where fishermen idly throw their nets and philologists row their boats, occupies a part of the valley bottom. There, the tumbling waterfall of Nietzsche is captured by the broad river of modern pragmatism. Towering above everything, the Gothic cathedral of St Thomas Aquinas’s Summae dominates the cathedral square of the city, in which the roofs and gables of Baroque speculations jostle one another. In the suburbs of this city, one catches sight of the Romantic, Realist and Modernist housing-blocks and factories of more recent litera¬ ture; somewhat apart from all these stands a small, apparently insignificant house resembling scaffolding more than a finished building: Wittgenstein’s building. This little house is called the Tractatus. This name isn’t the product of a one-track mind. For when one enters the house, one notices immediately that this is not a place that has lost track of things. Quite the opposite: It is a place of mirror- images. The house stands on six foundation pillars which support one another by means of cross-beams organized in a hierarchy. In the middle, however, there rises a seventh pillar whose function it is to cut through the building and free it from the ground. So the house with all its corners, angles and joints is protected, armoured and impregnable. And yet, and for that very reason, it is threatened with collapse and disappearance without trace – condemned in advance and from the outset. The building is set out: It consists of propositions. Every proposition presupposes all the preceding ones and is itself the 76 presupposition of all the following propositions. Proposition by proposition, anyone who enters progresses through the prescribed rooms, and his step is supported by consistencies. Suddenly, with one proposition, one single proposition, the ground gives way beneath his feet. He falls head first into the abyss. Wittgenstein’s house is situated in a suburb of that city whose cathedral square is dominated by the towers of Thomas Aquinas’s cathedral. The small, modest pillars of Wittgenstein’s house support one another according to the same logico- philosophical method as the pillars of the cathedral support one another. But there appears to be a world of difference between the cathedral and the little house: The cathedral is a ship pointing in the direction of heaven, and the little house is a trap-door pointing in the direction of a bottomless abyss. But be careful: May Thomas Aquinas not have been right in saying after his revelation that everything he had written before was like straw? May not the heaven above the cathedral be the same black hole as the abyss beneath the little house? May not Wittgenstein’s little house be the cathedral of today? And those mirrors whose images simultaneously mirror one another, may they not be our equivalent of stained-glass windows? The landscape portrayed in this essay, it goes without saying, is a metaphor. Is it possible to identify it as Vienna? And is it possible for anyone entering Wittgenstein’s little house in that unlikely place to make out a hint of the unsayable? What we cannot speak about we must pass over in silence. 77 |
Click the above image to enlarge.
See as well . . .
Update of 2:40 AM May 7, 2022 —
Flusser's seven "pillars" appear to be the main sections of the Tractatus
— numbered 1 through 7, with many intermediate numbered passages.
For a more geometric meditation on "the shape of things," see other
posts tagged "Shape Constant" in this journal.
*Byron Gogol is a tech magnate in the HBO series "Made for Love."
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Friday, July 30, 2021
The Secret Subterranean River
The "secret, subterranean river" of Shulevitz is
a flow of thought favorable to the cause of feminism,
but not necessarily to other "revolutionary" ideas.
Compare and contrast:
"Where Alph, the sacred river, ran"
— Coleridge, Kubla Khan
"Where Aleph the sacred symbol ran"
— Cullinane, "The Coxeter Aleph"
For group discussion:
How (if at all) is the "finitude" of Heidegger related to
mathematical finitude and The King of Infinite Space ?
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Thursday, March 5, 2020
Pythagorean Letter Meets Box of Chocolates
Friday, July 11, 2014Spiegel-Spiel des GeviertsFiled under: Uncategorized — m759 @ 12:00 PM See Cube Symbology.
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Monday, September 9, 2019
ART WARS at Harvard: The Wertham Professorship
See as well an obituary for Mrs. Wertham from 1987.
Related art —
Friday, July 11, 2014
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For further details, search the Web for "Wertham Professor" + Eck.
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Sunday, July 15, 2018
Jewish Oases
"… Lincoln Plaza Cinemas, the Juilliard String Quartet,
and the Strand Book Store remained oases
for cultural and intellectual stimulation."
— John S. Friedman in The Forward , Jan. 21, 2018
Read more:
https://forward.com/culture/392483/
how-fred-bass-dan-talbot-robert-mann
-shaped-new-york-culture/
From the Oasis in Steven Spielberg's "Ready Player One" (2018) —
I prefer, from a Log24 search for Flux Capacitor …
From "Raiders of the Lost Images" —
"The cube shape of the lost Mother Box,
also known as the Change Engine,
is shared by the Stone in a novel by
Charles Williams, Many Dimensions .
See the Solomon's Cube webpage."
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Thursday, June 14, 2018
Link, Not Wand.
"How frail the wand, but how profound the spell !"
— Clarence R. Wylie, Jr., "Paradox" (1948)
The above fanciful PlayStation symbols suggest an etymology —
See also Kipnis.
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Thursday, June 7, 2018
Saturday, May 19, 2018
Flux Capacitor
For Tom Hanks and Dan Brown —
From "Raiders of the Lost Images" —
"The cube shape of the lost Mother Box,
also known as the Change Engine,
is shared by the Stone in a novel by
Charles Williams, Many Dimensions .
See the Solomon's Cube webpage."
See as well a Google search for flux philosophy —
https://www.google.com/search?q=flux+philosophy.
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Tuesday, January 16, 2018
The Pentagram Papers
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Friday, January 5, 2018
Types of Ambiguity
From "The Principle of Sufficient Reason," by George David Birkhoff,
in "Three Public Lectures on Scientific Subjects,"
delivered at the Rice Institute, March 6, 7, and 8, 1940 —
From the same lecture —
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Up to the present point my aim has been to consider a variety of applications of the Principle of Sufficient Reason, without attempting any precise formulation of the Principle itself. With these applications in mind I will venture to formulate the Principle and a related Heuristic Conjecture in quasi-mathematical form as follows: PRINCIPLE OF SUFFICIENT REASON. If there appears in any theory T a set of ambiguously determined ( i e . symmetrically entering) variables, then these variables can themselves be determined only to the extent allowed by the corresponding group G. Consequently any problem concerning these variables which has a uniquely determined solution, must itself be formulated so as to be unchanged by the operations of the group G ( i e . must involve the variables symmetrically). HEURISTIC CONJECTURE. The final form of any scientific theory T is: (1) based on a few simple postulates; and (2) contains an extensive ambiguity, associated symmetry, and underlying group G, in such wise that, if the language and laws of the theory of groups be taken for granted, the whole theory T appears as nearly self-evident in virtue of the above Principle. The Principle of Sufficient Reason and the Heuristic Conjecture, as just formulated, have the advantage of not involving excessively subjective ideas, while at the same time retaining the essential kernel of the matter. In my opinion it is essentially this principle and this conjecture which are destined always to operate as the basic criteria for the scientist in extending our knowledge and understanding of the world. It is also my belief that, in so far as there is anything definite in the realm of Metaphysics, it will consist in further applications of the same general type. This general conclusion may be given the following suggestive symbolic form:
While the skillful metaphysical use of the Principle must always be regarded as of dubious logical status, nevertheless I believe it will remain the most important weapon of the philosopher. |
Related remarks by a founding member of the Metaphysical Club:
See also the previous post, "Seven Types of Interality."
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Tuesday, September 5, 2017
Annals of Critical Epistemology
"But unlike many who left the Communist Party, I turned left
rather than right, and returned—or rather turned for the first time—
to a critical examination of Marx's work. I found—and still find—
that his analysis of capitalism, which for me is the heart of his work,
provides the best starting point, the best critical tools, with which—
suitably developed—to understand contemporary capitalism.
I remind you that this year is also the sesquicentennial of the
Communist Manifesto , a document that still haunts the capitalist world."
— From "Autobiographical Reflections," a talk given on June 5, 1998, by
John Stachel at the Max Planck Institute for the History of Science in Berlin
on the occasion of a workshop honoring his 70th birthday,
"Space-Time, Quantum Entanglement and Critical Epistemology."
From a passage by Stachel quoted in the previous post —
From the source for Stachel's remarks on Weyl and coordinatization —
Note that Stachel distorted Weyl's text by replacing Weyl's word
"symbols" with the word "quantities." —
This replacement makes no sense if the coordinates in question
are drawn from a Galois field — a field not of quantities , but rather
of algebraic symbols .
"You've got to pick up every stitch… Must be the season of the witch."
— Donovan song at the end of Nicole Kidman's "To Die For"
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Tuesday, May 23, 2017
Logos Review
From Balboa Press —
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More than a pretty face designed to identify a product, a logo combines powerful elements super boosted with sophisticated branding techniques. Logos spark our purchasing choice and can affect our wellbeing. Lovingly detailed, researched and honed to deliver a specific intention, a logo contains a unique dynamic that sidesteps our conscious mind. We might not know why we prefer one product over another but the logo, designed to connect the heart of the brand to our own hearts, plays a vital part in our decision to buy. The power of symbols to sway us has been recognised throughout history. Found in caves and in Egyptian temples they are attributed with the strength to foretell and create the future, connect us with the divine and evoke emotions, from horror to ecstasy, at a glance. The new symbols we imbue with these awesome powers are our favourite brand logos. • Discover the unconscious effect of these modern symbols that thrust our most successful global corporations into the limelight and our lives. • Learn to make informed choices about brands. • Find out how a logo reflects the state of the brand and holds it to account. |
The date of the above remarks on a logo change, March 24, 2016,
suggests a review of a Log24 post from that date —
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Friday, March 10, 2017
Transformers
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Thursday, March 2, 2017
Stories
"We tell ourselves stories in order to live." — Joan Didion
The New York Times Magazine online today —
"As a former believer and now a nonbeliever, Carrère,
seeking answers, sets out, in The Kingdom , to tell
the story of the storytellers. He is trying to understand
what it takes to be able to tell a story, any story.
And what he finds, once again, is that you have to find
your role in it."
— Wyatt Mason in The New York Times Magazine ,
online March 2, 2017
Like Tom Hanks?
Click image for related posts.
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Saturday, February 18, 2017
Solid Symmetry (continued)
See Hanks + Cube in this journal … For instance …
Friday, July 11, 2014
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Monday, October 3, 2016
Ein Eck
Friday, July 11, 2014
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Wednesday, September 28, 2016
Logos
From RIP, a post of Wednesday, March 16, 2016 —
See also earlier posts tagged Sermon Weekend.
From Balboa Press —
|
More than a pretty face designed to identify a product, a logo combines powerful elements super boosted with sophisticated branding techniques. Logos spark our purchasing choice and can affect our wellbeing. Lovingly detailed, researched and honed to deliver a specific intention, a logo contains a unique dynamic that sidesteps our conscious mind. We might not know why we prefer one product over another but the logo, designed to connect the heart of the brand to our own hearts, plays a vital part in our decision to buy. The power of symbols to sway us has been recognised throughout history. Found in caves and in Egyptian temples they are attributed with the strength to foretell and create the future, connect us with the divine and evoke emotions, from horror to ecstasy, at a glance. The new symbols we imbue with these awesome powers are our favourite brand logos. • Discover the unconscious effect of these modern symbols that thrust our most successful global corporations into the limelight and our lives. • Learn to make informed choices about brands. • Find out how a logo reflects the state of the brand and holds it to account. |
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Friday, August 5, 2016
Sleight of Post
From an earlier Log24 post —
Friday, July 11, 2014
|
From a post of the next day, July 12, 2014 —
"So there are several different genres and tones
jostling for prominence within Lexicon :
a conspiracy thriller, an almost abstract debate
about what language can do, and an ironic
questioning of some of the things it’s currently used for."
— Graham Sleight in The Washington Post
a year earlier, on July 15, 2013
For the Church of Synchronology, from Log24 on the next day —
From a post titled Circles on the date of Marc Simont's death —
See as well Verhexung in this journal.
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Thursday, July 14, 2016
Symmetries and Correspondences
The title is that of a large-scale British research project
in mathematics. On a more modest scale …
"Hanks + Cube" in this journal —
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Friday, May 27, 2016
Peer Review
A review of the phrase "Innermost Kernel" in this journal
suggests the following meditation …
"Who am I?" — Existential cry
in "Zoolander" and "Zoolander 2."
A similar question occurs in "Peer Gynt" —
Ben Brantley in yesterday morning's print New York Times *
expressed a nihilistic view of Peer as an onion-peeler —
"Toward the end of Ibsen’s 'Peer Gynt,' a saga of self
under siege, the title character is discovered peeling
an onion, finding in the layers of that humble vegetable
a symbol for the chapters of an eventful life . . . .
… [the director’s] approach is the same one that Peer
applies to the onion: Keep stripping until you find the core.
Of course in Peer’s case what is finally found is
plenty of nothing, an apt conclusion for a man
for whom a solid self remains elusive."
I prefer a view from what Fitzgerald called
"the dark fields of the republic" — the Dordt College view —
* The Times — "A version of this review appears in print on May 26, 2016,
on page C3 of the New York edition with the headline:
'A Saga of Self-Identity, Stripped to Its Core, Still Provokes.' "
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Monday, December 8, 2014
Language Game
Continued from December 5 .
The previous post dealt with video game pioneer Ralph Baer.
Here is a link in honor of mathematician Reinhold Baer
(see Baer in Zero System , a post from the feast of St. Ignatius
Loyola in 2014.)
The posts in Reinhold 's link (those tagged "Yankee Puzzle")
include a reference to the Zero System post. The link tag was
suggested in part by the devil's claws in yesterday morning's post
The Kernel Conundrum and in part by last night's
Kennedy Center Honors tribute to Tom Hanks.
Hanks as the Harvard "symbologist" from the
novels of Dan Brown —
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Wednesday, September 17, 2014
Raiders of the Lost Articulation
Tom Hanks as Indiana Langdon in Raiders of the Lost Articulation :
An unarticulated (but colored) cube:
A 2x2x2 articulated cube:
A 4x4x4 articulated cube built from subcubes like
the one viewed by Tom Hanks above:
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Thursday, September 11, 2014
A Class by Itself
The American Mathematical Society yesterday:
Harvey Cohn (1923-2014)
Wednesday September 10th 2014
Cohn, an AMS Fellow and a Putnam Fellow (1942), died May 16 at the age of 90. He served in the Navy in World War II and following the war received his PhD from Harvard University in 1948 under the direction of Lars Ahlfors. He was a member of the faculty at Wayne State University, Stanford University, Washington University in St. Louis, the University of Arizona, and at City College of New York, where he was a distinguished professor. After retiring from teaching, he also worked for the NSA. Cohn was an AMS member since 1942.
Paid death notice from The New York Times , July 27, 2014:
COHN–Harvey. Fellow of the American Mathematical Society and member of the Society since 1942, died on May 16 at the age of 90. He was a brilliant Mathematician, an adoring husband, father and grandfather, and faithful friend and mentor to his colleagues and students. Born in New York City in 1923, Cohn received his B.S. degree (Mathematics and Physics) from CCNY in 1942. He received his M.S. degree from NYU (1943), and his Ph.D. from Harvard (1948) after service in the Navy (Electronic Technicians Mate, 1944-46). He was a member of Phi Beta Kappa (Sigma Chi), won the William Lowell Putnam Prize in 1942, and was awarded the Townsend Harris Medal in 1972. A pioneer in the intensive use of computers in an innovative way in a large number of classical mathematical problems, Harvey Cohn held faculty positions at Wayne State University, Stanford, Washington University Saint Louis (first Director of the Computing Center 1956-58), University of Arizona (Chairman 1958-1967), University of Copenhagen, and CCNY (Distinguished Professor of Mathematics). After his retirement from teaching, he worked in a variety of capacities for the National Security Agency and its research arm, IDA Center for Computing Sciences. He is survived by his wife of 63 years, Bernice, of Laguna Woods, California and Ft. Lauderdale, FL, his son Anthony, daughter Susan Cohn Boros, three grandchildren and one great-granddaughter.
— Published in The New York Times on July 27, 2014
See also an autobiographical essay found on the web.
None of the above sources mention the following book, which is apparently by this same Harvey Cohn. (It is dedicated to "Tony and Susan.")
Advanced Number Theory, by Harvey Cohn
Courier Dover Publications, 1980 – 276 pages
(First published by Wiley in 1962 as A Second Course in Number Theory )
Publisher's description:
" 'A very stimulating book … in a class by itself.'— American Mathematical Monthly
Advanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject.
The book is divided into three parts. Part I is concerned with background material — a synopsis of elementary number theory (including quadratic congruences and the Jacobi symbol), characters of residue class groups via the structure theorem for finite abelian groups, first notions of integral domains, modules and lattices, and such basis theorems as Kronecker's Basis Theorem for Abelian Groups.
Part II discusses ideal theory in quadratic fields, with chapters on unique factorization and units, unique factorization into ideals, norms and ideal classes (in particular, Minkowski's theorem), and class structure in quadratic fields. Applications of this material are made in Part III to class number formulas and primes in arithmetic progression, quadratic reciprocity in the rational domain and the relationship between quadratic forms and ideals, including the theory of composition, orders and genera. In a final concluding survey of more recent developments, Dr. Cohn takes up Cyclotomic Fields and Gaussian Sums, Class Fields and Global and Local Viewpoints.
In addition to numerous helpful diagrams and tables throughout the text, appendices, and an annotated bibliography, Advanced Number Theory also includes over 200 problems specially designed to stimulate the spirit of experimentation which has traditionally ruled number theory."
User Review –
"In a nutshell, the book serves as an introduction to Gauss' theory of quadratic forms and their composition laws (the cornerstone of his Disquisitiones Arithmeticae) from the modern point of view (ideals in quadratic number fields). I strongly recommend it as a gentle introduction to algebraic number theory (with exclusive emphasis on quadratic number fields and binary quadratic forms). As a bonus, the book includes material on Dirichlet L-functions as well as proofs of Dirichlet's class number formula and Dirichlet's theorem in primes in arithmetic progressions (of course this material requires the reader to have the background of a one-semester course in real analysis; on the other hand, this material is largely independent of the subsequent algebraic developments).
Better titles for this book would be 'A Second Course in Number Theory' or 'Introduction to quadratic forms and quadratic fields'. It is not a very advanced book in the sense that required background is only a one-semester course in number theory. It does not assume prior familiarity with abstract algebra. While exercises are included, they are not particularly interesting or challenging (if probably adequate to keep the reader engaged).
While the exposition is *slightly* dated, it feels fresh enough and is particularly suitable for self-study (I'd be less likely to recommend the book as a formal textbook). Students with a background in abstract algebra might find the pace a bit slow, with a bit too much time spent on algebraic preliminaries (the entire Part I—about 90 pages); however, these preliminaries are essential to paving the road towards Parts II (ideal theory in quadratic fields) and III (applications of ideal theory).
It is almost inevitable to compare this book to Borevich-Shafarevich 'Number Theory'. The latter is a fantastic book which covers a large superset of the material in Cohn's book. Borevich-Shafarevich is, however, a much more demanding read and it is out of print. For gentle self-study (and perhaps as a preparation to later read Borevich-Shafarevich), Cohn's book is a fine read."
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Saturday, July 12, 2014
Mars Package
“For me it is a sign that we have fundamentally different
conceptions of the work of the intelligence services.”
— Germany’s Chancellor Angela Merkel in
theguardian.com, Saturday, 12 July 2014, 14.32 EDT
Another sort of service, thanks to Dan Brown and Tom Hanks:
Friday, July 11, 2014 |
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Friday, July 11, 2014
Spiegel-Spiel des Gevierts
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Wednesday, January 15, 2014
Entertainment Theory
From "Entertainment," a 1981 story by M. A. Foster—
|
"For some time, Cormen had enjoyed a peculiar suspicion, which he had learned from his wanderings around the city, and cultivated with a little notebook, in which he had made a detailed series of notes and jottings, as well as crude, but effective, charts and maps of certain districts. 'Cormen's Problem,' as it was known, was familiar to the members of the circle in which he moved; in fact, if he had not been so effective with his productions and so engaging in his personality, they might have considered him a bore. It seemed, so the suspicion went, that the city was slowly shrinking, as evidenced by abandoned districts along the city edges. Beyond the empty houses were ruins, and beyond that, traces of foundations and street lines. Moreover, it had recently dawned on him that there were no roads out of the city, although there were no restraints. One hardly noticed this—it was the norm. But like many an easy assumption, once broken it became increasingly obvious. Cormen's acquaintances were tolerant of his aberration, but generally unsympathetic. What he needed was proof, something he could demonstrate in black and white—and color if required. But the city was reluctant, so it appeared, to give up its realities so easily. The Master Entertainment Center, MEC, would not answer direct queries about this, even though it would obediently show him presentations, pictorial or symbolic as he required, of the areas in question. But it was tiresome detail work, in which he had to proceed completely on his own." |
Lily Collins in City of Bones (2013)—
American Folk Art (see August 23, 2011) —
See as well Ballet Blanc .
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Saturday, November 23, 2013
Chess
Norwegian, 22, Takes World Chess Title
Quoted here on Thursday, the date of Kavli‘s death:
Herbert Mitgang’s New York Times
obituary of Cleanth Brooks—
“The New Critics advocated close reading of literary texts
and detailed analysis, concentrating on semantics, meter,
imagery, metaphor and symbol as well as references to
history, biography and cultural background.”
See also Steiner, Chess, and Death.
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Saturday, April 27, 2013
Mark and Remark
“Fact and fiction weave in and out of novels like a shell game.” —R.B. Kitaj
Not just novels.
Fact:
The mark preceding A8 in the above denotes the semidirect product.
 |
Symbol from the box-style I Ching (Cullinane, 1/6/89). This is Hexagram 55, “Abundance [Fullness].” |
The mathematical quote, from last evening’s Symmetry, is from Anne Taormina.
The I Ching remark is not.
Another version of Abbondanza —
Fiction:
Found in Translation and the giorno June 22, 2009, here.
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Friday, April 5, 2013
Reflections (continued)
From a search for Mirror-Play in this journal:
That search was suggested by a much lengthier
search, for Core, that itself was suggested
by yesterday's post (on Katherine Neville's birthday)
titled A Philosopher's Stone.
See, too, Tom Hanks (shown above as symbologist
Robert Langdon) in "Lucky Guy" (reviewed by TIME
yesterday), and a related poem:
Yes, you! You’re the Lucky One…
Prospective purchasers of the poet's work
may consult a press release from LSU Press
dated 4/4/2013. The poet died, apparently*
unlamented by his publisher, on 3/30.
* But only apparently.
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Wednesday, October 10, 2012
Melancholia, Depression, Ambiguity
Occurrences of the phrase "magic square" in Lowe-Porter's translation of the Thomas Mann novel Doctor Faustus—
"On the wall above the piano was an arithmetical diagram fastened with drawing-pins, something he had found in a second-hand shop: a so-called magic square, such as appears also in Dürer's Melancolia , along with the hour-glass, the circle, the scale, the polyhedron, and other symbols. Here as there, the figure was divided into sixteen Arabic-numbered fields, in such a way that number one was in the right-hand lower corner, sixteen in the upper left; and the magic, or the oddity, simply consisted in the fact that the sum of these numerals, however you added them, straight down, crosswise, or diagonally, always came to thirty-four. What the principle was upon which this magic uniformity rested I never made out, but by virtue of the prominent place Adrian had given it over the piano, it always attracted the eye, and I believe I never visited his room without giving a quick glance, slanting up or straight down and testing once more the invariable, incredible result."
….
"Adrian kept without changing during the whole four and a half years he spent in Leipzig his two-room quarters in Peterstrasse near the Collegium Beatae Virginis, where he had again pinned the magic square above his cottage piano."
….
" 'The decisive factor is that every note, without exception, has significance and function according to its place in the basic series or its derivatives. That would guarantee what I call the indifference to harmony and melody.'
'A magic square,' I said. 'But do you hope to have people hear all that?' "
….
" 'Extraordinarily Dürerish. You love it. First "how will I shiver after the sun"; and then the houre-glasse of the Melancolia . Is the magic square coming too?' "
….
"Here I will remind the reader of a conversation I had with Adrian on a long-ago day, the day of his sister's wedding at Buchel, as we walked round the Cow Trough. He developed for me— under pressure of a headache— his idea of the 'strict style,' derived from the way in which, as in the lied 'O lieb Madel, wie schlecht bist du ' melody and harmony are determined by the permutation of a fundamental five-note motif, the symbolic letters h, e, a, e, e-flat. He showed me the 'magic square' of a style of technique which yet developed the extreme of variety out of identical material and in which there is no longer anything unthematic, anything that could not prove itself to be a variation of an ever constant element. This style, this technique, he said, admitted no note, not one, which did not fulfil its thematic function in the whole structure— there was no longer any free note."
Review of related material—
Last night's midnight post (disambiguation), the followup 1 AM post (ambiguation), today's noon post (ambiguity), and Dürer in this journal.
The tesseracts of the noon post are related to the Dürer magic square by a well-known adjacency property.
"… the once stable 'father's depression' has been transmuted into a shifting reality that shimmered in a multiplicity of facets."
— Haim Omer, Tel-Aviv University, on Milanese ambiguation therapy,
p. 321 in "Three Styles of Constructive Therapy,"
Constructive Therapies, Vol. 2 , pp. 319-333,
ed. by Michael F. Hoyt (Guilford Press paperback, 1998)
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Tuesday, June 26, 2012
Looking Deeply
Last night's post on The Trinity of Max Black and the use of
the term "eightfold" by the Mathematical Sciences Research Institute
at Berkeley suggest a review of an image from Sept. 22, 2011—
The triskele detail above echoes a Buddhist symbol found,
for instance, on the Internet in an ad for meditation supplies—
Related remarks—
http://www.spencerart.ku.edu/about/dialogue/fdpt.shtml—
Mary Dusenbury (Radcliffe '64)—
"… I think a textile, like any work of art, holds a tremendous amount of information— technical, material, historical, social, philosophical— but beyond that, many works of art are very beautiful and they speak to us on many layers— our intellect, our heart, our emotions. I've been going to museums since I was a very small child, thinking about what I saw, and going back to discover new things, to see pieces that spoke very deeply to me, to look at them again, and to find more and more meaning relevant to me in different ways and at different times of my life. …
… I think I would suggest to people that first of all they just look. Linger by pieces they find intriguing and beautiful, and look deeply. Then, if something interests them, we have tried to put a little information around the galleries to give a bit of history, a bit of context, for each piece. But the most important is just to look very deeply."
http://en.wikipedia.org/wiki/Nikaya_Buddhism—
According to Robert Thurman, the term "Nikāya Buddhism" was coined by Professor Masatoshi Nagatomi of Harvard University, as a way to avoid the usage of the term Hinayana.[12] "Nikaya Buddhism" is thus an attempt to find a more neutral way of referring to Buddhists who follow one of the early Buddhist schools, and their practice.
12. The Emptiness That is Compassion:
An Essay on Buddhist Ethics, Robert A. F. Thurman, 1980
[Religious Traditions , Vol. 4 No. 2, Oct.-Nov. 1981, pp. 11-34]
http://dsal.uchicago.edu/cgi-bin/philologic/getobject.pl?c.2:1:6.pali—
Nikāya [Sk. nikāya, ni+kāya]
collection ("body") assemblage, class, group
http://en.wiktionary.org/wiki/नि—
Sanskrit etymology for नि (ni)
1 From Proto-Indo-European *ni …
Prefix
नि (ni)
- down
- back
- in, into
http://www.rigpawiki.org/index.php?title=Kaya—
Kaya (Skt. kāya ; སྐུ་, Tib. ku ; Wyl. sku ) —
the Sanskrit word kaya literally means ‘body’
but can also signify dimension, field or basis.
• structure, existentiality, founding stratum ▷HVG KBEU
Note that The Trinity of Max Black is a picture of a set—
i.e., of an "assemblage, class, group."
Note also the reference above to the word "gestalt."
"Was ist Raum, wie können wir ihn
erfassen und gestalten?"
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Saturday, April 21, 2012
Finding a Form
In "Contact," Dr. Arroway is shown the key to the Primer—
In this journal, fictional symbologist Robert Langdon is shown a cube—
"Confusion is nothing new." — Song lyric
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Wednesday, April 18, 2012
Adam in Eden
…. and John Golding, an authority on Cubism who "courted abstraction"—
"Adam in Eden was the father of Descartes." — Wallace Stevens
Fictional symbologist Robert Langdon and a cube—
From a Log24 post, "Eightfold Cube Revisited,"
on the date of Golding's death—
A related quotation—
"… quaternions provide a useful paradigm
for studying the phenomenon of 'triality.'"
— David A. Richter's webpage Zometool Triality
See also quaternions in another Log24 post
from the date of Golding's death— Easter Act.
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Monday, April 16, 2012
Carroll Thanks the Academy
Gary Gutting, "Arguing About Language," in "The Stone,"
The New York Times philosophy column, yesterday—
There's a sense in which we speak language
and a sense in which, in Mallarmé's famous phrase,
“language itself speaks.”
Famous? A Google Book Search for
"language itself speaks" Mallarmé
yields 2 results, neither helpful.
But a Google Book Search for
"language itself speaks" Heidegger
yields "about 312 results."
A related search yields the following—
Paul Valéry, encountering Un Coup de Dés in Mallarmé’s worksheets in 1897, described the text as tracing the pattern of thought itself:
It seemed to me that I was looking at the form and pattern of a thought, placed for the first time in finite space. Here space itself truly spoke, dreamed, and gave birth to temporal forms….
… there in the same void with them, like some new form of matter arranged in systems or masses or trailing lines, coexisted the Word! (Leonardo 309*)
* The page number is apparently a reference to The Collected Works of Paul Valéry: Leonardo, Poe, Mallarmé , translated by Malcolm Cowley and James R. Lawler, Princeton University Press, 1972. (As a temporal form, "309" might be interpreted as a reference to 3/09, March 9, the date of a webpage on the Void.)
For example—
Background:
Deconstructing Alice
and Symbology.
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Thursday, April 5, 2012
Leap Day of Faith
Presidential candidate Mitt Romney on Monday, April 2, 2012—
"I think there is in this country a war on religion.
I think there is a desire to establish a religion
in America known as secularism."
Nancy Haught of The Oregonian on Leap Day, Feb. 29, 2012—
|
William Hamilton, the retired theologian who declared in the 1960s that God was dead, died Tuesday [Feb. 28, 2012] in his downtown Portland apartment at 87. Hamilton said he'd been haunted by questions about God since he was a teenager. Years later, when his conclusion was published in the April 8, 1966, edition of Time Magazine, he found himself in a hornet's nest. Time christened the new movement "radical theology" and Hamilton, one of its key figures, received death threats and inspired angry letters to the editor in newspapers that carried the story. He encountered hostility at Colgate Rochester Crozer Divinity School, where he had been teaching theology, and lost his endowed chair in 1967. Hamilton moved on to teach religion at New College in Sarasota, Fla. |
(See also this journal on Leap Day.)
From New College: The Honors College of Florida—
|
Oct. 11, 1960: New College is founded as a private college 1961: Trustees obtain options to purchase the former Charles Ringling estate on Sarasota Bay and 12 acres of airport land facing U.S. 41 held by private interests. The two pieces form the heart of the campus Nov. 18, 1962: the campus is dedicated. Earth from Harvard is mixed with soil from New College as a symbol of the shared lofty ideals of the two institutions. |
See also, in this journal, "Greatest Show on Earth" and The Harvard Crimson—
| The Harvard Crimson, Online Edition |
Sunday, Oct. 8, 2006 |
|
POMP AND
Friday, Oct. 6:
The Ringling Bros. Barnum & Bailey Circus has come to town, and yesterday the animals were disembarked near MIT and paraded to their temporary home at the Banknorth Garden. |
OPINION At Last, a By THE CRIMSON STAFF The Trouble By SAHIL K. MAHTANI |
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Sunday, October 2, 2011
Emerson on Mathematics
From "The Poet" (1844)—
If the imagination intoxicates the poet, it is not inactive in other men. The metamorphosis excites in the beholder an emotion of joy.
The use of symbols has a certain power of emancipation and exhilaration for all men. We seem to be touched by a wand, which makes us dance and run about happily, like children. We are like persons who come out of a cave or cellar into the open air. This is the effect on us of tropes, fables, oracles, and all poetic forms. Poets are thus liberating gods. Men have really got a new sense, and found within their world, another world or nest of worlds; for the metamorphosis once seen, we divine that it does not stop. I will not now consider how much this makes the charm of algebra and the mathematics, which also have their tropes, but it is felt in every definition….
… Here is the difference betwixt the poet and the mystic, that the last nails a symbol to one sense, which was a true sense for a moment, but soon becomes old and false…. Mysticism consists in the mistake of an accidental and individual symbol for an universal one…. And the mystic must be steadily told,— All that you say is just as true without the tedious use of that symbol as with it. Let us have a little algebra, instead of this trite rhetoric,— universal signs, instead of these village symbols,— and we shall both be gainers.
See also Weyl on the use of symbols (in coordinate systems) and today's previous posts Birth of a Poet and Symmetric Generation Illustrated.
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Thursday, September 1, 2011
How It Works
“Design is how it works.” — Steven Jobs (See Symmetry and Design.)
“By far the most important structure in design theory is the Steiner system S(5, 8, 24).”
— “Block Designs,” by Andries E. Brouwer
The name Carmichael is not to be found in Booher’s thesis. A book he does cite for the history of S(5,8,24) gives the date of Carmichael’s construction of this design as 1937. It should be dated 1931, as the following quotation shows—
From Log24 on Feb. 20, 2010—
“The linear fractional group modulo 23 of order 24•23•11 is often represented as a doubly transitive group of degree 24 on the symbols ∞, 0, 1, 2,…, 22. This transitive group contains a subgroup of order 8 each element of which transforms into itself the set ∞, 0, 1, 3, 12, 15, 21, 22 of eight elements, while the whole group transforms this set into 3•23•11 sets of eight each. This configuration of octuples has the remarkable property that any given set of five of the 24 symbols occurs in one and just one of these octuples. The largest permutation group Γ on the 24 symbols, each element of which leaves this configuration invariant, is a five-fold transitive group of degree 24 and order 24•23•22•21•20•48. This is the Mathieu group of degree 24.”
– R. D. Carmichael, “Tactical Configurations of Rank Two,” in American Journal of Mathematics, Vol. 53, No. 1 (Jan., 1931), pp. 217-240
Epigraph from Ch. 4 of Design Theory , Vol. I:
“Es is eine alte Geschichte,
doch bleibt sie immer neu ”
—Heine (Lyrisches Intermezzo XXXIX)
See also “Do you like apples?“
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Friday, August 12, 2011
Into the Woods
"What’s best about us, I hope, is that we teach them
the ‘forest of symbols,’ to borrow deliberately from
a poem called ‘Correspondences,’ by Baudelaire."
— The late Stanley Bosworth, founding headmaster
of St. Ann's School in Brooklyn
Bosworth died Sunday.
Related material—
- Saturday's Correspondences,
- Sunday's Coordinated Steps, and
- Monday's Organizing the Mine Workers.
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Wednesday, July 13, 2011
The Sinatra Code
|
From The Da Vinci Code, Chapter 56 Sophie stared at Teabing a long moment and then turned to Langdon. “The Holy Grail is a person?” Langdon nodded. “A woman, in fact.” From the blank look on Sophie’s face, Langdon could tell they had already lost her. He recalled having a similar reaction the first time he heard the statement. It was not until he understood the symbology behind the Grail that the feminine connection became clear. Teabing apparently had a similar thought. “Robert, perhaps this is the moment for the symbologist to clarify?” He went to a nearby end table, found a piece of paper, and laid it in front of Langdon. Langdon pulled a pen from his pocket. “Sophie are you familiar with the modern icons for male and female?” He drew the common male symbol ♂ and female symbol ♀. “Of course,” she said. “These,” he said quietly, are not the original symbols for male and female. Many people incorrectly assume the male symbol is derived from a shield and spear, while the female represents a mirror reflecting beauty. In fact, the symbols originated as ancient astronomical symbols for the planet-god Mars and the planet-goddess Venus. The original symbols are far simpler.” Langdon drew another icon on the paper. ∧
“This symbol is the original icon for male ,” he told her. “A rudimentary phallus.” “Quite to the point,” Sophie said. “As it were,” Teabing added. Langdon went on. “This icon is formally known as the blade , and it represents aggression and manhood. In fact, this exact phallus symbol is still used today on modern military uniforms to denote rank.” “Indeed.” Teabing grinned. “The more penises you have, the higher your rank. Boys will be boys.” Langdon winced. “Moving on, the female symbol, as you might imagine, is the exact opposite.” He drew another symbol on the page. “This is called the ∨ Sophie glanced up, looking surprised. Langdon could see she had made the connection. “The chalice,” he said, “resembles a cup or vessel, and more important, it resembles the shape of a woman’s womb. This symbol communicates femininity, womanhood, and fertility.” Langdon looked directly at her now. “Sophie, legend tells us the Holy Grail is a chalice—a cup. But the Grail’s description as a chalice is actually an allegory to protect the true nature of the Holy Grail. That is to say, the legend uses the chalice as a metaphor for something far more important.” “A woman,” Sophie said. “Exactly.” Langdon smiled. “The Grail is literally the ancient symbol for womankind, and the Holy Grail represents the sacred feminine and the goddess, which of course has now been lost, virtually eliminated by the Church. The power of the female and her ability to produce life was once very sacred, but it posed a threat to the rise of the predominantly male Church, and so the sacred feminine was demonized and called unclean. It was man , not God, who created the concept of ‘original sin,’ whereby Eve tasted of the apple and caused the downfall of the human race. Woman, once the sacred giver of life, was now the enemy.” “I should add,” Teabing chimed, “that this concept of woman as life-bringer was the foundation of ancient religion. Childbirth was mystical and powerful. Sadly, Christian philosophy decided to embezzle the female’s creative power by ignoring biological truth and making man the Creator. Genesis tells us that Eve was created from Adam’s rib. Woman became an offshoot of man. And a sinful one at that. Genesis was the beginning of the end for the goddess.” “The Grail,” Langdon said, “is symbolic of the lost goddess. When Christianity came along, the old pagan religions did not die easily. Legends of chivalric quests for the lost Grail were in fact stories of forbidden quests to find the lost sacred feminine. Knights who claimed to be “searching for the chalice” were speaking in codes as a way to protect themselves from a Church that had subjugated women, banished the Goddess, burned nonbelievers, and forbidden pagan reverence for the sacred feminine.” |
Happy birthday to Harrison Ford.
One for my baby…
∧
One more for the road.
∨
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Sunday, May 1, 2011
Delos
The late translator Helen Lane in Translation Review , Vol. 5, 1980—
"Among the awards, I submit, should be one for the entire oeuvre of a lifetime "senior" translator— and one for the best first translation…. Similar organization, cooperation, and fund-finding for a first-rate replacement for the sorely missed Delos ."
This leads to one of the founders of Delos , the late Donald Carne-Ross, who died on January 9, 2010.
For one meditation on the date January 9, see Bridal Birthday (last Thursday).
Another meditation, from the date of Carne-Ross's death—
Saturday, January 9, 2010
Positional Meaning"The positional meaning of a symbol derives from its relationship to other symbols in a totality, a Gestalt, whose elements acquire their significance from the system as a whole." – Victor Turner, The Forest of Symbols , Ithaca, NY, Cornell University Press, 1967, p. 51, quoted by Beth Barrie in "Victor Turner." To everything, turn, turn, turn …
|
See also Delos in this journal.
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Saturday, April 23, 2011
Vigil
"The Easter Vigil is the most important liturgy on the church's calendar, when the faithful mark the passage from Christ's death to his resurrection on Easter Sunday. It is rich with symbols: fire and light signifying Jesus' resurrection, and the water used to baptize people into the faith….
This year, students of the Legion of Christ, the conservative order undergoing a major Vatican-mandated overhaul, provided the liturgical service at the vigil. The Vatican took over the Legion last May 1 after confirming its founder was a pedophile."
— AP story
See also Naples in this journal.
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Sunday, March 27, 2011
Frames
"I just seemed to have more frames per second than other kids."
— Mary Karr, "Facing Altars: Poetry and Prayer"
See also "Signs and Symbols."
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Friday, March 4, 2011
Infinite Jest
Two items from the August 5, 2005, anniversary
of the day Marilyn Monroe was found dead—
2. Literary Symbol —
See also related material on Hollywood.
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Wednesday, September 1, 2010
September Morn
For Alyssa Milano —
(Click here for cheesy Neil Diamond background music.)
For some related philosophical remarks, see Deconstructing Alice
and the new Pythagorean thriller The Thousand.
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Sunday, August 15, 2010
The Game
“We shall now give a brief summary of the beginnings of the Glass Bead Game. It appears to have arisen simultaneously in Germany and in England. In both countries, moreover, it was originally a kind of exercise employed by those small groups of musicologists and musicians who worked and studied in the new seminaries of musical theory. If we compare the original state of the Game with its subsequent developments and its present form, it is much like comparing a musical score of the period before 1500, with its primitive notes and absence of bar lines, with an eighteenth-century score, let alone with one from the nineteenth with its confusing excess of symbols for dynamics, tempi, phrasing, and so on, which often made the printing of such scores a complex technical problem.
The Game was at first nothing more than a witty method for developing memory and ingenuity among students and musicians. And as we have said, it was played both in England and Germany before it was ‘invented’ here in the Musical Academy of Cologne, and was given the name it bears to this day, after so many generations, although it has long ceased to have anything to do with glass beads.
The inventor, Bastian Perrot of Calw, a rather eccentric but clever, sociable, and humane musicologist, used glass beads instead of letters, numerals, notes, or other graphic symbols. Perrot, who incidentally has also bequeathed to us a treatise on the Apogee and Decline of Counterpoint, found that the pupils at the Cologne Seminary had a rather elaborate game they used to play. One would call out, in the standardized abbreviations of their science, motifs or initial bars of classical compositions, whereupon the other had to respond with the continuation of the piece, or better still with a higher or lower voice, a contrasting theme, and so forth. It was an exercise in memory and improvisation quite similar to the sort of thing probably in vogue among ardent pupils of counterpoint in the days of Schütz, Pachelbel, and Bach — although it would then not have been done in theoretical formulas, but in practice on the cembalo, lute, or flute, or with the voice.
Bastian Perrot in all probability was a member of the Journeyers to the East. He was partial to handicrafts and had himself built several pianos and clavichords in the ancient style. Legend has it that he was adept at playing the violin in the old way, forgotten since 1800, with a high-arched bow and hand-regulated tension of the bow hairs. Given these interests, it was perhaps only natural that he should have constructed a frame, modeled on a child’s abacus, a frame with several dozen wires on which could be strung glass beads of various sizes, shapes, and colors. The wires corresponded to the lines of the musical staff, the beads to the time-values of the notes, and so on. In this way he could represent with beads musical quotations or invented themes, could alter, transpose, and develop them, change them and set them in counterpoint to one another. In technical terms this was a mere plaything, but the pupils liked it; it was imitated and became fashionable in England too. For a time the game of musical exercises was played in this charmingly primitive manner. And as is so often the case, an enduring and significant institution received its name from a passing and incidental circumstance. For what later evolved out of that students’ sport and Perrot’s bead-strung wires bears to this day the name by which it became popularly known, the Glass Bead Game.“
“For although in a certain sense and for light-minded persons non-existent things can be more easily and irresponsibly represented in words than existing things, for the serious and conscientious historian it is just the reverse. Nothing is harder, yet nothing is more necessary, than to speak of certain things whose existence is neither demonstrable nor probable. The very fact that serious and conscientious men treat them as existing things brings them a step closer to existence and to the possibility of being born.”
— “Albertus Secundus,” epigraph to The Glass Bead Game
From DownloadThat.com—
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Tuesday, August 10, 2010
Architecture Continued
Yesterday's architectural entertainment coincided, more or less, with the New York Times article "The Hand of a Master Architect" (Online Sunday, Aug. 8, and in the print edition Monday, Aug. 9).
A search for some background on that architect (Philip Johnson, not Howard Roark) showed that the Art Libraries Society of North America published a notable graphic logo in 2005—
See this journal on April 7, 2005, for a related graphic design.
The ARLIS/NA 2005 page cited above says about Houston, Texas, that
"Just beyond the museum district lies Rice University, the city's most prestigious and oldest college….
Other campuses that contain significant architecture include St. Thomas University where Philip Johnson has made his mark for a period that extends more than forty years."
University of St. Thomas, Chapel of St. Basil
Applying Jungian synchronicity, we note that Johnson designed the Chapel of St. Basil at the University of St. Thomas, that the traditional date of the Feast of St. Basil is June 14, and that this journal on that date contained the following, from the aforementioned Rice University—
… a properly formulated Principle of Sufficient Reason plays
a fundamental role in scientific thought and, furthermore, is
to be regarded as of the greatest suggestiveness from the
philosophic point of view.2
… metaphysical reasoning always relies on the Principle of
Sufficient Reason, and… the true meaning of this Principle
is to be found in the “Theory of Ambiguity” and in the associated
mathematical “Theory of Groups.”
If I were a Leibnizian mystic, believing in his “preestablished
harmony,” and the “best possible world” so satirized by Voltaire
in “Candide,” I would say that the metaphysical importance of
the Principle of Sufficient Reason and the cognate Theory of Groups
arises from the fact that God thinks multi-dimensionally3
whereas men can only think in linear syllogistic series, and the
Theory of Groups is the appropriate instrument of thought to
remedy our deficiency in this respect.
The founder of the Theory of Groups was the mathematician
Evariste Galois….
2 As far as I am aware, only Scholastic Philosophy has fully recognized
and exploited this principle as one of basic importance for philosophic thought.
3 That is, uses multi-dimensional symbols beyond our grasp.
For more about Scholastic Philosophy, see the Center for Thomistic Studies at the University of St. Thomas.
For more about the graphic symbol shown (as above) by ARLIS and by Log24 in April 2005, see in this journal "rature sous rature ."
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Wednesday, July 21, 2010
Dream Names continued
From the 7/20 Harvard Crimson—
"The scholarly expeditions undertaken by modern-day explorer and Harvard Foundation Director S. Allen Counter will be featured in a biopic produced by actor Will Smith.
…. Debbie Allen is also producing the film, and Farhad Safinia will be penning the script, Variety magazine reported.
…. Counter said that Debbie Allen described his character as 'a mixture of Indiana Jones and Robert Langdon,' the fictional Harvard professor of symbology in Dan Brown’s novels."
Farhad Safinia is co-writer and co-producer, with Mel Gibson, of "Apocalypto."
From "The Envelope: The Awards Insider" at the LA Times, a review of the film based on Dan Brown's "Angels & Demons"—
"The script tips its hand too early, and can't quite turn Langdon into Indiana Langdon on his Last Crusade."
— , Orlando Sentinel movie critic, May 15, 2009
Related material:
The Robert Jones Code—
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Saturday, July 3, 2010
Beyond the Limits
"Human perception is a saga of created reality. But we were devising entities beyond the agreed-upon limits of recognition or interpretation…."
– Don DeLillo, Point Omega
Capitalized, the letter omega figures in the theology of two Jesuits, Teilhard de Chardin and Gerard Manley Hopkins. For the former, see a review of DeLillo. For the latter, see James Finn Cotter's Inscape and "Hopkins and Augustine."
The lower-case omega is found in the standard symbolic representation of the Galois field GF(4)—
A representation of GF(4) that goes beyond the standard representation—
Here the four diagonally-divided two-color squares represent the four elements of GF(4).
The graphic properties of these design elements are closely related to the algebraic properties of GF(4).
This is demonstrated by a decomposition theorem used in the proof of the diamond theorem.
To what extent these theorems are part of "a saga of created reality" may be debated.
I prefer the Platonist's "discovered, not created" side of the debate.
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Thursday, July 1, 2010
Plato’s Code
John Allen Paulos yesterday at Twitter—
"Plato's code cracked? http://bit.ly/ad6k1S
Fascinating if not a hoax or hype."
The story that Paulos linked to is about a British
academic who claims to have found some
symbolism hidden in Plato's writings by
splitting each into 12 parts and correlating
the 12 parts with semitones of a musical scale.
I prefer a different approach to Plato that is
related to the following hoax and hype—
HOAX:
From Dan Brown's novel Angels & Demons (2000)—
HYPE:
This four-elements diamond summarizes the classical
four elements and four qualities neatly, but some scholars
might call the figure "hype" since it deals with an academically
disreputable subject, alchemy, and since its origin is unclear.
For the four elements' role in some literature more respectable
than Dan Brown's, see Poetry's Bones.
Although an author like Brown might spin the remarks
below into a narrative— The Plato Code — they are
neither hoax nor hype.
NOT HOAX:
NOT HYPE:
For related non-hoax, non-hype remarks, see
The Rational Enterprise: Logos in Plato's Theaetetus,
by Rosemary Desjardins.
Those who prefer hoax and hype in their philosophy may consult
the writings of, say, Barbara Johnson, Rosalind Krauss, and—
in yesterday's NY Times's "The Stone" column— Nancy Bauer.
— The New York Times
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Saturday, June 19, 2010
Imago Creationis
In the above view, four of the tesseract's 16
vertices are overlaid by other vertices.
For views that are more complete and
moveable, see Smith's tesseract page.
Four-Part Tesseract Divisions—
The above figure shows how four-part partitions
of the 16 vertices of a tesseract in an infinite
Euclidean space are related to four-part partitions
of the 16 points in a finite Galois space
|
Euclidean spaces versus Galois spaces in a larger context—
Infinite versus Finite The central aim of Western religion —
"Each of us has something to offer the Creator...
the bridging of
masculine and feminine,
life and death.
It's redemption.... nothing else matters."
-- Martha Cooley in The Archivist (1998)
The central aim of Western philosophy —
Dualities of Pythagoras
as reconstructed by Aristotle:
Limited Unlimited
Odd Even
Male Female
Light Dark
Straight Curved
... and so on ....
"Of these dualities, the first is the most important; all the others may be seen as different aspects of this fundamental dichotomy. To establish a rational and consistent relationship between the limited [man, etc.] and the unlimited [the cosmos, etc.] is… the central aim of all Western philosophy." |
Another picture related to philosophy and religion—
Jung's Four-Diamond Figure from Aion—
This figure was devised by Jung
to represent the Self. Compare the
remarks of Paul Valéry on the Self—
|
Flight from Eden: The Origins of Modern Literary Criticism and Theory, by Steven Cassedy, U. of California Press, 1990, pages 156-157—
Valéry saw the mind as essentially a relational system whose operation he attempted to describe in the language of group mathematics. "Every act of understanding is based on a group," he says (C, 1:331). "My specialty— reducing everything to the study of a system closed on itself and finite" (C, 19: 645). The transformation model came into play, too. At each moment of mental life the mind is like a group, or relational system, but since mental life is continuous over time, one "group" undergoes a "transformation" and becomes a different group in the next moment. If the mind is constantly being transformed, how do we account for the continuity of the self? Simple; by invoking the notion of the invariant. And so we find passages like this one: "The S[elf] is invariant, origin, locus or field, it's a functional property of consciousness" (C, 15:170 [2:315]). Just as in transformational geometry, something remains fixed in all the projective transformations of the mind's momentary systems, and that something is the Self (le Moi, or just M, as Valéry notates it so that it will look like an algebraic variable). Transformation theory is all over the place. "Mathematical science… reduced to algebra, that is, to the analysis of the transformations of a purely differential being made up of homogeneous elements, is the most faithful document of the properties of grouping, disjunction, and variation in the mind" (O, 1:36). "Psychology is a theory of transformations, we just need to isolate the invariants and the groups" (C, 1:915). "Man is a system that transforms itself" (C, 2:896). O Paul Valéry, Oeuvres (Paris: Pléiade, 1957-60) C Valéry, Cahiers, 29 vols. (Paris: Centre National de le Recherche Scientifique, 1957-61) |
Note also the remarks of George David Birkhoff at Rice University
in 1940 (pdf) on Galois's theory of groups and the related
"theory of ambiguity" in Galois's testamentary letter—
|
… metaphysical reasoning always relies on the Principle of Sufficient Reason, and… the true meaning of this Principle is to be found in the “Theory of Ambiguity” and in the associated mathematical “Theory of Groups.” If I were a Leibnizian mystic, believing in his “preestablished harmony,” and the “best possible world” so satirized by Voltaire in “Candide,” I would say that the metaphysical importance of the Principle of Sufficient Reason and the cognate Theory of Groups arises from the fact that God thinks multi-dimensionally* whereas men can only think in linear syllogistic series, and the Theory of Groups is the appropriate instrument of thought to remedy our deficiency in this respect. * That is, uses multi-dimensional symbols beyond our grasp. |
Related material:
A medal designed by Leibniz to show how
binary arithmetic mirrors the creation by God
of something (1) from nothing (0).
Another array of 16 strings of 0's and 1's, this time
regarded as coordinates rather than binary numbers—
Some context by a British mathematician —
|
Imago by Wallace Stevens Who can pick up the weight of Britain, Who can move the German load Or say to the French here is France again? Imago. Imago. Imago. It is nothing, no great thing, nor man Of ten brilliancies of battered gold And fortunate stone. It moves its parade Of motions in the mind and heart, A gorgeous fortitude. Medium man In February hears the imagination's hymns And sees its images, its motions And multitudes of motions And feels the imagination's mercies, In a season more than sun and south wind, Something returning from a deeper quarter, A glacier running through delirium, Making this heavy rock a place, Which is not of our lives composed . . . Lightly and lightly, O my land, Move lightly through the air again. |
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Monday, June 14, 2010
Birkhoff on the Galois “Theory of Ambiguity”
The Principle of Sufficient Reason
from "Three Public Lectures on Scientific Subjects,"
delivered at the Rice Institute, March 6, 7, and 8, 1940
EXCERPT 1—
My primary purpose will be to show how a properly formulated
Principle of Sufficient Reason plays a fundamental
role in scientific thought and, furthermore, is to be regarded
as of the greatest suggestiveness from the philosophic point
of view.2
In the preceding lecture I pointed out that three branches
of philosophy, namely Logic, Aesthetics, and Ethics, fall
more and more under the sway of mathematical methods.
Today I would make a similar claim that the other great
branch of philosophy, Metaphysics, in so far as it possesses
a substantial core, is likely to undergo a similar fate. My
basis for this claim will be that metaphysical reasoning always
relies on the Principle of Sufficient Reason, and that
the true meaning of this Principle is to be found in the
“Theory of Ambiguity” and in the associated mathematical
“Theory of Groups.”
If I were a Leibnizian mystic, believing in his “preestablished
harmony,” and the “best possible world” so
satirized by Voltaire in “Candide,” I would say that the
metaphysical importance of the Principle of Sufficient Reason
and the cognate Theory of Groups arises from the fact that
God thinks multi-dimensionally3 whereas men can only
think in linear syllogistic series, and the Theory of Groups is
2 As far as I am aware, only Scholastic Philosophy has fully recognized and ex-
ploited this principle as one of basic importance for philosophic thought
3 That is, uses multi-dimensional symbols beyond our grasp.
______________________________________________________________________
the appropriate instrument of thought to remedy our deficiency
in this respect.
The founder of the Theory of Groups was the mathematician
Evariste Galois. At the end of a long letter written in
1832 on the eve of a fatal duel, to his friend Auguste
Chevalier, the youthful Galois said in summarizing his
mathematical work,4 “You know, my dear Auguste, that
these subjects are not the only ones which I have explored.
My chief meditations for a considerable time have been
directed towards the application to transcendental Analysis
of the theory of ambiguity. . . . But I have not the time, and
my ideas are not yet well developed in this field, which is
immense.” This passage shows how in Galois’s mind the
Theory of Groups and the Theory of Ambiguity were
interrelated.5
Unfortunately later students of the Theory of Groups
have all too frequently forgotten that, philosophically
speaking, the subject remains neither more nor less than the
Theory of Ambiguity. In the limits of this lecture it is only
possible to elucidate by an elementary example the idea of a
group and of the associated ambiguity.
Consider a uniform square tile which is placed over a
marked equal square on a table. Evidently it is then impossible
to determine without further inspection which one
of four positions the tile occupies. In fact, if we designate
its vertices in order by A, B, C, D, and mark the corresponding
positions on the table, the four possibilities are for the
corners A, B, C, D of the tile to appear respectively in the
positions A, B, C, D; B, C, D, A; C, D, A, B; and D, A, B, C.
These are obtained respectively from the first position by a
4 My translation.
5 It is of interest to recall that Leibniz was interested in ambiguity to the extent
of using a special notation v (Latin, vel ) for “or.” Thus the ambiguously defined
roots 1, 5 of x2-6x+5=0 would be written x = l v 5 by him.
______________________________________________________________________
null rotation ( I ), by a rotation through 90° (R), by a rotation
through 180° (S), and by a rotation through 270° (T).
Furthermore the combination of any two of these rotations
in succession gives another such rotation. Thus a rotation R
through 90° followed by a rotation S through 180° is equivalent
to a single rotation T through 270°, Le., RS = T. Consequently,
the "group" of four operations I, R, S, T has
the "multiplication table" shown here:
This table fully characterizes the group, and shows the exact
nature of the underlying ambiguity of position.
More generally, any collection of operations such that
the resultant of any two performed in succession is one of
them, while there is always some operation which undoes
what any operation does, forms a "group."
__________________________________________________
EXCERPT 2—
Up to the present point my aim has been to consider a
variety of applications of the Principle of Sufficient Reason,
without attempting any precise formulation of the Principle
itself. With these applications in mind I will venture to
formulate the Principle and a related Heuristic Conjecture
in quasi-mathematical form as follows:
PRINCIPLE OF SUFFICIENT REASON. If there appears
in any theory T a set of ambiguously determined ( i e .
symmetrically entering) variables, then these variables can themselves
be determined only to the extent allowed by the corresponding
group G. Consequently any problem concerning these variables
which has a uniquely determined solution, must itself be
formulated so as to be unchanged by the operations of the group
G ( i e . must involve the variables symmetrically).
HEURISTIC CONJECTURE. The final form of any
scientific theory T is: (1) based on a few simple postulates; and
(2) contains an extensive ambiguity, associated symmetry, and
underlying group G, in such wise that, if the language and laws
of the theory of groups be taken for granted, the whole theory T
appears as nearly self-evident in virtue of the above Principle.
The Principle of Sufficient Reason and the Heuristic Conjecture,
as just formulated, have the advantage of not involving
excessively subjective ideas, while at the same time
retaining the essential kernel of the matter.
In my opinion it is essentially this principle and this
conjecture which are destined always to operate as the basic
criteria for the scientist in extending our knowledge and
understanding of the world.
It is also my belief that, in so far as there is anything
definite in the realm of Metaphysics, it will consist in further
applications of the same general type. This general conclu-
sion may be given the following suggestive symbolic form:
While the skillful metaphysical use of the Principle must
always be regarded as of dubious logical status, nevertheless
I believe it will remain the most important weapon of the
philosopher.
___________________________________________________________________________
A more recent lecture on the same subject —
by Jean-Pierre Ramis (Johann Bernoulli Lecture at U. of Groningen, March 2005)
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Friday, March 19, 2010
Garden of Forking Paths
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Saturday, March 6, 2010
Deconstructing Alice
Alyssa is Wonderland
Manohla Dargis in The New York Times yesterday—
“Of course the character of Carroll’s original Alice is evident in each outrageous creation she dreams up in ‘Wonderland’ and in the sequel, ‘Through the Looking-Glass,’ which means that she’s a straight man to her own imagination. (She is Wonderland.)”
From Inside the White Cube—
“The sacramental nature of the space becomes clear, and so does one of the great projective laws of modernism: as modernism gets older, context becomes content. In a peculiar reversal, the object introduced into the gallery ‘frames’ the gallery and its laws.”
From Yogi Berra–
“When you come to a fork in the road, take it.”
Related material: For Baron Samedi and…
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Sunday, January 24, 2010
Today’s Sermon
More Than Matter
| Wheel in Webster’s Revised Unabridged Dictionary, 1913
(f) Poetry The burden or refrain of a song. ⇒ “This meaning has a low degree of authority, but is supposed from the context in the few cases where the word is found.” Nares. You must sing a-down a-down, An you call him a-down-a. O, how the wheel becomes it! Shak. |
“In one or other of G. F. H. Shadbold’s two published notebooks, Beyond Narcissus and Reticences of Thersites, a short entry appears as to the likelihood of Ophelia’s enigmatic cry: ‘Oh, how the wheel becomes it!’ referring to the chorus or burden ‘a-down, a-down’ in the ballad quoted by her a moment before, the aptness she sees in the refrain.”
— First words of Anthony Powell’s novel “O, How the Wheel Becomes It!” (See Library Thing.)
Related material:
Photo uploaded on January 14, 2009
with caption “This nothing’s more than matter”
and the following nothings from this journal
on the same date– Jan. 14, 2009—
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Friday, December 25, 2009
Brightness at Noon
New York Times online front page
Christmas morning:
"Arthur Koestler, Man of Darkness"–
The photo is of Koestler in 1931 on a zeppelin expedition to the North Pole.
"The Act of Creation is, I believe, a more truly creative work than any of Koestler’s novels…. According to him, the creative faculty in whatever form is owing to a circumstance which he calls ‘bisociation.’ And we recognize this intuitively whenever we laugh at a joke, are dazzled by a fine metaphor, are astonished and excited by a unification of styles, or ’see,’ for the first time, the possibility of a significant theoretical breakthrough in a scientific inquiry. In short, one touch of genius—or bisociation—makes the whole world kin. Or so Koestler believes.”
– Henry David Aiken, The Metaphysics of Arthur Koestler, New York Review of Books, Dec. 17, 1964
From Opus Postumum by Immanuel Kant, Eckart Förster, Cambridge U. Press, 1995, p. 260:
"In January 1697, Leibniz accompanied his New Year Congratulations to Rudolf August with the design of a medal with the duke's likeness on one side, and the 'image of Creation' in terms of the binary number system on the other. Concerning the inscription on this side, Leibniz writes: 'I have thought for a while about the Motto dell'impresa and finally have found it good to write this line: omnibus ex nihilo ducendis SUFFICIT UNUM [To make all things from nothing, UNITY SUFFICES], because it clearly indicates what is meant by the symbol, and why it is imago creationis' (G. F. Leibniz, Zwei Briefe über das binäre Zahlensystem und die chinesische Philosophie, ed. Renate Loosen and Franz Vonessen, Chr. Belser Verlag: Stuttgart 1968, p. 21)."
Figure from Rudolf Nolte’s
Gottfried Wilhelms Baron von Leibniz
Mathematischer Beweis der Erschaffung und
Ordnung der Welt in einem Medallion…
(Leipzig: J. C. Langenheim, 1734).
"And so that I won’t come entirely empty-handed this time, I enclose a design of that which I had the pleasure of discussing with you recently. It is in the form of a memorial coin or medallion; and though the design is mediocre and can be improved in accordance with your judgment, the thing is such, that it would be worth showing in silver now and unto future generations, if it were struck at your Highness’s command. Because one of the main points of the Christian Faith, and among those points that have penetrated least into the minds of the worldly-wise and that are difficult to make with the heathen is the creation of all things out of nothing through God’s omnipotence, it might be said that nothing is a better analogy to, or even demonstration of such creation than the origin of numbers as here represented, using only unity and zero or nothing. And it would be difficult to find a better illustration of this secret in nature or philosophy; hence I have set on the medallion design IMAGO CREATIONIS [in the image of creation]. It is no less remarkable that there appears therefrom, not only that God made everything from nothing, but also that everything that He made was good; as we can see here, with our own eyes, in this image of creation. Because instead of there appearing no particular order or pattern, as in the common representation of numbers, there appears here in contrast a wonderful order and harmony which cannot be improved upon….
Such harmonious order and beauty can be seen in the small table on the medallion up to 16 or 17; since for a larger table, say to 32, there is not enough room. One can further see that the disorder, which one imagines in the work of God, is but apparent; that if one looks at the matter with the proper perspective, there appears symmetry, which encourages one more and more to love and praise the wisdom, goodness, and beauty of the highest good, from which all goodness and beauty has flowed."
See also Parable.
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Thursday, September 17, 2009
Thursday September 17, 2009
“Nobody puts Baby in a corner.”
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Thursday, July 2, 2009
Thursday July 2, 2009
Hieron Grammaton, Part III*
The Old Man and the Light
In memory of
Ernest Hemingway,
who died on this date
in 1961, a story
in three parts:
I — Eye of Raven
Fermata
II — Psyche and Symbol
Leonard Baskin, detail of
cover for Jung’s
Psyche and Symbol
III — Raven Steals the Light
Detail from the story
“Raven Steals the Light”
Midrash:
“To the earnestness of death belongs precisely that capacity for awakening, that resonance of a profound mockery which, detached from the thought of the eternal, is an empty and often brash jest, but together with the thought of the eternal is just what it should be….” —Kierkegaard
* For Hieron Grammaton, Parts I and II, see the five Log24 entries from 6:29 PM Tuesday, June 23, to 1:00 AM Sunday, June 28.
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Saturday, March 7, 2009
Saturday March 7, 2009
One or Two Ideas
|
From James Joyce's A Portrait of the Artist as a Young Man:
he hearth and began to stroke his chin. –When may we expect to have something from you on the esthetic question? he asked. –From me! said Stephen in astonishment. I stumble on an idea once a fortnight if I am lucky. –These questions are very profound, Mr Dedalus, said the dean. It is like looking down from the cliffs of Moher into the depths. Many go down into the depths and never come up. Only the trained diver can go down into those depths and explore them and come to the surface again. –If you mean speculation, sir, said Stephen, I also am sure that there is no such thing as free thinking inasmuch as all thinking must be bound by its own laws. –Ha! –For my purpose I can work on at present by the light of one or two ideas of Aristotle and Aquinas. –I see. I quite see your point. |
Besides being Mondrian's birthday, today is also the dies natalis (in the birth-into-heaven sense) of St. Thomas Aquinas and, for those who believe worthy pre-Christians also enter heaven, possibly of Aristotle.
Pope Benedict XVI explained the dies natalis concept on Dec. 26, 2006:
"For believers the day of death, and even more the day of martyrdom, is not the end of all; rather, it is the 'transit' towards immortal life. It is the day of definitive birth, in Latin, dies natalis."
The Pope's remarks on that date
were in St. Peter's Square.
were in St. Peter's Square.
Pictorial version
of Hexagram 20,
Contemplation (View)
The square may be regarded as
symbolizing art itself.
(See Nov.30 – Dec.1, 2008.)
symbolizing art itself.
(See Nov.30 – Dec.1, 2008.)
In honor of
Aristotle and Aquinas,
here is a new web site,
illuminati-diamond.com,
with versions of the diamond shape
made famous by Mondrian —
— a shape symbolizing
possibility within modal logic
as well as the potentiality of
Aristotle's prima materia.
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Wednesday, December 10, 2008
Wednesday December 10, 2008
Sign
ho anax, hou to manteion esti
to en Delphois, oute legei oute
kruptei, alla sêmainei
— Heraclitus, DK 22 B 93,
Kahn XXXIII:
“The lord whose oracle is
at Delphi neither reveals nor
conceals, but gives a sign.“
A sign, perhaps of the sort
given by Apollo’s oracle:
Click on the sign for further details.
Related material:
… as well as
today’s previous entry —
“Symbol,” discussing Apollo
and a web page
by Nick Wedd —
and Wedd’s home page,
which states that
“I have now found a
source of Polish sandals.”
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Sunday, June 29, 2008
Sunday June 29, 2008
Big Rock
"I'm going to hit this problem
with a big rock."
|
A professor discusses a poem by Wallace Stevens:
"Professor Eucalyptus in 'Ordinary Evening' XIV, for example, 'seeks/ God in the object itself,' but this quest culminates in his own choosing of 'the commodious adjective/ For what he sees… the description that makes it divinity, still speech… not grim/ Reality but reality grimly seen/ And spoken in paradisal parlance new'…."
– Douglas Mao, Solid Objects:Modernism and the Test of Production, Princeton University Press, 1998, p. 242
"God in the object" seems
unlikely to be found in the artifact pictured on the cover of Mao's book: 
I have more confidence
These objects may be |
June 28, 2008:
These numbers can, of course,
be interpreted as symbols of
the dates 6/29 and 5/30.
The last Log24 entry of
6/29 (St. Peter's Day):
"The rock cannot be broken.
It is the truth."
– Wallace Stevens,
"Credences of Summer"
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Thursday, June 26, 2008
Thursday June 26, 2008
Review
Yesterday, June 25, was the 100th anniversay of W.V. Quine's birth and also the day on the calendar opposite Christmas– In the parlance of Quine's son Douglas, AntiChristmas.
Having survived that ominous date, I feel it is fitting to review what Wallace Stevens called "Credences of Summer"– religious principles for those who feel that faith and doubt are best reconciled by art.
|
"Credences of Summer," VII,
by Wallace Stevens, from
"Three times the concentred |
|
Definition of Epiphany
From James Joyce's Stephen Hero, first published posthumously in 1944. The excerpt below is from a version edited by John J. Slocum and Herbert Cahoon (New York: New Directions Press, 1959).
Three Times: … By an epiphany he meant a sudden spiritual manifestation, whether in the vulgarity of speech or of gesture or in a memorable phase of the mind itself. He believed that it was for the man of letters to record these epiphanies with extreme care, seeing that they themselves are the most delicate and evanescent of moments. He told Cranly that the clock of the Ballast Office was capable of an epiphany. Cranly questioned the inscrutable dial of the Ballast Office with his no less inscrutable countenance: — Yes, said Stephen. I will pass it time after time, allude to it, refer to it, catch a glimpse of it. It is only an item in the catalogue of Dublin's street furniture. Then all at once I see it and I know at once what it is: epiphany. — What? — Imagine my glimpses at that clock as the gropings of a spiritual eye which seeks to adjust its vision to an exact focus. The moment the focus is reached the object is epiphanised. It is just in this epiphany that I find the third, the supreme quality of beauty. — Yes? said Cranly absently. — No esthetic theory, pursued Stephen relentlessly, is of any value which investigates with the aid of the lantern of tradition. What we symbolise in black the Chinaman may symbolise in yellow: each has his own tradition. Greek beauty laughs at Coptic beauty and the American Indian derides them both. It is almost impossible to reconcile all tradition whereas it is by no means impossible to find the justification of every form of beauty which has ever been adored on the earth by an examination into the mechanism of esthetic apprehension whether it be dressed in red, white, yellow or black. We have no reason for thinking that the Chinaman has a different system of digestion from that which we have though our diets are quite dissimilar. The apprehensive faculty must be scrutinised in action. — Yes … — You know what Aquinas says: The three things requisite for beauty are, integrity, a wholeness, symmetry and radiance. Some day I will expand that sentence into a treatise. Consider the performance of your own mind when confronted with any object, hypothetically beautiful. Your mind to apprehend that object divides the entire universe into two parts, the object, and the void which is not the object. To apprehend it you must lift it away from everything else: and then you perceive that it is one integral thing, that is a thing. You recognise its integrity. Isn't that so? — And then? — That is the first quality of beauty: it is declared in a simple sudden synthesis of the faculty which apprehends. What then? Analysis then. The mind considers the object in whole and in part, in relation to itself and to other objects, examines the balance of its parts, contemplates the form of the object, traverses every cranny of the structure. So the mind receives the impression of the symmetry of the object. The mind recognises that the object is in the strict sense of the word, a thing, a definitely constituted entity. You see? — Let us turn back, said Cranly. They had reached the corner of Grafton St and as the footpath was overcrowded they turned back northwards. Cranly had an inclination to watch the antics of a drunkard who had been ejected from a bar in Suffolk St but Stephen took his arm summarily and led him away. — Now for the third quality. For a long time I couldn't make out what Aquinas meant. He uses a figurative word (a very unusual thing for him) but I have solved it. Claritas is quidditas. After the analysis which discovers the second quality the mind makes the only logically possible synthesis and discovers the third quality. This is the moment which I call epiphany. First we recognise that the object is one integral thing, then we recognise that it is an organised composite structure, a thing in fact: finally, when the relation of the parts is exquisite, when the parts are adjusted to the special point, we recognise that it is that thing which it is. Its soul, its whatness, leaps to us from the vestment of its appearance. The soul of the commonest object, the structure of which is so adjusted, seems to us radiant. The object achieves its epiphany. Having finished his argument Stephen walked on in silence. He felt Cranly's hostility and he accused himself of having cheapened the eternal images of beauty. For the first time, too, he felt slightly awkward in his friend's company and to restore a mood of flippant familiarity he glanced up at the clock of the Ballast Office and smiled: — It has not epiphanised yet, he said. |
|
Under the Volcano,
by Malcolm Lowry, "What have I got out of my life? Contacts with famous men… The occasion Einstein asked me the time, for instance. That summer evening…. smiles when I say I don't know. And yet asked me. Yes: the great Jew, who has upset the whole world's notions of time and space, once leaned down… to ask me… ragged freshman… at the first approach of the evening star, the time. And smiled again when I pointed out the clock neither of us had noticed."
An approach of
This figure is from a webpage,
As noted in yesterday's early- "The appearance of the evening star brings with it long-standing notions of safety within and danger without. In a letter to Harriet Monroe, written December 23, 1926, Stevens refers to the Sapphic fragment that invokes the genius of evening: 'Evening star that bringest back all that lightsome Dawn hath scattered afar, thou bringest the sheep, thou bringest the goat, thou bringest the child home to the mother.' Christmas, writes Stevens, 'is like Sappho's evening: it brings us all home to the fold' (Letters of Wallace Stevens, 248)."
— Barbara Fisher, |
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Saturday, June 21, 2008
Saturday June 21, 2008
for lifetime achievement
in arts and philosophy
this year goes to
Charles Taylor,
Montreal philosophy professor.
“The Kyoto Prize has been given in three domains since 1984:
advanced technology, basic sciences, and the arts and philosophy.
It is administered by the Inamori Foundation, whose president,
Kazuo Inamori, is founder and chairman emeritus of Kyocera and
KDDI Corporation, two Japanese telecommunications giants.”
 |
|
“The Kyocera brand symbol is composed of a corporate mark |
Related material —
Charles Taylor,
“Epiphanies of Modernism,”
Chapter 24 of Sources of the Self
(Cambridge U. Press, 1989, p. 477) —
“… the object sets up
a kind of frame or space or field
within which there can be epiphany.”
See also Talking of Michelangelo.
Comments Off on Saturday June 21, 2008
Sunday, May 25, 2008
Sunday May 25, 2008
Wechsler Cubes
"Confusion is nothing new."
— Song lyric, Cyndi Lauper
— Song lyric, Cyndi Lauper
Part I:
Magister Ludi
Magister Ludi
Hermann Hesse's 1943 The Glass Bead Game (Picador paperback, Dec. 6, 2002, pp. 139-140)–
"For the present, the Master showed him a bulky memorandum, a proposal he had received from an organist– one of the innumerable proposals which the directorate of the Game regularly had to examine. Usually these were suggestions for the admission of new material to the Archives. One man, for example, had made a meticulous study of the history of the madrigal and discovered in the development of the style a curved that he had expressed both musically and mathematically, so that it could be included in the vocabulary of the Game. Another had examined the rhythmic structure of Julius Caesar's Latin and discovered the most striking congruences with the results of well-known studies of the intervals in Byzantine hymns. Or again some fanatic had once more unearthed some new cabala hidden in the musical notation of the fifteenth century. Then there were the tempestuous letters from abstruse experimenters who could arrive at the most astounding conclusions from, say, a comparison of the horoscopes of Goethe and Spinoza; such letters often included pretty and seemingly enlightening geometric drawings in several colors."
Part II:
A Bulky Memorandum
A Bulky Memorandum
From Siri Hustvedt, author of Mysteries of the Rectangle: Essays on Painting (Princeton Architectural Press, 2005)– What I Loved: A Novel (Picador paperback, March 1, 2004, page 168)–
A description of the work of Bill Wechsler, a fictional artist:
"Bill worked long hours on a series of autonomous pieces about numbers. Like O's Journey, the works took place inside glass cubes, but these were twice as large– about two feet square. He drew his inspiration from sources as varied as the Cabbala, physics, baseball box scores, and stock market reports. He painted, cut, sculpted, distorted, and broke the numerical signs in each work until they became unrecognizable. He included figures, objects, books, windows, and always the written word for the number. It was rambunctious art, thick with allusion– to voids, blanks, holes, to monotheism and the individual, the the dialectic and yin-yang, to the Trinity, the three fates, and three wishes, to the golden rectangle, to seven heavens, the seven lower orders of the sephiroth, the nine Muses, the nine circles of Hell, the nine worlds of Norse mythology, but also to popular references like A Better Marriage in Five Easy Lessons and Thinner Thighs in Seven Days. Twelve-step programs were referred to in both cube one and cube two. A miniature copy of a book called The Six Mistakes Parents Make Most Often lay at the bottom of cube six. Puns appeared, usually well disguised– one, won; two, too, and Tuesday; four, for, forth; ate, eight. Bill was partial to rhymes as well, both in images and words. In cube nine, the geometric figure for a line had been painted on one glass wall. In cube three, a tiny man wearing the black-and-white prison garb of cartoons and dragging a leg iron has
— End of page 168 —
opened the door to his cell. The hidden rhyme is "free." Looking closely through the walls of the cube, one can see the parallel rhyme in another language: the German word drei is scratched into one glass wall. Lying at the bottom of the same box is a tiny black-and-white photograph cut from a book that shows the entrance to Auschwitz: ARBEIT MACHT FREI. With every number, the arbitrary dance of associations worked togethere to create a tiny mental landscape that ranged in tone from wish-fulfillment dream to nightmare. Although dense, the effect of the cubes wasn't visually disorienting. Each object, painting, drawing, bit of text, or sculpted figure found its rightful place under the glass according to the necessary, if mad, logic of numerical, pictorial, and verbal connection– and the colors of each were startling. Every number had been given a thematic hue. Bill had been interested in Goethe's color wheel and in Alfred Jensen's use of it in his thick, hallucinatory paintings of numbers. He had assigned each number a color. Like Goethe, he included black and white, although he didn't bother with the poet's meanings. Zero and one were white. Two was blue. Three was red, four was yellow, and he mixed colors: pale blue for five, purples in six, oranges in seven, greens in eight, and blacks and grays in nine. Although other colors and omnipresent newsprint always intruded on the basic scheme, the myriad shades of a single color dominated each cube.
The number pieces were the work of a man at the top of his form. An organic extension of everything Bill had done before, these knots of symbols had an explosive effect. The longer I looked at them, the more the miniature constructions seemed on the brink of bursting from internal pressure. They were tightly orchestrated semantic bombs through which Bill laid bare the arbitrary roots of meaning itself– that peculiar social contract generated by little squiggles, dashes, lines, and loops on a page."
Part III:
Wechsler Cubes
(named not for
Bill Wechsler, the
fictional artist above,
but for the non-fictional
David Wechsler) –
(named not for
Bill Wechsler, the
fictional artist above,
but for the non-fictional
David Wechsler) –
|
From 2002:
Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale "block design" subtest. |
Part IV:
A Magic Gallery
A Magic Gallery
|
ZZ
Figures from the
Poem by Eugen Jost:
Mit Zeichen und Zahlen
Numbers and Names,
With numbers and names English translation A related poem:
Alphabets
From time to time
But if a savage
— Hermann Hesse (1943), |
Comments Off on Sunday May 25, 2008
Tuesday, April 29, 2008
Tuesday April 29, 2008
Sacerdotal Jargon
at Harvard:
at Harvard:
Thomas Wolfe
(Harvard M.A., 1922)
versus
Rosalind Krauss
(Harvard M.A., 1964,
Ph.D., 1969)
on
"No culture has a pact with eternity."
— George Steiner, interview in
The Guardian of
"At that instant he saw,
in one blaze of light, an image
of unutterable conviction….
the core of life, the essential
pattern whence all other things
proceed, the kernel of eternity."
— Thomas Wolfe, Of Time
and the River, quoted in
Log24 on June 9, 2005
From today's online Harvard Crimson:
"… under the leadership of Faust,
Harvard students should look forward
to an ever-growing opportunity for
international experience
and artistic endeavor."
Pauli as Mephistopheles
in a 1932 parody of
Goethe's Faust at Niels Bohr's
institute in Copenhagen
From a recent book
on Wolfgang Pauli,
The Innermost Kernel:
A belated happy birthday
to the late
Felix Christian Klein
(born on April 25) —
Another Harvard figure quoted here on Dec. 5, 2002:
"The theory of poetry, that is to say, the total of the theories of poetry, often seems to become in time a mystical theology or, more simply, a mystique. The reason for this must by now be clear. The reason is the same reason why the pictures in a museum of modern art often seem to become in time a mystical aesthetic, a prodigious search of appearance, as if to find a way of saying and of establishing that all things, whether below or above appearance, are one and that it is only through reality, in which they are reflected or, it may be, joined together, that we can reach them. Under such stress, reality changes from substance to subtlety, a subtlety in which it was natural for Cézanne to say: 'I see planes bestriding each other and sometimes straight lines seem to me to fall' or 'Planes in color…. The colored area where shimmer the souls of the planes, in the blaze of the kindled prism, the meeting of planes in the sunlight.' The conversion of our Lumpenwelt went far beyond this. It was from the point of view of another subtlety that Klee could write: 'But he is one chosen that today comes near to the secret places where original law fosters all evolution. And what artist would not establish himself there where the organic center of all movement in time and space– which he calls the mind or heart of creation– determines every function.' Conceding that this sounds a bit like sacerdotal jargon, that is not too much to allow to those that have helped to create a new reality, a modern reality, since what has been created is nothing less."
— Wallace Stevens, Harvard College Class of 1901, "The Relations between Poetry and Painting" in The Necessary Angel (Knopf, 1951)
From a review of Rosalind Krauss's The Optical Unconscious (MIT Press hardcover, 1993):
Krauss is concerned to present Modernism less in terms of its history than its structure, which she seeks to represent by means of a kind of diagram: "It is more interesting to think of modernism as a graph or table than a history." The "table" is a square with diagonally connected corners, of the kind most likely to be familiar to readers as the Square of Opposition, found in elementary logic texts since the mid-19th century. The square, as Krauss sees it, defines a kind of idealized space "within which to work out unbearable contradictions produced within the real field of history." This she calls, using the inevitable gallicism, "the site of Jameson's Political Unconscious" and then, in art, the optical unconscious, which consists of what Utopian Modernism had to kick downstairs, to repress, to "evacuate… from its field."
— Arthur C. Danto in ArtForum, Summer 1993
Rosalind Kraus in The Optical Unconscious (MIT Press paperback, 1994):
For a presentation of the Klein Group, see Marc Barbut, "On the Meaning of the Word 'Structure' in Mathematics," in Introduction to Structuralism, ed. Michael Lane (New York: Basic Books, 1970). Claude Lévi-Strauss uses the Klein group in his analysis of the relation between Kwakiutl and Salish masks in The Way of the Masks, trans. Sylvia Modelski (Seattle: University of Washington Press, 1982), p. 125; and in relation to the Oedipus myth in "The Structural Analysis of Myth," Structural Anthropology, trans. Claire Jackobson [sic] and Brooke Grundfest Schoepf (New York: Basic Books, 1963). In a transformation of the Klein Group, A. J. Greimas has developed the semiotic square, which he describes as giving "a slightly different formulation to the same structure," in "The Interaction of Semiotic Constraints," On Meaning (Minneapolis: University of Minnesota Press, 1987), p. 50. Jameson uses the semiotic square in The Political Unconscious (see pp. 167, 254, 256, 277) [Fredric Jameson, The Political Unconscious: Narrative as a Socially Symbolic Act (Ithaca: Cornell University Press, 1981)], as does Louis Marin in "Disneyland: A Degenerate Utopia," Glyph, no. 1 (1977), p. 64.
For related non-sacerdotal jargon, see…
Wikipedia on the Klein group (denoted V, for Vierergruppe):
In this representation, V is a normal subgroup of the alternating group A4 (and also the symmetric group S4) on 4 letters. In fact, it is the kernel of a surjective map from S4 to S3. According to Galois theory, the existence of the Klein four-group (and in particular, this representation of it) explains the existence of the formula for calculating the roots of quartic equations in terms of radicals.
For radicals of another sort, see A Logocentric Meditation, A Mass for Lucero, and [update of 7 PM] Steven Erlanger in today's New York Times— "France Still Divided Over Lessons of 1968 Unrest."
For material related to Klee's phrase mentioned above by Stevens, "the organic center of all movement in time and space," see the following Google search:
Comments Off on Tuesday April 29, 2008
Tuesday, March 25, 2008
Tuesday March 25, 2008
Dancers and
the Dance
the Dance
The previous entry was inspired (see the "In the Details" link) by the philosophical musings of Julie Taymor… specifically, her recollection of Balinese dancers–
"… they were performing for God. Now God can mean whatever you want it to mean. But for me, I understood it so totally. The detail….
They did it from the inside to the outside. And from the outside to the in. And that profoundly moved me then. It was… it was the most important thing that I ever experienced."— Julie Taymor,
"Skewed Mirrors" interview
Here is some further commentary on the words of that entry–
On the phrase "Within You Without You"– the title of a song by George Harrison:
"Bernard’s understanding of reality connects to this idea of 'flow': he sees reality as a product of consciousness. He rejects the idea of an 'outer' world of unchanging objects and an 'inner' world of the mind and ideas. Rather, our minds are part of the world, and vice versa."
— Adrien Ardoin, SparkNote on
Virginia Woolf's The Waves
On "Death and the Apple Tree"– the title of the previous entry— in The Waves:
"The apple tree Neville is looking at as he overhears the servants at the school discussing a local murder becomes inextricably linked to his knowledge of death. Neville finds himself unable to pass the tree, seeing it as glimmering and lovely, yet sinister and 'implacable.' When he learns that Percival is dead, he feels he is face to face once again with 'the tree which I cannot pass.' Eventually, Neville turns away from the natural world to art, which exists outside of time and can therefore transcend death. The fruit of the tree appears only in Neville’s room on his embroidered curtain, a symbol itself of nature turned into artifice. The apple tree image also echoes the apple tree from the Book of Genesis in the Bible, the fruit of which led Adam and Eve to knowledge and, therefore, expulsion from Eden."
— Adrien Ardoin, op. cit.
Comments Off on Tuesday March 25, 2008
Wednesday, December 12, 2007
Wednesday December 12, 2007
Found in Translation:
Words and Images
Words and Images
From today’s New York Times:
“Thomas P. Whitney, a former diplomat and writer on Russian affairs who was best known for translating the work of the dissident writer Aleksandr Solzhenitsyn into English, died on [Sunday] Dec. 2 in Manhattan. He was 90….
During World War II, he was an analyst in Washington with the Office of Strategic Services, a forerunner of the Central Intelligence Agency….
In the late 1960s and afterward, he bred thoroughbred horses….
On one occasion, Mr. Whitney took Mr. Solzhenitsyn to Saratoga Racetrack….”
Related material:
Words
“Lewis began with
a number of haunted images….”
a number of haunted images….”
“The best of the books are the ones…
where the allegory is at a minimum
and the images just flow.”
“‘Everything began with images,’
Lewis wrote….”
Images
Yesterday’s entry on
Solzhenitsyn and The Golden Compass
and the following illustrations…
from Sunday in the Park with Death,
a Log24 entry commemorating
Trotsky’s birthday–
–and from Log24 on the date
of Whitney’s death,
Sunday, Dec. 2, 2007—
Personal Emblem
of psychiatrist
Harry Stack Sullivan
The horses may refer to
the Phaedrus of Plato.
See also Art Wars.
Friday, July 13, 2007
Friday July 13, 2007
Today’s birthday:
Harrison Ford is 65.
Harrison Ford is 65.
| “Three times the concentred self takes hold, three times The thrice concentred self, having possessed The object, grips it in savage scrutiny, Once to make captive, once to subjugate Or yield to subjugation, once to proclaim The meaning of the capture, this hard prize, Fully made, fully apparent, fully found.” — “Credences of Summer,” VII, |
“It was Plato who best expressed– who veritably embodied– the tension between the narrative arts and mathematics….
Plato clearly loved them both, both mathematics and poetry. But he approved of mathematics, and heartily, if conflictedly, disapproved of poetry. Engraved above the entrance to his Academy, the first European university, was the admonition: Oudeis ageometretos eiseto. Let none ignorant of geometry enter. This is an expression of high approval indeed, and the symbolism could not have been more perfect, since mathematics was, for Plato, the very gateway for all future knowledge. Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason. Mathematics is the threshold we cross to pass into the ideal, the truly real.”
— Rebecca Goldstein, Mathematics and the Character of Tragedy
Related material:
Previous entry,
entries of July 1, 2007,
and A Little Story
(9/30/06)
Comments Off on Friday July 13, 2007
Thursday, June 28, 2007
Thursday June 28, 2007
Real Numbers:
An Object Lesson
An Object Lesson
(continued from
AntiChristmas)
AntiChristmas)
A Cornell professor discusses a poem by Wallace Stevens:
"Professor Eucalyptus in 'Ordinary Evening' XIV, for example, 'seeks/ God in the object itself,' but this quest culminates in his own choosing of 'the commodious adjective/ For what he sees… the description that makes it divinity, still speech… not grim/ Reality but reality grimly seen/ And spoken in paradisal parlance new'…."
— Douglas Mao, Solid Objects:
Modernism and the Test
of Production,
Princeton University Press,
1998, p. 242
Modernism and the Test
of Production,
Princeton University Press,
1998, p. 242
"God in the object" seems
unlikely to be found in the
artifact pictured on the
cover of Mao's book:
unlikely to be found in the
artifact pictured on the
cover of Mao's book:
I have more confidence
that God is to be found
in the Ping Pong balls
of the New York Lottery.
that God is to be found
in the Ping Pong balls
of the New York Lottery.
These objects may be
regarded as supplying
a parlance that is, if not
paradisal, at least
intelligible– if only in
the context of my own
personal experience:
Journal entry dated 5/14:
Journal entries dated 3/09:
Comments Off on Thursday June 28, 2007
Thursday, March 8, 2007
Thursday March 8, 2007
Dia de la
Mujer Trabajadora
Mujer Trabajadora
“Yo es que nací un 8 de marzo,
Día de la Mujer Trabajadora,
y no he hecho más que
trabajar toda mi vida.”
For background on Aldecoa,
see a paper (pdf) by
Sara Brenneis:
“Josefina Aldecoa intertwines
history, collective memory
and individual testimony in her
historical memory trilogy…”
History:
The Triangle Shirtwaist Factory Fire in New York City on March 25, 1911, was the largest industrial disaster in the history of the city of New York, causing the death of 146 garment workers who either died in the fire or jumped to their deaths.
Propaganda, March 1977:
“On March 8, 1908, after the death of 128 women trapped in a fire at the Triangle Shirtwaist Factory in New York City, 15,000 women workers from the garment and textile industry marched echoing the demands of their sisters 50 years earlier…”
Propaganda, March 2006:
“First of all, on March 8th, 1857, a large number of factory workers in the United States took to the streets to demand their economic and political rights. The owners called the police who arrived immediately and opened fire, engaging in blind repression… Later on, in 1908, the same date of March 8th was once again a memorable date of struggle. On this day, capitalist bosses in Chicago set fire to a textile factory where over a thousand women worked. A very large number was terribly burnt. 120 died!”
Propaganda disguised as news, March 2007:
From today’s top story in 24 HoursTM, a commuter daily in Vancouver published by Sun Media Corporation:
Fight still on for equality
By Robyn Stubbs and Carly Krug
“International Women’s Day commemorates a march by female garment workers protesting low wages, 12-hour workdays and bad working conditions in New York City on March 8, 1857.
Then in 1908, after 128 women were trapped and killed in a fire at a New York City garment and textile factory, 15,000 women workers again took their protests to the street.”
Related historical fiction:
A version of the
I Ching’s Hexagram 19:
— Katherine Neville, The Eight
|
“What does this have to do with why we’re here?”
“I saw it in a chess book Mordecai showed me. The most ancient chess service ever discovered was found at the palace of King Minos on Crete– the place where the famous Labyrinth was built, named after this sacred axe. The chess service dates to 2000 B.C. It was made of gold and silver and jewels…. And in the center was carved a labrys.” … “But I thought chess wasn’t even invented until six or seven hundred A.D.,” I added. “They always say it came from Persia or India. How could this Minoan chess service be so old?” “Mordecai’s written a lot himself on the history of chess,” said Lily…. “He thinks that chess set in Crete was designed by the same guy who built the Labyrinth– the sculptor Daedalus….” Now things were beginning to click into place…. “Why was this axe carved on the chessboard?” I asked Lily, knowing the answer in my heart before she spoke. “What did Mordecai say was the connection?”…. “That’s what it’s all about,” she said quietly. “To kill the King.” The sacred axe was used to kill the King. The ritual had been the same since the beginning of time. The game of chess was merely a reenactment. Why hadn’t I recognized it before? |
Perhaps at the center of
Aldecoa’s labyrinth lurk the
capitalist bosses from Chicago
who, some say, set fire
to a textile factory
on this date in 1908.
For a Freudian perspective
on the above passage,
see yesterday’s entry
In the Labyrinth of Time,
with its link to
John Irwin‘s essay
“The False Artaxerxes:
Borges and the
Dream of Chess.”
Symbols
S. H. Cullinane
March 7, 2007
Today, by the way, is the
feast of a chess saint.
Comments Off on Thursday March 8, 2007
Friday, January 19, 2007
Friday January 19, 2007
Triple Kiss
| I bent to kiss the lovely Maid, | |
| And found a threefold kiss return’d. |
— “The Crystal Cabinet“
The above illustration of a classic Blake verse is for Anthony Daniels, a critic of Ezra Pound. The illustration may appeal to Daniels, since it is, like the persona presented by Daniels himself, petit-bourgeois and vulgar.
It was inspired by today’s two previous entries and by Daniels’s remarks, in this month’s New Criterion magazine, on Ezra Pound:
“Of his poetry I shall say nothing: not being fluent in Greek, Chinese, Italian, Farsi, and so forth, I do not feel much qualified to comment on it…. I shall merely confess to a petit-bourgeois partiality for comprehensibility and to what Pound himself called, in the nearest he ever came to a mea culpa with regard to his own ferocious anti-Semitism at a time of genocide, ‘a vulgar suburban prejudice’ against those who suppose that their thoughts are so profound that they justify a lifetime of exegesis if ever their meaning is to be even so much as glimpsed through a glass darkly.”
Daniels, here posing as a vulgar suburban petit-bourgeois, is unwilling to examine Pound’s poetry even “through a glass darkly.” This echoes the petit-bourgeois, but not vulgar, “confession” of today’s previous entry:
“I didn’t expect much–didn’t look out the window
At school more diligent than able–docile stable”
— “A Life,” by Zbigniew Herbert
Pound, editor of T. S. Eliot’s “The Waste Land”– published in the first issue of the original Criterion magazine in 1922– might refer Daniels to the ghost of Guy Davenport:
“‘The architectonics of a narrative,’ Davenport says, ‘are emphasized and given a role to play in dramatic effect when novelists become Cubists; that is, when they see the possibilities of making a hieroglyph, a coherent symbol, an ideogram of the total work. A symbol comes into being when an artist sees that it is the only way to get all the meaning in.’….
In his study of The Cantos, Davenport defines the Poundian ideogram as ‘a grammar of images, emblems, and symbols, rather than a grammar of logical sequence…. An idea unifies, dominates, and controls the particulars that make the ideogram’…. He insists on the intelligibility of this method: ‘The components of an ideogram cohere as particles in a magnetic field, independent of each other but not of the pattern in which they figure.'”
— Andre Furlani, “‘When Novelists Become Cubists’: The Prose Ideograms of Guy Davenport“
Related material:
A remark
on form and pattern
by T. S. Eliot
(friend of Pound
and founder of
the original
Criterion magazine)
A remark
on form and pattern
by T. S. Eliot
(friend of Pound
and founder of
the original
Criterion magazine)
Comments Off on Friday January 19, 2007
Tuesday, January 9, 2007
Tuesday January 9, 2007
For Balanchine's Birthday
(continued from
January 9, 2003)
George Balanchine
|
"What on earth is
a concrete universal?"
— Robert M. Pirsig
Review:
From Wikipedia's
"Upper Ontology"
and
Epiphany 2007:
"There is no neutral ground
that can serve as
a means of translating between
specialized (lower) ontologies."
There is, however,
"the field of reason"–
the 3×3 grid:
Click on grid
for details.
As Rosalind Krauss
has noted, some artists
regard the grid as
"a staircase to
the Universal."
Other artists regard
Epiphany itself as an
approach to
the Universal:
— Richard Kearney, 2005,
in The New Arcadia Review
Kearney (right) with
Martin Scorsese (left)
and Gregory Peck
in 1997.
"… one of the things that worried me about traditional metaphysics, at least as I imbibed it in a very Scholastic manner at University College Dublin in the seventies, is that philosophy was realism and realism was truth. What disturbed me about that was that everything was already acquired; truth was always a systematic given and it was there to be learned from Creation onwards; it was spoken by Jesus Christ and then published by St. Thomas Aquinas: the system as perfect synthesis. Hence, my philosophy grew out of a hunger for the 'possible' and it was definitely a reaction to my own philosophical formation. Yet that wasn't my only reaction. I was also reacting to what I considered to be the deep pessimism, and even at times 'nihilism' of the postmodern turn."
— Richard Kearney, interview (pdf) in The Leuven Philosophy Newsletter, Vol. 14, 2005-2006
For more on "the possible," see Kearney's The God Who May Be, Diamonds Are Forever, and the conclusion of Mathematics and Narrative:
|
"We symbolize
logical necessity with the box  )and logical possibility with the diamond  )."
"The possibilia that exist,
— Michael Sudduth, |
Sunday, January 7, 2007
Sunday January 7, 2007
Thursday, April 7, 2005 7:26 PM
In the Details
Wallace Stevens,
An Ordinary Evening in New Haven:
XXII
Professor Eucalyptus said, "The search
For reality is as momentous as
The search for God." It is the philosopher's search
For an interior made exterior
And the poet's search for the same exterior made
Interior….
… Likewise to say of the evening star,
The most ancient light in the most ancient sky,
That it is wholly an inner light, that it shines
From the sleepy bosom of the real, re-creates,
Searches a possible for its possibleness.
Julie Taymor, "Skewed Mirrors" interview:
"… they were performing for God. Now God can mean whatever you want it to mean. But for me, I understood it so totally. The detail….
They did it from the inside to the outside. And from the outside to the in. And that profoundly moved me then. It was…it was the most important thing that I ever experienced."
"Skewed Mirrors"
illustrated:
|
Click on the above to enlarge.
Details:
The above may be of interest to students
of iconology — what Dan Brown in
The Da Vinci Code calls "symbology" —
and of redheads.
The artist of Details,
"Brenda Starr" creator
Dale Messick, died on Tuesday,
April 5, 2005, at 98.
AP Photo
Dale Messick in 1982
For further details on
April 5, see
Art History:
The Pope of Hope
Comments Off on Sunday January 7, 2007
Friday, November 10, 2006
Friday November 10, 2006
Today's
numbers:
numbers:
Today is the day that
Stanley found Livingstone.
Click on picture for details.
"Stone 588,
I presume?"
Related material:
This afternoon's entry
on color symmetry
and
Click on picture for details.
See, too, the following from
a Log24 entry of last Monday–
"To von Eschenbach, the Grail
was never really a material cup,
but a jewel like the
jewel in the lotus,
a symbol of enlightenment,
of something intangible
and always beyond reach."
— Arcadian Functor
was never really a material cup,
but a jewel like the
jewel in the lotus,
a symbol of enlightenment,
of something intangible
and always beyond reach."
— Arcadian Functor
— in this context:
"Philosophers ponder the idea
of identity: what it is to give
something a name
on Monday
and have it respond
to that name
on Friday…."
— Bernard Holland in
The New York Times
Monday, May 20, 1996
something a name
on Monday
and have it respond
to that name
on Friday…."
— Bernard Holland in
The New York Times
Monday, May 20, 1996
Comments Off on Friday November 10, 2006
Wednesday, October 4, 2006
Wednesday October 4, 2006
Paul R. Halmos died
on Yom Kippur, 2006
on Yom Kippur, 2006
“Prof. Paul Halmos died of pneumonia early in the morning of October 2, 2006. He was 90 years old. He is survived by his wife, Virginia Halmos. An obituary may be found at the website of the Mathematical Association of America….”
— Halmos’s home page
at Santa Clara University
For a memorial of sorts, see
Lovely, Dark and Deep.
Update of 8 PM Oct. 4 —
From Google Book Search:
This is the source of the
“Halmos tombstone” symbol,
which has been described in a
different form at Wikipedia:
“The tombstone, or halmos–
symbol ∎ (Unicode U+220E)–
is used in mathematics to denote
the end of a proof.”
This Unicode character is rendered
as an empty square in Explorer
and as a black square in Firefox.
Related material:
Comments Off on Wednesday October 4, 2006
Tuesday, August 1, 2006
Tuesday August 1, 2006
Highway 1
Revisited
Revisited
John Constantine,
cartoon character, and
Donald E. Knuth,
Lutheran mathematician
“I need a photo-opportunity,
I want a shot at redemption.
Don’t want to end up a cartoon
In a cartoon graveyard.”
Mel Gibson,
7/28/06,
photo by
Los Angeles County
Sheriff’s Department
This meditation is prompted by memories of suicidal alcoholics Hunter S. Thompson and Ernest Hemingway, as well as by the title of Mel Gibson’s latest project, “Apocalypto.”
A search on Gibson’s film title leads to this quotation:
“And what does apocalypse mean? It means revelation: apocalypto means to open up and to show the truth. But it also means absolute violence, so the apocalypse is a violent revelation and a revelation of violence and immediately you see the relevance of this.”
— Interview with Rene Girard in the June 1996 issue of UCLA’s Anthropoetics: The Journal of Generative Anthropology
It is by no means clear that “apocalypse” means “violence,” let alone “absolute violence,” except in the Christian tradition.
For apocalyptic Christian violence, see “Apocalypse and Violence: The Evidence from the Reception History of the Book of Revelation” (pdf), by Christopher Rowland of Oxford University.
As for “the relevance of this,” see the definition of “generative anthropology” (GA) at
anthropoetics.ucla.edu/purpose.htm:
“The originary hypothesis of GA is that human language begins as an aborted gesture of appropriation representing–and thereby renouncing as sacred– an object of potential mimetic rivalry. The strength of our mimetic intelligence makes us the only creatures for whom intraspecific violence is a greater threat to survival than the external forces of nature. Human language defers potential conflict by permitting each to possess the sign of the unpossessable object of desire– the deferral of violence through representation.”
Compare with the remarks of Jung on Transformation Symbolism in the Mass:
Antecedents and parallels are found for the ritual of the Christian religious Mass in Aztec, Mithraic and pagan religious practices. “The Aztecs make a dough figure of the god Huitzilopochtli, which is then symbolically killed, divided and consumed….”
Collected Works of C. G. Jung, Vol. 11. 2nd ed., Princeton University Press, 1969. (pp. 222-225)
Mel Gibson’s interest in religion and violence is well known. His film “Apocalypto,” scheduled for release on Dec. 8, 2006, deals with human sacrifice among the Maya, rather than the Aztecs or Jews. (Cf. Abraham and “Highway 61 Revisited.”)
It seems unlikely that Mel will learn more about these issues in his recovery program. Too bad.
Comments Off on Tuesday August 1, 2006
Saturday, March 25, 2006
Saturday March 25, 2006
Built
In memory of Rolf Myller,
who died on Thursday,
March 23, 2006, at
Mount Sinai Hospital
in Manhattan:
Myller was,
according to the
New York Times,
an architect
whose eclectic pursuits
included writing
children’s books,
The Bible Puzzle Book, and
Fantasex: A Book of Erotic Games.
He also wrote, the Times says,
“Symbols and Their Meaning
(1978), a graphic overview of
children’s nonverbal communication.”
This is of interest in view of the
Log24 reference to “symbol-mongers”
on the date of Myller’s death.
In honor of Women’s History Month
and of Myller’s interests in the erotic
and in architecture, we present
the following work from a British gallery.
This work might aptly be
retitled “Brick Shithouse.”
Related material:
(1) the artist’s self-portrait
and, in view of the cover
illustration for Myller’s
The Bible Puzzle Book,
(2) the monumental treatise
by Leonard Shlain
The Alphabet Versus
the Goddess: The Conflict
Between Word and Image.
For devotees of women’s history
|
Liza Lou 03.03.06 – 08.04.06 White Cube is pleased to present the first UK solo exhibition by Los Angeles-based artist Liza Lou. Combining visionary, conceptual and craft approaches, Lou makes mixed-media sculptures and room-size installations that are suggestive of a transcendental reality. Lou’s work often employs familiar, domestic forms, crafted from a variety of materials such as steel, wood, papier-mâché and fibreglass, which is then covered with tiny glass beads that are painstakingly applied, one at a time, with tweezers. Dazzling and opulent and constantly glistening with refracted light, her sculptures bristle with what Peter Schjeldahl has aptly described as ‘surreal excrescence’. This exhibition, a meditation on the vulnerability of the human body and the architecture of confinement, will include several new figurative sculptures as well as two major sculptural installations. Security Fence (2005) is a large scale cage made up of four steel, chain link walls, topped by rings of barbed wire and Cell (2004-2006), as its name suggests, is a room based on the approximate dimensions of a death row prison cell, a kind of externalized map of the prisoner’s mind. Both Security Fence and Cell, like Lou’s immense earlier installations Kitchen (1991-1995) and Back Yard (1995-1999) are characterized by the absence of their real human subject. But whereas the absent subject in Kitchen and Back Yard could be imagined through the details and accessories carefully laid out to view, in Lou’s two new installations the human body is implied simply through the empty volume created by the surrounding architecture. Both Cell and Security Fence are monochromatic and employ iconic forms that make direct reference to Minimalist art in its use of repetition, formal perfection and materiality. In contrast to this, the organic form of a gnarled tree trunk, Scaffold (2005-2006), its surface covered with shimmering golden beads, juts directly out from the wall. Lou’s work has an immediate ‘shock’ content that works on different levels: first, an acknowledgement of the work’s sheer aesthetic impact and secondly the slower comprehension of the labour that underlies its construction. But whereas in Lou’s earlier works the startling clarity of the image is often a counterpoint to the lengthy process of its realization, for the execution of Cell, Lou further slowed down the process by using beads of the smallest variety with their holes all facing up in an exacting hour-by-hour approach in order to ‘use time as an art material’. Concluding this body of work are three male figures in states of anguish. In The Seer (2005-2006), a man becomes the means of turning his body back in on himself. Bent over double, his body becomes an instrument of impending self-mutilation, the surface of his body covered with silver-lined beads, placed with the exactitude and precision of a surgeon. In Homeostasis (2005-2006) a naked man stands prostrate with his hands up against the wall in an act of surrender. In this work, the dissolution between inside and outside is explored as the ornate surface of Lou’s cell-like material ‘covers’ the form while exposing the systems of the body, both corporeal and esoteric. In The Vessel (2005-2006), Christ, the universal symbol of torture and agony holds up a broken log over his shoulders. This figure is beheaded, and bejewelled, with its neck carved out, becoming a vessel into which the world deposits its pain and suffering. Lou has had numerous solo exhibitions internationally, including Museum Kunst Palast, Düsseldorf, Henie Onstad Kunstsenter, Oslo and Fondació Joan Miró, Barcelona. She was a 2002 recipient of the MacArthur Foundation Fellowship. Liza Lou’s film Born Again (2004), in which the artist tells the compelling and traumatic story* of her Pentecostal upbringing in Minnesota, will be screened at 52 Hoxton Square from 3 – 25 March courtesy of Penny Govett and Mick Kerr. Liza Lou will be discussing her work following a screening of her film at the ICA, The Mall, London on Friday 3 March at 7pm. Tickets are available from the ICA box office (+ 44 (0) 20 7930 3647). A fully illustrated catalogue, with a text by Jeanette Winterson and an interview with Tim Marlow, will accompany the exhibition. White Cube is open Tuesday to Saturday, 10.00 am to 6.00 pm.
For further information please contact Honey Luard or Susannah Hyman on + 44 (0) 20 7930 5373 * Warning note from Adrian Searle |
Comments Off on Saturday March 25, 2006
Thursday, March 23, 2006
Thursday March 23, 2006
Happy Birthday, Hassler Whitney
In honor of the late Hassler Whitney, mathematician and mountaineer, here is a link to the five Log24 entries ending with White, Geometric, and Eternal (Dec. 20, 2003).
Related material: the five Log24 entries ending with The Meadow (Dec. 18, 2005) and the five Log24 entries ending with Strange Attractor (Jan. 7, 2006).
The cross and the epiphany star in this last group of entries may interest the symbol-mongers among us.
Those more interested in substance than in symbols may prefer the following (click to enlarge):
This is apparently the original source for
the figure I cited on Dec. 20, 2003, as
from antiquark.com.
The connection with Whitney is
through the theory of matroids,
which Whitney founded in 1935.
See Hassler Whitney,
"On the abstract properties
of linear dependence,"
American Journal of Mathematics,
vol. 57 (1935), 509-533,
Collected Papers, vol. I, 147-171.
Comments Off on Thursday March 23, 2006
Monday, January 23, 2006
Monday January 23, 2006
In Defense of Hilbert
(On His Birthday)
Michael Harris (Log24, July 25 and 26, 2003) in a recent essay, Why Mathematics? You Might Ask (pdf), to appear in the forthcoming Princeton Companion to Mathematics:
“Mathematicians can… claim to be the first postmodernists: compare an art critic’s definition of postmodernism– ‘meaning is suspended in favor of a game involving free-floating signs’– with Hilbert’s definition of mathematics as ‘a game played according to certain simple rules with meaningless marks on paper.'”
Harris adds in a footnote:
“… the Hilbert quotation is easy to find but is probably apocryphal, which doesn’t make it any less significant.”
If the quotation is probably apocryphal, Harris should not have called it “Hilbert’s definition.”
For a much more scholarly approach to the concepts behind the alleged quotation, see Richard Zach, Hilbert’s Program Then and Now (pdf):
[Weyl, 1925] described Hilbert’s project as replacing meaningful mathematics by a meaningless game of formulas. He noted that Hilbert wanted to ‘secure not truth, but the consistency of analysis’ and suggested a criticism that echoes an earlier one by Frege: Why should we take consistency of a formal system of mathematics as a reason to believe in the truth of the pre-formal mathematics it codifies? Is Hilbert’s meaningless inventory of formulas not just ‘the bloodless ghost of analysis’?”
Some of Zach’s references:
[Ramsey, 1926] Frank P. Ramsey. Mathematical logic. The Mathematical Gazette, 13:185-94, 1926. Reprinted in [Ramsey, 1990, 225-244].
[Ramsey, 1990] Frank P. Ramsey. Philosophical Papers, D. H. Mellor, editor. Cambridge University Press, Cambridge, 1990
From Frank Plumpton Ramsey’s Philosophical Papers, as cited above, page 231:
“… I must say something of the system of Hilbert and his followers…. regarding higher mathematics as the manipulation of meaningless symbols according to fixed rules….
Mathematics proper is thus regarded as a sort of game, played with meaningless marks on paper rather like noughts and crosses; but besides this there will be another subject called metamathematics, which is not meaningless, but consists of real assertions about mathematics, telling us that this or that formula can or cannot be obtained from the axioms according to the rules of deduction….
Now, whatever else a mathematician is doing, he is certainly making marks on paper, and so this point of view consists of nothing but the truth; but it is hard to suppose it the whole truth.”
[Weyl, 1925] Hermann Weyl. Die heutige Erkenntnislage in der Mathematik. Symposion, 1:1-23, 1925. Reprinted in: [Weyl, 1968, 511-42]. English translation in: [Mancosu, 1998a, 123-42]….
[Weyl, 1968] Hermann Weyl. Gesammelte Abhandlungen, volume 1, K. Chandrasekharan, editor. Springer Verlag, Berlin, 1968.
[Mancosu, 1998a] Paolo Mancosu, editor. From Brouwer to Hilbert. The Debate on the Foundations of Mathematics in the 1920s. Oxford University Press, Oxford, 1998.
From Hermann Weyl, “Section V: Hilbert’s Symbolic Mathematics,” in Weyl’s “The Current Epistemogical Situation in Mathematics,” pp. 123-142 in Mancosu, op. cit.:
“What Hilbert wants to secure is not the truth, but the consistency of the old analysis. This would, at least, explain that historic phenomenon of the unanimity amongst all the workers in the vineyard of analysis.
To furnish the consistency proof, he has first of all to formalize mathematics. In the same way in which the contentual meaning of concepts such as “point, plane, between,” etc. in real space was unimportant in geometrical axiomatics in which all interest was focused on the logical connection of the geometrical concepts and statements, one must eliminate here even more thoroughly any meaning, even the purely logical one. The statements become meaningless figures built up from signs. Mathematics is no longer knowledge but a game of formulae, ruled by certain conventions, which is very well comparable to the game of chess. Corresponding to the chess pieces we have a limited stock of signs in mathematics, and an arbitrary configuration of the pieces on the board corresponds to the composition of a formula out of the signs. One or a few formulae are taken to be axioms; their counterpart is the prescribed configuration of the pieces at the beginning of a game of chess. And in the same way in which here a configuration occurring in a game is transformed into the next one by making a move that must satisfy the rules of the game, there, formal rules of inference hold according to which new formulae can be gained, or ‘deduced,’ from formulae. By a game-conforming [spielgerecht] configuration in chess I understand a configuration that is the result of a match played from the initial position according to the rules of the game. The analogue in mathematics is the provable (or, better, the proven) formula, which follows from the axioms on grounds of the inference rules. Certain formulae of intuitively specified character are branded as contradictions; in chess we understand by contradictions, say, every configuration which there are 10 queens of the same color. Formulae of a different structure tempt players of mathematics, in the way checkmate configurations tempt chess players, to try to obtain them through clever combination of moves as the end formula of a correctly played proof game. Up to this point everything is a game; nothing is knowledge; yet, to use Hilbert’s terminology, in ‘metamathematics,’ this game now becomes the object of knowledge. What is meant to be recognized is that a contradiction can never occur as an end formula of a proof. Analogously it is no longer a game, but knowledge, if one shows that in chess, 10 queens of one color cannot occur in a game-conforming configuration. One can see this in the following way: The rules are teaching us that a move can never increase the sum of the number of queens and pawns of one color. In the beginning this sum = 9, and thus– here we carry out an intuitively finite [anschaulich-finit] inference through complete induction– it cannot be more than this value in any configuration of a game. It is only to gain this one piece of knowledge that Hilbert requires contentual and meaningful thought; his proof of consistency proceeds quite analogously to the one just carried out for chess, although it is, obviously, much more complicated.
It follows from our account that mathematics and logic must be formalized together. Mathematical logic, much scorned by philosophers, plays an indispensable role in this context.”
Constance Reid says it was not Hilbert himself, but his critics, who described Hilbert’s formalism as reducing mathematics to “a meaningless game,” and quotes the Platonist Hardy as saying that Hilbert was ultimately concerned not with meaningless marks on paper, but with ideas:
“Hilbert’s program… received its share of criticism. Some mathematicians objected that in his formalism he had reduced their science to ‘a meaningless game played with meaningless marks on paper.’ But to those familiar with Hilbert’s work this criticism did not seem valid.
‘… is it really credible that this is a fair account of Hilbert’s view,’ Hardy demanded, ‘the view of the man who has probably added to the structure of significant mathematics a richer and more beautiful aggregate of theorems than any other mathematician of his time? I can believe that Hilbert’s philosophy is as inadequate as you please, but not that an ambitious mathematical theory which he has elaborated is trivial or ridiculous. It is impossible to suppose that Hilbert denies the significance and reality of mathematical concepts, and we have the best of reasons for refusing to believe it: “The axioms and demonstrable theorems,” he says himself, “which arise in our formalistic game, are the images of the ideas which form the subject-matter of ordinary mathematics.”‘”— Constance Reid in Hilbert-Courant, Springer-Verlag, 1986 (The Hardy passage is from “Mathematical Proof,” Mind 38, 1-25, 1929, reprinted in Ewald, From Kant to Hilbert.)
Harris concludes his essay with a footnote giving an unsourced Weyl quotation he found on a web page of David Corfield:
“.. we find ourselves in [mathematics] at exactly that crossing point of constraint and freedom which is the very essence of man’s nature.”
One source for the Weyl quotation is the above-cited book edited by Mancosu, page 136. The quotation in the English translation given there:
“Mathematics is not the rigid and petrifying schema, as the layman so much likes to view it; with it, we rather stand precisely at the point of intersection of restraint and freedom that makes up the essence of man itself.”
Corfield says of this quotation that he’d love to be told the original German. He should consult the above references cited by Richard Zach.
For more on the intersection of restraint and freedom and the essence of man’s nature, see the Kierkegaard chapter cited in the previous entry.
Comments Off on Monday January 23, 2006
Friday, November 18, 2005
Friday November 18, 2005
Crank Power!
One night in Bangkok
and the world’s your oyster…
Tonight’s Bangkok Post
on a new $100 laptop
from an MIT designer:
No logo for the initiative has yet been released, but designers could do worse than adopting as their symbol the bright yellow hand-crank that protrudes from the side of the laptop. This throwback to the days of the gramophone is designed to enable users to manually crank up electricity to run the laptop in places with irregular or non-existent access to the fixed electric power grid.
Details from Wired News
Kevin Poulsen, 12:58 PM Nov. 17, 2005 PT:
TUNIS, Tunisia — If tech luminary Nicholas Negroponte has his way, the pale light from rugged, hand-cranked $100 laptops will illuminate homes in villages and townships throughout the developing world, and give every child on the planet a computer of their own by 2010.
The MIT Media Lab and Wired magazine founder stood shoulder to shoulder with U.N. Secretary-General Kofi Annan to unveil the first working prototype of the “$100 laptop” — currently more like $110 — at the U.N. World Summit on the Information Society here Wednesday. The Linux-based machine instantly became the hit of the show, and Thursday saw diplomats and dignitaries, reporters and TV cameras perpetually crowded around the booth of One Laptop Per Child — Negroponte’s nonprofit — craning for a glimpse of the toy-like tote.
With its cheery green coloring and Tonka-tough shell, the laptop certainly looks cool. It boasts a 7-inch screen that swivels like a tablet PC, and an electricity-generating crank that provides 40 minutes of power from a minute of grinding.
Related material:
Certified Crank.
Certified Crank.
Comments Off on Friday November 18, 2005
Thursday, August 11, 2005
Thursday, April 7, 2005
Thursday April 7, 2005
In the Details
Wallace Stevens,
An Ordinary Evening in New Haven:
XXII
Professor Eucalyptus said, "The search
For reality is as momentous as
The search for God." It is the philosopher's search
For an interior made exterior
And the poet's search for the same exterior made
Interior….
… Likewise to say of the evening star,
The most ancient light in the most ancient sky,
That it is wholly an inner light, that it shines
From the sleepy bosom of the real, re-creates,
Searches a possible for its possibleness.
Julie Taymor, "Skewed Mirrors" interview:
"… they were performing for God. Now God can mean whatever you want it to mean. But for me, I understood it so totally. The detail….
They did it from the inside to the outside. And from the outside to the in. And that profoundly moved me then. It was…it was the most important thing that I ever experienced."
"Skewed Mirrors"
illustrated:
|
Click on the above to enlarge.
Details:
The above may be of interest to students
of iconology — what Dan Brown in
The Da Vinci Code calls "symbology" —
and of redheads.
The artist of Details,
"Brenda Starr" creator
Dale Messick, died on Tuesday,
April 5, 2005, at 98.
AP Photo
Dale Messick in 1982
For further details on
April 5, see
Art History:
The Pope of Hope
Sunday, January 9, 2005
Sunday January 9, 2005
Light at Bologna
“Others say it is a stone that posseses mysterious powers…. often depicted as a dazzling light. It’s a symbol representing power, a source of immense energy. It nourishes, heals, wounds, blinds, strikes down…. Some have thought of it as the philosopher’s stone of the alchemists….”
— Foucault’s Pendulum
by Umberto Eco,
Professor of Semiotics at
Europe’s oldest university,
the University of Bologna.
The Club Dumasby Arturo Perez-Reverte
|
Eclogues: Eight Stories
by Guy Davenport
Johns Hopkins paperback, 1993, page 127 —
Lo Splendore della Luce a Bologna, VI:
“In 1603, at Monte Paderno, outside Bologna, an alchemist (by day a cobbler) named Vicenzo Cascariolo discovered the Philosopher’s Stone, catalyst in the transformation of base metals into gold, focus of the imagination, talisman for abstruse thought. Silver in some lights, white in others, it glowed blue in darkness, awesome to behold.”
The Discovery of Luminescence:
The Bolognian Stone
Bologna, 16th Century
“For the University of Bologna hosting an International Conference on Bioluminescence and Chemiluminescence has a very special significance. Indeed, it is in our fair City that modern scientific research on these phenomena has its earliest roots….
‘After submitting the stone
to much preparation, it was not
the Pluto of Aristophanes
that resulted; instead, it was
the Luciferous Stone’ ”
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From one of the best books
of the 20th century: The Hawkline Monsterby Richard Brautigan
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Comments Off on Sunday January 9, 2005
Saturday, January 8, 2005
Saturday January 8, 2005
Splendor of the Light
The Beginning of a Story
by Guy Davenport
Lo Splendore della Luce a Bologna
“The locomotive bringing a trainload of philosophers to Bologna hissed and ground to a standstill in the long Appenine dusk to have its headlamps lit and to be dressed in the standards of the city and the university.”
Related material:
The train wreck at 12:50 pm local time (6:50 AM EST) Friday, Jan. 7, 2005, 25 miles north of Bologna.
A northbound freight train collided with a passenger train traveling south from Verona to Bologna.
From an essay on Davenport I found Friday morning, well before I learned on Friday afternoon (Eastern Standard Time) of the train wreck:
“A disciple of Ezra Pound, he adapts to the short story the ideogrammatic method of The Cantos, where a grammar of images, emblems, and symbols replaces that of logical sequence. This grammar allows for the grafting of particulars into a congeries of implied relation without subordination. In contrast to postmodernists, Davenport does not omit causal connection and linear narrative continuity for the sake of an aleatory play of signification but in order to intimate by combinational logic kinships and correspondences among eras, ideas and forces.”
— “When Novelists Become Cubists:
The Prose Ideograms of Guy Davenport,”
by Andre Furlani
The Prose Ideograms of Guy Davenport,”
by Andre Furlani
See also
Friday’s Log24 entries and
Davenport’s Express.
Comments Off on Saturday January 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:
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A web page
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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. |
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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.
Sunday, August 29, 2004
Sunday August 29, 2004
Olympic Arc
Thomas Becker, president of Chautauqua Institution, on Friday, Aug. 27, 2004:
“I’m really proud of this lecture platform this year. We started with Phil Wilcox on the first day of the season and finished with Sandra Day O’Connor. The arc of participation between them was really amazing.”
Phil Wilcox: See
Israel and Palestine:
Let’s Separate Myth from Reality,
by Philip C. Wilcox, Jr., President,
Foundation for Middle East Peace,
Chautauquan Daily, June 28, 2004
Sandra Day O’Connor: See
The Majesty of the Law:
Reflections of a
Supreme Court Justice,
by Sandra Day O’Connor
The O’Connor link above is to a page at the Chautauqua Bookstore.
For Justice O’Connor:
Reflections on Themis
(Log24, Aug. 17, 2004)
For Wilcox:
The Zen of Abraham
(Same entry, different title.)
I personally was at Chautauqua only one day this season — Friday, the 13th of August. My stops of course included the Chautauqua Bookstore, where I purchased the following:
Human cultural activity is mostly what Walker Percy astutely called “symbol-mongering.” Of the three books above, the central one offers the best symbols.
My own version of a
Chautauqua “Versus” symbol:
For further details, see the
For an “arc” symbol, see
Comments Off on Sunday August 29, 2004
Saturday, May 22, 2004
Saturday May 22, 2004
Star Wars
In memory of Melvin J. Lasky, editor, 1958-1990, of the CIA-funded journal Encounter:
“Once called as lively, and as bitchy, as a literary cocktail party, Encounter published articles of unrivalled authority on politics, history and literature.”
Lasky died on Wednesday, May 19, 2004. From a journal entry of my own on that date:
This newly-digitized diagram is from a
paper journal note of October 21, 1999.
Note that the diagram’s overall form is that of an eight-point star. Here is an excerpt from a Fritz Leiber story dealing with such a star, the symbol of a fictional organization:
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Time traveling, which is not quite the good clean boyish fun it’s cracked up to be, started for me when this woman with the sigil on her forehead looked in on me from the open doorway of the hotel bedroom where I’d hidden myself and the bottles and asked me, “Look, Buster, do you want to live?” Her right arm was raised and bent, the elbow touching the door frame, the hand brushing back the very dark bangs from her forehead to show me the sigil, as if that had a bearing on her question. The sigil was an eight-limbed asterisk made of fine dark lines and about as big as a silver dollar. An X superimposed on a plus sign. It looked permanent. … “Here is how it stacks up: You’ve bought your way with something other than money into an organization of which I am an agent….” “It’s a very big organization,” she went on, as if warning me. “Call it an empire or a power if you like. So far as you are concerned, it has always existed and always will exist. It has agents everywhere, literally. Space and time are no barriers to it. Its purpose, so far as you will ever be able to know it, is to change, for its own aggrandizement, not only the present and the future, but also the past. It is a ruthlessly competitive organization and is merciless to its employees.” “I. G. Farben?” I asked grabbing nervously and clumsily at humor. She didn’t rebuke my flippancy, but said, “And it isn’t the Communist Party or the Ku Klux Klan, or the Avenging Angels or the Black Hand, either, though its enemies give it a nastier name.” “Which is?” I asked. “The Spiders,” she said. That word gave me the shudders, coming so suddenly. I expected the sigil to step off her forehead and scuttle down her face and leap at me—something like that. She watched me. “You might call it the Double Cross,” she suggested, “if that seems better.” — Fritz Leiber, |
From last year’s entry,
Indiana Jones and the Hidden Coffer,
of 6/14:
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From Borges’s “The Aleph“:
From The Hunchback of Notre Dame:
Lena Olin and Harrison Ford |
Finally, from an excellent site
on the Knights Templar,
a quotation from Umberto Eco:
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When all the archetypes burst out shamelessly, we plumb the depths of Homeric profundity. Two cliches make us laugh but a hundred cliches move us because we sense dimly that the cliches are talking among themselves, celebrating a reunion . . . Just as the extreme of pain meets sensual pleasure, and the extreme of perversion borders on mystical energy, so too the extreme of banality allows us to catch a glimpse of the Sublime. — “Casablanca: Cult Movies and Intertextual Collage” (1984) from Travels in Hyperreality |
Comments Off on Saturday May 22, 2004
Tuesday, April 6, 2004
Tuesday April 6, 2004
Ideas and Art, Part III
The first idea was not our own. Adam
In Eden was the father of Descartes…
— Wallace Stevens, from
Notes Toward a Supreme Fiction
"Quaedam ex his tanquam rerum imagines sunt, quibus solis proprie convenit ideae nomen: ut cùm hominem, vel Chimaeram, vel Coelum, vel Angelum, vel Deum cogito."
— Descartes, Meditationes III, 5
"Of my thoughts some are, as it were, images of things, and to these alone properly belongs the name idea; as when I think [represent to my mind] a man, a chimera, the sky, an angel or God."
— Descartes, Meditations III, 5
Begin, ephebe, by perceiving the idea
Of this invention, this invented world,
The inconceivable idea of the sun.
You must become an ignorant man again
And see the sun again with an ignorant eye
And see it clearly in the idea of it.
— Wallace Stevens, from
Notes Toward a Supreme Fiction
"… Quinimo in multis saepe magnum discrimen videor deprehendisse: ut, exempli causâ, duas diversas solis ideas apud me invenio, unam tanquam a sensibus haustam, & quae maxime inter illas quas adventitias existimo est recensenda, per quam mihi valde parvus apparet, aliam verò ex rationibus Astronomiae desumptam, hoc est ex notionibus quibusdam mihi innatis elicitam, vel quocumque alio modo a me factam, per quam aliquoties major quàm terra exhibetur; utraque profecto similis eidem soli extra me existenti esse non potest, & ratio persuadet illam ei maxime esse dissimilem, quae quàm proxime ab ipso videtur emanasse."
— Descartes, Meditationes III, 11
"… I have observed, in a number of instances, that there was a great difference between the object and its idea. Thus, for example, I find in my mind two wholly diverse ideas of the sun; the one, by which it appears to me extremely small draws its origin from the senses, and should be placed in the class of adventitious ideas; the other, by which it seems to be many times larger than the whole earth, is taken up on astronomical grounds, that is, elicited from certain notions born with me, or is framed by myself in some other manner. These two ideas cannot certainly both resemble the same sun; and reason teaches me that the one which seems to have immediately emanated from it is the most unlike."
— Descartes, Meditations III, 11
"Et quamvis forte una idea ex aliâ nasci possit, non tamen hîc datur progressus in infinitum, sed tandem ad aliquam primam debet deveniri, cujus causa sit in star archetypi, in quo omnis realitas formaliter contineatur, quae est in ideâ tantùm objective."
— Descartes, Meditationes III, 15
"And although an idea may give rise to another idea, this regress cannot, nevertheless, be infinite; we must in the end reach a first idea, the cause of which is, as it were, the archetype in which all the reality [or perfection] that is found objectively [or by representation] in these ideas is contained formally [and in act]."
— Descartes, Meditations III, 15
Michael Bryson in an essay on Stevens's "Notes Toward a Supreme Fiction,"
The Quest for the Fiction of the Absolute:
"Canto nine considers the movement of the poem between the particular and the general, the immanent and the transcendent: "The poem goes from the poet's gibberish to / The gibberish of the vulgate and back again. / Does it move to and fro or is it of both / At once?" The poet, the creator-figure, the shadowy god-figure, is elided, evading us, "as in a senseless element." The poet seeks to find the transcendent in the immanent, the general in the particular, trying "by a peculiar speech to speak / The peculiar potency of the general." In playing on the senses of "peculiar" as particular and strange or uncanny, these lines play on the mystical relation of one and many, of concrete and abstract."
Brian Cronin in Foundations of Philosophy:
"The insight is constituted precisely by 'seeing' the idea in the image, the intelligible in the sensible, the universal in the particular, the abstract in the concrete. We pivot back and forth between images and ideas as we search for the correct insight."
— From Ch. 2, Identifying Direct Insights
Michael Bryson in an essay on Stevens's "Notes Toward a Supreme Fiction":
"The fourth canto returns to the theme of opposites. 'Two things of opposite natures seem to depend / On one another . . . . / This is the origin of change.' Change resulting from a meeting of opposities is at the root of Taoism: 'Tao produced the One. / The One produced the two. / The two produced the three. / And the three produced the ten thousand things' (Tao Te Ching 42) …."
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From an entry of March 7, 2004:
From the web page
Introduction to the I Ching– "He who has perceived the meaning of change fixes his attention no longer on transitory individual things but on the immutable, eternal law at work in all change. This law is the tao of Lao-tse, the course of things, the principle of the one in the many. That it may become manifest, a decision, a postulate, is necessary. This fundamental postulate is the 'great primal beginning' of all that exists, t'ai chi — in its original meaning, the 'ridgepole.' Later Chinese philosophers devoted much thought to this idea of a primal beginning. A still earlier beginning, wu chi, was represented by the symbol of a circle. Under this conception, t'ai chi was represented by the circle divided into the light and the dark, yang and yin,
This symbol has also played a significant part in India and Europe. However, speculations of a gnostic-dualistic character are foreign to the original thought of the I Ching; what it posits is simply the ridgepole, the line. With this line, which in itself represents oneness, duality comes into the world, for the line at the same time posits an above and a below, a right and left, front and back-in a word, the world of the opposites." The t'ai chi symbol is also illustrated on the web page Cognitive Iconology, which says that
"W.J.T. Mitchell calls 'iconology' A variation on the t'ai chi symbol appears in a log24.net entry for March 5:
The Line, See too my web page Logos and Logic, which has the following:
Logos Alogos, In the conclusion of Section 3, Canto X, of "Notes," Stevens says
This is the logoi alogoi of Simone Weil. |
.
In "Notes toward a Supreme Fiction,"
Wallace Stevens lists three criteria
for a work of the imagination:
It Must Be Abstract
The Line,
by S.H. Cullinane
It Must Change
It Must Give Pleasure
Related material:
Comments Off on Tuesday April 6, 2004
Thursday, March 4, 2004
Thursday March 4, 2004
ZZ
we measure heaven and earth
black
on white
we create new worlds
and universes
“Numbers and Names,
Wording and Words”
by Eugen Jost
Alphabets
From time to time we take our pen in hand
And scribble symbols on a blank white sheet
Their meaning is at everyone’s command;
It is a game whose rules are nice and neat.
But if a savage or a moon-man came
And found a page, a furrowed runic field,
And curiously studied lines and frame:
How strange would be the world that they revealed.
A magic gallery of oddities.
He would see A and B as man and beast,
As moving tongues or arms or legs or eyes,
Now slow, now rushing, all constraint released,
Like prints of ravens’ feet upon the snow.
He’d hop about with them, fly to and fro,
And see a thousand worlds of might-have-been
Hidden within the black and frozen symbols,
Beneath the ornate strokes, the thick and thin.
He’d see the way love burns and anguish trembles,
He’d wonder, laugh, shake with fear and weep
Because beyond this cipher’s cross-barred keep
He’d see the world in all its aimless passion,
Diminished, dwarfed, and spellbound in the symbols,
And rigorously marching prisoner-fashion.
He’d think: each sign all others so resembles
That love of life and death, or lust and anguish,
Are simply twins whom no one can distinguish …
Until at last the savage with a sound
Of mortal terror lights and stirs a fire,
Chants and beats his brow against the ground
And consecrates the writing to his pyre.
Perhaps before his consciousness is drowned
In slumber there will come to him some sense
Of how this world of magic fraudulence,
This horror utterly behind endurance,
Has vanished as if it had never been.
He’ll sigh, and smile, and feel all right again.
— Hermann Hesse (1943),
“Buchstaben” from Das Glasperlenspiel,
translated by Richard and Clara Winston
See also the previous entry,
on the dream
of El Pato-lógico.
Friday, February 20, 2004
Friday February 20, 2004
The Da Vinci Code
and Symbology at Harvard
The protagonist of the recent bestseller The Da Vinci Code is Robert Langdon, "a professor of Religious Symbology at Harvard University." A prominent part in the novel is played by the well-known Catholic organization Opus Dei. Less well known (indeed, like Langdon, nonexistent) is the academic discipline of "symbology." (For related disciplines that do exist, click here.) What might a course in this subject at Harvard be like?
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Harvard Crimson, April 10, 2003: While Opus Dei members said that they do not refer to their practices of recruitment as "fishing," the Work’s founder does describe the process of what he calls "winning new apostles" with an aquatic metaphor. Point #978 of The Way invokes a passage in the New Testament in which Jesus tells Peter that he will make him a "fisher of men." The point reads:
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Exercise for Symbology 101:
Describe the symmetry
in each of the pictures above.
Show that the second picture
retains its underlying structural
symmetry under a group of
322,560 transformations.
Having reviewed yesterday's notes
on Gombrich, Gadamer, and Panofsky,
discuss the astrological meaning of
the above symbols in light of
today's date, February 20.
Extra credit:
Relate the above astrological
symbolism to the four-diamond
symbol in Jung's Aion.
Happy metaphors!
Comments Off on Friday February 20, 2004
Thursday, February 5, 2004
Thursday February 5, 2004
Quantum Logic:
A memorial to the late Alan Bullock,
founding master of St. Catherine’s College,
Oxford, and historian of the Third Reich.
Bullock died on Groundhog Day.
From an obituary:
“Hitler: a Study in Tyranny was published in 1952 with the aphorism from Aristotle: ‘Men do not become tyrants in order to keep out the cold.’ In the same year Alan Bullock took up his appointment to the oddly-named office of ‘Censor’ of St. Catherine’s Society – a male society, constitutionally part of the University, with a handful of tutors and no residential accommodation. Ten years later it became a College….”
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Emblem of |
Quantum Oscillator |
Explaining what these Catherine wheels symbolize seems an appropriate task for Oxford philosophers. From the St. Catherine’s College site: “The College’s motto – Nova et Vetera (the new and the old) – sums up its unique quality among Oxford colleges.”
See also today’s previous entry, prompted by a recent MIT Press book on philosophy and quantum theory.
Comments Off on Thursday February 5, 2004
Thursday, November 6, 2003
Thursday November 6, 2003
Legacy Codes:
The Most Violent Poem
Lore of the Manhattan Project:
From The Trinity Site —
“I imagined Oppenheimer saying aloud,
‘Batter my heart, three person’d God,”
unexpectedly recalling John Donne’s ‘Holy Sonnet [14],’
and then he knew, ‘ “Trinity” will do.’
Memory has its reasons.
‘Batter my heart’ — I remember these words.
I first heard them on a fall day at Duke University in 1963.
Inside a classroom twelve of us were
seated around a long seminar table
listening to Reynolds Price recite this holy sonnet….
I remember Reynolds saying, slowly, carefully,
‘This is the most violent poem in the English language.’ ”
Related Entertainment
Today’s birthday:
director Mike Nichols
From a dead Righteous Brother:
“If you believe in forever
Then life is just a one-night stand.”
— Bobby Hatfield, found dead
in his hotel room at
7 PM EST Wednesday, Nov. 5, 2003,
before a concert scheduled at
Western Michigan University, Kalamazoo.
From a review of The Matrix Revolutions:
“You’d have to be totally blind at the end
to miss the Christian symbolism….
Trinity gets a glimpse of heaven…. And in the end…
God Put A Rainbow In The Clouds.”
Moral of the
Entertainment:
According to Chu Hsi [Zhu Xi],
“Li” is
“the principle or coherence
or order or pattern
underlying the cosmos.”
— Smith, Bol, Adler, and Wyatt,
Sung Dynasty Uses of the I Ching,
Princeton University Press, 1990
Related Non-Entertainment
Symmetry and a Trinity
(for the dotting-the-eye symbol above)
Introduction to Harmonic Analysis
(for musical and historical background)
Mathematical Proofs
(for the spirit of Western Michigan
University, Kalamazoo)
Moral of the
Non-Entertainment:
“Many kinds of entity
become easier to handle
by decomposing them into
components belonging to spaces
invariant under specified symmetries.”
— The importance of
mathematical conceptualisation
by David Corfield,
Department of History and
Philosophy of Science,
University of Cambridge
See, too,
Symmetry of Walsh Functions and
Geometry of the I Ching.
Comments Off on Thursday November 6, 2003
Monday, August 18, 2003
Monday August 18, 2003
Entries since Xanga’s
August 10 Failure:
Sunday, August 17, 2003 2:00 PM
A Thorny Crown of…
From the first episode of
the television series
“The West Wing“:
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Original airdate: Sept. 22, 1999 MARY MARSH CALDWELL MARY MARSH JOSH TOBY [A stunned silence. Everyone stares at Toby.] TOBY (CONT.) JOSH |
Going There, Part I
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Crown of Ideas Kirk Varnedoe, 57, art historian and former curator of the Museum of Modern Art, died Thursday, August 14, 2003. From his New York Times obituary: ” ‘He loved life in its most tangible forms, and so for him art was as physical and pleasurable as being knocked down by a wave,’ said Adam Gopnik, the writer and a former student of his who collaborated on Mr. Varnedoe’s first big show at the Modern, ‘High & Low.’ ‘Art was always material first — it was never, ever bound by a thorny crown of ideas.’ ” For a mini-exhibit of ideas in honor of Varnedoe, see Verlyn Klinkenborg on Varnedoe: “I was always struck by the tangibility of the words he used…. It was as if he were laying words down on the table one by one as he used them, like brushes in an artist’s studio. That was why students crowded into his classes and why the National Gallery of Art had overflow audiences for his Mellon Lectures earlier this year. Something synaptic happened when you listened to Kirk Varnedoe, and, remarkably, something synaptic happened when he listened to you. You never knew what you might discover together.” Perhaps even a “thorny crown of ideas“?
“Crown of Thorns” Varnedoe’s death coincided with “To what extent does this idea of a civic life produced by sense of adversity correspond to actual life in Brasília? I wonder if it is something which the city actually cultivates. Consider, for example the cathedral, on the monumental axis, a circular, concrete framed building whose sixteen ribs are both structural and symbolic, making a structure that reads unambiguously as a crown of thorns; other symbolic elements include the subterranean entrance, the visitor passing through a subterranean passage before emerging in the light of the body of the cathedral. And it is light, shockingly so….” — Modernist Civic Space: The Case of Brasilia, by Richard J. Williams, Department of History of Art, University of Edinburgh, Scotland |
Going There, Part II
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Simple, Bold, Clear Art historian Kirk Varnedoe was, of course, not the only one to die on the day of the Great Blackout. Claude Martel, 34, a senior art director of The New York Times Magazine, also died on Thursday, August 14, 2003. Janet Froelich, the magazine’s art director, describes below a sample of work that she and Martel did together: “A new world of ideas”
Froelich notes that “the elements are simple, bold, and clear.” For another example of elements with these qualities, see my journal entry The flag design in that entry
Note that the elements of the flag design have the qualities described so aptly by Froelich– simplicity, boldness, clarity:
They share these qualities with the Elements of Euclid, a treatise on geometrical ideas. For the manner in which such concepts might serve as, in Gopnik’s memorable phrase, a “thorny crown of ideas,” see “Geometry for Jews” in ART WARS: Geometry as Conceptual Art. See also the discussion of ideas in my journal entry on theology and art titled Understanding: On Death and Truth and the discussion of the word “idea” (as well as the word, and the concept, “Aryan”) in the following classic (introduced by poet W. H. Auden):
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Saturday, August 16, 2003 6:00 AM
Varnedoe’s Crown
Kirk Varnedoe, 57, art historian and former curator of the Museum of Modern Art, died Thursday, August 14, 2003.
From his New York Times obituary:
” ‘He loved life in its most tangible forms, and so for him art was as physical and pleasurable as being knocked down by a wave,’ said Adam Gopnik, the writer and a former student of his who collaborated on Mr. Varnedoe’s first big show at the Modern, ‘High & Low.’ ‘Art was always material first — it was never, ever bound by a thorny crown of ideas.’ “
For a mini-exhibit of ideas in honor of Varnedoe, see
Verlyn Klinkenborg on Varnedoe:
“I was always struck by the tangibility of the words he used…. It was as if he were laying words down on the table one by one as he used them, like brushes in an artist’s studio. That was why students crowded into his classes and why the National Gallery of Art had overflow audiences for his Mellon Lectures earlier this year. Something synaptic happened when you listened to Kirk Varnedoe, and, remarkably, something synaptic happened when he listened to you. You never knew what you might discover together.”
Perhaps even a “thorny crown of ideas”?
“Crown of Thorns”
Cathedral, Brasilia
Varnedoe’s death coincided with
the Great Blackout of 2003.
“To what extent does this idea of a civic life produced by sense of adversity correspond to actual life in Brasília? I wonder if it is something which the city actually cultivates. Consider, for example the cathedral, on the monumental axis, a circular, concrete framed building whose sixteen ribs are both structural and symbolic, making a structure that reads unambiguously as a crown of thorns; other symbolic elements include the subterranean entrance, the visitor passing through a subterranean passage before emerging in the light of the body of the cathedral. And it is light, shockingly so….”
— Modernist Civic Space: The Case of Brasilia, by Richard J. Williams, Department of History of Art, University of Edinburgh, Scotland
Friday, August 15, 2003 3:30 PM
ART WARS:
The Boys from Brazil
It turns out that the elementary half-square designs used in Diamond Theory
also appear in the work of artist Nicole Sigaud.
Sigaud’s website The ANACOM Project has a page that leads to the artist Athos Bulcão, famous for his work in Brasilia.
From the document
Conceptual Art in an
Authoritarian Political Context:
Brasilia, Brazil,
by Angélica Madeira:
“Athos created unique visual plans, tiles of high poetic significance, icons inseparable from the city.”
As Sigaud notes, two-color diagonally-divided squares play a large part in the art of Bulcão.
The title of Madeira’s article, and the remarks of Anna Chave on the relationship of conceptual/minimalist art to fascist rhetoric (see my May 9, 2003, entries), suggest possible illustrations for a more politicized version of Diamond Theory:
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Fahne, |
Dr. Mengele, |
Is it safe?
These illustrations were suggested in part by the fact that today is the anniversary of the death of Macbeth, King of Scotland, and in part by the following illustrations from my journal entries of July 13, 2003 comparing a MOMA curator to Lady Macbeth:
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Die Fahne Hoch, |
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Thursday, August 14, 2003 3:45 AM
Famous Last Words
The ending of an Aug. 14 Salon.com article on Mel Gibson’s new film, “The Passion”:
” ‘The Passion’ will most likely offer up the familiar puerile, stereotypical view of the evil Jew calling for Jesus’ blood and the clueless Pilate begging him to reconsider. It is a view guaranteed to stir anew the passions of the rabid Christian, and one that will send the Jews scurrying back to the dark corners of history.”
— Christopher Orlet
“Scurrying”?! The ghost of Joseph Goebbels, who famously portrayed Jews as sewer rats doing just that, must be laughing — perhaps along with the ghost of Lady Diana Mosley (née Mitford), who died Monday.
This goes well with a story that Orlet tells at his website:
“… to me, the most genuine last words are those that arise naturally from the moment, such as
Joseph Goebbels |
Voltaire’s response to a request that he foreswear Satan: ‘This is no time to make new enemies.’ ”
For a view of Satan as an old, familiar, acquaintance, see the link to Prince Ombra in my entry last October 29 for Goebbels’s birthday.
Wednesday, August 13, 2003 3:00 PM
Best Picture
For some reflections inspired in part by
- Today’s anniversary of a
1727 Moravian Pentecost, - An April 7, 2003,
lecture at Moravian College, and - St. Bonaventure’s 1259
remarks on the Trinity,
Tuesday, August 12, 2003 4:44 PM
Atonement:
A sequel to my entry “Catholic Tastes” of July 27, 2003.
Some remarks of Wallace Stevens that seem appropriate on this date:
“It may be that one life is a punishment
For another, as the son’s life for the father’s.”
— Esthétique du Mal, Wallace Stevens
“Unless we believe in the hero, what is there
To believe? ….
Devise, devise, and make him of winter’s
Iciest core, a north star, central
In our oblivion, of summer’s
Imagination, the golden rescue:
The bread and wine of the mind….”
— Examination of the Hero in a Time of War, Wallace Stevens
Etymology of “Atonement”:
“Middle English atonen, to be reconciled, from at one, in agreement“
At One
“… We found,
If we found the central evil, the central good….
… we and the diamond globe at last were one.”
— Asides on the Oboe, Wallace Stevens
Tuesday, August 12, 2003 1:52 PM
Franken & ‘Stein,
Attorneys at Law
“Tue August 12, 2003 04:10 AM ET
NEW YORK (Reuters) – Fox News Network is suing humor writer Al Franken for trademark infringement over the phrase ‘fair and balanced’ on the cover of his upcoming book, saying it has been ‘a signature slogan’ of the network since 1996.”
|
Franken: |
‘Stein: |
For answers, click on the pictures
of Franken and ‘Stein.
Comments Off on Monday August 18, 2003
Saturday, July 26, 2003
Saturday July 26, 2003
The Transcendent
Signified
“God is both the transcendent signifier
and transcendent signified.”
— Caryn Broitman,
Deconstruction and the Bible
“Central to deconstructive theory is the notion that there is no ‘transcendent signified,’ or ‘logos,’ that ultimately grounds ‘meaning’ in language….”
— Henry P. Mills,
The Significance of Language,
Footnote 2
“It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy. It structures Plato’s (realist) reaction to the sophists (nominalists). What is often called ‘postmodernism’ is really just nominalism, colourfully presented as the doctrine that there is nothing except texts. It is the variety of nominalism represented in many modern humanities, paralysing appeals to reason and truth.”
— Simon Blackburn, Think,
Oxford University Press, 1999, page 268
The question of universals is still being debated in Paris. See my July 25 entry,
That entry discusses an essay on
mathematics and postmodern thought
by Michael Harris,
professor of mathematics
at l’Université Paris 7 – Denis Diderot.
A different essay by Harris has a discussion that gets to the heart of this matter: whether pi exists as a platonic idea apart from any human definitions. Harris notes that “one might recall that the theorem that pi is transcendental can be stated as follows: the homomorphism
Harris illustrates this with
an X in a rectangle:
For the complete passage, click here.
If we rotate the Harris X by 90 degrees, we get a representation of the Christian Logos that seems closely related to the God-symbol of Arthur C. Clarke and Stanley Kubrick in 2001: A Space Odyssey. On the left below, we have a (1x)4×9 black monolith, representing God, and on the right below, we have the Harris slab, with X representing (as in “Xmas,” or the Chi-rho page of the Book of Kells) Christ… who is, in theological terms, also “the variable par excellence.”
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Kubrick’s |
Harris’s |
For a more serious discussion of deconstruction and Christian theology, see
Comments Off on Saturday July 26, 2003
Tuesday, June 17, 2003
Tuesday June 17, 2003
On actor Gregory Peck, who died Thursday, June 12, 2003:
"He had early success in 'The Keys of the Kingdom,' in which he played a priest."
As Peck noted in a videotape played at his memorial service June 16,
"As a professional," he added, "I think I'd like to be thought of as a good storyteller; that's what's always interested me."
June 16, besides being the day of Peck's memorial, was also Bloomsday. My entry for 1 PM on Bloomsday, a day celebrating the Ulysses of James Joyce, consists of the three words "Hickory, Dickory, Dock." A comment on that entry:
"I prefer the Wake."
The following, from the Discordian Scriptures, provides a connection between the Bloomsday mouse and the Wake of patriarch Gregory Peck.
Hickory Dickory Dock
Hickory, dickory, dock!
Here we are on higher ground at once. The clock symbolizes the spinal column, or if you prefer it, Time, chosen as one of the conditions of normal consciousness. The mouse is the Ego; "Mus", a mouse, being only "Sum", "I am", spelt Qabalistically backwards. This Ego or Prana or Kundalini force being driven up the spine, the clock strikes one, that is, the duality of consciousness is abolished. And the force again subsides to its original level. "Hickory, dickory, dock!" is perhaps the mantra which was used by the adept who constructed this rime, thereby hoping to fix it in the minds of men; so that they might attain to Samadhi by the same method. Others attribute to it a more profound significance — which is impossible to go into at this moment, for we must turn to:
Humpty Dumpty sat on a wall….
The Bloom of Ulysses has a certain philosophical kinship with Yale literary critic Harold Bloom. For material related to the latter Bloom's study of Gnosticism, see Chaos Matrix. For the conflict between Gnostic and Petrine approaches to religion, see Poul Anderson's Operation Chaos.
From an account of Peck's memorial service:
"Mourners included… Piper Laurie…."
OK, he's in.
Comments Off on Tuesday June 17, 2003
Saturday, June 14, 2003
Saturday June 14, 2003
 |
Indiana Jones |
In memory of Bernard Williams,
Oxford philosopher, who died Tuesday, June 10, 2003.
“…in… Truth and Truthfulness [September, 2002], he sought to speak plainly, and took on the post-modern, politically correct notion that truth is merely relative…”
“People have always longed for truths about the world — not logical truths, for all their utility; or even probable truths, without which daily life would be impossible; but informative, certain truths, the only ‘truths’ strictly worthy of the name. Such truths I will call ‘diamonds’; they are highly desirable but hard to find….
A new epistemology is emerging to replace the Diamond Theory of truth. I will call it the ‘Story Theory’ of truth: There are no diamonds. People make up stories about what they experience. Stories that catch on are called ‘true.’ The Story Theory of truth is itself a story that is catching on. It is being told and retold, with increasing frequency, by thinkers of many stripes…. My own viewpoint is the Story Theory….”
— Richard J. Trudeau, The Non-Euclidean Revolution, Birkhauser Boston, 1987
Today is the feast day of Saint Jorge Luis Borges (b. Buenos Aires, August 24, 1899 – d. Geneva, June 14, 1986).
From Borges’s “The Aleph“:
“The Faithful who gather at the mosque of Amr, in Cairo, are acquainted with the fact that the entire universe lies inside one of the stone pillars that ring its central court…. The mosque dates from the seventh century; the pillars come from other temples of pre-Islamic religions…. Does this Aleph exist in the heart of a stone?”
(“Los fieles que concurren a la mezquita de Amr, en el Cairo, saben muy bien que el universo está en el interior de una de las columnas de piedra que rodean el patio central…. la mezquita data del siglo VII; las columnas proceden de otros templos de religiones anteislámicas…. ¿Existe ese Aleph en lo íntimo de una piedra?”)
From The Hunchback of Notre Dame:
Un cofre de gran riqueza
Hallaron dentro un pilar,
Dentro del, nuevas banderas
Con figuras de espantar.*
* A coffer of great richness
In a pillar’s heart they found,
Within it lay new banners,
With figures to astound.
See also the figures obtained by coloring and permuting parts of the above religious symbol.
Lena Olin and Harrison Ford
in “Hollywood Homicide“
Sunday, May 25, 2003
Sunday May 25, 2003
STAR WARS
opened on this date in 1977.
From the web page Amande:
Le Christ et la Vierge apparurent souvent entourés d’une auréole en forme d’amande: la mandorle.
Étymologiquement, le mot amande est une altération de amandala, qui dérive lui-même du latin classique amygdala….
L’amande a… une connotation symbolique, celle du sexe féminin. Elle figure souvent la vulve. Elle est alors en analogie avec la yoni du vocabulaire de l’hindouisme, la vulve ou la matrice, représentée par une amande ou une noix coupée en deux.
Screenshot of the online
New York Times, May 25, 2003:
Ariel the Hutt and Princess Amygdala
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by Horia Cristescu and
The intersection of two geometric forms (lines, triangles, circles, etc.) represents forces that are even more intense than those generated by the simple forms. Such an interpenetration indicates a high level in the dynamic interaction of the correspondent energies. The empty spaces generated by such combinations are described as very efficient operational fields of the forces emanating from the central point of the YANTRA. That is why we can very often encounter representations of MANTRAS in such spaces. YANTRA and MANTRA are complementary aspects of SHIVA and their use together is much more efficient than the use of one alone.
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The Triangle (TRIKONA)
AMEN.
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Sunday May 25, 2003
— ART WARS —
Mental Health Month, Day 25:
Matrix of the Death God
Having dealt yesterday with the Death Goddess Sarah, we turn today to the Death God Abraham. (See Jacques Derrida, The Gift of Death, University of Chicago Press, 1996.) For a lengthy list of pictures of this damned homicidal lunatic about to murder his son, see The Text This Week.
See, too, The Matrix of Abraham, illustrated below. This is taken from a book by R. M. Abraham, Diversions and Pastimes, published by Constable and Company, London, in 1933.
The Matrix of Abraham
A summary of the religious import of the above from Princeton University Press:
“Moslems of the Middle Ages were fascinated by pandiagonal squares with 1 in the center…. The Moslems thought of the central 1 as being symbolic of the unity of Allah. Indeed, they were so awed by that symbol that they often left blank the central cell on which the 1 should be positioned.”
— Clifford A. Pickover, The Zen of Magic Squares, Circles, and Stars, Princeton U. Press, 2002, pp. 71-72
Other appearances of this religious icon on the Web:
A less religious approach to the icon may be found on page 393 of R. D. Carmichael’s Introduction to the Theory of Groups of Finite Order (Ginn, Boston, 1937, reprinted by Dover, 1956).
This matrix did not originate with Abraham but, unlike Neo, I have not yet found its Architect.
Wednesday, March 5, 2003
Wednesday March 5, 2003
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Ash |
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“Teach us to care and not to care.”
— T. S. Eliot, “Ash Wednesday“
From The Jerusalem Post, August 6, 2001:
In the movie Godfather II there is a scene when Michael Corleone is in Batista-ruled Havana. A Marxist rebel is arrested, and rather than be taken alive he explodes a grenade he had hidden in his jacket, killing himself and the officers arresting him.
His partner says: “Those rebels, you know, they’re lunatics.”
“Maybe so,” Michael Corleone says. “But it occurred to me. The soldiers are paid to fight – the rebels aren’t.”
“What does that tell you?” asks his partner.
“They can win,” he replies.
— Analysis by Arieh O’Sullivan
The date of the above analysis, August 6, was the date of the Christian Feast of the Transfiguration and the anniversary of the first use in warfare of a nuclear weapon.
“And the light shone in darkness and
Against the Word* the unstilled world still whirled
About the centre of the silent Word….
Where shall the word be found, where will the word
Resound?”
— T. S. Eliot, “Ash Wednesday,” 1930
Hiroshima, perhaps?
See also my entries for Transfiguration 2002.
* Eliot does not say what “Word” he is talking about. Perhaps it is “Arieh,” the name of the journalist who wrote the perceptive Havana passage above. A search for the meaning of this word reveals that it means “an adult lion, having paired, in search of his prey (Nahum 2:12; 2 Sam 17:10; Num 23:24).” This is from The Witness of the Stars, a work that views the constellation Leo as a symbol of the Messiah. A particularly relevant passage: “The brightest star… marks the heart of the Lion (hence sometimes called by the moderns, Cor Leonis, the heart of the Lion).” Cor Leonis, Corleone. Is this the “Word” you meant, T. S.?
Tuesday, March 4, 2003
Tuesday March 4, 2003
Fearful Symmetry
I just Googled this phrase and found the following site, which turns out to be related to my previous entry on the Bead Game and the death of John P. Thompson.
Fearful Symmetry:
The Music Master’s Lecture,
by Daniel d’Quincy.
This in turn links to an excerpt from The Glass Bead Game that includes this passage:
“I suddenly realized that in the language, or at any rate in the spirit of the Glass Bead Game, everything actually was all-meaningful, that every symbol and combination of symbols led not hither and yon, not to single examples, experiments, and proofs, but into the center, the mystery and innermost heart of the world, into primal knowledge. Every transition from major to minor in a sonata, every transformation of a myth or a religious cult, every classical or artistic formulation was, I realized in that flashing moment, if seen with a truly meditative mind, nothing but a direct route into the interior of the cosmic mystery, where in the alternation between inhaling and exhaling, between heaven and earth, between Yin and Yang, holiness is forever being created.”
It is very easy to get dangerously confused about holiness, but here are some relevant quotes:
“You will have to allow me to digress a bit in order to bring ourselves to a sufficiently elevated perspective… I warn you, it will require an attitude of playfulness on your part. Our approach will aim more at sincerity than seriousness. The attitude I’m aiming at is best expressed, I suppose, in the playing of a unique game, known by its German name as Das Glasperlenspiel, and which we may translate as the Glass Bead Game.”
— Daniel d’Quincy, Fearful Symmetry
“7:11”
— God himself said this, at least according to the previous entry and to my Jan. 28 entry, State of the Communion.
“Seven is heaven.”
— See my web page Eight is a Gate.
“An excellent example of a ‘universal’ in the sense of Charles Williams, Jung, or Plato is Hexagram 11 in China’s 3,000-year-old classic, the I Ching:
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‘Heaven and earth unite: |
— S. H. Cullinane, Plato, Pegasus, and the Evening Star
Thus we may associate the numbers 7 and 11 with the notions of heaven and peace; for a somewhat darker association of the time 7:11 with Kali as Time the Destroyer, see my last entry and also my previous entries
Fat Man and Dancing Girl (Feb. 18, 2003), and
Time and Eternity (Feb. 1, 2003).
Monday, January 20, 2003
Monday January 20, 2003
Shine On, Robinson Jeffers
"…be in nothing so moderate as in love of man,
a clever servant, insufferable master.
There is the trap that catches noblest spirits,
that caught — they say — God, when he walked on earth."
— Shine, Perishing Republic, by Robinson Jeffers
Robinson Jeffers died at Big Sur, California, on January 20, 1962 — a year to the day after Robert Frost spoke at the Kennedy inauguration.
"The poetry of Robinson Jeffers shines with a diamond's brilliance when he depicts Nature's beauty and magnificence. His verse also flashes with a diamond's hardness when he portrays human pain and folly."
— Gary Suttle
"Praise Him, He hath conferred aesthetic distance
Upon our appetites, and on the bloody
Mess of our birthright, our unseemly need,
Imposed significant form. Through Him the brutes
Enter the pure Euclidean kingdom of number…."
— Howard Nemerov,
Grace To Be Said at the Supermarket
"Across my foundering deck shone
A beacon, an eternal beam. | Flesh fade, and mortal trash
Fáll to the resíduary worm; | world's wildfire, leave but ash:
In a flash, at a trumpet crash,
I am all at once what Christ is |, since he was what I am, and
Thís Jack, jóke, poor pótsherd, | patch, matchwood,
immortal diamond,
Is immortal diamond."
— Gerard Manley Hopkins,
That Nature is a Heraclitean Fire and of the Comfort of the Resurrection
"In the last two weeks, I've been returning to Hopkins. Even in the 'world's wildfire,' he asserts that 'this Jack, joke, poor potsherd, patch, matchwood, immortal diamond,/Is immortal diamond.' A comfort."
— Michael Gerson, head White House speechwriter,
in Vanity Fair, May 2002, page 162
"There's none but truth can stead you. Christ is truth."
— Gerard Manley Hopkins
"The rock cannot be broken. It is the truth."
— Wallace Stevens
"My ghost you needn't look for; it is probably
Here, but a dark one, deep in the granite…."
— Robinson Jeffers, Tor House
On this date in 1993, the inauguration day of William Jefferson Clinton, Audrey Hepburn died.
"…today, the Rock cries out to us, clearly, forcefully…."
— Maya Angelou, January 20, 1993
"So, purposing each moment to retire,
She linger'd still. Meantime, across the moors,
Had come young Porphyro, with heart on fire"
— John Keats, The Eve of St. Agnes (January 20), IX
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Top view of |
Top view of |
What you see with a Hearts On Fire diamond is an unequalled marriage of math and physics, resulting in the world's most perfectly cut diamond. |
"Eightpointed symmetrical signs are ancient symbols for the Venus goddess or the planet Venus as either the Morning star or the Evening star."
— Symbols.com
"Set me as a seal upon your heart, as a seal upon your arm; for love is strong as death, passion fierce as the grave. Its flashes are flashes of fire, a raging flame."
— Song of Solomon
"The last words from the people in the towers and on the planes, over and over again, were 'I love you.' Over and over again, the message was the same, 'I love you.' …. Perhaps this is the loudest chorus from The Rock: we are learning just how powerful love really is, even in the face of death."
— The Rev. Kenneth E. Kovacs
"Then I'll get on my knees and pray
We don't get fooled again."
— The Who
See also my note, "Bright Star," of October 23, 2002.
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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
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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
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