Sunday, October 31, 2010
Diamond Theorem in Norway
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A Year Later
From this date last year—
Saturday, October 31, 2009Happy Harvard Halloween
Related material: This journal on the birthday of Kate Jackson ("Satan’s School for Girls") this year and in 2005. For more literary depth, see Spider Girl references on March 1, 2005 and August 2, 2009, as well as Raiders of the Lost Well (Feb. 18, 2009). Related religious symbolism: Follow the Harvard links of October 28 ("serious" and then "de facto university motto. [1]"). |
"By these Festival-rites, from the Age that is past,
To the Age that is waiting before…"
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Heaven’s Gate continues
In memory of Dutch author Harry Mulisch…
Mulisch died at his home in Amsterdam on the evening of October 30.
The Discovery of Heaven was made into a film in 2001 by Jeroen Krabbé,
brother of Tim Krabbé. The latter is the author of the novel The Cave
(1997, first published in English in 2000 by Farrar, Straus and Giroux).
The Cave is notable for a phrase, "a hole in time."
See also "starflight" in this journal.
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ART WARS —
Keanu vs. the Devil, continued
Al Pacino and Keanu Reeves in Devil's Advocate
For Keanu —
For Keanu's mentor —
… There is a Cave
Within the Mount of God, fast by his Throne,
Where light and darkness in perpetual round
Lodge and dislodge by turns, which makes through Heav'n
Grateful vicissitude, like Day and Night….
— Paradise Lost , by John Milton
|
Click on figure for details. |
Al Pacino in Devil's Advocate |
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Saturday, October 30, 2010
The Fall
On the recent death of prominent Israeli biblical archaeologist Ehud Netzer—
Matti Friedman, AP story at Yahoo News —
"Netzer was speaking with colleagues at the site on Sunday when a wooden safety railing broke and he fell several yards, suffering critical injuries, according to David Amit, a senior archaeologist at the Israel Antiquities Authority. He was rushed to a hospital but did not recover, and died Thursday."
Google Translate version of a ynet.co.il report in Hebrew —
"On Monday, after a staff meeting Excavators Herodion, sat Professor Netzer on what is called a steel pipe … Theatre Royal cabin Herodium. Witnesses said that the mood was very cheerful – until suddenly broke a few screws and railing, archaeologist fell backwards on my back and hurt himself in the head. Then fell again, and hurt the neck vertebrae."
Hillel Fendel at IsraelNationalNews.com —
"Prof. Netzer slipped and fell on Tuesday, sustaining severe injuries."
So, according to Jewish legend-in-the-making, this biblical fall may have occurred on Sunday, Monday, or Tuesday. There seems to be agreement at least that the resulting death occurred on Thursday.
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Keanu vs. the Devil
(Continued from Little Buddha (1994), The Matrix (1999), and Constantine (2005))
This post was suggested by yesterday's post on Habermas and by his 1962 book The Structural Transformation of the Public Sphere (English translation, 1989).
The "public sphere" of Habermas has come to pass; it is, of course, the World-Wide Web.
For October 30, the day leading up to Devil's Night, a more private sphere—though in a public setting— seems appropriate…
The Day the Earth Stood Still (2008)
A Keanu Reeves scene related to this image—
"The low point of the movie’s persuasiveness is the single scene with Professor Barnhardt (John Cleese) — in the original an Einstein-like scientist who impresses Klaatu with his highly evolved thinking, here a caricature of professorial enlightenment. Helen decides to bring Klaatu to Professor Barnhardt when Klaatu professes his disappointment with earth’s leaders. 'Those aren’t our leaders!' she protests earnestly. 'Let me take you to one of our leaders!'"
A perhaps more persuasive scene, from today's New York Times—
Prize in Hand, He Keeps His Eye on Teaching
Nobel winner Mario Vargas Llosa teaches
a seminar on Borges at Princeton
(Photo by James Leynse for The New York Times )
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Friday, October 29, 2010
Kulturkampf at the Times
Some background:
Stanley Fish in the Times on April 12, 2010.
See also this journal on that date —
"Fact and fiction weave in and out of novels
like a shell game." –R. B. Kitaj
Not just novels.
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Church Logic
"The law of excluded middle is the logical principle in
accordance with which every proposition is either true or
false. This principle is used, in particular, whenever a proof
is made by the method of reductio ad absurdum . And it is
this principle, also, which enables us to say that the denial of
the denial of a proposition is equivalent to the assertion of
the proposition."
— Alonzo Church, "On the Law of Excluded Middle,"
Bulletin of the American Mathematical Society ,
Vol. 34, No. 1 (Jan.–Feb. 1928), pp. 75–78
It seems reasonable to define a Euclidean geometry as one describing what mathematicians now call a Euclidean space.
What sort of geometry
is the following?
Four points and six lines,
with parallel lines indicated
by being colored alike.
Consider the proposition "The finite geometry with four points and six lines is non-Euclidean."
Consider its negation. Absurd? Of course.
"Non-Euclidean," therefore, does not apply only to geometries that violate Euclid's parallel postulate.
The problem here is not with geometry, but with writings about geometry.
"In the plainest terms, non-Euclidean geometry
took something that was rather simple and straightforward
(Euclidean geometry) and made it endlessly more difficult."
Had the Greeks investigated finite geometry before Euclid came along, the reverse would be true.
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Word Study
Commentary on Revelation 6:8—
And I looked, and behold a pale horse:
and his name that sat on him was Death,
and Hell followed with him.
| Vincent's Word Studies
Pale (χλωρὸς) Only in Revelation, except Mark 6:39. Properly, greenish-yellow, like young grass or unripe wheat. Homer applies it to honey, and Sophocles to the sand. Generally, pale, pallid. Used of a mist, of sea-water, of a pale or bilious complexion. Thucydides uses it of the appearance of persons stricken with the plague (ii., 49). In Homer it is used of the paleness of the face from fear, and so as directly descriptive of fear ("Iliad," x., 376; xv., 4). Of olive wood ("Odyssey," ix., 320, 379) of which the bark is gray. Gladstone says that in Homer it indicates rather the absence than the presence of definite color. In the New Testament, always rendered green, except here. See Mark 6:39; Revelation 8:7; Revelation 9:4. Hell Properly, Hades. The realm of the dead personified. See on Matthew 16:18. |
Related material:
Death toll climbs to 394 in Indonesian tsunami
See also, in this journal, Pale Rider and Hereafter.
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Thursday, October 28, 2010
A Sort of Mirror
"Whence God is to be understood as a sort of mirror in which all things succeeding one another in the whole course of time have images shining back, a mirror indeed directly beholding itself and all the images existing in it."
— Peter de Rivo, quoted in Wild Materialism , p. 102 (below)
"The stakes were high…. …the status, indeed, the ownership, of logic, a term common to the Faculties of Theology and Art, was in dispute…."
— Wild Materialism: The Ethic of Terror and the Modern Republic , by Jacques Lezra, Fordham University Press, 2010, chapter on "The Logic of Sovereignty," page 102
See also Borges on the Aleph.
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Wednesday, October 27, 2010
Lyrics
"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…"
"Un cofre de gran riqueza
Hallaron dentro un pilar,
Dentro del, nuevas banderas
Con figuras de espantar"
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Language and Form
In memory of S. Neil Fujita, who died last Saturday—
Fujita did the cover art for this edition.
Another book by Langer with a striking cover (artist unknown)—
Note that the background may be constructed from
any of four distinct motifs. For another approach to these
motifs in a philosophical context, see June 8, 2010.
"Visual forms— lines, colors, proportions, etc.— are just as capable of articulation , i.e. of complex combination, as words. But the laws that govern this sort of articulation are altogether different from the laws of syntax that govern language. The most radical difference is that visual forms are not discursive . They do not present their constituents successively, but simultaneously, so the relations determining a visual structure are grasped in one act of vision."
— Susanne K. Langer, Philosophy in a New Key
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Review
A mathematical review—
— Gian-Carlo Rota
A science fiction—
— Alfred Bester
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Monday, October 25, 2010
The Embedding*
A New York Times "The Stone" post from yesterday (5:15 PM, by John Allen Paulos) was titled—
Stories vs. Statistics
Related Google searches—
"How to lie with statistics"— about 148,000 results
"How to lie with stories"— 2 results
What does this tell us?
Consider also Paulos's phrase "imbedding the God character." A less controversial topic might be (with the spelling I prefer) "embedding the miraculous." For an example, see this journal's "Mathematics and Narrative" entry on 5/15 (a date suggested, coincidentally, by the time of Paulos's post)—
* Not directly related to the novel The Embedding discussed at Tenser, said the Tensor on April 23, 2006 ("Quasimodo Sunday"). An academic discussion of that novel furnishes an example of narrative as more than mere entertainment. See Timothy J. Reiss, "How can 'New' Meaning Be Thought? Fictions of Science, Science Fictions," Canadian Review of Comparative Literature , Vol. 12, No. 1, March 1985, pp. 88-126. Consider also on this, Picasso's birthday, his saying that "Art is a lie that makes us realize truth…."
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Saturday, October 23, 2010
Paranormal Jackass
The follow-up to last year's runaway horror hit, "Paranormal Activity 2," kicked off its first weekend in theaters with a major haul. The creepy tale… pulled in $20.1 million on Friday.
Trailing behind "Paranormal" is last week's box-office busting debut "Jackass 3D. " The prank-fest, which landed about $50 million its first weekend in theaters, slipped to the second-place slot….
…
The Clint Eastwood-helmed ensemble drama "Hereafter" landed in fourth place. Exploring the lives of three people who are dealing with death and the afterlife in several ways, including the story of a psychic played by Matt Damon, the screen legend's latest turn in the director's chair made approximately $4.1 million on Friday.
Related material—
Margaret Atwood on Lewis Hyde's Trickster Makes This World: Mischief, Myth, and Art—
"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)
What is "the next world"? It might be the Underworld….
The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation and art all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254) If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist. Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.
George P. Hansen on Martin Gardner and the paranormal.
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Friday, October 22, 2010
But Seriously…
Happy Birthday, Jean Simmons … Jan. 31, 2008
Elmer Gantry … Hollywood's view of the Foursquare Church
Resurrection … An August 2003 post inspired by KHYI, then broadcasting from Plano, Texas
For what it's worth, some free advice for Matt Damon…
GET QUOTES
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Moreover
Google News this afternoon—
Related material:
- Celebration of Mind (Oct. 20)
- Problem Picture (Oct. 21)
- Hereafter (Oct. 22)
- The Gypsy in The French Mathematician
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Thursday, October 21, 2010
St. Ursula’s Day
Mathematics and Narrative continued
A search for Ursula in this journal yields a story…
“The main character is a slave woman who discovers new patterns in the mosaics.”
Other such stories: Plato’s Meno and Changing Woman —
|
“Kaleidoscope turning…
Shifting pattern within — Roger Zelazny, Eye of Cat |
Philosophical postscript—
“That Lévi-Strauss should have been able to transmute the romantic passion of Tristes Tropiques into the hypermodern intellectualism of La Pensée Sauvage is surely a startling achievement. But there remain the questions one cannot help but ask. Is this transmutation science or alchemy? Is the ‘very simple transformation’ which produced a general theory out of a personal disappointment real or a sleight of hand? Is it a genuine demolition of the walls which seem to separate mind from mind by showing that the walls are surface structures only, or is it an elaborately disguised evasion necessitated by a failure to breach them when they were directly encountered? Is Lévi-Strauss writing, as he seems to be claiming in the confident pages of La Pensée Sauvage, a prolegomenon to all future anthropology? Or is he, like some uprooted neolithic intelligence cast away on a reservation, shuffling the debris of old traditions in a vain attempt to revivify a primitive faith whose moral beauty is still apparent but from which both relevance and credibility have long since departed?”
— Clifford Geertz, conclusion of “The Cerebral Savage: On the Work of Claude Lévi-Strauss“
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Line
The NY Times recently discussed "Longing for the Lines That Had Us at Hello"
and “We land in Albuquerque at 4 a.m. That’s strictly a 9 o’clock town.”
And so…
"How much story do you want?" — George Balanchine
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Problem Picture
The above image was suggested by yesterday's
Celebration of Mind and by Plan 9 From Outer Space
in yesterday's New York Times and in this journal.
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Wednesday, October 20, 2010
Celebration of Mind
"Martin Gardner passed away on May 22, 2010."
Imaginary movie poster from stoneship.org
Context— The Gardner Tribute.
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Tuesday, October 19, 2010
Savage Logic continued…
CHAPTER V
"This is an account of the discrete groups generated by reflections…."
— Regular Polytopes , by H.S.M. Coxeter (unabridged and corrected 1973 Dover reprint of the 1963 Macmillan second edition)
"In this article, we begin a theory linking hyperplane arrangements and invariant forms for reflection groups over arbitrary fields…. Let V be an n-dimensional vector space over a field F, and let G ≤ Gln (F) be a finite group…. An element of finite order in Gl(V ) is a reflection if its fixed point space in V is a hyperplane, called the reflecting hyperplane. There are two types of reflections: the diagonalizable reflections in Gl(V ) have a single nonidentity eigenvalue which is a root of unity; the nondiagonalizable reflections in Gl(V ) are called transvections and have determinant 1 (note that they can only occur if the characteristic of F is positive)…. A reflection group is a finite group G generated by reflections."
— Julia Hartmann and Anne V. Shepler, "Reflection Groups and Differential Forms," Mathematical Research Letters , Vol. 14, No. 6 (Nov. 2007), pp. 955-971
"… the class of reflections is larger in some sense over an arbitrary field than over a characteristic zero field. The reflections in Gl(V ) not only include diagonalizable reflections (with a single nonidentity eigenvalue), but also transvections, reflections with determinant 1 which can not be diagonalized. The transvections in Gl(V ) prevent one from developing a theory of reflection groups mirroring that for Coxeter groups or complex reflection groups."
— Julia Hartmann and Anne V. Shepler, "Jacobians of Reflection Groups," Transactions of the American Mathematical Society , Vol. 360, No. 1 (2008), pp. 123-133 (Pdf available at CiteSeer.)
See also A Simple Reflection Group of Order 168 and this morning's Savage Logic.
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Savage Logic…
and the New York Lottery
A search in this journal for yesterday's evening number in the New York Lottery, 359, leads to…
The Cerebral Savage:
On the Work of Claude Lévi-Strauss
by Clifford Geertz
Shown below is 359, the final page of Chapter 13 in
The Interpretation of Cultures: Selected Essays by Clifford Geertz,
New York, 1973: Basic Books, pp. 345-359 —
This page number 359 also appears in this journal in an excerpt from Dan Brown's novel Angels & Demons—
See this journal's entries for March 1-15, 2009, especially…
| Sunday, March 15, 2009 5:24 PM
Philosophy and Poetry: The Origin of Change A note on the figure
"Two things of opposite natures seem to depend On one another, as a man depends On a woman, day on night, the imagined On the real. This is the origin of change. Winter and spring, cold copulars, embrace And forth the particulars of rapture come." -- Wallace Stevens, "Notes Toward a Supreme Fiction," Canto IV of "It Must Change" Sunday, March 15, 2009 11:00 AM Ides of March Sermon: Angels, Demons,
"Symbology" "On Monday morning, 9 March, after visiting the Mayor of Rome and the Municipal Council on the Capitoline Hill, the Holy Father spoke to the Romans who gathered in the square outside the Senatorial Palace…
'… a verse by Ovid, the great Latin poet, springs to mind. In one of his elegies he encouraged the Romans of his time with these words: "Perfer et obdura: multo graviora tulisti." "Hold out and persist: (Tristia, Liber V, Elegia XI, verse 7).'" This journal
on 9 March:
Note the color-interchange Related material: |
The symmetry of the yin-yang symbol, of the diamond-theorem symbol, and of Brown's Illuminati Diamond is also apparent in yesterday's midday New York lottery number (see above).
"Savage logic works like a kaleidoscope…." — Clifford Geertz on Lévi-Strauss
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Monday, October 18, 2010
For St. Luke’s Day —
The Turning
"To everything, turn, turn, turn…
… there is a season, turn, turn, turn…"
For less turning and more seasons, see a search in this journal for
fullness + multitude + "cold mountain."
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Sunday, October 17, 2010
An Intricate Reflection
"Humanity's fascination with numbers is ancient and complex. Our present relationship with numbers reveals both a highly developed tool and a highly developed user, working together to measure, create, and predict both ourselves and the world around us. But like every symbiotic couple, the tool we would like to believe is separate from us (and thus objective) is actually an intricate reflection of our thoughts, interests, and capabilities."
— The Secret Lives of Numbers, by New Radio and Performing Arts
(recommended on the Frivolous Linkages page at Daniel Gilbert's Harvard website)
Other linkages:
New York Lottery on October 16: Midday 706, Evening 684.
Related material — 7/06, 2007, and post no. 684 in this journal.
The above "Secret Lives of Numbers" quotation was suggested by Gilbert's "Magic by Numbers" op-ed piece in today's New York Times—
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Saturday, October 16, 2010
Quaternion Day
Brightness at Noon continued
— Sir William Rowan Hamilton, Oct. 16, 1843
See also this journal on 1/09, 2010.
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The Mandelbrot Numbers
Benoît Mandelbrot died on Oct. 14.
— New York Lottery on Thursday, Oct. 14, 2010
Related material on 109: See 1/09, 2009.
Related material on 060: See Hexagram 60 of the I Ching and…
Margaret Atwood on Lewis Hyde's Trickster Makes This World: Mischief, Myth, and Art—
"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)
What is "the next world"? It might be the Underworld….
The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation and art all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254) If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist. Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.
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Friday, October 15, 2010
Mathematics and Narrative, continued
The Story of N
Roberta Smith in the New York Times of July 7, 2006—
Art Review
Endgame Art? It's Borrow, Sample and Multiply in an Exhibition at Bard College
"… The show has an endgame, end-time mood, as if we are looking at the end of the end of the end of Pop, hyperrealism and appropriation art. The techniques of replication and copying have become so meticulous that they are beside the point. This is truly magic realism: the kind you can't see, that has to be explained. It is also a time when artists cultivate hybridism and multiplicity and disdain stylistic coherence, in keeping with the fashionable interest in collectivity, lack of ego, the fluidity of individual identity. But too often these avoidance tactics eliminate the thread of a personal sensibility or focus.
I would call all these strategies fear of form, which can be parsed as fear of materials, of working with the hands in an overt way and of originality. Most of all originality. Can we just say it? This far from Andy Warhol and Duchamp, the dismissal of originality is perhaps the oldest ploy in the postmodern playbook. To call yourself an artist at all is by definition to announce a faith, however unacknowledged, in some form of originality, first for yourself, second, perhaps, for the rest of us.
Fear of form above all means fear of compression— of an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible. With a few exceptions, forms of collage and assemblage dominate this show: the putting together (or simply putting side by side) of existing images and objects prevails. The consistency of this technique in two and three dimensions should have been a red flag for the curators. Collage has driven much art since the late 1970's. Lately, and especially in this exhibition, it often seems to have become so distended and pulled apart that its components have become virtually autonomous and unrelated, which brings us back to square one. This is most obvious in the large installations of graphic works whose individual parts gain impact and meaning from juxtaposition but are in fact considered distinct artworks."
Margaret Atwood on art and the trickster—
"The pleasures of fabulation, the charming and playful lie— this line of thought leads Hyde* to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation and art all come from the same ancient root, a word meaning 'to join,' 'to fit,' and 'to make.' If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist. Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart."
* Lewis Hyde, Trickster Makes This World: Mischief, Myth, and Art, Farrar Straus & Giroux, January 1998
Smith mentions "an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible."
Atwood mentions "a seamless whole."
For some related remarks, see "A Study in Art Education" and the central figure pictured above. (There "N" can stand for "number," "nine," or "narrative.")
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Thursday, October 14, 2010
Diamond Theory and Magic Squares
"A world of made
is not a world of born— pity poor flesh
and trees, poor stars and stones, but never this
fine specimen of hypermagical
ultraomnipotence."
— e. e. cummings, 1944
For one such specimen, see The Matrix of Abraham—
a 5×5 square that is hypermagical… indeed, diabolical.
Related material on the algebra and geometry underlying some smaller structures
that have also, unfortunately, become associated with the word "magic"—
- Finite Geometry of the Square and Cube
- Clifford Pickover on a 4×4 square
-
Christopher J. Henrich on the geometry of 4×4 magic squares
(without any mention of [1] above or related work dating back to 1976)
" … listen: there's a hell
of a good universe next door; let's go"
— e. e. cummings
Happy birthday, e. e.
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