“The About page contains detailed descriptions of the project….”
— The Illustris project on constructing a model of the universe
For the mathematics of a simpler traditional Chinese model
of everything, see
Definition: A diamond space — informal phrase denoting
a subspace of AG(6, 2), the six-dimensional affine space
over the two-element Galois field.
The reason for the name:
Click to enlarge.
Part I: The New Yorker
Passages from The New Yorker issue dated March 17, 2014—
"Both autism and psychopathy entail a lack of empathy. Psychologists, though, distinguish between the 'cognitive empathy' deficits of autism (difficulty understanding what emotions are, trouble interpreting other people’s nonverbal signs) and the 'emotional empathy' deficits of psychopathy (lack of concern about hurting other people, an inability to share their feelings). The subgroup of people with neither kind of empathy appears to be small, but such people may act out their malice in ways that can feel both guileless and brutal." — "The Reckoning," by Andrew Solomon
"The question of what constitutes a story is troublesome." — "Long Story Short," by Dana Goodyear
Part II: The New York Times
Part III: Log24
From New World Encyclopedia —
See also Tetragrammaton in this journal.
For further context, see Solomon's Cube and Oct. 16, 2013.
Meanwhile…
|
Log24 on Sunday, October 5, 2008— “In a game of chess, the knight’s move is unique because it alone goes around corners. In this way, it combines the continuity of a set sequence with the discontinuity of an unpredictable turn in the middle. This meaningful combination of continuity and discontinuity in an otherwise linear set of possibilities has led some to refer to the creative act of discovery in any field of research as a ‘knight’s move’ in intelligence.” Related material: Terence McKenna: “Schizophrenia is not a psychological disorder peculiar to human beings. Schizophrenia is not a disease at all but rather a localized traveling discontinuity of the space time matrix itself. It is like a travelling whirl-wind of radical understanding that haunts time. It haunts time in the same way that Alfred North Whitehead said that the color dove grey ‘haunts time like a ghost.’” Anonymous author: “‘Knight’s move thinking’ is a psychiatric term describing a thought disorder where in speech the usual logical sequence of ideas is lost, the sufferer jumping from one idea to another with no apparent connection. It is most commonly found in schizophrenia.” |
Related journalism—
"What's the 'S' stand for?" — Amy Adams
Last midnight's post quoted poet John Hollander
on Cervantes—
"… the Don’s view of the world is correct at midnight,
and Sancho’s at noon."
The post concluded with a figure that might, if
rotated slightly, be regarded as a sort of Star of
David or Solomon's Seal. The figure's six vertices
may be viewed as an illustration of Pascal's
"mystic hexagram."
Pacal's hexagram is usually described
as a hexagon inscribed in a conic
(such as a circle). Clearly the hexagon
above may be so inscribed.
The figure suggests that last midnight's Don be
played by the nineteenth-century mathematician
James Joseph Sylvester. His 1854 remarks on
the nature of geometry describe a different approach
to the Pascal hexagram—
| "… the celebrated theorem of Pascal known under the name of the Mystic Hexagram, which is, that if you take two straight lines in a plane, and draw at random other straight lines traversing in a zigzag fashion between them, from A in the first to B in the second, from B in the second to C in the first, from C in the first to D in the second, from D in the second to E in the first, from E in the first to F in the second and finally from F in the second back again to A the starting point in the first, so as to obtain ABCDEF a twisted hexagon, or sort of cat's-cradle figure and if you arrange the six lines so drawn symmetrically in three couples: viz. the 1st and 4th in one couple, the 2nd and 5th in a second couple, the 3rd and 6th in a third couple; then (no matter how the points ACE have been selected upon one of the given lines, and BDF upon the other) the three points through which these three couples of lines respectively pass, or to which they converge (as the case may be) will lie all in one and the same straight line." |
For a Sancho view of Sylvester's "cat's cradle," see some twentieth-century
remarks on "the most important configuration of all geometry"—
"Now look, your grace," said Sancho,
"what you see over there aren't giants,
but windmills, and what seems to be arms
are just their sails, that go around in the wind
and turn the millstone."
"Obviously," replied Don Quijote,
"you don't know much about adventures.”
Beneath the word "When" above, there appears
the date of a journal post— "July 27, 2012."
A check of synchronicity for this journal on that date
yields two posts related to this morning's remarks.
The configurations recently discussed in
Classical Geometry in Light of Galois Geometry
are not unrelated to the 27 "Solomon's Seal Lines"
extensively studied in the 19th century.
See, in particular—
The following figures supply the connection of Henderson's six-set
to the Galois geometry previously discussed in "Classical Geometry…"—
From a review in the April 2013 issue of
Notices of the American Mathematical Society—
"The author clearly is passionate about mathematics
as an art, as a creative process. In reading this book,
one can easily get the impression that mathematics
instruction should be more like an unfettered journey
into a jungle where an individual can make his or her
own way through that terrain."
From the book under review—
"Every morning you take your machete into the jungle
and explore and make observations, and every day
you fall more in love with the richness and splendor
of the place."
— Lockhart, Paul (2009-04-01). A Mathematician's Lament:
How School Cheats Us Out of Our Most Fascinating and
Imaginative Art Form (p. 92). Bellevue Literary Press.
Kindle Edition.
Related material: Blackboard Jungle in this journal.
See also Galois Space and Solomon's Mines.
Last Wednesday's 11 PM post mentioned the
adjacency-isomorphism relating the 4-dimensional
hypercube over the 2-element Galois field GF(2) to
the 4×4 array made up of 16 square cells, with
opposite edges of the 4×4 array identified.
A web page illustrates this property with diagrams that
enjoy the Karnaugh property— adjacent vertices, or cells,
differ in exactly one coordinate. A brief paper by two German
authors relates the Karnaugh property to the construction
of a magic square like that of Dürer (see last Wednesday).
In a similar way (search the Web for Karnaugh + cube ),
vertex adjacency in the 6-dimensional hypercube over GF(2)
is isomorphic to cell adjacency in the 4x4x4 cube, with
opposite faces of the 4x4x4 cube identified.
The above cube may be used to illustrate some properties
of the 64-point Galois 6-space that are more advanced
than those studied by enthusiasts of "magic" squares
and cubes.
See
Those who prefer narrative to mathematics may
consult posts in this journal containing the word "Cuber."
In diamond-narrative news today…
"Among the low points of his career was his performance
in the disastrous 1985 remake of “King Solomon’s Mines….”
— David Belcher in today's online New York Times
The second Logos figure in the previous post
summarized affine group actions on partitions
that generate a group of about 1.3 trillion
permutations of a 4x4x4 cube (shown below)—
Click for further details.
Wikipedia on a magical ring—
Background— The Ring and the Stone, a story linked to here Wednesday.
"By then he was familiar with the work of the Vienna Actionists….
He once said that he had his first taste of the movement
when he heard the screams of his mother’s dental patients
from her office next door to the family’s apartment."
— Obituary of a Viennese artist who reportedly died Wednesday
For those who prefer fiction:
"Many Dimensions (1931) — An evil antiquarian illegally purchases
the fabled Stone of Suleiman (Williams uses this Muslim form
rather than the more familiar King Solomon) from its Islamic guardian
in Baghdad and returns to England to discover not only that the Stone
can multiply itself infinitely without diminishing the original, but that it
also allows its possessor to transcend the barriers of space and time."
— Wikipedia article on the author Charles Williams
(Not Olympus )
(Continued from Mythopoetic, a post of April 12)
This post was suggested by a 2010 film about fictional Olympians,
by today's New York Times obituaries, and by a bar brawl at the Olympian
New York Athletic Club in "the wee hours of April 13."
Rick Riordan in the image below advertises another large
"Demigod Gathering" on October 12, 2010.
The Riordan image is from a post at ComposersCave.com
made on October 3, 2010.
Applying Jung's principle of synchronicity to this demigod material,
we find the October 3, 2010, Log24 post Search for the Basic Picture
and the October 12, 2010, Log24 post King Solomon's Mind.
Note that the latter October date is that of the traditional
Columbus Day, and that the 2010 film of The Lightning Thief
was directed by Chris Columbus of 1492 Pictures.
The film's release was earlier in 2010, on February 12.
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
…. 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.
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.
"Is Space Digital?"
— Cover story, Scientific American magazine, February 2012
"The idea that space may be digital
is a fringe idea of a fringe idea
of a speculative subfield of a subfield."
— Physicist Sabine Hossenfelder
at her weblog on Feb. 5, 2012
"A quantization of space/time
is a holy grail for many theorists…."
— Peter Woit in a comment at his physics weblog today
See also
* See yesterday's Steiner's Systems.
The showmanship of Nicki Minaj at Sunday's
Grammy Awards suggested the above title,
that of a novel by the author of The Exorcist .
The Ninth Configuration —
The ninth* in a list of configurations—
"There is a (2d-1)d configuration
known as the Cox configuration."
— MathWorld article on "Configuration"
For further details on the Cox 326 configuration's Levi graph,
a model of the 64 vertices of the six-dimensional hypercube γ6 ,
see Coxeter, "Self-Dual Configurations and Regular Graphs,"
Bull. Amer. Math. Soc. Vol. 56, pages 413-455, 1950.
This contains a discussion of Kummer's 166 as it
relates to γ6 , another form of the 4×4×4 Galois cube.
See also Solomon's Cube.
* Or tenth, if the fleeting reference to 113 configurations is counted as the seventh—
and then the ninth would be a 153 and some related material would be Inscapes.
“Examples galore of this feeling must have arisen in the minds of the people who extended the Magic Cube concept to other polyhedra, other dimensions, other ways of slicing. And once you have made or acquired a new ‘cube’… you will want to know how to export a known algorithm , broken up into its fundamental operators , from a familiar cube. What is the essence of each operator? One senses a deep invariant lying somehow ‘down underneath’ it all, something that one can’t quite verbalize but that one recognizes so clearly and unmistakably in each new example, even though that example might violate some feature one had thought necessary up to that very moment. In fact, sometimes that violation is what makes you sure you’re seeing the same thing , because it reveals slippabilities you hadn’t sensed up till that time….
… example: There is clearly only one sensible 4 × 4 × 4 Magic Cube. It is the answer; it simply has the right spirit .”
— Douglas R. Hofstadter, 1985, Metamagical Themas: Questing for the Essence of Mind and Pattern (Kindle edition, locations 11557-11572)
See also Many Dimensions in this journal and Solomon’s Cube.
Some related resources from Malcolm Lowry—
"…his eyes ranged the Consul's books disposed quite neatly… on high shelves around the walls: Dogme et Ritual de la Haute Magie , Serpent and Siva Worship in Central America , there were two long shelves of this, together with the rusty leather bindings and frayed edges of the numerous cabbalistic and alchemical books, though some of them looked fairly new, like the Goetia of the Lemegaton of Solomon the King , probably they were treasures, but the rest were a heterogeneous collection…."
— Under the Volcano , Chapter VI
— and from Matilde Marcolli—
Seven books on analytical psychology
See also Marcolli in this morning's previous post, The Garden Path.
For the relevance of alchemy to form, see Alchemy in this journal.
This year's Black Friday Prize for Literature went to…
The title describes two philosophical events (one major, one minor) from the same day— Thursday, July 5, 2007. Some background from 2001:
"Are the finite simple groups, like the prime numbers, jewels strung on an as-yet invisible thread? And will this thread lead us out of the current labyrinthine proof to a radically new proof of the Classification Theorem?" (p. 345)
— Ronald Solomon, "A Brief History of the Classification of Finite Simple Groups," Bulletin of the American Mathematical Society , Vol. 38 No. 3 (July 2001), pp. 315-352
The major event— On July 5, 2007, Cambridge University Press published Robert T. Curtis's Symmetric Generation of Groups.*
Curtis's book does not purport to lead us out of Solomon's labyrinth, but its publication date may furnish a Jungian synchronistic clue to help in exiting another nightmare labyrinth— that of postmodernist nominalism.
The minor event— The posting of Their Name is Legion in this journal on July 5, 2007.
* This is the date given by Amazon.co.uk and by BookDepository.com. Other sources give a later July date, perhaps applicable to the book's publication in the U.S. rather than Britain.
From http://msa-x.msa-x.org/?p=1064 —
"Exit Art New York, The Labyrinth Wall:
From Mythology to Reality" —
From tonight's online New York Times obituaries —
Ms. Ingberman died Wednesday. Related material—
Symmetry (Wednesday), Design (Thursday), Solomon's Labyrinth (Friday).
See also an essay by John Haber —
"Exit Art may yet offer an alternative: shut them up in the labyrinth, with the Minotaur and, as in Iraq, no Ariadne's thread to guide them out. Jeannette Ingberman and Papo Colo line the space with 'The Labyrinth Wall: From Mythology to Reality,' inviting fifty-one artists to cover its sixty-two panels."
— "Marlene Dumas, The Labyrinth Wall, and Emily Jacir"
Haber (ibid .) also describes artist Marlene Dumas, a recent winner of a Royal Swedish Academy Schock Prize. For a fellow Schock winner— mathematician Michael Aschbacher— see Thursday's Design.)
* For another version of the title, see this morning's front page.
The previous posts, Design and Solomon's Labyrinth,
refer, respectively, to concepts of Tits ("buildings") and
of Thompson (imagining a future Origin of Groups ).
This suggests a review of Norway's 2008 Abel Prize,
presented to Thompson and Tits on May 20, 2008.
Poster display before the 2008 Abel Prize ceremony—
A poster of sorts in this journal on the same day, May 20, 2008—
|
Bright Star – … Todo lo sé por el lucero puro – Rubén Darío 
Image adapted from |
Related material— Epiphany Revisited, Four Winds,
and Where Entertainment is God (continued).
"… the Jews have discovered a way to access a fourth spatial dimension."
— Clifford Pickover, description of his novel Jews in Hyperspace
"If you have built castles in the air, your work need not be lost;
that is where they should be. Now put the foundations under them.”
— Henry David Thoreau
"King Solomon's Mines," 1937—
The image above is an illustration from "Romancing the Hyperspace," May 4, 2010.
Happy birthday to the late Salomon Bochner.
This screenshot was suggested by the word "metalibrarianship" in a Bloomsday 2011 post by artist Steve Richards.
Note the words in the search field.
The phrase "Dublin Core metadata" refers to a city in Ohio, not in Ireland.
Related material— The highlighted phrase below is in the epigraph to Borges's "The Library of Babel"—
"I would, for these causes, wish him that is melancholy, to use both humane and divine authors, voluntarily to impose some taske upon himself, to divert his melancholy thoughts; to study the art of memory, Cosmus Rosselius, Pet. Ravennas, Scenkelius Detectus, or practise brachygraphy, &c. that will aske a great deal of attention: or let him demonstrate a proposition in Euclide in his five last books, extract a square root, or studie Algebra: than which, as gClavius holds, in all humane disciplines nothing can be more excellent and pleasant, so abstruse and recondite, so bewitching, so miraculous, so ravishing, so easie withal and full of delight, omnem humanum captum superare videtur . By this means you may define ex ungue leonem , as the diverbe is, by his thumb alone the bigness of Hercules, or the true dimensions of the great hColossus, Solomons temple, and Domitians amphitheater, out of a little part. By this art you may contemplate the variation of the 23 letters…."
g Ad. 2. definit.2. elem. In disciplinis humanis nihil praestantius reperitur: quippe miracula quaedam numerorum eruit tam abstrusa et recondita, tanta nihilo minus facilitate et voluptate, ut, &c.
h Which contained 1080000 weight of brass.
— The Anatomy of Melancholy, Part. 2, Sec. 2, Mem. 4
"Plato acknowledges how khora challenges our normal categories
of rational understanding. He suggests that we might best approach it
through a kind of dream consciousness."
—Richard Kearney, quoted here yesterday afternoon
"You make me feel like I'm living a teenage dream."
— Song at last night's Grammy awards
Richard Kiley in "Blackboard Jungle" (1955)
Note the directive on the blackboard.
Quoted here last year on this date—
Alexandre Borovik's Mathematics Under the Microscope (American Mathematical Society, 2010)—
"Once I mentioned to Gelfand that I read his Functions and Graphs ; in response, he rather sceptically asked me what I had learned from the book. He was delighted to hear my answer: 'The general principle of always looking at the simplest possible example.'….
So, let us look at the principle in more detail:
Always test a mathematical theory on the simplest possible example…
This is a banality, of course. Everyone knows it; therefore, almost no one follows it."
Related material— Geometry Simplified and A Simple Reflection Group of Order 168.
"Great indeed is the riddle of the universe.
Beautiful indeed is the source of truth."
– Shing-Tung Yau, Chairman,
Department of Mathematics, Harvard University
"Always keep a diamond in your mind."
– King Solomon at the Paradiso
Image from stoneship.org
The following is a new illustration for Cubist Geometries—
(For elementary cubism, see Pilate Goes to Kindergarten and The Eightfold Cube.
For advanced, see Solomon's Cube and Geometry of the I Ching .)
"Spaces and geometries, those which we perceive,
which we can’t perceive, or which only some of us perceive,
are a recurring theme in Against the Day ."
"大哉大哉 宇宙之谜
美哉美哉 真理之源"
"Great indeed is the riddle of the universe.
Beautiful indeed is the source of truth."
— Shing-Tung Yau, Chairman,
Department of Mathematics, Harvard University
"Always keep a diamond in your mind."
— King Solomon at the Paradiso
Image from stoneship.org
David Brooks's column in today's New York Times suggests a search for the origin of the phrase used as the title of a book Brooks is reviewing— All Things Shining , by philosophy professors Hubert Dreyfus and Sean Dorrance Kelly.
The phrase occurred, notably, in Terrence Malick's 1998 film "The Thin Red Line." I have not yet found an earlier usage.
(A search within the book for "title" yielded no relevant results, and such searches for "Malick" and for "Thin Red Line" yielded no results.)
For some background, see an August 20 weblog post by Kelly, Shining in Homer.
For some other background, see an August 20 post in this weblog.
Update: The phrase occurs in Stephen Mitchell's 1989 translation from the Odes of Solomon—
And you have made all things new;
you have showed me all things shining.
Suggested by Dan Brown's remarks in today's Science Times special section on puzzles—
|
For a fanciful linkage of the dreidel 's concept of chance
to The Stone 's concept of invariant law, note that the New York Lottery evening number on Dec. 1 (the beginning of Hanukkah) was 840. See also the number 840 in the final post (July 20, 2002) of a search for Solomon's Cube. |
|
The Dreidel Is Cast
The Nietzschean phrase "ruling and Caesarian spirits" occurred in yesterday morning's post "Novel Ending."
That post was followed yesterday morning by a post marking, instead, a beginning— that of Hanukkah 2010. That Jewish holiday, whose name means "dedication," commemorates the (re)dedication of the Temple in Jerusalem in 165 BC.
The holiday is celebrated with, among other things, the Jewish version of a die— the dreidel . Note the similarity of the dreidel to an illustration of The Stone* on the cover of the 2001 Eerdmans edition of Charles Williams's 1931 novel Many Dimensions—
For mathematics related to the dreidel , see Ivars Peterson's column on this date fourteen years ago.
For mathematics related (if only poetically) to The Stone , see "Solomon's Cube" in this journal.
Here is the opening of Many Dimensions—
For a fanciful linkage of the dreidel 's concept of chance to The Stone 's concept of invariant law, note that the New York Lottery yesterday evening (the beginning of Hanukkah) was 840. See also the number 840 in the final post (July 20, 2002) of the "Solomon's Cube" search.
Some further holiday meditations on a beginning—
Today, on the first full day of Hanukkah, we may or may not choose to mark another beginning— that of George Frederick James Temple, who was born in London on this date in 1901. Temple, a mathematician, was President of the London Mathematical Society in 1951-1953. From his MacTutor biography—
"In 1981 (at the age of 80) he published a book on the history of mathematics. This book 100 years of mathematics (1981) took him ten years to write and deals with, in his own words:-
those branches of mathematics in which I had been personally involved.
He declared that it was his last mathematics book, and entered the Benedictine Order as a monk. He was ordained in 1983 and entered Quarr Abbey on the Isle of Wight. However he could not stop doing mathematics and when he died he left a manuscript on the foundations of mathematics. He claims:-
The purpose of this investigation is to carry out the primary part of Hilbert's programme, i.e. to establish the consistency of set theory, abstract arithmetic and propositional logic and the method used is to construct a new and fundamental theory from which these theories can be deduced."
For a brief review of Temple's last work, see the note by Martin Hyland in "Fundamental Mathematical Theories," by George Temple, Philosophical Transactions of the Royal Society, A, Vol. 354, No. 1714 (Aug. 15, 1996), pp. 1941-1967.
The following remarks by Hyland are of more general interest—
"… one might crudely distinguish between philosophical and mathematical motivation. In the first case one tries to convince with a telling conceptual story; in the second one relies more on the elegance of some emergent mathematical structure. If there is a tradition in logic it favours the former, but I have a sneaking affection for the latter. Of course the distinction is not so clear cut. Elegant mathematics will of itself tell a tale, and one with the merit of simplicity. This may carry philosophical weight. But that cannot be guaranteed: in the end one cannot escape the need to form a judgement of significance."
— J. M. E. Hyland. "Proof Theory in the Abstract." (pdf)
Annals of Pure and Applied Logic 114, 2002, 43-78.
Here Hyland appears to be discussing semantic ("philosophical," or conceptual) and syntactic ("mathematical," or structural) approaches to proof theory. Some other remarks along these lines, from the late Gian-Carlo Rota—
See also "Galois Connections" at alpheccar.org and "The Galois Connection Between Syntax and Semantics" at logicmatters.net.
* Williams's novel says the letters of The Stone are those of the Tetragrammaton— i.e., Yod, He, Vau, He (cf. p. 26 of the 2001 Eerdmans edition). But the letters on the 2001 edition's cover Stone include the three-pronged letter Shin , also found on the dreidel . What esoteric religious meaning is implied by this, I do not know.
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.
David Levine's portrait of Arthur Koestler (see Dec. 30, 2009) —
See also this morning's post as well as
Monday's post quoting George David Birkhoff —
"If I were a Leibnizian mystic… I would say that…
God thinks multi-dimensionally — that is,
uses multi-dimensional symbols beyond our grasp."
(Continued from April 23, 2009, and February 13, 2010.)
Paul Valéry as quoted in yesterday’s post:
“The S[elf] is invariant, origin, locus or field, it’s a functional property of consciousness” (Cahiers, 15:170 [2: 315])
The geometric example discussed here yesterday as a Self symbol may seem too small to be really impressive. Here is a larger example from the Chinese, rather than European, tradition. It may be regarded as a way of representing the Galois field GF(64). (“Field” is a rather ambiguous term; here it does not, of course, mean what it did in the Valéry quotation.)
From Geometry of the I Ching—
The above 64 hexagrams may also be regarded as
the finite affine space AG(6,2)— a larger version
of the finite affine space AG(4,2) in yesterday’s post.
That smaller space has a group of 322,560 symmetries.
The larger hexagram space has a group of
1,290,157,424,640 affine symmetries.
From a paper on GL(6,2), the symmetry group
of the corresponding projective space PG(5,2),*
which has 1/64 as many symmetries—
For some narrative in the European tradition
related to this geometry, see Solomon’s Cube.
* Update of July 29, 2011: The “PG(5,2)” above is a correction from an earlier error.
Paul Robeson in
"King Solomon's Mines," 1937—
The image above is an illustration from
"Romancing the Hyperspace," May 4, 2010.
This illustration, along with Georgia Brown's
song from "Cabin in the Sky"—
"There's honey in the honeycomb"—
suggests the following picture.
"What might have been and what has been
Point to one end, which is always present."
— Four Quartets
Romancing the
Non-Euclidean Hyperspace
Backstory —
Mere Geometry, Types of Ambiguity,
Dream Time, and Diamond Theory, 1937
For the 1937 grid, see Diamond Theory, 1937.
The grid is, as Mere Geometry points out, a non-Euclidean hyperspace.
For the diamonds of 2010, see Galois Geometry and Solomon’s Cube.
It is well known that the seven
Similarly, recent posts* have noted that the thirteen
These three cubes, with 8, 27, and 64 subcubes, thus serve as geometric models in a straightforward way– first as models of finite linear spaces, hence as models for small Galois geometries derived from the linear spaces. (The cubes with 8 and 64 subcubes also serve in a less straightforward, and new, way as finite-geometry models– see The Eightfold Cube, Block Designs, and Solomon's Cube.)
A group of collineations** of the 21-point plane is one of two nonisomorphic simple groups of order 20,160. The other is the linear group acting on the linear 4-space over the two-element Galois field GF(2). The 1899 paper establishing the nonisomorphism notes that "the expression Galois Field is perhaps not yet in general use."
Coordinates of the 4×4×4 cube's subcubes can, of course, be regarded as elements of the Galois field GF(64).
The preceding remarks were purely mathematical. The "dreams" of this post's title are not. See…
See also Geometry of the I Ching and a search in this journal for
* February 27 and March 13
** G20160 in Mitchell 1910, LF(3,22) in Edge 1965
— Mitchell, Ulysses Grant, "Geometry and Collineation Groups
of the Finite Projective Plane PG(2,22),"
Princeton Ph.D. dissertation (1910)
— Edge, W. L., "Some Implications of the Geometry of
the 21-Point Plane," Math. Zeitschr. 87, 348-362 (1965)
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…
Jeremy Gray, Plato's Ghost: The Modernist Transformation of Mathematics, Princeton, 2008–
"Here, modernism is defined as an autonomous body of ideas, having little or no outward reference, placing considerable emphasis on formal aspects of the work and maintaining a complicated— indeed, anxious— rather than a naïve relationship with the day-to-day world, which is the de facto view of a coherent group of people, such as a professional or discipline-based group that has a high sense of the seriousness and value of what it is trying to achieve. This brisk definition…."
Brisk? Consider Caesar's "The die is cast," Gray in "Solomon's Cube," and yesterday's post—
This is the group of "8 rigid motions
generated by reflections in midplanes"
of Solomon's Cube.
Related material:
"… the action of G168 in its alternative guise as SL(3; Z/2Z) is also now apparent. This version of G168 was presented by Weber in [1896, p. 539],* where he attributed it to Kronecker."
— Jeremy Gray, "From the History of a Simple Group," in The Eightfold Way, MSRI Publications, 1998
Here MSRI, an acronym for Mathematical Sciences Research Institute, is pronounced "Misery." See Stephen King, K.C. Cole, and Heinrich Weber.
*H. Weber, Lehrbuch der Algebra, Vieweg, Braunschweig, 1896. Reprinted by Chelsea, New York, 1961.
Truth, Geometry, Algebra
The following notes are related to A Simple Reflection Group of Order 168.
1. According to H.S.M. Coxeter and Richard J. Trudeau
“There is a pleasantly discursive treatment of Pontius Pilate’s unanswered question ‘What is truth?’.”
— Coxeter, 1987, introduction to Trudeau’s The Non-Euclidean Revolution
1.1 Trudeau’s Diamond Theory of Truth
1.2 Trudeau’s Story Theory of Truth
2. According to Alexandre Borovik and Steven H. Cullinane
2.1 Coxeter Theory according to Borovik
2.1.1 The Geometry–
Mirror Systems in Coxeter Theory
2.1.2 The Algebra–
Coxeter Languages in Coxeter Theory
2.2 Diamond Theory according to Cullinane
2.2.1 The Geometry–
Examples: Eightfold Cube and Solomon’s Cube
2.2.2 The Algebra–
Examples: Cullinane and (rather indirectly related) Gerhard Grams
Summary of the story thus far:
Diamond theory and Coxeter theory are to some extent analogous– both deal with reflection groups and both have a visual (i.e., geometric) side and a verbal (i.e., algebraic) side. Coxeter theory is of course highly developed on both sides. Diamond theory is, on the geometric side, currently restricted to examples in at most three Euclidean (and six binary) dimensions. On the algebraic side, it is woefully underdeveloped. For material related to the algebraic side, search the Web for generators+relations+”characteristic two” (or “2“) and for generators+relations+”GF(2)”. (This last search is the source of the Grams reference in 2.2.2 above.)
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
Annals of Deconstruction —
Click on image for background.
Related material
for Baron Samedi —
The Found Symbol
Solomons Dance
Bridge caption from Flickr —
"William Hogarth theorized a perfect curve– his 'curve of beauty'– in the 18th century. I'm not sure the designer of this bridge took that into account, but Hogarth's curve is definitely there…."
Dance caption from Brooklyn Academy of Music —
"Elegant and uncompromising"
A graphic novel reviewed in the current Washington Post features Alfred North Whitehead and Bertrand Russell–
Related material:
Whitehead on Fano’s finite projective three-space:
“This is proved by the consideration of a three dimensional geometry in which there are only fifteen points.”
—The Axioms of Projective Geometry , Cambridge University Press, 1906
Further reading:
See Solomon’s Cube and the link at the end of today’s previous entry, then compare and contrast the above portraits of Whitehead and Russell with Charles Williams’s portraits of Sir Giles Tumulty and Lord Arglay in the novel Many Dimensions .
As noted here yesterday, Claude Levi-Strauss may have died on Devil's Night, on Halloween, or on All Saints' Day. He was apparently a myth-transformer to the end.
The Independent says today he died on Sunday, All Saints' Day. Its eulogy, by Adam Kuper, is well-written, noting that linguist Roman Jakobson was a source of Levi-Strauss's theory of oppositions in myth, and observing that
"… binary oppositions tend to accumulate to form structures…."
Yes, they do. Examples:
I. The structures in the Diamond Puzzle…
Click on image for Jungian background.
II: The structure on a recent cover of Semiotica…
The Semiotica article by mathematical linguist Solomon Marcus is a defense of the Levi-Strauss canonic formula mentioned here yesterday.
It is available online for $40.
A less expensive, and possibly more informative, look at oppositions in linguistics is available for free online in a 1984 master's thesis (pdf, 8+ mb)–
"Language, Linguistics, and Philosophy: A Comparison of the Work of Roman Jakobson and the Later Wittgenstein, with Some Attention to the Philosophy of Charles Saunders Peirce," by Miles Spencer Kimball.
A search for “Chinese Cube” (based on the the previous entry’s title) reveals the existence of a most interesting character, who…
“… has attempted in his books to produce a Science and Art of Reasoning using the simplest of the Platonic solids, the Cube. [His] model also parallels, in some ways, the Cube of Space constructed from the Sepher Yetzirah’s attributions for the Hebrew letters and their direction. [He] elucidated his theories at great length….”
— More…
For related remarks, see the link to Solomon’s Cube from the previous entry.
Then of course there is…
Click on figure for details.
From the Bulletin of the American Mathematical Society, Jan. 26, 2005:
What is known about unit cubes
by Chuanming Zong, Peking University
Abstract: Unit cubes, from any point of view, are among the simplest and the most important objects in n-dimensional Euclidean space. In fact, as one will see from this survey, they are not simple at all….
From Log24, now:
What is known about the 4×4×4 cube
by Steven H. Cullinane, unaffiliated
Abstract: The 4×4×4 cube, from one point of view, is among the simplest and the most important objects in n-dimensional binary space. In fact, as one will see from the links below, it is not simple at all.
The Klein Correspondence, Penrose Space-Time, and a Finite Model
Related material:
Monday's entry Just Say NO and a poem by Stevens,
Knight Moves
Deborah Solomon, New York Times Magazine, Sunday, June 27, 1999:
Christopher Knight, LA Times art critic, on Solomon:
A reference to Solomon’s piece appeared in this journal in 2003.
See also yesterday’s entry, today’s 9 AM entry, and (for the Academy) an example of knight’s move thinking.
The following remark this evening by Ann Hornaday of The Washington Post serves as an instant review of today's previous cinematic Log24 offering starring the late Patrick Swayze:
"Watch it, forget it, move on."
A perhaps more enduring tribute:
(Cover slightly changed.)
Background —
SAT
Part I:
Part II:
|
|
Part III:
From August 25th —
"Boo, boo, boo,
square root of two."
From Mitchell Stephens, author of a website mentioned here yesterday:
“This paper is designed to be a conversation….
The ideas are organized loosely around a single theme: the Roman leader Pompey’s forced entry into the most sacred place of the Jewish temple. At issue are the origins and prevalence of doubt, even at the heart of religion….
The paper will be initially presented, with comments and additions, to the working group on ‘Secularism, Religious Authority, and the Mediation of Knowledge’ of the Center for Religion and Media at New York University on December 8, 2006.”
From the paper itself:
“All Pompey’s intrusion into the Holy of Holies will leave behind is one sentence in Tacitus; still, it is not hard to imagine it as a media show. As he enters this hidden room in the Temple of those weird, unGreek, Asian, tribal Jews, this cosmopolitan, sophisticated Roman is not just the insensitive anthropologist. He wants, to continue our imagining, to display the lack of contents of the Holy of Holies in a museum, to take them, like the treasures of Tutankhamen’s tomb, on tour. This all-powerful Roman wields klieg lights; he brings the press. He exposes. His expedition is something of an exposé. The whole scene feels as if it might have been filmed: like Dorothy’s peek behind the curtain at the diminutive Wizard of Oz. It feels as if it might have been televised: like Geraldo Rivera’s opening of Al Capone’s ‘secret vault.’ Pompey has in common with all journalists a desire to shove a microphone in God’s face. He wants to rant about what he has learned on his blog.
In his desecration of the Holy of Holies, Pompey has with him, in other words, what Jacques Derrida, in his essay ‘Faith and Knowledge,’ calls the ‘powers of abstraction’: ‘deracination, delocalization, disincarnation, formalization, universalizing schematization, objectification, telecommunication etc.'”
Related material:
Solomon's Cube
continued
"There is a book… called A Fellow of Trinity, one of series dealing with what is supposed to be Cambridge college life…. There are two heroes, a primary hero called Flowers, who is almost wholly good, and a secondary hero, a much weaker vessel, called Brown. Flowers and Brown find many dangers in university life, but the worst is a gambling saloon in Chesterton run by the Misses Bellenden, two fascinating but extremely wicked young ladies. Flowers survives all these troubles, is Second Wrangler and Senior Classic, and succeeds automatically to a Fellowship (as I suppose he would have done then). Brown succumbs, ruins his parents, takes to drink, is saved from delirium tremens during a thunderstorm only by the prayers of the Junior Dean, has much difficulty in obtaining even an Ordinary Degree, and ultimately becomes a missionary. The friendship is not shattered by these unhappy events, and Flowers's thoughts stray to Brown, with affectionate pity, as he drinks port and eats walnuts for the first time in Senior Combination Room."
— G. H. Hardy, A Mathematician's Apology
"The Solomon Key is the working title of an unreleased novel in progress by American author Dan Brown. The Solomon Key will be the third book involving the character of the Harvard professor Robert Langdon, of which the first two were Angels & Demons (2000) and The Da Vinci Code (2003)." — Wikipedia
"One has O+(6) ≅ S8, the symmetric group of order 8! …."
— "Siegel Modular Forms and Finite Symplectic Groups," by Francesco Dalla Piazza and Bert van Geemen, May 5, 2008, preprint.
"The complete projective group of collineations and dualities of the [projective] 3-space is shown to be of order [in modern notation] 8! …. To every transformation of the 3-space there corresponds a transformation of the [projective] 5-space. In the 5-space, there are determined 8 sets of 7 points each, 'heptads' …."
— George M. Conwell, "The 3-space PG(3, 2) and Its Group," The Annals of Mathematics, Second Series, Vol. 11, No. 2 (Jan., 1910), pp. 60-76
"It must be remarked that these 8 heptads are the key to an elegant proof…."
— Philippe Cara, "RWPRI Geometries for the Alternating Group A8," in Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference (July 16-21, 2000), Kluwer Academic Publishers, 2001, ed. Aart Blokhuis, James W. P. Hirschfeld, Dieter Jungnickel, and Joseph A. Thas, pp. 61-97
Diamond-Faceted:
Transformations
of the Rock
|
A discussion of Stevens's late poem "The Rock" (1954) in Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 120:
For Stevens, the poem "makes meanings of the rock." In the mind, "its barrenness becomes a thousand things/And so exists no more." In fact, in a peculiar irony that only a poet with Stevens's particular notion of the imagination's function could develop, the rock becomes the mind itself, shattered into such diamond-faceted brilliance that it encompasses all possibilities for human thought:
The rock is the gray particular of man's life,
The stone from which he rises, up—and—ho,
The step to the bleaker depths of his descents ...
The rock is the stern particular of the air,
The mirror of the planets, one by one,
But through man's eye, their silent rhapsodist,
Turquoise the rock, at odious evening bright
With redness that sticks fast to evil dreams;
The difficult rightness of half-risen day.
The rock is the habitation of the whole,
Its strength and measure, that which is near,
point A
In a perspective that begins again
At B: the origin of the mango's rind.
(Collected Poems, 528)
|
For some explanation of the
groups of 8 and 24
motions referred to in the note,
see an earlier note from 1981.
For the Perlis "diamond facets,"
see the Diamond 16 Puzzle.
For a much larger group
of motions, see
Solomon's Cube.
As for "the mind itself"
and "possibilities for
human thought," see
Geometry of the I Ching.
A footprint from Germany:
|
Germany Python-urllib |
/504856559/item.html |
12/6/2008 1:21 PM |
The link in the above footprint leads
to an entry of July 5, 2006.
The access method:
The urllib Module
|
For a larger and more sophisticated
relative of that object,
see Solomon's Cube and
the related three presents
from the German link's target:
|
1. Many Dimensions 2. Boggle 3. My Space |
From the Grave
in yesterday's New York Times:
"From the grave, Albert Einstein
poured gasoline on the culture wars
between science and religion this week…."
An announcement of a
colloquium at Princeton:
Above: a cartoon,
"Coxeter exhuming Geometry,"
with the latter's tombstone inscribed
"GEOMETRY
600 B.C. —
1900 A.D.
R.I.P."
The above is from
The Paradise of Childhood,
a work first published in 1869.
"I need a photo-opportunity,
I want a shot at redemption.
Don't want to end up a cartoon
In a cartoon graveyard."
— Paul Simon
Albert Einstein,
1879-1955:
"It is quite clear to me that the religious paradise of youth, which was thus lost, was a first attempt to free myself from the chains of the 'merely-personal,' from an existence which is dominated by wishes, hopes and primitive feelings. Out yonder there was this huge world, which exists independently of us human beings and which stands before us like a great, eternal riddle, at least partially accessible to our inspection and thinking. The contemplation of this world beckoned like a liberation…."
— Autobiographical Notes, 1949
Related material:
A commentary on Tom Wolfe's
"Sorry, but Your Soul Just Died"–
"The Neural Buddhists," by David Brooks,
in the May 13 New York Times:
"The mind seems to have
the ability to transcend itself
and merge with a larger
presence that feels more real."
A New Yorker commentary on
a new translation of the Psalms:
"Suddenly, in a world without
Heaven, Hell, the soul, and
eternal salvation or redemption,
the theological stakes seem
more local and temporal:
'So teach us to number our days.'"
and a May 13 Log24 commentary
on Thomas Wolfe's
"Only the Dead Know Brooklyn"–
"… all good things — trout as well as
eternal salvation — come by grace
and grace comes by art
and art does not come easy."
"Art isn't easy."
— Stephen Sondheim,
quoted in
Solomon's Cube.
For further religious remarks,
consult Indiana Jones and the
Kingdom of the Crystal Skull
and The Librarian:
Return to King Solomon's Mines.
"… the startling thesis of Mr. Brosterman's new book, 'Inventing Kindergarten' (Harry N. Abrams, $39.95): that everything the giants of modern art and architecture knew about abstraction they learned in kindergarten, thanks to building blocks and other educational toys designed by Friedrich Froebel, a German educator, who coined the term 'kindergarten' in the 1830's."
— "Was Modernism Born
in Toddler Toolboxes?"
by Trip Gabriel, New York Times,
April 10, 1997
Figure 1 —
Concept from 1819:
(Footnotes 1 and 2)
Figure 2 —
The Third Gift, 1837:
Froebel, the inventor of
kindergarten, worked as
an assistant to the
crystallographer Weiss
mentioned in Fig. 1.
(Footnote 3)
Figure 3 —
The Third Gift, 1906:
Figure 4 —
Solomon's Cube,
1981 and 1983:
Figure 5 —
Design Cube, 2006:
The above screenshot shows a
moveable JavaScript display
of a space of six dimensions
(over the two-element field).
(To see how the display works,
try the Kaleidoscope Puzzle first.)
— The missing last words
of Inman in Cold Mountain,
added here on the
Feast of St. Luke, 2004
7: In that night did God appear unto Solomon, and said unto him, Ask what I shall give thee.
8: And Solomon said unto God, Thou hast shewed great mercy unto David my father, and hast made me to reign in his stead.
9: Now, O LORD God, let thy promise unto David my father be established: for thou hast made me king over a people like the dust of the earth in multitude.
10: Give me now wisdom and knowledge, that I may go out and come in before this people: for who can judge this thy people, that is so great?
"At 42– a professor with no museum experience– he was named curator of painting and sculpture at the Museum of Modern Art. It was, and is, the most influential job in the fluid, insular, fiercely contentious world of modern art. Just two decades past his last Amherst game, the lineman from Savannah was sitting in the chair where the most critical decisions in his profession are made– 'the conscientious, continuous, resolute distinction of quality from mediocrity,' according to his Olympian predecessor Alfred Barr. The Modern and its chief curator serve the American art establishment as a kind of aesthetic Supreme Court, and most of their rulings are beyond appeal."
On Quality
Varnedoe, in his final
Mellon lecture at
the National Gallery,
quoted "Blade Runner"–
"I've seen things
you people wouldn't believe….
"Frank Rich of The New York Times
on the United States of America:
"A country where
entertainment is god."
Rich's description may or may not
be true of the United States, but
it certainly seems true of
The New York Times:
Click on image to enlarge.
Related material:
Greetings.
“The greatest sorcerer (writes Novalis memorably)
would be the one who bewitched himself to the point of
taking his own phantasmagorias for autonomous apparitions.
Would not this be true of us?”
–Jorge Luis Borges, “Avatars of the Tortoise”
“El mayor hechicero (escribe memorablemente Novalis)
sería el que se hechizara hasta el punto de
tomar sus propias fantasmagorías por apariciones autónomas.
¿No sería este nuestro caso?”
–Jorge Luis Borges, “Los Avatares de la Tortuga“
At Midsummer Noon:“In Many Dimensions (1931)
Williams sets before his reader the
mysterious Stone of King Solomon,
an image he probably drew from
a brief description in Waite’s
The Holy Kabbalah (1929) of
a supernatural cubic stone
on which was inscribed
‘the Divine Name.’”
 Related material:
|
| It is not enough to cover the rock with leaves. We must be cured of it by a cure of the ground Or a cure of ourselves, that is equal to a cure Of the ground, a cure beyond forgetfulness. And if we ate the incipient colorings – Wallace Stevens, “The Rock” |
Hofstadter’s cover.
Click on image for details.
(Continued from June 23)
Related material:
The Klein Correspondence,
Penrose Space-Time,
and a Finite Model
Symbol from a
website on
“Presbyterian
Creedal Standards”
The above symbol
appeared here
on 11/8/02.
Related material:
1. The remarks of
Bradley Whitford
at Princeton’s
Class Day yesterday:
2. An illustration from
Log 24 on 11/10/06:
|
|
|
|
Paul Robeson in |
3. The Whirligig of Time
(1/5/03):
4. Natalie Angier, priestess of Scientism
(5/26/07), and her new book
The Canon: A Whirligig Tour of
the Beautiful Basics of Science
(available as a special from
Amazon.com):
| Better Together Buy this book with God Is Not Great: How Religion Poisons Everything by Christopher Hitchens today!
|
Our Judeo-Christian
Heritage –
Lottery
Hermeneutics
Part I: Judeo
| The Lottery 12/9/06 | Mid-day | Evening |
| New York | 036
See |
331
See 3/31— “square crystal” and “the symbolism could not have been more perfect.” |
| Pennsylvania | 602
See 6/02— Walter Benjamin |
111
See 1/11— “Related material:
|
Part II: Christian
| The Lottery 4/3/07 | Mid-day | Evening |
| New York | 115
See 1/15— |
017
See
|
| Pennsylvania | 604
See |
714
See |
Related material:
It is perhaps relevant to
this Holy Week that the
date 6/04 (2006) above
refers to both the Christian
holy day of Pentecost and
to the day of the
facetious baccalaureate
of the Class of 2006 in
the University Chapel
at Princeton.
For further context for the
Log24 remarks of that same
date, see June 1-15, 2006.
The next novel starring
Robert Langdon, Harvard author
of "the renowned collegiate
texbook Religious Iconology"
is said to be titled
The Solomon Key.
Related material–
The Harvard Crimson online:
| Fishburne To Receive Honors at Cultural Rhythms Acclaimed actor and humanitarian chosen as the Harvard Foundation's Artist of the Year By DORIS A. HERNANDEZ Friday, February 16, 2007 9:37 PM Tony and Emmy Award-winning actor Laurence Fishburne will take the stage later this month as the 2007 Artist of the Year during the 22nd annual Cultural Rhythms festival, the Harvard Foundation for Intercultural and Race Relations announced Friday afternoon. |
Fishburne
as Morpheus
"Metaphor for Morphean morphosis,
Dreams that wake, transform, and die,
Calm and lucid this psychosis,
Joyce's nightmare in Escher's eye….
Dabo claves regni caelorum. By silent shore
Ripples spread from castle rock. The metaphor
For metamorphosis no keys unlock."
— Steven H. Cullinane,
November 7, 1986,
"Endgame"
More on metamorphosis–
Cat's Yarn
(Log24, June 20, 2006):
"The end is where
we start from."
plus.maths.org
and
Garfield 2003-06-24
See also:
Zen Koan
and
Blue Dream.
Update of 5:24 PM
Feb. 18, 2007:
A Xanga footprint from France
this afternoon (3:47 PM EST)
indicates that someone there
may be interested in the above
poem's "claves regni caelorum."
The visitor from France viewed
"Windmills" (Nov. 15, 2005).
Material related to that entry
may be found in various places
at Log24.com. See particularly
"Shine On, Hermann Weyl," and
entries for Women's History
Month last year that include
"Christ at the Lapin Agile."
From this morning’s
New York Times:
Tim Weiner in today’s New York Times:
“Mr. Hunt was intelligent, erudite, suave and loyal to his friends….
Everette Howard Hunt Jr. was born in Hamburg, N.Y., on Oct. 9, 1918, the son of a lawyer and a classically trained pianist who played church organ. He graduated from Brown University in June 1940 and entered the United States Naval Academy as a midshipman in February 1941.
He worked as a wartime intelligence officer in China, a postwar spokesman for the Marshall Plan in Paris and a screenwriter in Hollywood. Warner Brothers had just bought his fourth novel, ‘Bimini Run,’ a thriller set in the Caribbean, when he joined the fledgling C.I.A. in April 1949.
Mr. Hunt was immediately assigned to train C.I.A. recruits…. He moved to Mexico City, where he became chief of station in 1950. He brought along another rookie C.I.A. officer, William F. Buckley Jr., later a prominent conservative author and publisher, who became godfather and guardian to the four children of Mr. Hunt and his wife, the former Dorothy L. Wetzel.
In 1954, Mr. Hunt helped plan the covert operation that overthrew the elected president of Guatemala….
By the time of the coup, Mr. Hunt had been removed from responsibility. He moved on to uneventful stints in Japan and Uruguay. Not until 1960 was Mr. Hunt involved in an operation that changed history.
The C.I.A. had received orders from both President Dwight D. Eisenhower and his successor, President John F. Kennedy, to alter or abolish the revolutionary government of Fidel in Cuba. Mr. Hunt’s assignment was to create a provisional Cuban government that would be ready to take power once the C.I.A.’s cadre of Cuban shock troops invaded the island….
He retired from the C.I.A. in 1970 and secured a job with an agency-connected public relations firm in Washington. Then, a year later, came a call from the White House….
Mr. Hunt’s last book, ‘American Spy: My Secret History in the C.I.A., Watergate and Beyond,’ written with Greg Aunapu, is to be published on March 16 with a foreword by his old friend William F. Buckley Jr.
Late in life, he said he had no regrets, beyond the Bay of Pigs.”
Related Material:
Game Boy,
Philosophy Wars,
and the following:
“The most prominent critic
of the modal notions is Quine.
Throughout his career, he has
argued against the use of notions
like necessity and possibility.”
— Michael J. Loux,
Note 1 of Chapter 5,
“The Necessary and the Possible,”
in Metaphysics:
A Contemporary Introduction
(Routledge, second edition,
January 1, 2002)
“Personality is a synthesis of
possibility and necessity.”
— Soren Kierkegaard,
The Sickness Unto Death
Related material:
Plato, Pegasus,
and the Evening Star
Diamonds Are Forever
Dream a Little Dream
Update of 3:45 PM:
From Arts & Letters Daily
this afternoon–
“Existentialism is not all gloom,
even if Heidegger looks pretty sour
in those photos. It’s a philosophy
that America needs now, says
the late Robert Solomon…
more … obit”
See also Jan. 2,
the date of
Solomon’s death
in Switzerland,
and click on the
following symbol
from that date:
Time and Chance
on the 90th Birthday
of Kirk Douglas,
star of
“The Garden of Allah“
| The Lottery 12/9/06 | Mid-day | Evening |
| New York | 036
See |
331
See 3/31— “square crystal” and “the symbolism could not have been more perfect.” |
| Pennsylvania | 602
See 6/02— Walter Benjamin |
111
See 1/11— “Related material: |
Livingstone
On this date:
In 1871, journalist-explorer Henry M. Stanley found Scottish missionary David Livingstone, who had not been heard from for years, near Lake Tanganyika in central Africa.
— AP “Today in History,” Nov. 10
1 Peter 2, on the
“living stone.”
— NIV Bible
|
|
|
|
Paul Robeson in |
See also Wednesday’s
Grave Matters.
First to Illuminate
“From the History of a Simple Group” (pdf), by Jeremy Gray:
“The American mathematician A. B. Coble [1908; 1913]* seems to have been the first to illuminate the 27 lines and 28 bitangents with the elementary theory of geometries over finite fields.
The combinatorial aspects of all this are pleasant, but the mathematics is certainly not easy.”
* [Coble 1908] A. Coble, “A configuration in finite geometry isomorphic with that of the 27 lines on a cubic surface,” Johns Hopkins University Circular 7:80-88 (1908), 736-744.
[Coble 1913] A. Coble, “An application of finite geometry to the characteristic theory of the odd and even theta functions,” Trans. Amer. Math. Soc. 14 (1913), 241-276.
From The Harvard Crimson,
Monday, October 30, 2006 6:09 AM
“Why is the Task Force on General Education afraid of teaching religion? True, their report did recommend a reason and faith requirement, but the committee has clearly shied away from teaching religious principles and has treated the study of religion itself with contempt….
In the general education report… there is no mention of the fundamental principles of religious thought, even though the general education report stresses that students are affected by religion and should think critically about it.”
Screenshot of doctoryau.com
Here is a rather different
approach to religious thought–
|
Yesterday’s numbers
in the Empire State:
These suggest the
religious contemplation of Log24, 6/16– Hero of His Own Story— and of Log24, 6/30– Summers Revels Ended. |
For more on Harvard’s
real religion, Scientism,
and the political background
in which it thrives,
click on the picture below.
.
(Title of an interview with
the late Paul Halmos, mathematician)
From a 1990 interview:
“What’s the best part of being a mathematician? I’m not a religious man, but it’s almost like being in touch with God when you’re thinking about mathematics. God is keeping secrets from us, and it’s fun to try to learn some of the secrets.”
I personally prefer Annie Dillard on God:
“… if Holy the Firm is matter at its dullest, Aristotle’s materia prima, absolute zero, and since Holy the Firm is in touch with the Absolute at base, then the circle is unbroken. And it is…. Holy the Firm is in short the philosopher’s stone.”
Some other versions of
the philosopher’s stone:
This last has the virtue of
being connected with Halmos
via his remarks during the
“In Touch with God” interview:
See also the remark of Halmos that serves as an epigraph to Theme and Variations.
has also served
at least one interpreter
as a philosopher’s stone,
and is also the original
“Halmos tombstone.”
Public Space
"… the Danish cartoons crisis last March showed 'two world views colliding in public space with no common point of reference.'"
— George Carey, Archbishop of Canterbury from 1991 to 2002, quoted in today's London Times.
Related material:
Geometry and Christianity
(Google search yielding
"about 1,540,000" results)
Geometry and Islam
(Google search yielding
"about 1,580,000" results)
A Public Space
— Motto of
Plato's Academy
|
If we replace the Chinese word "I" (change, transformation) with the word "permutation," the relevance of Western mathematics (which some might call "the Logos") to the I Ching ("Changes Classic") beomes apparent.
Related material:
Hitler's Still Point, Jung's Imago, Solomon's Cube, Geometry of the I Ching, and Globe Award. |
For the relevance of Plato to
Islam, see David Wade's
Pattern in Islamic Art
and a Google search on
Plato and Islam
("about 1,680,000" results).
— Heraclitus of Ephesus, about 500 B.C.
And now, from
the author of Sphere…
He beomes aware of something else… some other presence.
“Anybody here?” he says.
I am here.
He almost jumps, it is so loud. Or it seems loud. Then he wonders if he has heard anything at all.
“Did you speak?”
No.
How are we communicating? he wonders.
The way everything communicates with everything else.
Which way is that?
Why do you ask if you already know the answer?
— Sphere, by Michael Crichton, Harvard ’64
“… when I went to Princeton things were completely different. This chapel, for instance– I remember when it was just a clearing, cordoned off with sharp sticks. Prayer was compulsory back then, and you couldn’t just fake it by moving your lips; you had to know the words, and really mean them. I’m dating myself, but this was before Jesus Christ.”
— Baccalaureate address at Princeton, Pentecost 2006, reprinted in The New Yorker, edited by David Remnick, Princeton ’81
Related figures:
For further details,
see Solomon’s Cube
and myspace.com/affine.
For further details,
see Jews on Buddhism
and
Adventures in Group Theory.
“In this way we are offered
a formidable lesson
for every Christian community.”
Pope Benedict XVI
on Pentecost,
June 4, 2006,
St. Peter’s Square.
Part I:
The Game
Part II:
Many People
For further details,
see Solomon’s Cube
and myspace.com/affine.
“The rock cannot be broken.
It is the truth.”
— Wallace Stevens
“… we have condensed six dimensions into four, then we either work by analogy into six, or we have to use math that apparently nobody but Jake and my cousin Ed understands. Unless you can think of some way to project six dimensions into three– you seem to be smart at such projections.”
I closed my eyes and thought hard. “Zebbie, I don’t think it can be done. Maybe Escher could have done it.”
The above screenshot shows a
moveable JavaScript display
of a space of six dimensions
(over the 2-element field).
(To see how the display works,
try the Kaleidoscope Puzzle first.)
Compare and contrast:
Solomon’s Cube, the five
Log24 entries ending on 3/14,
and the
American Mathematical Society
on Mathematical Imagery.
Related material:
A more extensive excerpt from
The Number of the Beast, and
“There is a pleasantly discursive treatment
of Pontius Pilate’s unanswered question
‘What is truth?'”
— H. S. M. Coxeter, 1987, introduction to
Richard J. Trudeau’s remarks on
the “Story Theory” of truth
as opposed to
the “Diamond Theory” of truth
in The Non-Euclidean Revolution
A Serious Position
“‘Teitelbaum,’ in German,
is ‘date palm.'”
— Generations, Jan. 2003
“In Hasidism, a mystical brand
of Orthodox Judaism, the grand rabbi
is revered as a kinglike link to God….”
— Today’s New York Times obituary
of Rabbi Moses Teitelbaum,
who died on April 24, 2006
(Easter Monday in the
Orthodox Church)
From Wikipedia, an unsigned story:
“In 1923 Alfred Teitelbaum and his brother Wacław changed their surnames to Tarski, a name they invented because it sounded very Polish, was simple to spell and pronounce, and was unused. (Years later, he met another Alfred Tarski in northern California.) The Tarski brothers also converted to Roman Catholicism, the national religion of the Poles. Alfred did so, even though he was an avowed atheist, because he was about to finish his Ph.D. and correctly anticipated that it would be difficult for a Jew to obtain a serious position in the new Polish university system.”
“Diabolique” (1996), starring
For related material on St. Anselm
and mathematics at Princeton, see
Modal Theology and the
April 2006 AMS Notices
on
Today’s birthdays:
Sharon Stone and
Gregory La Cava.
Finitegeometry.org Update
(Revised May 21, 2006)
Finitegeometry.org now has permutable JavaScript views of the 2x2x2 and 4x4x4 design cubes. Solomon’s Cube presented a claim that the 4x4x4 design cube retains symmetry under a group of about 1.3 trillion transformations. The JavaScript version at finitegeometry.org/sc/64/view/ lets the reader visually verify this claim. The reader should first try the Diamond 16 Puzzle. The simpler 2x2x2 design cube, with its 1,344 transformations, was described in Diamonds and Whirls; the permutable JavaScript version is at finitegeometry.org/sc/8/view/.
These topics may be illuminated
by a study of the Chinese classics.
If we replace the Chinese word "I"
(change, transformation) with the
word "permutation," the relevance
of Western mathematics (which
some might call "the Logos") to
the I Ching ("Changes Classic")
beomes apparent.
Related material:
Hitler's Still Point,
Jung's Imago,
Solomon's Cube,
Geometry of the I Ching,
and Globe Award.
Yesterday's Valentine
may also have some relevance.
Time in the Rock
"a world of selves trying to remember the self
before the idea of self is lost–
Walk with me world, upon my right hand walk,
speak to me Babel, that I may strive to assemble
of all these syllables a single word
before the purpose of speech is gone."
— Conrad Aiken, "Prelude" (1932),
later part of "Time in the Rock,
or Preludes to Definition, XIX" (1936),
in Selected Poems, Oxford U. Press
paperback, 2003, page 156
"The rock is the habitation of the whole,
Its strength and measure, that which is near, point A
In a perspective that begins again
At B: the origin of the mango's rind.
It is the rock where tranquil must adduce
Its tranquil self, the main of things, the mind,
The starting point of the human and the end,
That in which space itself is contained, the gate
To the enclosure, day, the things illumined
By day, night and that which night illumines,
Night and its midnight-minting fragrances,
Night's hymn of the rock, as in a vivid sleep."
— Wallace Stevens in The Rock (1954)
"Poetry is an illumination of a surface,
the movement of a self in the rock."
— Wallace Stevens, introduction to
The Necessary Angel, 1951
The following may help illuminate the previous entry:
"I want, as a man of the imagination, to write poetry with all the power of a monster equal in strength to that of the monster about whom I write. I want man's imagination to be completely adequate in the face of reality."
— Wallace Stevens, 1953 (Letters 790)
The "monster" of the previous entry is of course not Reese Witherspoon, but rather Vox Populi itself.
In memory of Humphrey Carpenter, author of The Inklings, who attended The Dragon School. Carpenter died a year ago today.
"Lewis began with 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…."
From Paul Preuss,
Broken Symmetries
(see previous entry):
From
Verbum Sat Sapienti?
"…his eyes ranged the Consul's books disposed quite neatly… on high shelves around the walls: Dogme et Ritual de la Haute Magie, Serpent and Siva Worship in Central America, there were two long shelves of this, together with the rusty leather bindings and frayed edges of the numerous cabbalistic and alchemical books, though some of them looked fairly new, like the Goetia of the Lemegaton of Solomon the King, probably they were treasures, but the rest were a heterogeneous collection…."
— Malcolm Lowry, Under the Volcano, Chapter VI
"… when Saul does reach for a slim leather-bound volume Eliza cannot help but feel that something momentous is about to happen. There is care in the way he carries the book on the short journey from its shelf, as if it were constructed not of leather and parchment but of flesh and blood….
"Otzar Eden HaGanuz," Saul says. "The Hidden Eden. In this book, Abulafia describes the process of permutation…. Once you have mastered it, you will have mastered words, and once you have mastered words, you will be ready to receive shefa."
"In the Inner Game, we call the Game Dhum Welur, the Mind of God."
— The Gameplayers of Zan, a novel featuring games based on cellular automata
"Regarding cellular automata, I'm trying to think in what SF books I've seen them mentioned. Off the top of my head, only three come to mind:
The Gameplayers of Zan M.A. Foster
Permutation City Greg Egan
Glory Season David Brin"
— Jonathan L. Cunningham, Usenet
"If all that 'matters' are fundamentally mathematical relationships, then there ceases to be any important difference between the actual and the possible. (Even if you aren't a mathematical Platonist, you can always find some collection of particles of dust to fit any required pattern. In Permutation City this is called the 'logic of the dust' theory.)….
… Paul Durham is convinced by the 'logic of the dust' theory mentioned above, and plans to run, just for a few minutes, a complex cellular automaton (Permutation City) started in a 'Garden of Eden' configuration — one which isn't reachable from any other, and which therefore must have been the starting point of a simulation…. I didn't understand the need for this elaborate set-up, but I guess it makes for a better story than 'well, all possible worlds exist, and I'm going to tell you about one of them.'"
— Danny Yee, review of Permutation City
"Y'know, I never imagined the competition version involved so many tricky permutations."
— David Brin, Glory Season, 1994 Spectra paperback, p. 408
|
Figure 2
"… matter is consciousness expressed in the intermixing of force and form, but so heavily structured and constrained by form that its behaviour becomes describable using the regular and simple laws of physics. This is shown in Figure 2. |
Figure 3
"This quaternary is a Kabbalistic representation of God-the-Knowable, in the sense that it the most abstract representation of God we are capable of comprehending…. — A Depth of Beginning: Notes on Kabbalah by Colin Low (pdf) |
See also
Cognitive Blending and the Two Cultures,
Mathematics and Narrative,
Deep Game,
and the previous entry.
Contrapuntal Themes
in a Shadowland
(See previous entry.)
Douglas Hofstadter on his magnum opus:
"… I realized that to me, Gödel and Escher and Bach were only shadows cast in different directions by some central solid essence. I tried to reconstruct the central object, and came up with this book."
Hofstadter's cover
Here are three patterns,
"shadows" of a sort,
derived from a different
"central object":
For details, see
Solomon's Cube.
Related material:
The reference to a
"permutation fugue"
(pdf) in an article on
Gödel, Escher, Bach.
Born today: Laurence Fishburne
Yale Daily News, Jan. 11, 2001:
“When New Haven was founded, the city was laid out into a grid of nine squares surrounded by a great wilderness.
Last year History of Art Professor Emeritus Vincent Scully said the original town plan reflected a feeling that the new city should be sacred.
Scully said the colony’s founders thought of their new Puritan settlement as a ‘nine-square paradise on Earth, heaven on earth, New Haven, New Jerusalem.'”
“Real and unreal are two in one:
New Haven
Before and after one arrives….”
— Wallace Stevens,
“An Ordinary Evening in New Haven,’ XXVIII
|
Fade to Black “…that ineffable constellation of talents that makes the player of rank: a gift for conceiving abstract schematic possibilities; a sense of mathematical poetry in the light of which the infinite chaos of probability and permutation is crystallized under the pressure of intense concentration into geometric blossoms; the ruthless focus of force on the subtlest weakness of an opponent.” — Trevanian, Shibumi
“‘Haven’t there been splendidly elegant colors in Japan since ancient times?’ ‘Even black has various subtle shades,’ Sosuke nodded.” — Yasunari Kawabata, The Old Capital
An Ad Reinhardt painting
Ad Reinhardt, The viewer may need to tilt “The grid is a staircase to the Universal…. We could think about Ad Reinhardt, who, despite his repeated insistence that ‘Art is art,’ ended up by painting a series of… nine-square grids in which the motif that inescapably emerges is a Greek cross.  Greek Cross There is no painter in the West who can be unaware of the symbolic power of the cruciform shape and the Pandora’s box of spiritual reference that is opened once one uses it.” — Rosalind Krauss,
|
In memory of
St. William Golding
(Sept. 19, 1911 – June 19, 1993)
or, The Eightfold Cube
Every permutation of the plane's points that preserves collinearity is a symmetry of the plane. The group of symmetries of the Fano plane is of order 168 and is isomorphic to the group PSL(2,7) = PSL(3,2) = GL(3,2). (See Cameron on linear groups (pdf).)
The above model indicates with great clarity six symmetries of the plane– those it shares with the equilateral triangle. It does not, however, indicate where the other 162 symmetries come from.
Shown below is a new model of this same projective plane, using partitions of cubes to represent points:
The second model is useful because it lets us generate naturally all 168 symmetries of the Fano plane by splitting a cube into a set of four parallel 1x1x2 slices in the three ways possible, then arbitrarily permuting the slices in each of the three sets of four. See examples below.
(Note that this procedure, if regarded as acting on the set of eight individual subcubes of each cube in the diagram, actually generates a group of 168*8 = 1,344 permutations. But the group's action on the diagram's seven partitions of the subcubes yields only 168 distinct results. This illustrates the difference between affine and projective spaces over the binary field GF(2). In a related 2x2x2 cubic model of the affine 3-space over GF(2) whose "points" are individual subcubes, the group of eight translations is generated by interchanges of parallel 2x2x1 cube-slices. This is clearly a subgroup of the group generated by permuting 1x1x2 cube-slices. Such translations in the affine 3-space have no effect on the projective plane, since they leave each of the plane model's seven partitions– the "points" of the plane– invariant.)
To view the cubes model in a wider context, see Galois Geometry, Block Designs, and Finite-Geometry Models.
For another application of the points-as-partitions technique, see Latin-Square Geometry: Orthogonal Latin Squares as Skew Lines.
For more on the plane's symmetry group in another guise, see John Baez on Klein's Quartic Curve and the online book The Eightfold Way. For more on the mathematics of cubic models, see Solomon's Cube.
Seal
The Log24 entry for yesterday, the date of Prince Rainier’s funeral, discussed a figure sometimes called “Solomon’s seal.” Here are some further reflections.
In memory of Leonardo and of Chen Yifei (previous entry), a link to the Sino-Judaic Institute’s review of Chen’s film “Escape to
Related material
from Log24.net:
Saturday, December 27, 2003 10:21 PM
Toy
“If little else, the brain is an educational toy. While it may be a frustrating plaything — one whose finer points recede just when you think you are mastering them — it is nonetheless perpetually fascinating, frequently surprising, occasionally rewarding, and it comes already assembled; you don’t have to put it together on Christmas morning.
The problem with possessing such an engaging toy is that other people want to play with it, too. Sometimes they’d rather play with yours than theirs. Or they object if you play with yours in a different manner from the way they play with theirs. The result is, a few games out of a toy department of possibilities are universally and endlessly repeated. If you don’t play some people’s game, they say that you have ‘lost your marbles,’ not recognizing that,
while Chinese checkers is indeed a fine pastime, a person may also play dominoes, chess, strip poker, tiddlywinks, drop-the-soap or Russian roulette with his brain.
One brain game that is widely, if poorly, played is a gimmick called ‘rational
“I took the number twenty-four and there’s twenty-four ways of expressing the numbers one, two, three, four. And I assigned one kind of line to one, one to two, one to three, and one to four. One was a vertical line, two was a horizontal line, three was diagonal left to right, and four was diagonal right to left. These are the basic kind of directions that lines can take…. the absolute ways that lines can be drawn. And I drew these things as parallel lines very close to one another in boxes. And then there was a system of changing them so that within twenty-four pages there were different arrangements of actually sixteen squares, four sets of four. Everything was based on four. So this was kind of a… more of a… less of a rational… I mean, it gets into the whole idea of methodology.”
Yes, it does.
See Art Wars, Poetry’s Bones, and Time Fold.
Friday, December 26, 2003 7:59 PM
ART WARS, St. Stephen’s Day:
The Magdalene Code
Got The Da Vinci Code for Xmas.
From page 262:
When Langdon had first seen The Little Mermaid, he had actually gasped aloud when he noticed that the painting in Ariel’s underwater home was none other than seventeenth-century artist Georges de la Tour’s The Penitent Magdalene — a famous homage to the banished Mary Magdalene — fitting decor considering the movie turned out to be a ninety-minute collage of blatant symbolic references to the lost sanctity of Isis, Eve, Pisces the fish goddess, and, repeatedly, Mary Magdalene.
Related Log24 material —
The Da Vinci Code, pages 445-446:
“The blade and chalice?” Marie asked. “What exactly do they look like?”
Langdon sensed she was toying with him, but he played along, quickly describing the symbols.
A look of vague recollection crossed her face. “Ah, yes, of course. The blade represents all that is masculine. I believe it is drawn like this, no?” Using her index finger, she traced a shape on her palm.
“Yes,” Langdon said. Marie had drawn the less common “closed” form of the blade, although Langdon had seen the symbol portrayed both ways.
“And the inverse,” she said, drawing again upon her palm, “is the chalice, which represents the feminine.”
“Correct,” Langdon said….
… Marie turned on the lights and pointed….
“There you are, Mr. Langdon. The blade and chalice.”….
“But that’s the Star of Dav–“
Langdon stopped short, mute with amazement as it dawned on him.
The blade and chalice.
Fused as one.
The Star of David… the perfect union of male and female… Solomon’s Seal… marking the Holy of Holies, where the male and female deities — Yahweh and Shekinah — were thought to dwell.
Related Log24 material —
Relativity Blues
Today, February 20, is the 19th anniversary of my note The Relativity Problem in Finite Geometry. Here is some related material.
In 1931, the Christian writer Charles Williams grappled with the theology of time, space, free will, and the many-worlds interpretation of quantum mechanics (anticipating by many years the discussion of this topic by physicists beginning in the 1950's).
(Some pure mathematics — untainted by physics or theology — that is nevertheless related, if only by poetic analogy, to Williams's 1931 novel, Many Dimensions, is discussed in the above-mentioned note and in a generalization, Solomon's Cube.)
On the back cover of Williams's 1931 novel, the current publisher, William B. Eerdmans Publishing Company of Grand Rapids, Michigan, makes the following statement:
"Replete with rich religious imagery, Many Dimensions explores the relation between predestination and free will as it depicts different human responses to redemptive transcendence."
One possible response to such statements was recently provided in some detail by a Princeton philosophy professor. See On Bullshit, by Harry G. Frankfurt, Princeton University Press, 2005.
A more thoughtful response would take into account the following:
1. The arguments presented in favor of philosopher John Calvin, who discussed predestination, in The Death of Adam: Essays on Modern Thought, by Marilynne Robinson
2. The physics underlying Einstein's remarks on free will, God, and dice
3. The physics underlying Rebecca Goldstein's novel Properties of Light and Paul Preuss's novels Secret Passages and Broken Symmetries
4. The physics underlying the recent so-called "free will theorem" of John Conway and Simon Kochen of Princeton University
5. The recent novel Gilead, by Marilynne Robinson, which deals not with philosophy, but with lives influenced by philosophy — indirectly, by the philosophy of the aforementioned John Calvin.
From a review of Gilead by Jane Vandenburgh:
"In The Death of Adam, Robinson shows Jean Cauvin to be the foremost prophet of humanism whose Protestant teachings against the hierarchies of the Roman church set in motion the intellectual movements that promoted widespread literacy among the middle and lower classes, led to both the American and French revolutions, and not only freed African slaves in the United States but brought about suffrage for women. It's odd then that through our culture's reverse historicism, the term 'Calvinism' has come to mean 'moralistic repression.'"
For more on what the Calvinist publishing firm Eerdmans calls "redemptive transcendence," see various July 2003 Log24.net entries. If these entries include a fair amount of what Princeton philosophers call bullshit, let the Princeton philosophers meditate on the summary of Harvard philosophy quoted here on November 5 of last year, as well as the remarks of November 5, 2003, and those of November 5, 2002.
From Many Dimensions (Eerdmans paperback, 1963, page 53):
"Lord Arglay had a suspicion that the Stone would be purely logical. Yes, he thought, but what, in that sense, were the rules of its pure logic?"
A recent answer:
"We symbolize logical necessity
with the box 
)
and logical possibility
with the diamond 
).
— Keith Allen Korcz,
(Log24.net, 1/25/05)
And what do we
symbolize by 
?
"The possibilia that exist,
and out of which
the Universe arose,
are located in
a necessary being…."
— Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)
Today’s New York Times on a rabbi who died in Jerusalem on Sunday, Dec. 5:
“In the 1950’s, he was a vocal advocate for the relaxation of New York City’s blue laws, which forbade many kinds of commerce on Sundays but not on Saturdays. The laws were repealed in the 1970’s. Solomon Joseph Sharfman was born on Nov. 1, 1915, in Treblinka, Poland; his family immigrated to the United States five years later. His father, Rabbi Label Sharfman, worked as a shochet, or ritual slaughterer….”
Saturday’s lottery numbers from Pennsylvania, the State of Grace:
A Sunday Sermon:
Related material:
(See Song in Red and Gray
and The Dot and the Line.)
Nothing Nothings
(Again)
Background: recent Log24 entries (beginning with Chorus from the Rock on Dec. 5, 2004) and Is Nothing Sacred? (quotations compiled on March 9, 2000).
From an obituary of Paul Edwards, a writer on philosophy, in this morning's New York Times:
"Heidegger's Confusions, a collection of Professor Edwards's scholarly articles, was published last month by Prometheus."
Edwards, born in Vienna in 1923 to Jewish parents, died on December 9.
Some sites I visited earlier this evening, before reading of Edwards's death:
The above link is in memory of
Iris Chang,
who ended her life at 36
on Nov. 9, 2004.
A central concept of Zen
is satori, or “awakening.”
For a rude awakening, see
Satori at Pearl Harbor.
|
Fade to Black See, too, my entries of “…that ineffable constellation of talents that makes the player of rank: a gift for conceiving abstract schematic possibilities; a sense of mathematical poetry in the light of which the infinite chaos of probability and permutation is crystallized under the pressure of intense concentration into geometric blossoms; the ruthless focus of force on the subtlest weakness of an opponent.” — Trevanian, Shibumi
” ‘Haven’t there been splendidly elegant colors in Japan since ancient times?’ ‘Even black has various subtle shades,’ Sosuke nodded.’ “ — Yasunari Kawabata, The Old Capital An Ad Reinhardt painting
Ad Reinhardt,
|
The Quality of Diamond
On February 3, 2004, archivist and abstract painter Ward Jackson died at 75. From today’s New York Times:
“Inspired by painters like Piet Mondrian and Josef Albers, Mr. Jackson made austere, hard-edged geometric compositions, typically on diamond-shaped canvases.”
|
On a 2003 exhibit by Pablo Helguera that included Mr. Jackson: Parallel Lives recounts and recontextualizes real episodes from the lives of five disparate individuals including Florence Foster Jenkins, arguably the world’s worst opera singer; Giulio Camillo, a Renaissance mystic who aimed to build a memory container for all things; Friedrich Froebel, the inventor of the kindergarten education system, the members of the last existing Shaker community, and Ward Jackson, the lifelong archivist of the Solomon R. Guggenheim Museum. Parallel Lives pays homage to Hans-Georg Gadamer (1900-2002) and his system of philosophical hermeneutics built through an exploration of historicity, language, and art. This exhibition, which draws its title from the classic work by Plutarch, is a project that explores biography as a medium, drawing from the earlier innovation of the biographical practice in works like Marcel Schwob’s “Imaginary Lives” (1896) and John Aubrey’s “Brief Lives” (1681). Through display means, the project blends the lives of these individuals into one basic story, visually stating the relationship between individualism and society as best summarized by Gadamer’s famous phrase: “we all are others, and we all are a self.” |
On February 3, the day that Jackson died, there were five different log24.net entries:
Parallels with the Helguera exhibit:
Florence Foster Jenkins: Janet Jackson in (2) above.
Giulio Camillo: Myself as compiler of the synchronistic excerpts in (5).
Friedrich Froebel: David Wade in (4).
The last Shakers: Christopher Alexander and his acolytes in (1).
Ward Jackson: On Feb. 3, Jackson became a permanent part of
Some thoughts of Hans-Georg Gadamer
relevant to Jackson’s death:
|
by G.T. Karnezis The pleasure it [art] elicits “is the joy of knowledge.” It does not operate as an enchantment but “a transformation into the true.” Art, then, would seem to be an essentializing agent insofar as it reveals what is essential. Gadamer asks us to see reality as a horizon of “still undecided possibilities,” of unfulfilled expectations, of contingency. If, in a particular case, however, “a meaningful whole completes and fulfills itself in reality,” it is like a drama. If someone sees the whole of reality as a closed circle of meaning” he will be able to speak “of the comedy and tragedy of life” (genres becoming ways of conceiving reality). In such cases where reality “is understood as a play, there emerges the reality of what play is, which we call the play of art.” As such, art is a realization: “By means of it everyone recognizes that that is how things are.” Reality, in this viewpoint, is what has not been transformed. Art is defined as “the raising up of this reality to its truth.” |
As noted in entry (3) above
on the day that Jackson died,
“All the world’s a stage.”
ART WARS, St. Stephen’s Day:
The Magdalene Code
Got The Da Vinci Code for Xmas.
From page 262:
When Langdon had first seen The Little Mermaid, he had actually gasped aloud when he noticed that the painting in Ariel’s underwater home was none other than seventeenth-century artist Georges de la Tour’s The Penitent Magdalene — a famous homage to the banished Mary Magdalene — fitting decor considering the movie turned out to be a ninety-minute collage of blatant symbolic references to the lost sanctity of Isis, Eve, Pisces the fish goddess, and, repeatedly, Mary Magdalene.
Related Log24 material —
The Da Vinci Code, pages 445-446:
“The blade and chalice?” Marie asked. “What exactly do they look like?”
Langdon sensed she was toying with him, but he played along, quickly describing the symbols.
A look of vague recollection crossed her face. “Ah, yes, of course. The blade represents all that is masculine. I believe it is drawn like this, no?” Using her index finger, she traced a shape on her palm.
“Yes,” Langdon said. Marie had drawn the less common “closed” form of the blade, although Langdon had seen the symbol portrayed both ways.
“And the inverse,” she said, drawing again upon her palm, “is the chalice, which represents the feminine.”
“Correct,” Langdon said….
… Marie turned on the lights and pointed….
“There you are, Mr. Langdon. The blade and chalice.”….
“But that’s the Star of Dav–“
Langdon stopped short, mute with amazement as it dawned on him.
The blade and chalice.
Fused as one.
The Star of David… the perfect union of male and female… Solomon’s Seal… marking the Holy of Holies, where the male and female deities — Yahweh and Shekinah — were thought to dwell.
Related Log24 material —
Symmetry in Diamond Theory:
Robbing Peter to Pay Paul
"Groups arise in most areas of pure and applied mathematics, usually as a set of operators or transformations of some structure. The appearance of a group generally reflects some kind of symmetry in the object under study, and such symmetry may be considered one of the fundamental notions of mathematics."
"Counter-change is sometimes known as Robbing Peter to Pay Paul."
|
|
|
|
Paul Robeson in |
For a look at the Soviet approach
to counterchange symmetry, see
The Kishinev School of Discrete Geometry.
The larger cultural context:
See War of Ideas (Oct. 24),
The Hunt for Red October (Oct. 25),
On the Left (Oct. 25), and
ART WARS for Trotsky's Birthday (Oct. 26).
ART WARS, 5:09
The Word in the Desert
For Harrison Ford in the desert.
(See previous entry.)
Words strain,
Crack and sometimes break,
under the burden,
Under the tension, slip, slide, perish,
Will not stay still. Shrieking voices
Scolding, mocking, or merely chattering,
Always assail them.
The Word in the desert
Is most attacked by voices of temptation,
The crying shadow in the funeral dance,
The loud lament of
the disconsolate chimera.— T. S. Eliot, Four Quartets
The link to the word "devilish" in the last entry leads to one of my previous journal entries, "A Mass for Lucero," that deals with the devilishness of postmodern philosophy. To hammer this point home, here is an attack on college English departments that begins as follows:
"William Faulkner's Snopes trilogy, which recounts the generation-long rise of the drily loathsome Flem Snopes from clerk in a country store to bank president in Jefferson, Mississippi, teems with analogies to what has happened to English departments over the past thirty years."
For more, see
The Word in the Desert,
by Glenn C. Arbery.
See also the link on the word "contemptible," applied to Jacques Derrida, in my Logos and Logic page.
This leads to an National Review essay on Derrida,
The Philosopher as King,
by Mark Goldblatt.
A reader's comment on my previous entry suggests the film "Scotland, PA" as viewing related to the Derrida/Macbeth link there.
I prefer the following notice of a 7-11 death, that of a powerful art museum curator who would have been well cast as Lady Macbeth:
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Die Fahne Hoch, |
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From the Whitney Museum site:
"Max Anderson: When artist Frank Stella first showed this painting at The Museum of Modern Art in 1959, people were baffled by its austerity. Stella responded, 'What you see is what you see. Painting to me is a brush in a bucket and you put it on a surface. There is no other reality for me than that.' He wanted to create work that was methodical, intellectual, and passionless. To some, it seemed to be nothing more than a repudiation of everything that had come before—a rational system devoid of pleasure and personality. But other viewers saw that the black paintings generated an aura of mystery and solemnity.
The title of this work, Die Fahne Hoch, literally means 'The banner raised.' It comes from the marching anthem of the Nazi youth organization. Stella pointed out that the proportions of this canvas are much the same as the large flags displayed by the Nazis.
But the content of the work makes no reference to anything outside of the painting itself. The pattern was deduced from the shape of the canvas—the width of the black bands is determined by the width of the stretcher bars. The white lines that separate the broad bands of black are created by the narrow areas of unpainted canvas. Stella's black paintings greatly influenced the development of Minimalism in the 1960s."
From Play It As It Lays:
She took his hand and held it. "Why are you here."
"Because you and I, we know something. Because we've been out there where nothing is. Because I wanted—you know why."
"Lie down here," she said after a while. "Just go to sleep."
When he lay down beside her the Seconal capsules rolled on the sheet. In the bar across the road somebody punched King of the Road on the jukebox again, and there was an argument outside, and the sound of a bottle breaking. Maria held onto BZ's hand.
"Listen to that," he said. "Try to think about having enough left to break a bottle over it."
"It would be very pretty," Maria said. "Go to sleep."
I smoke old stogies I have found…
Cigar Aficionado on artist Frank Stella:
" 'Frank actually makes the moment. He captures it and helps to define it.'
This was certainly true of Stella's 1958 New York debut. Fresh out of Princeton, he came to New York and rented a former jeweler's shop on Eldridge Street on the Lower East Side. He began using ordinary house paint to paint symmetrical black stripes on canvas. Called the Black Paintings, they are credited with paving the way for the minimal art movement of the 1960s. By the fall of 1959, Dorothy Miller of The Museum of Modern Art had chosen four of the austere pictures for inclusion in a show called Sixteen Americans."
For an even more austere picture, see
For more on art, Derrida, and devilishness, see Deborah Solomon's essay in the New York Times Magazine of Sunday, June 27, 1999:
"Blame Derrida and
his fellow French theorists…."
See, too, my site
Art Wars: Geometry as Conceptual Art.
For those who prefer a more traditional meditation, I recommend
("Behold the Wood of the Cross")
For more on the word "road" in the desert, see my "Dead Poet" entry of Epiphany 2003 (Tao means road) as well as the following scholarly bibliography of road-related cultural artifacts (a surprising number of which involve Harrison Ford):
Of Time and the River
Today is the feast day of Saint Gerard Manley Hopkins, “immortal diamond.”
“At that instant he saw, in one blaze of light, an image of unutterable conviction, the reason why the artist works and lives and has his being–the reward he seeks–the only reward he really cares about, without which there is nothing. It is to snare the spirits of mankind in nets of magic, to make his life prevail through his creation, to wreak the vision of his life, the rude and painful substance of his own experience, into the congruence of blazing and enchanted images that are themselves the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”
“entered the university at Chapel Hill at fifteen ‘an awkward, unhappy misfit.’ By the time he graduated, he was editor of the college newspaper….”
Jeff MacNelly, who died on this date in the Year of Our Lord 2000,
“in 1977 started drawing the comic strip ‘Shoe‘…. The strip was named in honor of the legendary Jim Shumaker, for whom MacNelly worked at the Chapel Hill Weekly.”
From my Monday, June 2, 2003 entry:
Two quotations from “The Diamond Project“:
“We all know that something is eternal,” the Stage Manager says. “And it ain’t houses and it ain’t names, and it ain’t earth, and it ain’t even stars—everybody knows in their bones that something is eternal, and that something has to do with human beings.”
— John Lahr, review of “Our Town““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
Here are some other thoughts from the same date, but a different time, fictional time, Faulkner time:
Where the shadow of the bridge fell I could see down for a long way, but not as far as the bottom. When you leave a leaf in water a long time after a while the tissue will be gone and the delicate fibers waving slow as the motion of sleep. They dont touch one another, no matter how knotted up they once were, no matter how close they lay once to the bones. And maybe when He says Rise the eyes will come floating up too, out of the deep quiet and the sleep, to look on glory.
— William Faulkner, The Sound and the Fury
The concluding link from my June 2, 2003, entry furnishes a clue to the timelessness of Quentin Compson‘s thoughts above:
Glory… Song of Songs 8. 7-8
From the King James Bible‘s rendition of the Song of Songs:
8:7 Many waters cannot quench love, neither can the floods drown it: if a man would give all the substance of his house for love, it would utterly be contemned.
8:8 We have a little sister, and she hath no breasts: what shall we do for our sister in the day when she shall be spoken for?
For Quentin Compson’s thoughts on his little sister Caddy, consult the online hypertext edition of
Fearful Meditation —
A follow-up to yesterday
afternoon's entry of
| 03:04 |
O fearful meditation! Where, alack,
Shall time's best jewel from time's chest lie hid?
— Shakespeare, Sonnet 65
Pop Culture's answer:
"Flashes of fire,
a raging flame!"
— Song of Solomon
|
Click on the album title "0304" for details.
A different answer:
| 03/04 |
Click on the date "03/04" for details.
Solomon’s Seal —
A follow-up to my May 28 entry,
“The Eightfold Way and Solomon’s Seal.”
From the New York Times of May (Mental Health Month) 31, 2003:
By DOUGLAS MARTIN
Martha Scott, who created the role of the sweet, ethereal Emily in the original Broadway production of Thornton Wilder’s “Our Town” and was nominated for an Oscar for repeating it in the film version, died on Wednesday [May 28, 2003] in Los Angeles. She was 88.
United Artists
Martha Scott with William Holden
in the 1940 film of “Our Town.”
A quotation from Hemingway’s Death in the Afternoon:
“Madame, all stories, if continued far enough, end in death, and he is no true-story teller who would keep that from you.”
Two quotations from “The Diamond Project“:
“We all know that something is eternal,” the Stage Manager says. “And it ain’t houses and it ain’t names, and it ain’t earth, and it ain’t even stars—everybody knows in their bones that something is eternal, and that something has to do with human beings.”
— John Lahr, review of “Our Town”“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
Mental Health Month, Day 28:
The Eightfold Way and
Solomon's Seal
For a continuation of the mathematical and religious themes in yesterday's entry, click on the figure below.
Mental Health Month, Day 27:
Conspiracy Theory and
Solomon's Seal
In our journey through Mental Health Month, we have now arrived at day 27. This number, the number of lines on a non-singular cubic surface in complex projective 3-space, suggests it may be time to recall the following note (a sort of syllabus for an imaginary course) from August 1997, the month that the Mel Gibson film "Conspiracy Theory" was released.
Conspiracy Theory 101
August 13, 1997
Fiction:
| (A) | Masks of the Illuminati, by Robert Anton Wilson, Pocket Books, New York, 1981. Freemasonry meets The Force (starring James Joyce and Albert Einstein). |
| (B) | The Number of the Beast, by Robert A. Heinlein, Ballantine Books, New York, 1980. "Pantheistic multiple solipsism" and transformation groups in n-dimensional space combine to yield "the ultimate total philosophy." (p. 438). |
| (C) | The Essential Blake, edited by Stanley Kunitz, MJF Books, New York, 1987. "Fearful symmetry" in context. |
Fact:
| (1) | The Cosmic Trigger, by Robert Anton Wilson, Falcon Press, Phoenix, 1986 (first published 1977). Page 245 reveals that "the most comprehensive conspiracy theory," that of the physicist Sir Arthur Eddington, is remarkably similar to Heinlein's theory in (B) above. |
| (2) | The Development of Mathematics, by E. T. Bell, 2nd. ed., McGraw-Hill, New York, 1945. See the discussion of "Solomon's seal," a geometric configuration in complex projective 3-space. This is as good a candidate as any for Wilson's "Holy Guardian Angel" in (A) above. |
| (3) | Finite Projective Spaces of Three Dimensions, by J. W. P. Hirschfeld, Clarendon Press, Oxford, 1985. Chapter 20 shows how to represent Solomon's seal in the 63-point 5-dimensional projective space over the 2-element field. (The corresponding 6-dimensional affine space, with 64 points, is reminiscent of Heinlein's 6-dimensional space.) |
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See also China's 3,000-year-old "Book of Transformations," the I Ching, for more philosophy and lore of the affine 6-dimensional space over the binary field. © 1997 S. H. Cullinane |
For a more up-to-date and detailed look at the mathematics mentioned above, see
Abstract Configurations
in Algebraic Geometry,
by Igor Dolgachev.
"Art isn't easy." — Stephen Sondheim
ART WARS:
Readings for Bach's Birthday
Larry J. Solomon:
Symmetry as a Compositional Determinant,
Chapter VIII: New Transformations
In Solomon's work, a sequence of notes is represented as a set of positions within a Latin square:
Transformations of the Latin square correspond to transformations of the musical notes. For related material, see The Glass Bead Game, by Hermann Hesse, and Charles Cameron's sites on the Game.
Steven H. Cullinane:
Dorothy Sayers:
"The function of imaginative speech is not to prove, but to create–to discover new similarities, and to arrange them to form new entities, to build new self-consistent worlds out of the universe of undifferentiated mind-stuff." (Christian Letters to a Post-Christian World, Grand Rapids: Eerdmans, 1969, p. xiii)
— Quoted by Timothy A. Smith, "Intentionality and Meaningfulness in Bach's Cyclical Works"
Edward Sapir:
"…linguistics has also that profoundly serene and satisfying quality which inheres in mathematics and in music and which may be described as the creation out of simple elements of a self-contained universe of forms. Linguistics has neither the sweep nor the instrumental power of mathematics, nor has it the universal aesthetic appeal of music. But under its crabbed, technical, appearance there lies hidden the same classical spirit, the same freedom in restraint, which animates mathematics and music at their purest."
— "The Grammarian and his Language,"
American Mercury 1:149-155, 1924
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
|
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.
Story
"How much story do you want?"
— George Balanchine
While researching yesterday's entry on Balanchine, Apollo, and the nine Muses, I came across this architect's remarks, partially quoted yesterday and continued here:
"The icon that I use for this element is the nine-fold square…. This is the garden of Apollo, the field of Reason…. This is the Temple of Solomon, as inscribed, for example, by a nine-fold compartmentation to provide the ground plan of Yale, as described to me by Professor Hersey."
Checking this out yesterday, I came across the following at a Yale University Art Gallery site:
"This exhibition of nine boldly colored, asymmetrically designed quilts selected from a private collection will be displayed in the Matrix Gallery….
With the guidance of Professor Maude Southwell Wahlman, author of 'Signs and Symbols: African Images in African American Quilts,' the collector has explored and gathered examples…."
Exploring and gathering examples myself today, I received a book in the mail — W. M. Spackman's On the Decay of Humanism (Rutgers University Press, 1967) — and picked up a second-hand book at a sale — Barbara Michaels's Stitches in Time (Harper Collins Publishers, 1995).
The Spackman book includes the following poem at the end:
In sandarac etui for sepulchre
lies the cered body of a poisoned queen;
and in her mouth and hair, and at her feet,
and in the grey folds of her winding-sheet,
there sifts a dreamy powder, smooth and green,
the magic of an idle sorcerer,
an ancient spell, cast when the shroud was spun.
In death her hands clasp amourously a bowl
that still contains the fragments of her soul,
a tale of Beauty sought, and Beauty won,
his false lips kissed, and Beauty dead for her.
— Alexander B. Griswold, Princeton '28, in the
Nassau Literary Magazine of December 1925
From a synopsis of Michaels's Stitches in Time:
"Michaels follows Rachel, a graduate student studying women's crafts–weaving, spinning, quilting, embroidery–and the superstitions connected with them. Linking all important rites of passage to the garments created as markers of these occasions leads Rachel to her theory: in societies in which magic was practiced, the garment was meant to protect its wearer. She gains evidence that her theory is valid when an evil antique bridal quilt enters her life."
Although Stitches in Time is about a quilt — stitched, not spun — Griswold's line
"an ancient spell, cast when the shroud was spun"
is very closely related to the evil spell in Michaels's book.
The above events display a certain synchronicity that Wallace Stevens might appreciate, especially in light of the following remark in a review of Stitches in Time:
"…the premise is too outlandish for even the suspension of disbelief…." (Publishers Weekly, 4/24/95)
Stevens might reply,
The very man despising honest quilts
Lies quilted to his poll in his despite.— "The Comedian as the Letter C," Part V
Finally, those who prefer stories to the more formal qualities of pure dance (ballet) pure mathematics (see previous entry), pure (instrumental) music, and pure (abstract, as in quilt designs) art, can consult the oeuvre of Jodie Foster — as in my
Pearl Harbor Day entry on Buddhism.
An art historian named Griswold — perhaps that very same Griswold quoted above — might have a thing or two to say to Jodie on her recent film "Anna and the King." In the April, 1957, issue of The Journal of the Siam Society, Alexander B. Griswold takes issue with Broadway's and Hollywood's "grotesque caricature" of Siamese society, and ultimately with Anna herself:
"The real fault lies in the two books they ultimately spring from — The English Governess at the Court of Siam and The Romance of the Harem — both written by Mrs. Anna Leonowens.''
See also The Diamond 16 Puzzle for some quilt designs.
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Initial Xanga entry. Updated Nov. 18, 2006.
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