Subject and Predicates "A Chu space is a set X of subjects and a set A of predicates on those subjects. These stand in a symbiotic relationship in which the nature of each is determined by the other. Each subject is characterized by the values the predicates take on it, while each predicate is characterized by its values on subjects." -- Vaughan Pratt, Chu Spaces It would seem that Pratt and Sambin need to reconcile their similar predicates for the same subject. For some background on Sambin's approach to the subject, see
Mathematical Modal Logic:
A View of its Evolution (pdf), by Robert Goldblatt at Victoria University of Wellington's Centre for Logic, Language, and Computation For some background on Pratt's approach to the subject, see
Information Transfer Across Chu Spaces (pdf), by Johan van Benthem at the University of Amsterdam's Institute for Logic, Language, and Computation For a gloss on Sambin's words see the Log24 entry of Epiphany, 2005. Posted 5/31/2005 at 1:06 PM |
Just Say Non "French opposition to the draft European constitution
is being undermined by an onslaught of state-funded propaganda 'worthy
of Fidel Castro,' according to France's most eurosceptic leader of the
Right, Philippe de Villiers."
de Villiers -- telegraph.co.uk May 4, 2005 -- telegraph.co.uk May 30, 2005 Posted 5/29/2005 at 10:00 PM |
Immoveable Feast Today is a holiday of the Roman Catholic Church: the feast of St. Germain, Bishop of Paris. St. Germain is now known for the neighborhood that bears his name, home to what is said to be the oldest church in Paris, and a boulevard... "... I met Joyce who was walking along the Boulevard St.-Germain after having been to a matinée alone. He liked to listen to the actors, although he could not see them. He asked me to have a drink with him and we went to the Deux-Magots...." -- Ernest Hemingway, A Moveable Feast Two writers walk into a bar.... Posted 5/28/2005 at 12:25 PM |
Birth and Death Today's birthdays: Kylie Minogue and John Fogerty. Get well soon, Bad Moon. And in memory of Eddie Albert, a talented actor who died on Thursday, May 26, 2005, at his home in California and was born on April 22, 1906, in Rock Island, Illinois: you gotta ride it like you find it. Get your ticket at the station of the Rock Island Line. Among his films:
Posted 5/28/2005 at 12:00 AM |
Drama of the Diagonal, Wednesday's entry The Turning discussed a work by Roger Cooke. Cooke presents aPart Deux The History of Mathematics is the title of the Cooke book."fanciful story (based on Plato's dialogue Meno)." Associated Press thought for today: "History is not, of course, a cookbook offering pretested recipes. It teaches by analogy, not by maxims. It can illuminate the consequences of actions in comparable situations, yet each generation must discover for itself what situations are in fact comparable." — Henry Kissinger (whose birthday is today) For Henry Kissinger on his birthday: a link to Geometry for Jews. This link suggests a search for material on the art of Sol LeWitt, which leads to an article by Barry Cipra, The "Sol LeWitt" Puzzle: A Problem in 16 Squares (ps), a discussion of a 4x4 array of square linear designs. Cipra says that "If you like, there are three symmetry groups
lurking within the LeWitt puzzle: the rotation/reflection group
of order 8, a toroidal group of order 16, and an 'existential'* group
of order 16. The first group is the most obvious. The
third, once you see it, is also obvious." * Jean-Paul Sartre, Being and Nothingness, Philosophical Library, 1956 [reference by Cipra] For another famous group lurking near, if not within, a 4x4 array, click on Kissinger's birthday link above. Kissinger's remark (above) on analogy suggests the following analogy to the previous entry's (Drama of the Diagonal) figure: Logos Alogos II: Horizon This figure in turn, together with Cipra's reference to Sartre, suggests the following excerpts (via Amazon.com)-- From Sartre's Being and Nothingness, translated by Hazel E. Barnes, 1993 Washington Square Press reprint edition:
For more on the horizon, being, and nothingness, see Posted 5/27/2005 at 12:25 PM |
Drama of the Diagonal
"The beautiful in mathematics resides in contradiction. Incommensurability, logoi alogoi, was the first splendor in mathematics." -- Simone Weil, Oeuvres Choisies, éd. Quarto , Gallimard, 1999, p. 100 Logos Alogos -- Dennis Guedj, abstract of "The Drama of Mathematics," a talk to be given this July at the Mykonos conference on mathematics and narrative. For the drama of the diagonal of the square, see
Posted 5/26/2005 at 4:23 PM |
The Changing
The previous entry dealt with a transformation of the diamond figure from Plato's Meno into a visual proof of the Pythagorean theorem:
Here is a transformation of Plato's diamond
into the "gyronny" pattern of heraldry: For the mathematics dealing with this sort of transformation, see The Diamond 16 Puzzle and Diamond Theory. Posted 5/26/2005 at 4:00 AM |
The Turning Readers who have an Amazon.com account may view book pages relevant to the previous entry. See page 77 of The Way We Think, by Fauconnier and Turner (Amazon search term = Meno). This page discusses both the Pythagorean theorem and Plato's diamond figure in the Meno, but fails to "blend" these two topics. See also page 53 of The History of Mathematics, by Roger Cooke (first edition), where these two topics are in fact blended (Amazon search term = Pythagorean). The illustration below is drawn from the Cooke book. Cooke demonstrates how the Pythagorean theorem might have been derived by "blending" Plato's diamond (left) with the idea of moving the diamond's corners (right).
The previous entry dealt with a conference on mathematics and narrative. Above is an example I like of mathematics.... Here is an example I like of narrative: Kate felt quite dizzy. She didn't know exactly what it was-- Douglas Adams, The Long Dark Tea-Time of the Soul And here is a blend of the concepts "Asgard" and "conference": "Asgard During the Interuniverse Society conference, a bridge was opened to Valhalla...." Bifrost In Norse myth, the rainbow bridge that connected Earth to Asgard, home of the gods. It was extended to Tellus Tertius during the Interuniverse Society conference" -- From A Heinlein Concordance -- Front page picture from a local morning newspaper published today, Wednesday, May 25, 2005
As George Balanchine once asked,
"How much story do you want?" Posted 5/25/2005 at 2:22 PM |
"Poetry is a satisfying of the desire for resemblance.... If resemblance is described as a partial similarity between two dissimilar things, it complements and reinforces that which the two dissimilar things have in common. It makes it brilliant." -- Wallace Stevens, "Three Academic Pieces" in The Necessary Angel (1951) Two dissimilar things: 1. A talk to be given at a conference on "Mathematics and Narrative" in Mykonos in July: Mark Turner, "The Role of Narrative Imagining in Blended Mathematical Concepts" -- Abstract: "The Way We Think (Gilles Fauconnier and Mark Turner; Basic Books, 2002) presents a theory of conceptual integration, or "blending," as a basic mental operation. See http://blending.stanford.edu. This talk will explore some ways in which narrative imagining plays a role in blended mathematical concepts." 2. An application of the "conceptual blending" of Fauconnier and Turner to some journal entries of 2004: Cognitive Blending and the Two Cultures. Posted 5/25/2005 at 12:00 AM |
Final Arrangements, continued:
Two PolesFrom today's New York Times: From erraticimpact.com on Paul Ricoeur: "Ricoeur reserves his greatest admiration for
the narratologist Algirdas-Julien Greimas. [See below.]
Ricoeur also explores
the relationship
between the philosophical and religious domains, attempting to reconcile the two poles in his thought."
Elementary Art
continued: From Log24 on May 2, 2005: "... it is not in isolation that the rhetorical power of such oppositions resides, but in their articulation in relation to other oppositions. In Aristotle's Physics the four elements of earth, air, fire and water were said to be opposed in pairs. For more than two thousand years oppositional patterns based on these four elements were widely accepted as the fundamental structure underlying surface reality.... The structuralist semiotician Algirdas Greimas introduced the semiotic square (which he adapted from the 'logical square' of scholastic philosophy) as a means of analysing paired concepts more fully...." -- Daniel Chandler, Semiotics for Beginners Related material:
Poetry's Bones and Theme and Variations. Other readings on polarity: Log24, May 24, 2003, and from July 26, 2003:
Posted 5/24/2005 at 2:00 PM |
From the J. Paul Getty Trust:
"I've recently had it brought to my attention that the current accepted primary colors are magenta, cyan, and yellow. I teach elementary art and I'm wondering if I really need to point out that fact or if I should continue referring to the primary colors the way I always have -- red, yellow, and blue! Anyone have an opinion?" "There is a fundamental difference between color and pigment. Color represents energy radiated.... Pigments, as opposed to colors, represent energy that is not absorbed...." Another good background page
for elementary color education: Colored Shadow Explorations. A good starting point for non-elementary education: The "Color" category in Wikipedia. Further background: From "The Relations between "The theory of poetry, that is to say, the total of the
theories of poetry, often seems to become in time a mystical theology
or, more simply, a mystique. The reason for this must by now be clear.
The reason is the same reason why the pictures in a museum of modern
art often seem to become in time a mystical aesthetic, a prodigious
search of appearance, as if to find a way of saying and of establishing
that all things, whether below or above appearance, are one and that it
is only through reality, in which they are reflected or, it may be,
joined together, that we can reach them. Under such stress, reality
changes from substance to subtlety, a subtlety in which it was natural
for Cézanne to say: 'I see planes bestriding each other and sometimes
straight lines seem to me to fall' or 'Planes in color. . . . The
colored area where shimmer the souls of the planes, in the blaze of the
kindled prism, the meeting of planes in the sunlight.' The conversion
of our Lumpenwelt went far beyond this. It was from the point
of view of another subtlety that Klee could write: 'But he is one
chosen that today comes near to the secret places where original law
fosters all evolution. And what artist would not establish himself
there where the organic center of all movement in time and space—which
he calls the mind or heart of creation— determines every function.'
Conceding that this sounds a bit like sacerdotal jargon, that is not
too much to allow to those that have helped to create a new reality, a
modern reality, since what has been created is nothing less."
Posted 5/23/2005 at 1:00 PM |
Final Arrangements continued: Elements:
"Elegant." -- The Daily Telegraph Posted 5/23/2005 at 2:56 AM |
The Diamond in the Labyrinth From the labyrinth of Solitude:
Posted 5/22/2005 at 4:09 PM |
The Shining
of Friday the 13th From Margalit Fox in today's New York Times: "Eddie Barclay, who for three decades after World War II was arguably the most powerful music mogul in Europe and inarguably the most flamboyant, died on [Friday] May 13 in Paris. He was 84.... ... Mr. Barclay was best known for three things: popularizing American jazz in France in the postwar years; keeping the traditional French chanson alive into the age of rock 'n' roll; and presiding over parties so lavish that they were considered just the tiniest bit excessive even by the standards of the French Riviera....Among the guests at some of his glittering parties... Jack Nicholson...." Related material: "Joyce’s confidant in Zurich in 1918, Frank Budgen, luckily
for us described the process of writing Ulysses.... 'Not
Bloom, not Stephen is here the principal personage, but Dublin itself…
All towns are labyrinths…' While working...
Joyce bought a game called Labyrinth, which he played every evening
for a time with his daughter, Lucia. From this game he cataloged
the six main errors of judgment into which one might fall in seeking
a way out of a maze." -- quoted by Bruce Graham from The Creators by Daniel Boorstin "We'll always have Paris." -- An Invariant Feast, Log24, Sept. 6, 2004 Posted 5/22/2005 at 12:25 PM |
Icarus at Boardwalk
"As in Monopoly, the fortunes of -- Eileen Smith, Sept. 6, 2004 A link from Log24 last night: A Throw of the Dice: From Log24 on Aug. 29, 2003:
From today's online New York Times: 4 Killed as Small Plane Crashes narratives, I do not know. For Mallarmé's own views, see Un coup de Dés jamais n’abolira le Hasard. Posted 5/21/2005 at 10:29 PM |
History As She Is Writ "Finally, there is the matter of players changing history as she is writ." -- "Historical Fantasy Campaigns for Role Playing Simulations," published in Phantasmagoria, Murdoch Alternative Reality Society Annual, 2004, pp. 32-38 Franken is best known as the author of Lies and the Lying Liars Who Tell Them. Posted 5/21/2005 at 12:35 PM |
From a March 10, 2004, entry: "Language was no more than a collection of meaningless conventional signs, and life could absurdly end at any moment. [Mallarmé] became aware, in Millan's* words, 'of the extremely fine line
separating absence and presence, being and nothingness, life and death,
which -- John Simon, Squaring the Circle For those who prefer
Related material: Posted 5/21/2005 at 12:16 AM |
The Shining of Apollo "Plato's most significant passage may be found in Phaedrus 265b: 'And we made four divisions of the divine madness, ascribing them to four gods, saying that prophecy was inspired by Apollo, the mystic madness by Dionysos, the poetic by the Muses, and the madness of love [...] by Aphrodite and Eros' (trans. by H.N. Fowler, in the Loeb Classical Library)." -- Saverio Marchignoli, note on section 20, paragraphs 115-119, of the Discourse on the Dignity of Man (Oratio de hominis dignitate) (1486) by Pico della Mirandola, considered the "Manifesto of the Renaissance." Related material: A Mass for Lucero, The Shining of May 29, Shining Forth, Sermon for St. Patrick's Day, and the phrase Diamond Struck by the Sun. Posted 5/20/2005 at 1:20 PM |
Shining Through "Schon in der Antike gab es zwei Definitionen der
Schönheit, die in einem gewissen Gegensatz zueinander standen.... Die
eine bezeichnet die Schönheit als die richtige Übereinstimmung der
Teile miteinander und mit dem Ganzen. Die andere, auf Plotin
zurückgehend, ohne jede Bezugnahme auf Teile, bezeichnet sie als das
Durchleuchten des ewigen Glanzes des 'Einen' durch die materielle
Erscheinung."
-- Werner Heisenberg "Heisenberg sets down his glass. 'Perhaps I may remind you of the
second definition of beauty, which stems from Plotinus: "Beauty is the
translucence, through the material phenomenon, of the eternal splendor
of the One."'....
It's that translucence, that light shining through, that brings us to tears, wherever we find it.... As Sidney Bechet put it, 'You've got to be in the sun to feel the sun.'" -- Matt Glaser, Satchmo, the Philosopher, Posted 5/19/2005 at 10:10 AM |
"Beauty is
the proper conformity
of the parts to one another and to the whole." -- Werner Heisenberg, "Die Bedeutung des Schönen in der exakten Naturwissenschaft," address delivered to the Bavarian Academy of Fine Arts, Munich, 9 Oct. 1970, reprinted in Heisenberg's Across the Frontiers, translated by Peter Heath, Harper & Row, 1974 Related material: The Eightfold Cube Posted 5/18/2005 at 11:07 PM |
"The Garden of Eden is behind us and there is no road back to innocence; we can only go forward." — Anne Morrow Lindbergh, Earth Shine, p. xii Posted 5/18/2005 at 4:00 PM |
The Nine
"Nine is a very powerful Nordic number."
in The Magic Circle "To live is to defend a form." ("Leben, das heisst eine Form verteidigen") -- attributed to Hölderlin In defense of the nine-square grid:
For details on the above picture, see Posted 5/14/2005 at 9:00 PM |
Paths to the Absolute: Mondrian, Malevich, Kandinsky, Pollock, Newman, Rothko, and Still by John Golding Cloth | 2000 | $65.00 | ISBN: 0-691-04896-7 240 pp. | 7 x 10 | 63 color plates 109 halftones This may illuminate Krauss's remarks on Mondrian and Malevich at the conclusion of the previous entry. Posted 5/14/2005 at 4:00 PM |
Today's New York Times: "Horton Marlais Davies, Putnam professor emeritus of religion at
Princeton and an author of many books about church history, died on
Wednesday at his home in Princeton, N.J. He was 89.... Dr. Davies specialized in the impact of Christianity on the arts." A book edited by Horton Davies,
apparently first published by Eerdmans at Grand Rapids, Michigan, in 1990 The Catholic Encyclopedia (1908) on the communion of saints: "One cannot read the parables of the kingdom (Matt., xiii) without perceiving its corporate nature and the continuity which links together the kingdom in our midst and the kingdom to come. The nature of that communion, called by St. John a fellowship with one another ('a fellowship with Related material: Religious art in the entry Art History of 11 AM Wednesday, May 11, the date of Davies's death. See also the following direct and indirect links from that entry: To a cruciform artifact from the current film Kingdom of Heaven, to an entry quoting John xv, Nine is a Vine, and to Art Theory for Yom Kippur. For less-religious material on the number nine, see the entries and links in the Log24 archive for June 17-30, 2004.
From Rosalind Krauss, "Grids": "If we open any tract-- Plastic Art and Pure Plastic Art or The Non-Objective World, for instance-- we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter. They are talking about Being or Mind or Spirit." Amen. Posted 5/14/2005 at 1:00 PM |
Powers From today's New York Times -- Francesco Marchisano, made a cardinal on October 21, 2003: "All the saints have powers." Tonight at 8 PM ET on Fox: X-Men. Posted 5/13/2005 at 4:00 PM |
"Si me de veras quieres, (See Shining Forth.) Today's birthdays -- Natasha Richardson, Martha Quinn, Frances Fisher -- remind me of
Posted 5/11/2005 at 7:11 PM |
... y eres tú y soy yo
y es un caminarte en círculo dar a tus hechos dimensión de arco y a solas con tu impulso decirte la palabra. -- Homero Aridjis For Lucero:
Posted 5/11/2005 at 3:00 PM |
Art History
Reuters - "Joe Grant, a legendary Disney artist who designed the Queen/Witch in 'Snow White and the Seven Dwarfs,' died of a heart attack while doing what he loved most, drawing, the Walt Disney Co. said Monday. "With a little effort, anything can be
shown to connect with anything else: existence is infinitely cross-referenced." -- Opening sentence of From Log24 last Friday, Click on picture for details. Columbia University's Click on pictures for details. Related material: Nine is a Vine3. 1, 2, 3 Today's birthdays:
1 Natasha Richardson, born 11 May 1963, Jedi wife and costar of Nell 2 Martha Quinn, born 11 May 1959, MTV wit 3 Frances Fisher, born 11 May 1952, dazzling redhead Posted 5/11/2005 at 11:00 AM |
Europe Marks Nazis' Surrender -- Boston Globe on events of Sunday, May 8, 2005 "After all, tomorrow is another day." -- Gone with the Wind
St. Ephrem the Syrian (about 306 AD - 373 AD) "He... acquired honor as a Christian musician and poet. He was so accomplished in both arts that he was called the 'lyre of the Holy Spirit.'" -- Pope Benedict XV Posted 5/9/2005 at 12:12 PM |
Today's Sermon: "Holl, Adolf" pneumatology. Posted 5/8/2005 at 10:31 AM |
Geometry and Theology See
Mark Olson's article is at the website of the New England Science Fiction Association, publisher of Ingathering: The Complete People Stories of Zenna Henderson. This book, by one of my favorite science-fiction authors, was apparently edited by the same Mark Olson. The following remarks seem relevant to the recurring telepathy theme in Henderson: From the first article cited above, David L. Neuhouser, Higher Dimensions in the Writings of C. S. Lewis (pdf): "If we are three-dimensional cross-sections of four-dimensional reality, perhaps we are parts of the same body. In fact, we know we are parts of the same body in some way, this four-dimensional idea just may help us to see it more clearly. Remember the preceding comments are mine, not Lewis's. He puts it this way, 'That we can die "in" Adam and live "in" Christ seems to me to imply that man as he really is differs a good deal from man as our categories of thought and our three-dimensional imaginations represent him; that the separateness... which we discern between individuals, is balanced, in absolute reality, by some kind of inter-inanimation of which we have no conception at all. It may be that the acts and sufferings of great archetypal individuals such as Adam and Christ are ours, not by legal fiction, metaphor, or causality, but in some much deeper fashion. There is no question, of course, of individuals melting down into a kind of spiritual continuum such as Pantheistic systems believe in; that is excluded by the whole tenor of our faith.'" From Webster's Unabridged, 1913 edition: inanimate, [Pref. in- in (or intensively) + animate.] inanimation, n. animation; inspiration. The inanimation of Christ living and breathing within us. -- Bp. Hall. Related words... Also from the 1913 Webster's: circumincession, n. of the three persons of the Trinity. From an online essay: perichoresis "The term means mutual indwelling or, better, mutual interpenetration and refers to the understanding of both the Trinity and Christology. In the divine perichoresis, each person has 'being in each other without coalescence' (John of Damascus ca. 650). The roots of this doctrine are long and deep." -- Bert Waggoner coinherence, n.
-- Timothy Ware, Bishop Kallistos of Diokleia, Posted 5/8/2005 at 12:00 AM |
Fugues "To improvise an eight-part fugue is really beyond human capability." -- Douglas R. Hofstadter, Gödel, Escher, Bach Order of a projective automorphism group: 168 "There are possibilities of contrapuntal arrangement of subject-matter." -- T. S. Eliot, quoted in Origins of Form in Four Quartets. Order of a projective automorphism group: 20,160 Posted 5/6/2005 at 7:28 PM |
Involved
"Difficult to understand because of intricacy: byzantine, complex, complicated, convoluted, daedal, Daedalian, elaborate, intricate, involute, knotty, labyrinthine, tangled." -- Roget's II: The New Thesaurus, Third Edition Posted 5/6/2005 at 2:56 PM |
From the West Wing time slot:
"It's ... extremely weird how the previously- -- The Flick Filosopher Posted 5/6/2005 at 1:01 PM |
Crystalline
"In Francis Ford Coppola's film, Col. Kurtz tells how after his medics inoculated a small village, the Reds chopped off every child's left arm. 'My God, the genius of that. The genius,' Kurtz said. 'The will to do that. Perfect, genuine, complete, crystalline, pure! And then I realized they were stronger than me because they could stand it.'" -- Col. David Hackworth on Tuesday, April 9, 2002. Col. Hackworth died at 74 on Wednesday, May 4, 2005. Click on pictures for details. Posted 5/6/2005 at 10:18 AM |
The Fano Plane Revisualized: or, The Eightfold Cube Here is the usual model of the seven points and seven lines (including the circle) of the smallest finite projective plane (the Fano plane): 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 cubes' partitioning planes are added in binary (1+1=0) fashion. Three partitioned cubes are collinear if and only if their partitioning planes' binary sum equals zero.
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. For a proof that such permutations generate the 168 symmetries, see Binary Coordinate Systems. (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. For a large downloadable folder with many other related web pages, see Notes on Finite Geometry.
Posted 5/4/2005 at 1:00 PM |
Posted 5/3/2005 at 9:29 AM |
A Dance Results
"Professor Krauss even uses many of the same decorations with which she festooned earlier volumes. Bataille’s photograph of a big toe, for example, which I like to think of as her mascot, reappears. As does her favorite doodle, a little graph known as a 'Klein Group' or 'L Schema' whose sides and diagonals sport arrows pointing to corners labeled with various opposing pairs: e.g., 'ground' and 'not ground,' 'figure' and 'not figure.' Professor Krauss seems to believe that this device, lifted from the pages of structuralist theory, illuminates any number of deep mysteries: the nature of modernism, to begin with, but also the essence of gender relations, self-consciousness, perception, vision, castration anxiety, and other pressing conundrums that, as it happens, she has trouble distinguishing from the nature of modernism. Altogether, the doodle is a handy thing to have around. One is not surprised that Professor Krauss reproduces it many times in her new book."
From Drid Williams,
-- Daniel Chandler, Semiotics for Beginners.The Semiotics of Human Action, Ritual, and Dance: This is closely related to
Beckett's "Quad" figure
and to the Greimas "semiotic square":
"People have believed in the fundamental character of binary oppositions since at least classical times. For instance, in his Metaphysics Aristotle advanced as primary oppositions: form/matter, natural/unnatural, active/passive, whole/part, unity/variety, before/after and being/not-being.* But it is not in isolation that the rhetorical power of such oppositions resides, but in their articulation in relation to other oppositions. In Aristotle's Physics the four elements of earth, air, fire and water were said to be opposed in pairs. For more than two thousand years oppositional patterns based on these four elements were widely accepted as the fundamental structure underlying surface reality.... The structuralist semiotician Algirdas Greimas introduced the semiotic square (which he adapted from the 'logical square' of scholastic philosophy) as a means of analysing paired concepts more fully...." * Compare Chandler's list of Aristotle's primary oppositions with Aristotle's list (also in the Metaphysics) of Pythagorean oppositions (see Midrash Jazz Quartet). Posted 5/2/2005 at 11:00 AM |
Logos
Harvard's Barry Mazur on one mathematical style: "It’s the barest, most Beckett-like vocabulary that incorporates the theory and nothing else." Samuel Beckett, Quad (1981): A Jungian on this six-line logo: "They are the same six lines that exist in the I Ching.... Now observe the square more closely: four of the lines are of equal length, the other two are longer.... For this reason symmetry cannot be statically produced and a dance results." -- Marie-Louise von Franz, Number and Time (1970), Northwestern U. Press paperback, 1979, p. 108 A related logo from Columbia University's Department of Art History and Archaeology: Also from that department: Rosalind Krauss, Meyer Schapiro Professor of Modern Art and Theory: "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." "In the garden of Adding live Even and Odd..." -- The Midrash Jazz Quartet in City of God, by E. L. Doctorow THE GREEK CROSS A cross in which all the arms
are the same length. Here, for reference, is a Greek cross Related religious meditation for illustrated in Wikipedia under "cross": From designboom.com: THE BAPTISMAL CROSS
is a cross with eight arms: a Greek cross, which is superimposed on a Greek 'chi,' the first letter of the Greek word for 'Christ.' Since the number eight is symbolic of rebirth or regeneration, this cross is often used as a baptismal cross. Related material: Fritz Leiber's "spider" or "double cross" logo. See Why Me? and A Shot at Redemption. Happy Orthodox Easter. Posted 5/1/2005 at 1:11 PM |
Hooray, Hooray... Posted 5/1/2005 at 12:00 AM |