Vide —
Saturday, December 26, 2020
As It Were
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Sunday, January 4, 2015
As It Were
A search for antimetaphoric yields…
"And I heard, as it were, the noise of thunder."
See also other instances of "As It Were" in this journal.
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Saturday, September 17, 2011
As It Were
Historic plane crashes at West Virginia air show
"The T-28 aircraft crashed at about 2:40 p.m.
during an acrobatic demonstration at the 2011
Thunder Over the Blue Ridge Open House & Air Show…."
See also Themes—
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Friday, November 17, 2023
Classicism Continued: An Apotheosis of Modernity
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From Chapter 23, "Poetry," by Adam Parkes, in Writing in 1910–11, the English poet and critic T. E. Hulme claimed that the two major traditions in poetry, romanticism and classicism, were as different as a well and a bucket. According to the romantic party, Hulme explained, humankind is “intrinsically good, spoilt by circumstance”; that is, our nature is “a well, a reservoir full of possibilities.” For the classical party, however, human nature is “like a bucket”; it is “intrinsically limited, but disciplined by order and tradition to something fairly decent” (Hulme 1987: 117). But it was not only that romanticism and classicism were as dissimilar as a well and a bucket; their contents were different, too. To draw water from the well of romanticism was, in effect, to pour a “pot of treacle over the dinner table,” while the classical bucket was more likely to be full of little stones – or jewels, perhaps. Romanticism, in Hulme’s view, was the result of displaced religious fervor; it represented the return of religious instincts that the “perverted rhetoric of Rationalism” had suppressed, so that “concepts that are right and proper in their own sphere are spread over, and so mess up, falsify and blur the clear outlines of human experience” (Hulme 1987: 118). Classicism, by contrast, traded in dry goods – dry, hard goods, to be precise. Hulme left little doubt as to which side he was on. “It is essential to prove,” he argued, “that beauty may be in small, dry things. The great aim is accurate, precise and definite description. . . . I prophesy that a period of dry, hard, classical verse is coming” (Hulme 1987: 131–3). If by “dry, hard, classical verse” Hulme meant poems looking like the fragments of Sappho, he didn’t have to wait long to see his prophecy fulfilled.
The hard sand breaks,
Far off over the leagues of it, 228
playing on the wide shore, So wrote Hilda Doolittle in “Hermes of the Ways,” the first poem that she signed “H. D., Imagiste” at the behest of her fellow American expatriate Ezra Pound. From Pound’s perspective, the Imagist movement that he co-founded in 1912 with H. D. and the English poet Richard Aldington was finished well before the First World War began in August 1914; throughout this war-torn decade, however, Imagism continued to spawn the poetry of “small, dry things” whose coming Hulme had predicted a few years before. Indeed, modernist poets weren’t content merely to break down the extended heroic narratives – the “spilt religion,” as Hulme put it – of their treacly nineteenthcentury predecessors; they insisted on breaking down small things into ever-smaller particles and subparticles. This logic of disintegration is clearly at work in poems like “Hermes of the Ways,” where each line is metrically unique, creating a sense of perpetual freshness – an apotheosis of modernity, as it were. REFERENCE Hulme, T. E. (1987). Speculations: Essays on Humanism and the Philosophy of Art, ed. Herbert Read. London and New York: Routledge and Kegan Paul. First published 1924. |
Compare and contrast:
Jeremy Gray,
Plato's Ghost: The Modernist Transformation of Mathematics,
Princeton University Press, first edition Sept. 22, 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…."
(Quoted at the webpage Solomon's Cube.)
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Friday, October 13, 2023
Turn, Turn, Turn
The conclusion of a Hungarian political figure's obituary in
tonight's online New York Times, written by Clay Risen —
"A quietly religious man, he spent his last years translating
works dealing with Roman Catholic canon law."
This journal on the Hungarian's date of death, October 8,
a Sunday, dealt in part with the submission to Wikipedia of
the following brief article . . . and its prompt rejection.
|
The Cullinane diamond theorem is a theorem
The theorem also explains symmetry properties of the Reference
1. Cullinane diamond theorem at |
Some quotations I prefer to Catholic canon law —
|
Ludwig Wittgenstein,
97. Thought is surrounded by a halo. * See the post Wittgenstein's Diamond. Related language in Łukasiewicz (1937)—
|
See as well Diamond Theory in 1937.
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Friday, January 13, 2023
LMS Gresham
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Posted on 13/01/2023 by Peter Cameron My last major job at Queen Mary University of London more than ten years ago was designing and presenting a new first-semester first-year module to be taken by all students on mathematics programmes or joint programmes involving mathematics. I discussed it in my LMS-Gresham lecture. |
LMS
Gresham
"… seeds having fallen on barren rock, as it were" . . .
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Sunday, October 18, 2020
The Limits of Language
Wittgenstein, Philosophical Investigations 118-119 —
| 118. | Where does our investigation get its importance from, since it seems only to destroy everything interesting, that is, all that is great and important? (As it were all the buildings, leaving behind only bits of stone and rubble.) What we are destroying is nothing but houses of cards and we are clearing up the ground of language on which they stand. |
| 119. | The results of philosophy are the uncovering of one or another piece of plain nonsense and of bumps that the understanding has got by running its head up against the limits of language. These bumps make us see the value of the discovery. |
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Wednesday, February 13, 2019
April 18, 2003 (Good Friday), Continued
"The purpose of mathematics cannot be derived from an activity
inferior to it but from a higher sphere of human activity, namely,
religion."
— Igor Shafarevitch, 1973 remark published as above in 1982.
"Perhaps."
— Steven H. Cullinane, February 13, 2019
|
From Log24 on Good Friday, April 18, 2003 — . . . What, indeed, is truth? I doubt that the best answer can be learned from either the Communist sympathizers of MIT or the “Red Mass” leftists of Georgetown. For a better starting point than either of these institutions, see my note of April 6, 2001, Wag the Dogma. See, too, In Principio Erat Verbum , which notes that “numbers go to heaven who know no more of God on earth than, as it were, of sun in forest gloom.” Since today is the anniversary of the death of MIT mathematics professor Gian-Carlo Rota, an example of “sun in forest gloom” seems the best answer to Pilate’s question on this holy day. See
“Examples are the stained glass windows Motto of Plato’s Academy † The Exorcist, 1973 |
Detail from an image linked to in the above footnote —
"And the darkness comprehended it not."
Id est :
A Good Friday, 2003, article by
a student of Shafarevitch —
"… there are 25 planes in W . . . . Of course,
replacing {a,b,c} by the complementary set
does not change the plane. . . ."
Of course.
See. however, Six-Set Geometry in this journal.
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Sunday, September 25, 2016
Introduction to Pragmatism
Stanford Encyclopedia of Philosophy
on the origins of Pragmatism:
"Pragmatism had been born in the discussions at
a ‘metaphysical club’ in Harvard around 1870
(see Menand…*). Peirce and James participated
in these discussions along with some other philosophers
and philosophically inclined lawyers. As we have
already noted, Peirce developed these ideas in his
publications from the 1870s."
|
From "How to Make Our Ideas Clear," "The very first lesson that we have a right to demand that logic shall teach us is, how to make our ideas clear; and a most important one it is, depreciated only by minds who stand in need of it. To know what we think, to be masters of our own meaning, will make a solid foundation for great and weighty thought. It is most easily learned by those whose ideas are meagre and restricted; and far happier they than such as wallow helplessly in a rich mud of conceptions. A nation, it is true, may, in the course of generations, overcome the disadvantage of an excessive wealth of language and its natural concomitant, a vast, unfathomable deep of ideas. We may see it in history, slowly perfecting its literary forms, sloughing at length its metaphysics, and, by virtue of the untirable patience which is often a compensation, attaining great excellence in every branch of mental acquirement. The page of history is not yet unrolled which is to tell us whether such a people will or will not in the long-run prevail over one whose ideas (like the words of their language) are few, but which possesses a wonderful mastery over those which it has. For an individual, however, there can be no question that a few clear ideas are worth more than many confused ones. A young man would hardly be persuaded to sacrifice the greater part of his thoughts to save the rest; and the muddled head is the least apt to see the necessity of such a sacrifice. Him we can usually only commiserate, as a person with a congenital defect. Time will help him, but intellectual maturity with regard to clearness comes rather late, an unfortunate arrangement of Nature, inasmuch as clearness is of less use to a man settled in life, whose errors have in great measure had their effect, than it would be to one whose path lies before him. It is terrible to see how a single unclear idea, a single formula without meaning, lurking in a young man's head, will sometimes act like an obstruction of inert matter in an artery, hindering the nutrition of the brain, and condemning its victim to pine away in the fullness of his intellectual vigor and in the midst of intellectual plenty. Many a man has cherished for years as his hobby some vague shadow of an idea, too meaningless to be positively false; he has, nevertheless, passionately loved it, has made it his companion by day and by night, and has given to it his strength and his life, leaving all other occupations for its sake, and in short has lived with it and for it, until it has become, as it were, flesh of his flesh and bone of his bone; and then he has waked up some bright morning to find it gone, clean vanished away like the beautiful Melusina of the fable, and the essence of his life gone with it. I have myself known such a man; and who can tell how many histories of circle-squarers, metaphysicians, astrologers, and what not, may not be told in the old German story?" |
Peirce himself may or may not have been entirely successful
in making his ideas clear. See Where Credit Is Due (Log24,
June 11, 2016) and the Wikipedia article Categories (Peirce).
* Menand, L., 2001. The Metaphysical Club : A Story of
Ideas in America , New York: Farrar, Straus and Giroux
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Friday, October 30, 2015
For Scientific Witch Hunters*
Motto selected by an Oslo artist —
Illustration selected by The Boston Globe —
Notes on perspective selected at Log24 —
* I.e. , those who hunt witches scientifically,
or those who hunt scientific witches —
a matter of, as it were, perspective.
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Tuesday, October 23, 2012
Labyrinth 23
The title refers to a search (see below)
suggested by three things—
- David Foster Wallace biographer D. T. Max—
"There's a note in one of my files where he says something like,
'Infinite Jest was just a means to Mary Karr's end, as it were.' " - "There is a body on the cross in my church ." —Mary Karr
- A body.
The search— Labyrinth 23.
(Within the search results, note particularly the post "The Infinity Point.")
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Monday, May 21, 2012
Wittgenstein’s Kindergarten
A web search for the author Cameron McEwen mentioned
in today's noon post was unsuccessful, but it did yield an
essay, quite possibly by a different Cameron McEwen, on
"The fundamental difference between analog
and digital systems may be understood as
underlying philosophical discourse since the Greeks."
The University of Bergen identifies the Wittgenstein
McEwen as associated with InteLex of Charlottesville.
The title of this post may serve to point out an analogy*
between the InteLex McEwen's analog-digital contrast
and the Euclidean-Galois contrast discussed previously
in this journal.
The latter contrast is exemplified in Pilate Goes to Kindergarten.
* An analogy, as it were, between analogies.
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Friday, December 23, 2011
About the People
(Continued from April 5, 2009)
"Thought can as it were fly , it doesn't have to walk."
— Ludwig Wittgenstein, Zettel , fragment 273
See also a related song.
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Friday, September 23, 2011
Kali’s Thunder
NY Lottery this evening—
Continued from Themes of Sept. 17—
"And I heard, as it were, the noise of thunder."
Lottery hermeneutics for this evening—
747 — Source of the sound effect in a post of April 28, 2009:
"And Kali, ‘The Dark One,’ addressed him with the voice of a cloud of thunder…"
— The King and the Corpse , by Heinrich Zimmer
3695 — Number of a post on Steps Toward Salvation (Dec. 14, 2008)
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Saturday, September 17, 2011
Themes
"'Ain’t No Grave' is Johnny’s final studio recording. The album and its title track
deal heavily with themes of mortality, resurrection, and everlasting life.
The Johnny Cash Project pays tribute to these themes."
And sells products!
Click image to enlarge.
I prefer "And I heard, as it were, the noise of thunder."
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Tuesday, August 30, 2011
Boundary
A comment yesterday on the New York Times philosophy column “The Stone” quoted Karl Barth—
“Man is the creature of the boundary between heaven and earth.”
See also Plato’s theory of ideas (or “forms”) and the I Ching—
The eight trigrams are images not so much of objects as of states of change. This view is associated with the concept expressed in the teachings of Lao-tse, as also in those of Confucius, that every event in the visible world is the effect of an “image,” that is, of an idea in the unseen world. Accordingly, everything that happens on earth is only a reproduction, as it were, of an event in a world beyond our sense perception; as regards its occurrence in time, it is later than the suprasensible event. The holy men and sages, who are in contact with those higher spheres, have access to these ideas through direct intuition and are therefore able to intervene decisively in events in the world. Thus man is linked with heaven, the suprasensible world of ideas, and with earth, the material world of visible things, to form with these a trinity of the primal powers.
— Richard Wilhelm, Introduction to the I Ching
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Wednesday, July 20, 2011
Cover Art
The Misalignment of Mars and Venus
A death in Sarasota on Sunday leads to a weblog post from Tuesday
that suggests a review of Dan Brown's graphic philosophy—
|
From The Da Vinci Code : Langdon pulled a pen from his pocket. “Sophie are you familiar with the modern icons for male and female?” He drew the common male symbol ♂ and female symbol ♀. “Of course,” she said. “These,” he said quietly, are not the original symbols for male and female. Many people incorrectly assume the male symbol is derived from a shield and spear, while the female represents a mirror reflecting beauty. In fact, the symbols originated as ancient astronomical symbols for the planet-god Mars and the planet-goddess Venus. The original symbols are far simpler.” Langdon drew another icon on the paper. ∧
“This symbol is the original icon for male ,” he told her. “A rudimentary phallus.” “Quite to the point,” Sophie said. “As it were,” Teabing added. Langdon went on. “This icon is formally known as the blade , and it represents aggression and manhood. In fact, this exact phallus symbol is still used today on modern military uniforms to denote rank.” “Indeed.” Teabing grinned. “The more penises you have, the higher your rank. Boys will be boys.”
Langdon winced. “Moving on, the female symbol, as you might imagine, is the exact opposite.” He drew another symbol on the page. “This is called the ∨ Sophie glanced up, looking surprised. Langdon could see she had made the connection. “The chalice,” he said, “resembles a cup or vessel, and more important, it resembles the shape of a woman’s womb. This symbol communicates femininity, womanhood, and fertility.” |
Langdon's simplified symbols, in disguised form, illustrate
a musical meditation on the misalignment of Mars and Venus—
This was adapted from an album cover by "Meyers/Monogram"—
See also Secret History and The Story of N.
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Wednesday, July 13, 2011
The Sinatra Code
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From The Da Vinci Code, Chapter 56 Sophie stared at Teabing a long moment and then turned to Langdon. “The Holy Grail is a person?” Langdon nodded. “A woman, in fact.” From the blank look on Sophie’s face, Langdon could tell they had already lost her. He recalled having a similar reaction the first time he heard the statement. It was not until he understood the symbology behind the Grail that the feminine connection became clear. Teabing apparently had a similar thought. “Robert, perhaps this is the moment for the symbologist to clarify?” He went to a nearby end table, found a piece of paper, and laid it in front of Langdon. Langdon pulled a pen from his pocket. “Sophie are you familiar with the modern icons for male and female?” He drew the common male symbol ♂ and female symbol ♀. “Of course,” she said. “These,” he said quietly, are not the original symbols for male and female. Many people incorrectly assume the male symbol is derived from a shield and spear, while the female represents a mirror reflecting beauty. In fact, the symbols originated as ancient astronomical symbols for the planet-god Mars and the planet-goddess Venus. The original symbols are far simpler.” Langdon drew another icon on the paper. ∧
“This symbol is the original icon for male ,” he told her. “A rudimentary phallus.” “Quite to the point,” Sophie said. “As it were,” Teabing added. Langdon went on. “This icon is formally known as the blade , and it represents aggression and manhood. In fact, this exact phallus symbol is still used today on modern military uniforms to denote rank.” “Indeed.” Teabing grinned. “The more penises you have, the higher your rank. Boys will be boys.” Langdon winced. “Moving on, the female symbol, as you might imagine, is the exact opposite.” He drew another symbol on the page. “This is called the ∨ Sophie glanced up, looking surprised. Langdon could see she had made the connection. “The chalice,” he said, “resembles a cup or vessel, and more important, it resembles the shape of a woman’s womb. This symbol communicates femininity, womanhood, and fertility.” Langdon looked directly at her now. “Sophie, legend tells us the Holy Grail is a chalice—a cup. But the Grail’s description as a chalice is actually an allegory to protect the true nature of the Holy Grail. That is to say, the legend uses the chalice as a metaphor for something far more important.” “A woman,” Sophie said. “Exactly.” Langdon smiled. “The Grail is literally the ancient symbol for womankind, and the Holy Grail represents the sacred feminine and the goddess, which of course has now been lost, virtually eliminated by the Church. The power of the female and her ability to produce life was once very sacred, but it posed a threat to the rise of the predominantly male Church, and so the sacred feminine was demonized and called unclean. It was man , not God, who created the concept of ‘original sin,’ whereby Eve tasted of the apple and caused the downfall of the human race. Woman, once the sacred giver of life, was now the enemy.” “I should add,” Teabing chimed, “that this concept of woman as life-bringer was the foundation of ancient religion. Childbirth was mystical and powerful. Sadly, Christian philosophy decided to embezzle the female’s creative power by ignoring biological truth and making man the Creator. Genesis tells us that Eve was created from Adam’s rib. Woman became an offshoot of man. And a sinful one at that. Genesis was the beginning of the end for the goddess.” “The Grail,” Langdon said, “is symbolic of the lost goddess. When Christianity came along, the old pagan religions did not die easily. Legends of chivalric quests for the lost Grail were in fact stories of forbidden quests to find the lost sacred feminine. Knights who claimed to be “searching for the chalice” were speaking in codes as a way to protect themselves from a Church that had subjugated women, banished the Goddess, burned nonbelievers, and forbidden pagan reverence for the sacred feminine.” |
Happy birthday to Harrison Ford.
One for my baby…
∧
One more for the road.
∨
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Sunday, July 10, 2011
Wittgenstein’s Diamond
Philosophical Investigations (1953)—
97. Thought is surrounded by a halo.
—Its essence, logic, presents an order,
in fact the a priori order of the world:
that is, the order of possibilities * ,
which must be common to both world and thought.
But this order, it seems, must be
utterly simple . It is prior to all experience,
must run through all experience;
no empirical cloudiness or uncertainty can be allowed to affect it
——It must rather be of the purest crystal.
But this crystal does not appear as an abstraction;
but as something concrete, indeed, as the most concrete,
as it were the hardest thing there is
(Tractatus Logico-Philosophicus No. 5.5563).
— Translation by G.E.M. Anscombe
All propositions of our colloquial language
are actually, just as they are, logically completely in order.
That simple thing which we ought to give here is not
a model of the truth but the complete truth itself.
(Our problems are not abstract but perhaps
the most concrete that there are.)
97. Das Denken ist mit einem Nimbus umgeben.
—Sein Wesen, die Logik, stellt eine Ordnung dar,
und zwar die Ordnung a priori der Welt,
d.i. die Ordnung der Möglichkeiten ,
die Welt und Denken gemeinsam sein muß.
Diese Ordnung aber, scheint es, muß
höchst einfach sein. Sie ist vor aller Erfahrung;
muß sich durch die ganze Erfahrung hindurchziehen;
ihr selbst darf keine erfahrungsmäßige Trübe oder Unsicherheit anhaften.
——Sie muß vielmehr vom reinsten Kristall sein.
Dieser Kristall aber erscheint nicht als eine Abstraktion;
sondern als etwas Konkretes, ja als das Konkreteste,
gleichsam Härteste . (Log. Phil. Abh. No. 5.5563.)
Related language in Łukasiewicz (1937)—
* Updates of 9:29 PM ET July 10, 2011—
A mnemonic from a course titled “Galois Connections and Modal Logics“—
“Traditionally, there are two modalities, namely, possibility and necessity.
The basic modal operators are usually written 
(square) for necessarily
and 
(diamond) for possibly. Then, for example, P can be read as
‘it is possibly the case that P .'”
| See also Intensional Semantics , lecture notes by Kai von Fintel and Irene Heim, MIT, Spring 2007 edition—
“The diamond ⋄ symbol for possibility is due to C.I. Lewis, first introduced in Lewis & Langford (1932), but he made no use of a symbol for the dual combination ¬⋄¬. The dual symbol □ was later devised by F.B. Fitch and first appeared in print in 1946 in a paper by his doctoral student Barcan (1946). See footnote 425 of Hughes & Cresswell (1968). Another notation one finds is L for necessity and M for possibility, the latter from the German möglich ‘possible.’” Barcan, Ruth C.: 1946. “A Functional Calculus of First Order Based on Strict Implication.” Journal of Symbolic Logic, 11(1): 1–16. URL http://www.jstor.org/pss/2269159. Hughes, G.E. & Cresswell, M.J.: 1968. An Introduction to Modal Logic. London: Methuen. Lewis, Clarence Irving & Langford, Cooper Harold: 1932. Symbolic Logic. New York: Century. |
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Wednesday, May 4, 2011
Unity and Multiplicity
Continued from Crimson Walpurgisnacht.
Epigraphs— Two quotations from
Shakespeare's Birthday last year—
|
"I was reading Durant's section on Plato, struggling to understand his theory of the ideal Forms that lay in inviolable perfection out beyond the phantasmagoria. (That was the first, and I think the last, time that I encountered that word.)" |
|
"We tell ourselves stories in order to live…. We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the 'ideas' with which we have learned to freeze the shifting phantasmagoria which is our actual experience." |
From Thomas Mann, "Schopenhauer," 1938, in Essays of Three Decades , translated by H. T. Lowe-Porter, Alfred A. Knopf, 1947, pp. 372-410—
Page 372: THE PLEASURE we take in a metaphysical system, the gratification purveyed by the intellectual organization of the world into a closely reasoned, complete, and balanced structure of thought, is always of a pre-eminently aesthetic kind. It flows from the same source as the joy, the high and ever happy satisfaction we get from art, with its power to shape and order its material, to sort out life's manifold confusions so as to give us a clear and general view.
Truth and beauty must always be referred the one to the other. Each by itself, without the support given by the other, remains a very fluctuating value. Beauty that has not truth on its side and cannot have reference to it, does not live in it and through it, would be an empty chimera— and "What is truth?"
….
Page 376: … the life of Plato was a very great event in the history of the human spirit; and first of all it was a scientific and a moral event. Everyone feels that something profoundly moral attaches to this elevation of the ideal as the only actual, above the ephemeralness and multiplicity of the phenomenal, this devaluation of the senses to the advantage of the spirit, of the temporal to the advantage of the eternal— quite in the spirit of the Christianity that came after it. For in a way the transitory phenomenon, and the sensual attaching to it, are put thereby into a state of sin: he alone finds truth and salvation who turns his face to the eternal. From this point of view Plato's philosophy exhibits the connection between science and ascetic morality.
But it exhibits another relationship: that with the world of art. According to such a philosophy time itself is merely the partial and piecemeal view which an individual holds of ideas— the latter, being outside time, are thus eternal. "Time"— so runs a beautiful phrase of Plato— "is the moving image of eternity." And so this pre-Christian, already Christian doctrine, with all its ascetic wisdom, possesses on the other hand extraordinary charm of a sensuous and creative kind; for a conception of the world as a colourful and moving phantasmagoria of pictures, which are transparencies for the ideal and the spiritual, eminently savours of the world of art, and through it the artist, as it were, first comes into his own.
From last night's online NY Times obituaries index—
"How much story do you want?" — George Balanchine
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Monday, December 27, 2010
Church Diamond
Also known, roughly speaking, as confluence or the Church-Rosser property.
From “NYU Lambda Seminar, Week 2” —
[See also the parent page Seminar in Semantics / Philosophy of Language or:
What Philosophers and Linguists Can Learn From Theoretical Computer Science But Didn’t Know To Ask)]
A computational system is said to be confluent, or to have the Church-Rosser or diamond property, if, whenever there are multiple possible evaluation paths, those that terminate always terminate in the same value. In such a system, the choice of which sub-expressions to evaluate first will only matter if some of them but not others might lead down a non-terminating path.
The untyped lambda calculus is confluent. So long as a computation terminates, it always terminates in the same way. It doesn’t matter which order the sub-expressions are evaluated in.
A computational system is said to be strongly normalizing if every permitted evaluation path is guaranteed to terminate. The untyped lambda calculus is not strongly normalizing: ω ω doesn’t terminate by any evaluation path; and (\x. y) (ω ω) terminates only by some evaluation paths but not by others.
But the untyped lambda calculus enjoys some compensation for this weakness. It’s Turing complete! It can represent any computation we know how to describe. (That’s the cash value of being Turing complete, not the rigorous definition. There is a rigorous definition. However, we don’t know how to rigorously define “any computation we know how to describe.”) And in fact, it’s been proven that you can’t have both. If a computational system is Turing complete, it cannot be strongly normalizing.
There is no connection, apart from the common reference to an elementary geometric shape, between the use of “diamond” in the above Church-Rosser sense and the use of “diamond” in the mathematics of (Cullinane’s) Diamond Theory.
Any attempt to establish such a connection would, it seems, lead quickly into logically dubious territory.
Nevertheless, in the synchronistic spirit of Carl Jung and Arthur Koestler, here are some links to such a territory —
Link One — “Insane Symmetry” (Click image for further details)—
See also the quilt symmetry in this journal on Christmas Day.
Link Two — Divine Symmetry
(George Steiner on the Name in this journal on Dec. 31 last year (“All about Eve“)) —
“The links are direct between the tautology out of the Burning Bush, that ‘I am’ which accords to language the privilege of phrasing the identity of God, on the one hand, and the presumptions of concordance, of equivalence, of translatability, which, though imperfect, empower our dictionaries, our syntax, our rhetoric, on the other. That ‘I am’ has, as it were, at an overwhelming distance, informed all predication. It has spanned the arc between noun and verb, a leap primary to creation and the exercise of creative consciousness in metaphor. Where that fire in the branches has gone out or has been exposed as an optical illusion, the textuality of the world, the agency of the Logos in logic—be it Mosaic, Heraclitean, or Johannine—becomes ‘a dead letter.'”
– George Steiner, Grammars of Creation
(See also, from Hanukkah this year, A Geometric Merkabah and The Dreidel is Cast.)
Link Three – Spanning the Arc —
Part A — Architect Louis Sullivan on “span” (see also Kindergarten at Stonehenge)
Part B — “Span” in category theory at nLab —
Also from nLab — Completing Spans to Diamonds
“It is often interesting whether a given span in some partial ordered set can be completed into a diamond. The property of a collection of spans to consist of spans which are expandable into diamonds is very useful in the theory of rewriting systems and producing normal forms in algebra. There are classical results e.g. Newman’s diamond lemma, Širšov-Bergman’s diamond lemma (Širšov is also sometimes spelled as Shirshov), and Church-Rosser theorem (and the corresponding Church-Rosser confluence property).”
The concepts in this last paragraph may or may not have influenced the diamond theory of Rudolf Kaehr (apparently dating from 2007).
They certainly have nothing to do with the Diamond Theory of Steven H. Cullinane (dating from 1976).
For more on what the above San Francisco art curator is pleased to call “insane symmetry,” see this journal on Christmas Day.
For related philosophical lucubrations (more in the spirit of Kaehr than of Steiner), see the New York Times “The Stone” essay “Span: A Remembrance,” from December 22—
“To understand ourselves well,” [architect Louis] Sullivan writes, “we must arrive first at a simple basis: then build up from it.”
Around 300 BC, Euclid arrived at this: “A point is that which has no part. A line is breadthless length.”
See also the link from Christmas Day to remarks on Euclid and “architectonic” in Mere Geometry.
Comments Off on Church Diamond
Wednesday, February 10, 2010
Mathematics and Religion, continued
But Seriously…
From "Georg Cantor and the Battle for Transfinite Set Theory," by Joseph W. Dauben (pdf)–
"It is easy, of course, to misinterpret the religious element in Cantor's thinking, as popularizers often do. This was certainly the case in an article that appeared not long ago in the French magazine La Recherche, which supplied [the above] caricatures to illustrate an expository article about Cantor, his religious convictions, psychological illness and transfinite set theory.* The first drawing depicts Cantor in ecstasy, as it were, receiving the divine message. In the second illustration, the figure with the gun of course is meant to be Kronecker– with God helping Cantor to maintain his balance– all of which rests precariously on a transfinite aleph. But there is a very serious side to all of this…."
* Pierre Thuillier, “Dieu, Cantor et l'Infini,” La Recherche, (December, 1977), pp. 1110-1116.
Everything and More: A Compact History of Infinity, by David Foster Wallace–
"In modern medical terms, it's fairly clear that G.F.L.P. Cantor suffered from manic-depressive illness at a time when nobody knew what this was, and that his polar cycles were aggravated by professional stresses and disappointments, of which Cantor had more than his share. Of course, this makes for less interesting flap copy than Genius Driven Mad by Attempts to Grapple with ∞. The truth, though, is that Cantor's work and its context are so totally interesting and beautiful that there's no need for breathless Prometheusizing of the poor guy's life. The real irony is that the view of ∞ as some forbidden zone or road to insanity– which view was very old and powerful and haunted math for 2000+ years– is precisely what Cantor's own work overturned. Saying that ∞ drove Cantor mad is sort of like mourning St. George's loss to the dragon: it's not only wrong but insulting."
Related entertainment:
David Foster Wallace,
Influential Writer, Dies at 46
and the film "Neverwas"–
Comments Off on Mathematics and Religion, continued
Thursday, December 31, 2009
All About Eve
Genesis 3:24—
So he drove out the man; and he placed
at the east of the garden of Eden Cherubims,
and a flaming sword which turned every way,
to keep the way of the tree of life.
|
"The links are direct between the tautology out of the Burning Bush, that 'I am' which accords to language the privilege of phrasing the identity of God, on the one hand, and the presumptions of concordance, of equivalence, of translatability, which, though imperfect, empower our dictionaries, our syntax, our rhetoric, on the other. That 'I am' has, as it were, at an overwhelming distance, informed all predication. It has spanned the arc between noun and verb, a leap primary to creation and the exercise of creative consciousness in metaphor. Where that fire in the branches has gone out or has been exposed as an optical illusion, the textuality of the world, the agency of the Logos in logic—be it Mosaic, Heraclitean, or Johannine—becomes 'a dead letter.'" |
Carlene Hatcher Polite–
"Shall I help you?" asked a bass voice.
"If you can," answered a contralto.
"Trace down this tree. Let me show you
men in its stead. Leaf through this bush,
extinguish the burning fire…"
— The Flagellants, page 8
"How much story do you want?"
— George Balanchine
Comments Off on All About Eve
Friday, July 3, 2009
Friday July 3, 2009
Damnation Morning
continued
“The tigers of wrath are wiser
than the horses of instruction.”
continued
“The tigers of wrath are wiser
than the horses of instruction.”
— Blake
“… the moment is not
properly an atom of time
but an atom of eternity.
It is the first reflection
of eternity in time, its first
attempt, as it were, at
stopping time….”
— Kierkegaard
|
Symmetry Axes
of the Square: 
From the cover of the
|
A Monolith
for Kierkegaard:  |
Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.
— Rubén Darío
Related material:
The deaths of
Ernest Hemingway
on the morning of
Sunday, July 2, 1961,
and of Alexis Arguello
on the morning of
Wednesday, July 1, 2009.
See also philosophy professor
Clancy Martin in the
London Review of Books
(issue dated July 9, 2009)
on AA members as losers—
“the ‘last men,’ the nihilists,
the hopeless ones.”
Comments Off on Friday July 3, 2009
Thursday, July 2, 2009
Thursday July 2, 2009
Meditation
on a joke by George Carlin,
a passage by Kierkegaard,
and the death on this date
12 years ago
of actor James Stewart
The Catholic Carlin:
“Thank you, Mr. Twain. Have your people call my people.” –George Carlin on learning he had won the Mark Twain award. Twain’s people were Protestant, Carlin’s Catholic.
The Protestant Kierkegaard:
“… the moment is not properly an atom of time but an atom of eternity. It is the first reflection of eternity in time, its first attempt, as it were, at stopping time….
Once here in Copenhagen there were two actors who probably never thought that their performance could have a deeper significance. They stepped forth onto the stage, placed themselves opposite each other, and then began the mimical representation of one or another passionate conflict. When the mimical act was in full swing and the spectators’ eyes followed the story with expectation of what was to follow, they suddenly stopped and remained motionless as though petrified in the mimical expression of the moment. The effect of this can he exceedingly comical, for the moment in an accidental way becomes commensurable with the eternal.”
Catholic tableau
(with Vivien Leigh
representing the Church)
of Salvation by Works —
Protestant tableau
(with James Stewart
as Protestant Pilgrim)
of Salvation by Grace —
Click on either tableau
for a (much) larger image.
* Thanks to University Diaries for an entry on Clancy Martin, a philosophy professor in the “show me” state, and his experiences with AA. For a sample of Martin’s style, see a piece he wrote on Fabergé Easter eggs. For other Easter egg material, see this journal and (via a link) The Harvard Crimson, Easter 2008. A valuable philosophical remark by Martin in a recent interview:
“An unscrupulous jeweler will swap diamonds for cheaper ones when jewelry is dropped off to be sized or repaired, he said.
‘It happens all the time,’ Martin said. ‘Nobody’s watching.'”
Comments Off on Thursday July 2, 2009
Saturday, December 6, 2008
Saturday December 6, 2008
Shining Forth
| Abstraction and Faith On Kirk Varnedoe’s National Gallery lectures in 2003 (Philip Kennicott, Washington Post, Sunday, May 18, 2003): “Varnedoe’s lectures were ultimately about faith, about his faith in the power of abstraction, and abstraction as a kind of anti-religious faith in itself.”
|
et lux in tenebris lucet
et tenebrae eam non conprehenderunt
… the mirroring …
is to be conceived of as
a shining forth, a play of mirror flashes,
as it were…. The four “mirrors”
emerge into presence as light
at the same time that they converge….
The above image:
Axes of Reflection
and Annunciation,
the latter being a detail
of a fresco by Giotto
on the cover of
The Pearly Gates of Cyberspace.
Happy Feast of St. Nicholas.
Comments Off on Saturday December 6, 2008
Sunday, September 14, 2008
Sunday September 14, 2008
On John McCain’s presidential campaign eight years ago:
“He always pauses a second for effect and then says: ‘I’m going to tell you something. I may have said some things here today that maybe you don’t agree with, and I might have said some things you hopefully do agree with. But I will always. Tell you. The truth.’ This is McCain’s closer, his last big reverb on the six-string as it were. And the frenzied standing-O it always gets from his audience is something to see. But you have to wonder. Why do these crowds from Detroit to Charleston cheer so wildly at a simple promise not to lie?
Well, it’s obvious why. When McCain says it, the people are cheering not for him so much as for how good it feels to believe him. They’re cheering the loosening of a weird sort of knot in the electoral tummy. McCain’s resume and candor, in other words, promise not empathy with voters’ pain but relief from it. Because we’ve been lied to and lied to, and it hurts to be lied to. It’s ultimately just about that complicated. It hurts.
We learn this at like age four– it’s grownups’ first explanation to us of why it’s bad to lie (‘How would you like it if…?’). And we keep learning for years, from hard experience, that getting lied to sucks– that it diminishes you, denies you respect for yourself, for the liar, for the world. Especially if the lies are chronic, systemic, if experience seems to teach that everything you’re supposed to believe in’s really just a game based on lies….
… It’s painful to believe that the would-be ‘public servants’ you’re forced to choose between are all phonies… who will lie so outrageously and with such a straight face that you know they’ve just got to believe you’re an idiot.”
Part II:
Macbeth
by William Shakespeare
Macbeth
by William Shakespeare
Related material:
Log24 last Wednesday
Comments Off on Sunday September 14, 2008
Friday, April 18, 2008
Friday April 18, 2008
In memory of
Gian-Carlo Rota,
mathematician, who died
at 66 on this date in 1999
Gian-Carlo Rota,
mathematician, who died
at 66 on this date in 1999
"Numbers go to heaven
who know no more
of God on earth than,
as it were,
of sun in forest gloom."
— Meister Eckhart,
In Principio Erat Verbum
Related material:
yesterday's entry, and
Comments Off on Friday April 18, 2008
Friday, June 2, 2006
Friday June 2, 2006
'Ursprache' beats 'weltschmerz'
to win American spelling bee
Weltschmerz
and the
Ursprache
to win American spelling bee
Weltschmerz
and the
Ursprache
From eudaemonist.com,
a quotation from
Paul Zanker's
The Mask of Socrates:
"Zanker describes the photograph [above] as 'Walter Benjamin looking out at the viewer, his head propped on his hand, his face filled with loneliness and weltschmerz.'"
Benjamin was a Jewish Marxist. For a Jewish perspective on spelling, see Log24, Nov. 11, 2005. For a leftist perspective on Benjamin and last night's crucial spelling word "Ursprache," see "Ground Zero, an American Origin," by Mary Caputi (Poroi, 2, 1, August 2003):
The Baroque sensibility of ruin emphasizes a meaninglessness that too many possibilities deliver. Aimlessness and malaise make life into exhausting toil in the absence of coherence. In overdetermined realities, meaning appears arbitrary and erratic, as the world's connection to God seems lost or withheld. At the extreme, everyday life is as full of noise and commotion as it is devoid of intrinsic meaning. Connections among people wither with the onset of overabundance and despair. Recognition of this condition induces acedia, a weariness of life. Here the malaise of modernity and ruins ties to Benjamin's interest in Trauerspiel, German tragic drama, and the tragedies of Shakespeare. All respond to a plague of lost spiritual connections and a meaningless earthly existence where incessant toil and trouble — "tomorrow and tomorrow and tomorrow" — contribute to a chronic, wearing sense of pain.
Benjamin's interest in this form of melancholia, from suffering a sort of spiritual exile, is evident in his 1916 essay "On Language as Such and On the Language of Man." In this text, he explains that the Ursprache, our "original" language, is "blissful" precisely because it lacks the arbitrariness that results from overdetermination. Ur-speech is Adamic language, the linguistic power that God gives to Adam to confer identity on the material world. It contains no arbitrary component, but reveals the unity between God's divine plan and the world as it exists. Before ruins and fragments, there is no overdetermination to induce the melancholy of acedia. Instead the originary language implies a unity of transcendent and immanent realms. "With the creative omnipotence of language it begins, and at the end of language, as it were, assimilates the created, names it. Language is therefore both the creative and the finished creation; it is word and nature."6
This blissful state between the world and its creator as expressed in Adamic language has its end, of course, in the Fall. The "ignorance" introduced into the world that ultimately drives our melancholic state of acedia has its inception with the Fall away from the edenic union that joins God's plan to the immediacy of the material world. What ensues, says Benjamin, is an overabundance of conventional languages, a prattle of meanings now localized hence arbitrary. A former connection to a defining origin has been lost; and an overdetermined, plethoric state of melancholia forms. Over-determination stems from over-naming. "Things have no proper names except in God. . . . In the language of men, however, they are overnamed." Overnaming becomes "the linguistic being of melancholy."7
6 Walter Benjamin, "On Language as Such and On the Languages of Man," Edmund Jephcott, tr., Walter Benjamin, Selected Writings, Volume I: 1913-1926, Marcus Bullock and Michael W. Jennings, eds., Cambridge, MA, Harvard University Press, 1997, p. 68. 7 Ibid., p. 73.
For a Christian perspective on Adamic language, see Charles Williams's The Place of the Lion.
Float like a butterfly,
sting like a
Comments Off on Friday June 2, 2006
Saturday, March 11, 2006
Saturday March 11, 2006
|
Holy the Firm
by Annie Dillard Esoteric Christianity, I read, posits a substance. It is a created substance, lower than metals and minerals on a “spiritual scale” and lower than salts and earths, occurring beneath salts and earths in the waxy deepness of planets, but never on the surface of planets where men could discern it; and it is in touch with the Absolute, at base. In touch with the Absolute! At base. The name of this substance is Holy the Firm. These are only ideas, by the single handful. Lines, lines, and their infinite points! Hold hands and crack the whip, and yank the Absolute out of there and into the light, God pale and astounded, spraying a spiral of salts and earths, God footloose and flung. And cry down the line to his passing white ear, “Old Sir! Do you hold space from buckling by a finger in its hole? O Old! Where is your other hand?” His right hand is clenching, calm, round the exploding left hand of Holy the Firm. — Annie Dillard, Holy the Firm, Harper & Row 1977, reissued by Harper Perennial Library in 1988 as a paperback, pp. 68-71. |
Comments Off on Saturday March 11, 2006
Thursday, December 8, 2005
Thursday December 8, 2005
Aion Flux
That Nature is a Heraclitean Fire…
— Poem title, Gerard Manley Hopkins
— Poem title, Gerard Manley Hopkins
From Jung’s Map of the Soul, by Murray Stein:
“… Jung thinks of the self as undergoing continual transformation during the course of a lifetime…. At the end of his late work Aion, Jung presents a diagram to illustrate the dynamic movements of the self….”
“The formula presents a symbol of the self, for the self is not just a stable quantity or constant form, but is also a dynamic process. In the same way, the ancients saw the imago Dei in man not as a mere imprint, as a sort of lifeless, stereotyped impression, but as an active force…. The four transformations represent a process of restoration or rejuvenation taking place, as it were, inside the self….”
“The formula reproduces exactly the essential features of the symbolic process of transformation. It shows the rotation of the mandala, the antithetical play of complementary (or compensatory) processes, then the apocatastasis, i.e., the restoration of an original state of wholeness, which the alchemists expressed through the symbol of the uroboros, and finally the formula repeats the ancient alchemical tetrameria, which is implicit in the fourfold structure of unity.
What the formula can only hint at, however, is the higher plane that is reached through the process of transformation and integration. The ‘sublimation’ or progress or qualitative change consists in an unfolding of totality into four parts four times, which means nothing less than its becoming conscious. When psychic contents are split up into four aspects, it means that they have been subjected to discrimination by the four orienting functions of consciousness. Only the production of these four aspects makes a total description possible. The process depicted by our formula changes the originally unconscious totality into a conscious one.”
— Jung, Collected Works,
Vol. 9, Part 2, Aion: Researches into the Phenomenology of the Self (1951)
Related material:
“Although ‘wholeness’ seems at first sight to be nothing but an abstract idea (like anima and animus), it is nevertheless empirical in so far as it is anticipated by the psyche in the form of spontaneous or autonomous symbols. These are the quaternity or mandala symbols, which occur not only in the dreams of modern people who have never heard of them, but are widely disseminated in the historical recods of many peoples and many epochs. Their significance as symbols of unity and totality is amply confirmed by history as well as by empirical psychology. What at first looks like an abstract idea stands in reality for something that exists and can be experienced, that demonstrates its a priori presence spontaneously. Wholeness is thus an objective factor that confronts the subject independently of him… Unity and totality stand at the highest point on the scale of objective values because their symbols can no longer be distinguished from the imago Dei. Hence all statements about the God-image apply also to the empirical symbols of totality.”
— Jung, Aion, as quoted in
Carl Jung and Thomas Merton
Comments Off on Thursday December 8, 2005
Sunday, April 3, 2005
Sunday April 3, 2005
Wager
Pennsylvania Lottery Daily Number
for yesterday evening,
Saturday, April 2, 2005:
613
Pennsylvania Lottery Daily Number
for yesterday evening,
Saturday, April 2, 2005:
613
Related material:
From 6/13 2004 —
An 8-rayed star:
Another 8-rayed star:
St. Peter’s Square in Rome
From 6/13 2003 —
A link to a 2001 First Things essay,
“Here is the heart of the matter:
The underwriting of Hebraic–Hellenic literacy, of the normative analogue between divine and mortal acts of creation, was, in the fullest sense, theological. As was the wager (pronounced lost in deconstruction and postmodernism) on ultimate possibilities of accord between sign and sense, between word and meaning, between form and phenomenality. The links are direct between the tautology out of the Burning Bush, that ‘I am’ which accords to language the privilege of phrasing the identity of God, on the one hand, and the presumptions of concordance, of equivalence, of translatability, which, though imperfect, empower our dictionaries, our syntax, our rhetoric, on the other. That ‘I am’ has, as it were, at an overwhelming distance, informed all predication. It has spanned the arc between noun and verb, a leap primary to creation and the exercise of creative consciousness in metaphor. Where that fire in the branches has gone out or has been exposed as an optical illusion, the textuality of the world, the agency of the Logos in logic—be it Mosaic, Heraclitean, or Johannine—becomes ‘a dead letter.’
That passage bears rereading.”
— Richard John Neuhaus quoting
George Steiner’s Grammars of Creation
(Yale University Press, April 1, 2001)
Comments Off on Sunday April 3, 2005
Tuesday, April 6, 2004
Tuesday April 6, 2004
Ideas and Art, Part III
The first idea was not our own. Adam
In Eden was the father of Descartes…
— Wallace Stevens, from
Notes Toward a Supreme Fiction
"Quaedam ex his tanquam rerum imagines sunt, quibus solis proprie convenit ideae nomen: ut cùm hominem, vel Chimaeram, vel Coelum, vel Angelum, vel Deum cogito."
— Descartes, Meditationes III, 5
"Of my thoughts some are, as it were, images of things, and to these alone properly belongs the name idea; as when I think [represent to my mind] a man, a chimera, the sky, an angel or God."
— Descartes, Meditations III, 5
Begin, ephebe, by perceiving the idea
Of this invention, this invented world,
The inconceivable idea of the sun.
You must become an ignorant man again
And see the sun again with an ignorant eye
And see it clearly in the idea of it.
— Wallace Stevens, from
Notes Toward a Supreme Fiction
"… Quinimo in multis saepe magnum discrimen videor deprehendisse: ut, exempli causâ, duas diversas solis ideas apud me invenio, unam tanquam a sensibus haustam, & quae maxime inter illas quas adventitias existimo est recensenda, per quam mihi valde parvus apparet, aliam verò ex rationibus Astronomiae desumptam, hoc est ex notionibus quibusdam mihi innatis elicitam, vel quocumque alio modo a me factam, per quam aliquoties major quàm terra exhibetur; utraque profecto similis eidem soli extra me existenti esse non potest, & ratio persuadet illam ei maxime esse dissimilem, quae quàm proxime ab ipso videtur emanasse."
— Descartes, Meditationes III, 11
"… I have observed, in a number of instances, that there was a great difference between the object and its idea. Thus, for example, I find in my mind two wholly diverse ideas of the sun; the one, by which it appears to me extremely small draws its origin from the senses, and should be placed in the class of adventitious ideas; the other, by which it seems to be many times larger than the whole earth, is taken up on astronomical grounds, that is, elicited from certain notions born with me, or is framed by myself in some other manner. These two ideas cannot certainly both resemble the same sun; and reason teaches me that the one which seems to have immediately emanated from it is the most unlike."
— Descartes, Meditations III, 11
"Et quamvis forte una idea ex aliâ nasci possit, non tamen hîc datur progressus in infinitum, sed tandem ad aliquam primam debet deveniri, cujus causa sit in star archetypi, in quo omnis realitas formaliter contineatur, quae est in ideâ tantùm objective."
— Descartes, Meditationes III, 15
"And although an idea may give rise to another idea, this regress cannot, nevertheless, be infinite; we must in the end reach a first idea, the cause of which is, as it were, the archetype in which all the reality [or perfection] that is found objectively [or by representation] in these ideas is contained formally [and in act]."
— Descartes, Meditations III, 15
Michael Bryson in an essay on Stevens's "Notes Toward a Supreme Fiction,"
The Quest for the Fiction of the Absolute:
"Canto nine considers the movement of the poem between the particular and the general, the immanent and the transcendent: "The poem goes from the poet's gibberish to / The gibberish of the vulgate and back again. / Does it move to and fro or is it of both / At once?" The poet, the creator-figure, the shadowy god-figure, is elided, evading us, "as in a senseless element." The poet seeks to find the transcendent in the immanent, the general in the particular, trying "by a peculiar speech to speak / The peculiar potency of the general." In playing on the senses of "peculiar" as particular and strange or uncanny, these lines play on the mystical relation of one and many, of concrete and abstract."
Brian Cronin in Foundations of Philosophy:
"The insight is constituted precisely by 'seeing' the idea in the image, the intelligible in the sensible, the universal in the particular, the abstract in the concrete. We pivot back and forth between images and ideas as we search for the correct insight."
— From Ch. 2, Identifying Direct Insights
Michael Bryson in an essay on Stevens's "Notes Toward a Supreme Fiction":
"The fourth canto returns to the theme of opposites. 'Two things of opposite natures seem to depend / On one another . . . . / This is the origin of change.' Change resulting from a meeting of opposities is at the root of Taoism: 'Tao produced the One. / The One produced the two. / The two produced the three. / And the three produced the ten thousand things' (Tao Te Ching 42) …."
|
From an entry of March 7, 2004:
From the web page
Introduction to the I Ching– "He who has perceived the meaning of change fixes his attention no longer on transitory individual things but on the immutable, eternal law at work in all change. This law is the tao of Lao-tse, the course of things, the principle of the one in the many. That it may become manifest, a decision, a postulate, is necessary. This fundamental postulate is the 'great primal beginning' of all that exists, t'ai chi — in its original meaning, the 'ridgepole.' Later Chinese philosophers devoted much thought to this idea of a primal beginning. A still earlier beginning, wu chi, was represented by the symbol of a circle. Under this conception, t'ai chi was represented by the circle divided into the light and the dark, yang and yin,
This symbol has also played a significant part in India and Europe. However, speculations of a gnostic-dualistic character are foreign to the original thought of the I Ching; what it posits is simply the ridgepole, the line. With this line, which in itself represents oneness, duality comes into the world, for the line at the same time posits an above and a below, a right and left, front and back-in a word, the world of the opposites." The t'ai chi symbol is also illustrated on the web page Cognitive Iconology, which says that
"W.J.T. Mitchell calls 'iconology' A variation on the t'ai chi symbol appears in a log24.net entry for March 5:
The Line, See too my web page Logos and Logic, which has the following:
Logos Alogos, In the conclusion of Section 3, Canto X, of "Notes," Stevens says
This is the logoi alogoi of Simone Weil. |
.
In "Notes toward a Supreme Fiction,"
Wallace Stevens lists three criteria
for a work of the imagination:
It Must Be Abstract
The Line,
by S.H. Cullinane
It Must Change
It Must Give Pleasure
Related material:
Comments Off on Tuesday April 6, 2004
Friday, April 18, 2003
Friday April 18, 2003
To the Society of Jesus (also known as the Jesuits):
Have a Good Friday, Traitors
†
Prompted by Pilate’s question “What is truth?” and by my March 24 attack on Noam Chomsky, I decided this afternoon to further investigate what various people have written about Chomsky’s posing of what he calls “Plato’s problem” and “Orwell’s problem.” The former concerns linguistics, the latter, politics. As my March 24 entry indicates, I have nothing but contempt for both Chomsky’s linguistics and Chomsky’s politics. What I discovered this afternoon is that Georgetown University, a Jesuit institution, in 2001 appointed a Chomskyite, David W. Lightfoot, as Dean of the Graduate School of Arts and Sciences.
“Why do we know so much more than we have evidence for in certain areas, and so much less in others? In tackling these questions — Plato’s and Orwell’s problem — Chomsky again demonstrates his unequalled capacity to integrate vast amounts of material.” — David W. Lightfoot, review of Chomsky’s Knowledge of Language
What, indeed, is truth? I doubt that the best answer can be learned from either the Communist sympathizers of MIT or the “Red Mass” leftists of Georgetown. For a better starting point than either of these institutions, see my note of April 6, 2001, Wag the Dogma.
See, too, In Principio Erat Verbum, which notes that “numbers go to heaven who know no more of God on earth than, as it were, of sun in forest gloom.”
Since today is the anniversary of the death of MIT mathematics professor Gian-Carlo Rota, an example of “sun in forest gloom” seems the best answer to Pilate’s question on this holy day. See
“Examples are the stained glass windows of knowledge.” — Vladimir Nabokov
Motto of Plato’s Academy
† The Exorcist, 1973
Comments Off on Friday April 18, 2003
Thursday, October 31, 2002
Thursday October 31, 2002
|
Plato's |
|
From The Unknowable (1999), by Gregory J. Chaitin, who has written extensively about his constant, which he calls Omega:
"What is Omega? It's just the diamond-hard distilled and crystallized essence of mathematical truth! It's what you get when you compress tremendously the coal of redundant mathematical truth…"
Charles H. Bennett has written about Omega as a cabalistic number.
Here is another result with religious associations which, historically, has perhaps more claim to be called the "diamond-hard essence" of mathematical truth: The demonstration in Plato's Meno that a diamond inscribed in a square has half the area of the square (or that, vice-versa, the square has twice the area of the diamond).
From Ivars Peterson's discussion of Plato's diamond and the Pythagorean theorem:
"In his textbook The History of Mathematics, Roger Cooke of the University of Vermont describes how the Babylonians might have discovered the Pythagorean theorem more than 1,000 years before Pythagoras.
Basing his account on a passage in Plato's dialogue Meno, Cooke suggests that the discovery arose when someone, either for a practical purpose or perhaps just for fun, found it necessary to construct a square twice as large as a given square…."
From "Halving a Square," a presentation of Plato's diamond by Alexander Bogomolny, the moral of the story:
SOCRATES: And if the truth about reality is always in our soul, the soul must be immortal….
From "Renaissance Metaphysics and the History of Science," at The John Dee Society website:
Galileo on Plato's diamond:
"Cassirer, drawing attention to Galileo's frequent use of the Meno, particularly the incident of the slave's solving without instruction a problem in geometry by 'natural' reason stimulated by questioning, remarks, 'Galileo seems to accept all the consequences drawn by Plato from this fact…..'"
Roger Bacon on Plato's diamond:
"Fastening on the incident of the slave in the Meno, which he had found reproduced in Cicero, Bacon argued from it 'wherefore since this knowledge (of mathematics) is almost innate and as it were precedes discovery and learning or at least is less in need of them than other sciences, it will be first among sciences and will precede others disposing us towards them.'"
It is perhaps appropriate to close this entry, made on All Hallows' Eve, with a link to a page on Dr. John Dee himself.
Friday, August 2, 2002
Friday August 2, 2002
Double Day… August 2, 2002
“Time cannot exist without a soul (to count it).” — Aristotle
The above quotation appears in my journal note of August 2, 1995, as an epigraph on the reproduced title page of The Sense of an Ending, by Frank Kermode (Oxford University Press, 1967).
August 2, 1995, was the fortieth anniversary of Wallace Stevens’s death. On the same date in 1932 — seventy years ago today — actor Peter O’Toole was born. O’Toole’s name appears, in a suitably regal fashion, in my journal note of August 2, 1995, next to the heraldic crest of Oxford University, which states that “Dominus illuminatio mea.” Both the crest and the name appear below the reproduced title page of Kermode’s book — forming, as it were, a foundation for what Harvard professor Marjorie Garber scornfully called “the Church of St. Frank” (letters to the editor, New York Times Book Review, July 30, 1995).
Meditations for today, August 2, 2002:
From page 60 of Why I Am a Catholic, by Gary Wills (Houghton Mifflin, 2002):
“Was Jesus teasing Peter when he called him ‘Rocky,’ naming him ab opposito, as when one calls a not-so-bright person Einstein?”
From page 87 of The Third Word War, by Ian Lee (A&W Publishers, Inc., New York, 1978):
“Two birds… One stone (EIN STEIN).”
From “Seventy Years Later,” Section I of “The Rock,” a poem by Wallace Stevens:
A theorem proposed between the two —
Two figures in a nature of the sun….
From page 117 of The Sense of an Ending:
“A great many different kinds of writing are called avant-garde…. The work of William Burroughs, for instance, is avant-garde. His is the literature of withdrawal, and his interpreters speak of his hatred for life, his junk nihilism, his treatment of the body as a corpse full of cravings. The language of his books is the language of an ending world, its aim… ‘self-abolition.'”
From “Today in History,” by The Associated Press:
“Five years ago: ‘Naked Lunch’ author William S. Burroughs, the godfather of the ‘Beat generation,’ died in Kansas City, Mo., at age 83.”
Part of the above statement is the usual sort of AP disinformation, due not to any sinister intent but to stupidity and carelessness. Burroughs actually died in Lawrence, Kansas. For the location of Lawrence, click on the link below. Location matters.
From page 118 of The Sense of an Ending:
“Somewhere, then, the avant-garde language must always rejoin the vernacular.”
From the Billie Holiday songbook:
“Good mornin’, heartache.”
From page 63 of The New Yorker issue dated August 5, 2002:
“Birthday, death-day — what day is not both?” — John Updike
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