Log24

Thursday, April 20, 2017

Stone Logic

Filed under: Uncategorized — m759 @ 9:48 PM

See also "Romancing the Omega" —

Image- Josefine Lyche work (with 1986 figures by Cullinane) in a 2009 exhibition in Oslo

Related mathematics — Guitart in this journal —

From 'Moving Logic, from Boole to Galois,' by René Guitart, 2005

See also Weyl + Palermo in this journal —

http://www.log24.com/log/pix11B/110922-TriquetrumCube.jpg

Sunday, March 26, 2017

Four-Year* Date

Filed under: Uncategorized — m759 @ 11:00 AM

"Eigenvalues. Fixed points. Stable equilibria.
Mathematicians like things that stay put.
And if they can't stay put, the objects of study
should at least repeat themselves on a regular basis. . . ."

— Barry Cipra, "A Moveable Feast," SIAM News , Jan. 14, 2006

Tuesday, March 18, 2014

Class of 64 continues…

Uncategorized — m759 @ 12:00 PM 

Mathematician Norbert Wiener reportedly
died on this date in 1964.

“Mathematics is too arduous and uninviting a field
to appeal to those to whom it does not give great rewards.
These rewards are of exactly the same character as
those of the artist. To see a difficult uncompromising material
take living shape and meaning is to be Pygmalion,
whether the material is stone or hard, stonelike logic."
. . . .

Wednesday, March 18, 2015

Play Is Not Playing Around

Uncategorized — m759 @ 1:00 PM

(A saying of Friedrich Fröbel)


. . . .

Friday, March 18, 2016

Southwestern Noir

Uncategorized — m759 @ 2:56 PM 

Kyle Smith on April 15, 2015, in the New York Post —

"The ludicrous action thriller 'Beyond the Reach'
fails to achieve the Southwestern noir potency
of 'No Country for Old Men,' but there’s no denying
it brings to mind another Southwestern classic
about malicious pursuit: the Road Runner cartoons."
. . . .

Saturday, March 18, 2017

Back to the Past

Uncategorized — Tags:  — m759 @ 7:35 PM 

"Old men ought to be explorers" — T. S. Eliot

. . . .

* For a full  four years, see also March 18, 2013.

Monday, February 27, 2017

Logic for Jews

Filed under: Uncategorized — Tags: — m759 @ 9:07 PM

(Continued)

Adam Gopnik in The New Yorker  today reacts to the startling
outcomes of three recent contests: the presidential election,
the Super Bowl, and the Oscar for Best Picture —

"The implicit dread logic is plain."

Related material —

Transformers in this journal and

“Lord Arglay had a suspicion that the Stone would be
purely logical.  Yes, he thought, but what, in that sense,
were the rules of its pure logic?”

Many Dimensions  (1931), by Charles Williams

See also

The above figure is from Ian Stewart's 1996 revision of a 1941 classic, 
What Is Mathematics? , by Richard Courant and Herbert Robbins.

One wonders how the confused slave boy of Plato's Meno  would react
to Stewart's remark that

"The number of copies required to double an
 object's size depends on its dimension."

Saturday, January 28, 2017

Cranking It Up

Filed under: Uncategorized — m759 @ 12:17 PM

From "Core," a post of St. Lucia's Day, Dec. 13, 2016 —

'We are rooted in yoga and love the magic that happens when that practice is cranked up to eleven.'

In related news yesterday —

California yoga mogul’s mysterious death:
Trevor Tice’s drunken last hours detailed

"Police found Tice dead on the floor in his home office,
blood puddled around his head. They also found blood
on walls, furniture, on a sofa and on sheets in a nearby
bedroom, where there was a large bottle of Grey Goose
vodka under several blood-stained pillows on the floor."

See as well an image from "The Stone," a post of March 18, 2016 —

Some backstory —

“Lord Arglay had a suspicion that the Stone would be
purely logical.  Yes, he thought, but what, in that sense,
were the rules of its pure logic?”

Many Dimensions  (1931), by Charles Williams

Wednesday, August 10, 2016

Narratives

Filed under: Uncategorized — m759 @ 1:00 PM

The novel Blood on Snow , set in Oslo, was published
by Knopf on April 7, 2015.  This journal on that date —

Log24 on Tuesday, April 7, 2015

Logic

Filed under: Uncategorized — m759 @ 7:00 PM 

Seven years ago in this journal —

The above links:  the Stone,  the rules.

A related image —

Sunday, April 17, 2016

The Thing and I

Filed under: Uncategorized — m759 @ 2:01 PM

The New York Times  philosophy column yesterday —

The Times's philosophy column "The Stone" is named after the legendary
"philosophers' stone." The column's name, and the title of its essay yesterday
"Is that even a thing?" suggest a review of the eightfold cube  as "The object
most closely resembling a 'philosophers' stone' that I know of" (Page 51 of
the current issue of a Norwegian art quarterly, KUNSTforum.as).

The eightfold cube —

Definition of Epiphany

From James Joyce’s Stephen Hero , first published posthumously in 1944. The excerpt below is from a version edited by John J. Slocum and Herbert Cahoon (New York: New Directions Press, 1959).

Three Times:

… By an epiphany he meant a sudden spiritual manifestation, whether in the vulgarity of speech or of gesture or in a memorable phase of the mind itself. He believed that it was for the man of letters to record these epiphanies with extreme care, seeing that they themselves are the most delicate and evanescent of moments. He told Cranly that the clock of the Ballast Office was capable of an epiphany. Cranly questioned the inscrutable dial of the Ballast Office with his no less inscrutable countenance:

— Yes, said Stephen. I will pass it time after time, allude to it, refer to it, catch a glimpse of it. It is only an item in the catalogue of Dublin’s street furniture. Then all at once I see it and I know at once what it is: epiphany.

— What?

— Imagine my glimpses at that clock as the gropings of a spiritual eye which seeks to adjust its vision to an exact focus. The moment the focus is reached the object is epiphanised. It is just in this epiphany that I find the third, the supreme quality of beauty.

— Yes? said Cranly absently.

— No esthetic theory, pursued Stephen relentlessly, is of any value which investigates with the aid of the lantern of tradition. What we symbolise in black the Chinaman may symbolise in yellow: each has his own tradition. Greek beauty laughs at Coptic beauty and the American Indian derides them both. It is almost impossible to reconcile all tradition whereas it is by no means impossible to find the justification of every form of beauty which has ever been adored on the earth by an examination into the mechanism of esthetic apprehension whether it be dressed in red, white, yellow or black. We have no reason for thinking that the Chinaman has a different system of digestion from that which we have though our diets are quite dissimilar. The apprehensive faculty must be scrutinised in action.

— Yes …

— You know what Aquinas says: The three things requisite for beauty are, integrity, a wholeness, symmetry and radiance. Some day I will expand that sentence into a treatise. Consider the performance of your own mind when confronted with any object, hypothetically beautiful. Your mind to apprehend that object divides the entire universe into two parts, the object, and the void which is not the object. To apprehend it you must lift it away from everything else: and then you perceive that it is one integral thing, that is a  thing. You recognise its integrity. Isn’t that so?

— And then?

— That is the first quality of beauty: it is declared in a simple sudden synthesis of the faculty which apprehends. What then? Analysis then. The mind considers the object in whole and in part, in relation to itself and to other objects, examines the balance of its parts, contemplates the form of the object, traverses every cranny of the structure. So the mind receives the impression of the symmetry of the object. The mind recognises that the object is in the strict sense of the word, a thing , a definitely constituted entity. You see?

— Let us turn back, said Cranly.

They had reached the corner of Grafton St and as the footpath was overcrowded they turned back northwards. Cranly had an inclination to watch the antics of a drunkard who had been ejected from a bar in Suffolk St but Stephen took his arm summarily and led him away.

— Now for the third quality. For a long time I couldn’t make out what Aquinas meant. He uses a figurative word (a very unusual thing for him) but I have solved it. Claritas is quidditas . After the analysis which discovers the second quality the mind makes the only logically possible synthesis and discovers the third quality. This is the moment which I call epiphany. First we recognise that the object is one  integral thing, then we recognise that it is an organised composite structure, a thing  in fact: finally, when the relation of the parts is exquisite, when the parts are adjusted to the special point, we recognise that it is that  thing which it is. Its soul, its whatness, leaps to us from the vestment of its appearance. The soul of the commonest object, the structure of which is so adjusted, seems to us radiant. The object achieves its epiphany.

Having finished his argument Stephen walked on in silence. He felt Cranly’s hostility and he accused himself of having cheapened the eternal images of beauty. For the first time, too, he felt slightly awkward in his friend’s company and to restore a mood of flippant familiarity he glanced up at the clock of the Ballast Office and smiled:

— It has not epiphanised yet, he said.

Sunday, April 3, 2016

Logic

Filed under: Uncategorized — m759 @ 9:29 PM

See also Stone Logical Dimensions 

“Lord Arglay had a suspicion that the Stone
would be purely logical.  Yes, he thought,
but what, in that sense, were the rules of its pure logic?”

Many Dimensions  (1931), by Charles Williams

Tuesday, March 8, 2016

Ripples

Filed under: Uncategorized — m759 @ 2:00 AM

From the New York Times  philosophy column "The Stone"
yesterday morning —

"Our knowledge of the universe and ourselves expands
like a ripple surrounding a pebble dropped in a pool.
As we move away from the center of the spreading circle,
its area, representing our secure knowledge, grows.
But so does its circumference, representing the border
where knowledge blurs into uncertainty and speculation,
and methodological confusion returns. Philosophy patrols
the border, trying to understand how we got there and to
conceptualize our next move.  Its job is unending."

— Scott Soames, "Philosophy's True Home"

Related ripples —

       From the previous Log24 post:

From a passage by Nietzsche quoted here on June 9, 2012:

For Soames's "unending" job of philosophy and Nietzsche's 
"maieutic and educational influences on noble youths," 
consult the lyrics played over the end credits of "Monster" —

"Oh, the movie never ends
It goes on, and on, and on, and on"

Friday, January 15, 2016

Local and Global

Filed under: Uncategorized — m759 @ 9:00 PM

The American Mathematical Society today —

George E. Weaver (1942-2015) 
Friday January 15th 2016

Weaver was a philosophy professor at Bryn Mawr College before retiring in 2008. He had an interest in mathematics, among other fields, and taught discrete mathematics and mathematical logic at Bryn Mawr. A colleague said that Weaver "taught with passion and rigor, and cared deeply about his courses and the students. Students who studied with him had a deep respect and admiration for him." Weaver was an AMS member since 1972. Read more about his life in an obituary published in the Philadelphia Inquirer.

Weaver reportedly died on December 4, 2015.

Related material in this journal on the date of Weaver's death —

Friday, December 4, 2015

Symbology for the Vatican Gift Shop

Filed under: Uncategorized —  m759 @ 8:00 PM 

(Title adapted from a 1996 Stone Temple Pilots album)

See Symbols, Local and Global (September 26, 2015),
Change Descends (April 11, 2014), and Altar (August 27, 2014).

Saturday, November 7, 2015

Clarifying Dyson

Filed under: Uncategorized — m759 @ 12:00 PM

The previous post quoted a passage from Turing's Cathedral ,
a 2012 book by George Dyson —

A passage in 'Turing's Cathedral' that recalls the Go chip in 'Wild Palms'

It should be noted that Dyson's remarks on "two species of
bits," space, time, "structure and sequence" and logic gates
are from his own idiosyncratic attempt to create a philosophy
based on the workings of computers.  These concepts are not,
so far as I can tell, part of anyone else's approach to the subject.

For a more standard introduction to how computers work, see
(for instance) a book by an author Dyson admires:

The Pattern on the Stone , by W. Daniel Hillis (Basic Books, 1998).

PREFACE: MAGIC IN THE STONE

I etch a pattern of geometric shapes onto a stone.
To the uninitiated, the shapes look mysterious and
complex, but I know that when arranged correctly
they will give the stone a special power, enabling it
to respond to incantations in a language no human
being has ever spoken. I will ask the stone questions
in this language, and it will answer by showing me a
vision: a world created by my spell, a world imagined
within the pattern on the stone.

A few hundred years ago in my native New England,
an accurate description of my occupation would have
gotten me burned at the stake. Yet my work involves
no witchcraft; I design and program computers. The
stone is a wafer of silicon, and the incantations are
software. The patterns etched on the chip and the
programs that instruct the computer may look
complicated and mysterious, but they are generated
according to a few basic principles that are easily
explained. . . . .

Hillis's title suggests some remarks unrelated to computers —

See Philosopher + Stone in this journal.

Saturday, October 31, 2015

Raiders of the Lost Crucible

Filed under: Uncategorized — m759 @ 10:15 AM

Stanford Encyclopedia of Philosophy
on the date Friday, April 5, 2013 —

Paraconsistent Logic

"First published Tue Sep 24, 1996;
substantive revision Fri Apr 5, 2013"

This  journal on the date Friday, April 5, 2013 —

The object most closely resembling a "philosophers' stone"
that I know of is the eightfold cube .

For some related philosophical remarks that may appeal 
to a general Internet audience, see (for instance) a website
by I Ching  enthusiast Andreas Schöter that displays a labeled
eightfold cube in the form of a lattice diagram —

Related material by Schöter —

A 20-page PDF, "Boolean Algebra and the Yi Jing."
(First published in The Oracle: The Journal of Yijing Studies ,
Vol 2, No 7, Summer 1998, pp. 19–34.)

I differ with Schöter's emphasis on Boolean algebra.
The appropriate mathematics for I Ching  studies is,
I maintain, not Boolean algebra  but rather Galois geometry.

See last Saturday's post Two Views of Finite Space.
Unfortunately, that post is, unlike Schöter's work, not  
suitable for a general Internet audience.

Tuesday, April 7, 2015

Logic

Filed under: Uncategorized — m759 @ 7:00 PM

Seven years ago in this journal —

The above links:  the Stone,  the rules.

Saturday, July 26, 2014

OOPs

Filed under: Uncategorized — m759 @ 2:01 PM

Or:  Two Rivets Short of a Paradigm

Detail from an author photo:

IMAGE- 'House of Cards,' book on Bear Stearns, author photo, with two missing rivets

From rivet-rivet.net:

The philosopher Graham Harman is invested in re-thinking the autonomy of objects and is part of a movement called Object-Oriented-Philosophy (OOP). Harman wants to question the authority of the human being at the center of philosophy to allow the insertion of the inanimate into the equation. With the aim of proposing a philosophy of objects themselves, Harman puts the philosophies of Bruno Latour and Martin Heidegger in dialogue. Along these lines, Harman proposes an unconventional reading of the tool-being analysis made by Heidegger. For Harman, the term tool does not refer only to human-invented tools such as hammers or screwdrivers, but to any kind of being or thing such as a stone, dog or even a human. Further, he uses the terms objects, beings, tools and things, interchangeably, placing all on the same ontological footing. In short, there is no “outside world.”

Harman distinguishes two characteristics of the tool-being: invisibility and totality. Invisibility means that an object is not simply used but is: “[an object] form(s) a cosmic infrastructure of artificial and natural and perhaps supernatural forces, power by which our last action is besieged.” For instance, nails, wooden boards and plumbing tubes do their work to keep a house “running” silently (invisibly) without being viewed or noticed. Totality means that objects do not operate alone but always in relation to other objects–the smallest nail can, for example, not be disconnected from wooden boards, the plumbing tubes or from the cement. Depending on the point of view of each entity (nail, tube, etc.) a different reality will emerge within the house. For Harman, “to refer to an object as a tool-being is not to say that it is brutally exploited as a means to an end, but only that it is torn apart by the universal duel between the silent execution of an object’s reality and the glistening aura of its tangible surface.”

— From “The Action of Things,” an M.A. thesis at the Center for Curatorial Studies, Bard College, by Manuela Moscoso, May 2011, edited by Sarah Demeuse

From Wikipedia, a programming paradigm:

See also posts tagged Turing’s Cathedral, and Alley  Oop (Feb. 11, 2003).

Tuesday, March 18, 2014

Class of 64 continues…

Filed under: Uncategorized — m759 @ 12:00 PM

Mathematician Norbert Wiener reportedly died on this date in 1964.

“Mathematics is too arduous and uninviting a field to appeal to those to whom it does not give great rewards. These rewards are of exactly the same character as those of the artist. To see a difficult uncompromising material take living shape and meaning is to be Pygmalion, whether the material is stone or hard, stonelike logic. To see meaning and understanding come where there has been no meaning and no understanding is to share the work of a demiurge. No amount of technical correctness and no amount of labour can replace this creative moment, whether in the life of a mathematician or of a painter or musician. Bound up with it is a judgment of values, quite parallel to the judgment of values that belongs to the painter or the musician. Neither the artist nor the mathematician may be able to tell you what constitutes the difference between a significant piece of work and an inflated trifle; but if he is not able to recognise this in his own heart, he is no artist and no mathematician.”

— Wiener, Ex-Prodigy

Wednesday, January 22, 2014

A Riddle for Davos

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

Hexagonale Unwesen

Einstein and Thomas Mann, Princeton, 1938


IMAGE- Redefining the cube's symmetry planes: 13 planes, not 9.


See also the life of Diogenes Allen, a professor at Princeton
Theological Seminary, a life that reportedly ended on the date—
January 13, 2013— of the above Log24 post.

January 13 was also the dies natalis  of St. James Joyce.

Some related reflections —

"Praeterit figura huius mundi  " — I Corinthians 7:31 —

Conclusion of of "The Dead," by James Joyce—

The air of the room chilled his shoulders. He stretched himself cautiously along under the sheets and lay down beside his wife. One by one, they were all becoming shades. Better pass boldly into that other world, in the full glory of some passion, than fade and wither dismally with age. He thought of how she who lay beside him had locked in her heart for so many years that image of her lover's eyes when he had told her that he did not wish to live.

Generous tears filled Gabriel's eyes. He had never felt like that himself towards any woman, but he knew that such a feeling must be love. The tears gathered more thickly in his eyes and in the partial darkness he imagined he saw the form of a young man standing under a dripping tree. Other forms were near. His soul had approached that region where dwell the vast hosts of the dead. He was conscious of, but could not apprehend, their wayward and flickering existence. His own identity was fading out into a grey impalpable world: the solid world itself, which these dead had one time reared and lived in, was dissolving and dwindling.

A few light taps upon the pane made him turn to the window. It had begun to snow again. He watched sleepily the flakes, silver and dark, falling obliquely against the lamplight. The time had come for him to set out on his journey westward. Yes, the newspapers were right: snow was general all over Ireland. It was falling on every part of the dark central plain, on the treeless hills, falling softly upon the Bog of Allen and, farther westward, softly falling into the dark mutinous Shannon waves. It was falling, too, upon every part of the lonely churchyard on the hill where Michael Furey lay buried. It lay thickly drifted on the crooked crosses and headstones, on the spears of the little gate, on the barren thorns. His soul swooned slowly as he heard the snow falling faintly through the universe and faintly falling, like the descent of their last end, upon all the living and the dead.

Tuesday, September 3, 2013

“The Stone” Today Suggests…

Filed under: Uncategorized — m759 @ 12:31 PM

A girl's best friend?

The Philosopher's Gaze , by David Michael Levin,
U. of California Press, 1999, in III.5, "The Field of Vision," pp. 174-175—

The post-metaphysical question—question for a post-metaphysical phenomenology—is therefore: Can the perceptual field, the ground of perception, be released  from our historical compulsion to represent it in a way that accommodates our will to power and its need to totalize and reify the presencing of being? In other words: Can the ground be experienced as  ground? Can its hermeneutical way of presencing, i.e., as a dynamic interplay of concealment and unconcealment, be given appropriate  respect in the receptivity of a perception that lets itself  be appropriated by  the ground and accordingly lets  the phenomenon of the ground be  what and how it is? Can the coming-to-pass of the ontological difference that is constitutive of all the local figure-ground differences taking place in our perceptual field be made visible hermeneutically, and thus without violence to its withdrawal into concealment? But the question concerning the constellation of figure and ground cannot be separated from the question concerning the structure of subject and object. Hence the possibility of a movement beyond metaphysics must also think the historical possibility of breaking out of this structure into the spacing of the ontological difference: différance , the primordial, sensuous, ekstatic écart . As Heidegger states it in his Parmenides lectures, it is a question of "the way historical man belongs within the bestowal of being (Zufügung des Seins ), i.e., the way this order entitles him to acknowledge being and to be the only being among all beings to see  the open" (PE* 150, PG** 223. Italics added). We might also say that it is a question of our response-ability, our capacity as beings gifted with vision, to measure up to the responsibility for perceptual responsiveness laid down for us in the "primordial de-cision" (Entscheid ) of the ontological difference (ibid.). To recognize the operation of the ontological difference taking place in the figure-ground difference of the perceptual Gestalt  is to recognize the ontological difference as the primordial Riß , the primordial Ur-teil  underlying all our perceptual syntheses and judgments—and recognize, moreover, that this rift, this  division, decision, and scission, an ekstatic écart  underlying and gathering all our so-called acts of perception, is also the only "norm" (ἀρχή ) by which our condition, our essential deciding and becoming as the ones who are gifted with sight, can ultimately be judged.

* PE: Parmenides  of Heidegger in English— Bloomington: Indiana University Press, 1992

** PG: Parmenides  of Heidegger in German— Gesamtausgabe , vol. 54— Frankfurt am Main: Vittorio Klostermann, 1992

Examples of "the primordial Riß " as ἀρχή  —

For an explanation in terms of mathematics rather than philosophy,
see the diamond theorem. For more on the Riß  as ἀρχή , see
Function Decomposition Over a Finite Field.

Friday, June 15, 2012

Elements

Filed under: Uncategorized — m759 @ 3:00 AM

In memory of Paul Sussman, author of archaeological 
mystery novels about Egypt—

IMAGE- Harvard Divinity School bookplate dated 1910

"… the sacred symbols of the cosmic elements
were hid away hard by the secrets of Osiris."  

Thrice-Great Hermes: Excerpts and Fragments ,
      by George Robert Stowe Mead,
     Theosophical Publishing Society, 1906   

Sussman's last novel, not yet published, was

The Labyrinth of Osiris .

Sussman, 45, reportedly died suddenly on May 31, 2012.

A perhaps relevant thought—

"A world of made
is not a world of born— pity poor flesh
and trees, poor stars and stones, but never this
fine specimen of hypermagical 
ultraomnipotence."

– e. e. cummings, 1944

Monday, June 4, 2012

Rigor and Respect

Filed under: Uncategorized — m759 @ 7:00 PM

"… Western academic philosophy will likely come to appear
utterly parochial in the coming years if it does not find a way
to approach non-Western traditions that is much more rigorous
and respectful than the tokenism that reigns at present."

— Justin E. H. Smith in the New York Times  philosophy
    column "The Stone" yesterday

For example—

Selected Bibliography on Ancient Chinese Logic

Monday, May 21, 2012

Child’s Play (continued*)

Filed under: Uncategorized — m759 @ 7:59 PM

You and I …

we are just like a couple of tots…

Sinatra

JOSEFINE LYCHE

Born 1973 in Bergen. Lives and works in Oslo.

Education

2000 – 2004 National Academy of Fine Arts, Oslo
1998 – 2000 Strykejernet Art School, Oslo, NO
1995 – 1998 Philosophy, University of Bergen

University of Bergen—

 It might therefore seem that the idea of digital and analogical systems as rival fundaments to human experience is a new suggestion and, like digital technology, very modern. In fact, however, the idea is as old as philosophy itself (and may be much older). In his Sophist, Plato sets out the following ‘battle’ over the question of ‘true reality’:

What we shall see is something like a battle of gods and giants going on between them over their quarrel about reality [γιγαντομαχία περì της ουσίας] ….One party is trying to drag everything down to earth out of heaven and the unseen, literally grasping rocks and trees in their hands, for they lay hold upon every stock and stone and strenuously affirm that real existence belongs only to that which can be handled and offers resistance to the touch. They define reality as the same thing as body, and as soon as one of the opposite party asserts that anything without a body is real, they are utterly contemptuous and will not listen to another word. (…) Their adversaries are very wary in defending their position somewhere in the heights of the unseen, maintaining with all their force that true reality [την αληθινήν ουσίαν] consists in certain intelligible and bodiless forms. In the clash of argument they shatter and pulverize those bodies which their opponents wield, and what those others allege to be true reality they call, not real being, but a sort of moving process of becoming. On this issue an interminable battle is always going on between the two camps [εν μέσω δε περι ταυτα απλετος αμφοτέρων μάχη τις (…) αει συνέστηκεν]. (…) It seems that only one course is open to the philosopher who values knowledge and truth above all else. He must refuse to accept from the champions of the forms the doctrine that all reality is changeless [and exclusively immaterial], and he must turn a deaf ear to the other party who represent reality as everywhere changing [and as only material]. Like a child begging for 'both', he must declare that reality or the sum of things is both at once [το όν τε και το παν συναμφότερα] (Sophist 246a-249d).

The gods and the giants in Plato’s battle present two varieties of the analog position. Each believes that ‘true reality’ is singular, that "real existence belongs only to" one side or other of competing possibilities. For them, difference and complexity are secondary and, as secondary, deficient in respect to truth, reality and being (την αληθινήν ουσίαν, το όν τε και το παν). Difference and complexity are therefore matters of "interminable battle" whose intended end for each is, and must be (given their shared analogical logic), only to eradicate the other. The philosophical child, by contrast, holds to ‘both’ and therefore represents the digital position where the differentiated two yet belong originally together. Here difference, complexity and systematicity are primary and exemplary.

It is an unfailing mark of the greatest thinkers of the tradition, like Plato, that they recognize the digital possibility and therefore recognize the principal difference of it from analog possibilities.

— Cameron McEwen, "The Digital Wittgenstein,"
    The Wittgenstein Archives at the University of Bergen

* See that phrase in this journal.

Monday, May 14, 2012

Mathematics, Logic, and Faith

Filed under: Uncategorized — m759 @ 4:44 PM

From the NY Times  philosophy column "The Stone" 
yesterday at 5 PM—

Timothy Williamson, Wykeham Professor of Logic at Oxford,
claims that all the theorems of mathematics

"… are ultimately derived from a few simple axioms
by chains of logical reasoning, some of them
hundreds of pages long…."

Williamson gives as an example recent (1986-1995)
work on Fermat's conjecture.

He does not, however, cite any axioms or "chains of
logical reasoning" in support of his claim that 
a proof of Fermat's conjecture can be so derived.

Here is a chain of reasoning that forms a crucial part
of recent arguments for the truth of Fermat's conjecture—

K. A. Ribet, "On modular representations of Gal(Q̄/Q)
arising from modular forms
," Invent. Math. 100 (1990), 431-476.

Whether this chain of reasoning is in fact logical  is no easy question.
It is not the sort of argument easily reduced to a series of purely
logical symbol-strings that could be checked by a computer.

Few mathematicians, even now, can follow each step
in the longer chain of reasoning that led to a June 1993 claim
that Fermat's conjecture is true. 

Williamson is not a mathematician, and his view of
Fermat's conjecture as a proven fact is clearly based
not on logic, but on faith.

Friday, April 27, 2012

Paradigms Lost continues…

Filed under: Uncategorized — m759 @ 9:00 PM

This post was suggested by Paradigms Lost
(a post cited here a year ago today),
by David Weinberger's recent essay "Shift Happens,"
and by today's opening of "The Raven."

David Weinberger in The Chronicle of Higher Education April 22

"… Kuhn was trying to understand how Aristotle could be such a brilliant natural scientist except when it came to understanding motion. Aristotle's idea that stones fall and fire rises because they're trying to get to their natural places seems like a simpleton's animism.

Then it became clear to Kuhn all at once. Ever since Newton, we in the West have thought movement changes an object's position in neutral space but does not change the object itself. For Aristotle, a change in position was a change in a quality of the object, and qualitative change tended toward an asymmetric actualization of potential: an acorn becomes an oak, but an oak never becomes an acorn. Motion likewise expressed a tendency for things to actualize their essence by moving to their proper place. With that, 'another initially strange part of Aristotelian doctrine begins to fall into place,' Kuhn wrote in The Road Since Structure ."

Dr. John Raven (of Raven's Progressive Matrices)

"… these tools cannot be immediately applied within our current workplaces, educational systems, and public management systems because the operation of these systems is determined, not by personal developmental or societal needs, but by a range of latent, rarely discussed, and hard to influence sociological forces.

But this is not a cry of despair: It points to another topic which has been widely neglected by psychologists: It tells us that human behaviour is not  mainly determined by internal  properties— such as talents, attitudes, and values— but by external  social forces. Such a transformation in psychological thinking and theorising is as great as the transformation Newton introduced into physics by noting that the movement of inanimate objects is not determined by internal, 'animistic,' properties of the objects but by invisible external forces which act upon them— invisible forces that can nevertheless be mapped, measured, and harnessed to do useful work for humankind.

So this brings us to our fourth conceptualisation and measurement topic: How are these social forces to be conceptualised, mapped, measured, and harnessed in a manner analogous to the way in which Newton made it possible to harness the destructive forces of the wind and the waves to enable sailing boats to get to their destinations?"

Before Newton, boats never arrived?

Friday, April 20, 2012

Complex Reflection

Filed under: Uncategorized — m759 @ 11:32 AM

Yesterday's post in memory of Octavio Paz

… the free-standing, two-sided “Life-Death Figure,”
carved from stone in Mexico some time between
A.D. 900 and 1250, 
has multiple personalities.

Holland Cotter,  New York Times 

An earlier post yesterday, Fashion Notes, linked to a Sting video—

IMAGE- Sting meets his own reflection in a mirror in 'We'll Be Together' video

From "Loo Ree," by Zenna Henderson

"It's so hard to explain–"

"Oh, foof!" I cried defiantly, taking off my glasses and, smearing the tears across both lenses with a tattered Kleenex. "So I'm a dope, a moron! If I can explain protective coloration to my six-year-olds and the interdependence of man and animals, you can tell me something of what the score is!" I scrubbed the back of my hand across my blurry eyes. "If you have to, start out 'Once upon a time."' I sat down– hard.  

Loo Ree smiled and sat down, too. "Don't cry, teacher. Teachers aren't supposed to have tears."  

"I know it," I sniffed. "A little less than human-that's us."

"A little more than human, sometimes." Loo Ree corrected gently. "Well then, you must understand that I'll have to simplify. You will have to dress the bare bones of the explanation according to your capabilities.  

"Once upon a time there was a classroom. Oh, cosmic in size, but so like yours that you would smile in recognition if you could see it all. And somewhere in the classroom something was wrong. Not the whispering and murmuring– that's usual. Not the pinching and poking and tattling that goes on until you get so you don't even hear it." I nodded. How well I knew.  

"It wasn't even the sudden blow across the aisle or the unexpected wrestling match in the back of the room. That happens often, too. But something else was wrong. It was an undercurrent, a stealthy, sly sort of thing that has to be caught early or it disrupts the whole classroom and tarnishes the children with a darkness that will never quite rub off.  

"The teacher could feel it –as all good teachers can– and she spoke to the principal. He, being a good principal, immediately saw the urgency of the matter and also saw that it was beyond him, so he called in an Expert." "You?" I asked, feeling quite bright because I had followed the analogy so far.  

Loo Ree smiled. "Well, I'm part of the Expert."  

"If you have to, start out 'Once upon a time.'"

Yesterday's Paz post was at 6:48 PM EDT.

For the autistic, here is some related mathematics.

Yesterday's Fashion Notes post was at 1:06 PM  EDT.

A related chronological note from Rolling Stone  yesterday—

"Levon Helm, singer and drummer for the Band,
 died on April 19th in New York of throat cancer.
 He was 71. 

"He passed away peacefully at 1:30 this afternoon…."

Helm and The Band performing "The Weight"—

"I pulled into Nazareth, I was a-feelin' 'bout half past dead…"

Thursday, December 1, 2011

Paranoia Strikes Deep

Filed under: Uncategorized — m759 @ 2:02 PM

Tens of Millions of Smartphones Come With Spyware
Preinstalled, Security Analyst Says

Published December 01, 2011 – FoxNews.com

For details, see comments at YouTube.

Related entertainment—

1. Tara Fitzgerald in "New World Disorder" (1999)—

http://www.log24.com/log/pix11C/111201-NewWorldDisorder-TaraFitzgerald.jpg

We skipped the light fandango
turned cartwheels 'cross the floor
I was feeling kinda seasick
but the crowd called out for more

2. Tara Fitzgerald in "Broken Glass" (2011)—

http://www.log24.com/log/pix11C/111201-TaraFitgerald-BrokenGlass.jpg

And so it was that later
as the miller told his tale
that her face, at first just ghostly,
turned a whiter shade of pale

Procul Harum song at beginning and end of "The Net" (1995)

“Lord Arglay had a suspicion that the Stone
would be purely logical.  Yes, he thought,
but what, in that sense, were the rules of its pure logic?”

Many Dimensions  (1931), by Charles Williams,
   quoted here on Kristallnacht 2011

See also, from "The Net"—

Decompiling Wolfenstein

http://www.log24.com/log/pix11C/111201-DecompilingWolfenstein.jpg

"In Wolfenstein 3D , the player assumes the role of an American soldier
of Polish descent… attempting to escape from the Nazi stronghold of
Castle Wolfenstein." — Wikipedia

Wednesday, November 9, 2011

Polish Logic–

Filed under: Uncategorized — Tags: — m759 @ 11:23 AM

The Big Lukasiewicz

“Lord Arglay had a suspicion that the Stone
would be purely logical.  Yes, he thought,
but what, in that sense, were the rules of its pure logic?”

Many Dimensions  (1931), by Charles Williams

See also Łukasiewicz in Wikipedia and Lukasiewicz in this journal.

The latter's Christian references seem preferable to yesterday's
link to a scene from the Coen brothers' film "The Big Lebowski."

For those who prefer  a Christ-for-Jews there is
also Harvard's version. See The Crimson Passion.

Monday, July 11, 2011

The Witch of And/Or

Filed under: Uncategorized — m759 @ 12:00 PM

AND: Logical conjunction, symbolized as… 

OR:    Logical disjunction, symbolized as…  

AND/OR: Logical confusion, symbolized as…  IMAGE- AND and OR symbols combined as Lacanian AND/OR lozenge
according to a woman Lacanian analyst in this journal.

See also another female disciple of Lacan
writing as co-author with a philosophy professor
in Saturday's online New York Times 's "The Stone"—

"Let Be: An Answer to Hamlet’s Question."

Perhaps they thought the question was…

 

http://www.log24.com/log/pix11B/110711-ANDOR.jpg

http://www.log24.com/log/pix11B/110711-Wikipedia_Portrait_of_Simon_Critchley.jpg

Wikipedia portrait of New School
philosopher Simon Critchley

"To be and/or not to be?"

For a more philosophically respectable approach to
the same shape, see Sunday morning's Wittgenstein's Diamond.

"We're gonna need more holy water." —Hollywood saying

Tuesday, March 1, 2011

Women’s History Month

Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

Susanne for Suzanne

From pages 7-8 of William York Tindall’s Literary Symbolism  (Columbia U. Press, 1955)—

                                     ... According to Cassirer's Essay 
on Man, as we have seen, art is a symbolic form, parallel in respect 
of this to religion or science. Each of these forms builds up a universe 
that enables man to interpret and organize his experience; and each 
is a discovery, because a creation, of reality. Although similar in func- 
tion, the forms differ in the kind of reality built. Whereas science
builds it of facts, art builds it of feelings, intuitions of quality, and 
the other distractions of our inner life— and in their degrees so do 
myth and religion. What art, myth, and religion are, Cassirer con- 
fesses, cannot be expressed by a logical definition. 

Nevertheless, let us see what Clive Bell says about art. He calls 
it "significant form," but what that is he is unable to say. Having 
no quarrel with art as form, we may, however, question its signifi- 
cance. By significant he cannot mean important in the sense of 
having import, nor can he mean having the function of a sign; 
for to him art, lacking reference to nature, is insignificant. Since, 
however, he tells us that a work of art "expresses" the emotion of 
its creator and "provokes" an emotion in its contemplator,he seems 
to imply that his significant means expressive and provocative. The 
emotion expressed and provoked is an "aesthetic emotion," contem- 
plative, detached from all concerns of utility and from all reference. 

Attempting to explain Bell's significant form, Roger Fry, equally 
devoted to Whistler and art for art's sake, says that Flaubert's "ex- 
pression of the idea" is as near as he can get to it, but neither Flaubert 
nor Fry tells what is meant by idea. To "evoke" it, however, the artist 
creates an "expressive design" or "symbolic form," by which the 
spirit "communicates its most secret and indefinable impulses." 

Susanne Langer,who occupies a place somewhere between Fry 
and Cassirer, though nearer the latter, once said in a seminar that a 
work of art is an "unassigned syntactical symbol." Since this defini- 

End of page 7 

tion does not appear in her latest book, she may have rejected it, but 
it seems far more precise than Fry's attempt. By unassigned she prob- 
ably intends insignificant in the sense of lacking sign value or fixed 
reference; syntactical implies a form composed of parts in relation- 
ship to one another; and a symbol, according to Feeling and Form, 
is "any device whereby we are enabled to make an abstraction." Too 
austere for my taste, this account of symbol seems to need elaboration, 
which, to be sure, her book provides. For the present, however, taking 
symbol to mean an outward device for presenting an inward state, 
and taking unassigned and syntactical as I think she uses them, let 
us tentatively admire her definition of the work of art.

http://www.log24.com/log/pix11/110301-VegaSongsSm.jpg

http://www.log24.com/log/pix11/110301-Diamond-RedOnGray.bmp

Oh, the red leaf looks to the hard gray stone
To each other, they know what they mean

— Suzanne Vega, “Song in Red and Gray

Monday, December 27, 2010

Church Diamond

Filed under: Uncategorized — m759 @ 3:09 PM

IMAGE- The diamond property

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)—

http://www.log24.com/log/pix10B/101227-InsaneSymmetry.jpg

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 —

http://www.log24.com/log/pix10B/101227-nLabSpanImage.jpg

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.

Thursday, December 2, 2010

Caesarian

Filed under: Uncategorized — m759 @ 8:00 AM

The Dreidel Is Cast

The Nietzschean phrase "ruling and Caesarian spirits" occurred in yesterday morning's post "Novel Ending."

That post was followed yesterday morning by a post marking, instead, a beginning— that of Hanukkah 2010. That Jewish holiday, whose name means "dedication," commemorates the (re)dedication of the Temple in Jerusalem in 165 BC.

The holiday is celebrated with, among other things, the Jewish version of a die—  the dreidel . Note the similarity of the dreidel  to an illustration of The Stone*  on the cover of the 2001 Eerdmans edition of  Charles Williams's 1931 novel Many Dimensions

http://www.log24.com/log/pix10B/101202-DreidelAndStone.jpg

For mathematics related to the dreidel , see Ivars Peterson's column on this date fourteen years ago.
For mathematics related (if only poetically) to The Stone , see "Solomon's Cube" in this journal.

Here is the opening of Many Dimensions

http://www.log24.com/log/pix10B/101202-WilliamsChOne.jpg

For a fanciful linkage of the dreidel 's concept of chance to The Stone 's concept of invariant law, note that the New York Lottery yesterday evening (the beginning of Hanukkah) was 840. See also the number 840 in the final post (July 20, 2002) of the "Solomon's Cube" search.

Some further holiday meditations on a beginning—

Today, on the first full day of Hanukkah, we may or may not choose to mark another beginning— that of George Frederick James Temple, who was born in London on this date in 1901. Temple, a mathematician, was President of the London Mathematical Society in 1951-1953. From his MacTutor biography

"In 1981 (at the age of 80) he published a book on the history of mathematics. This book 100 years of mathematics (1981) took him ten years to write and deals with, in his own words:-

those branches of mathematics in which I had been personally involved.

He declared that it was his last mathematics book, and entered the Benedictine Order as a monk. He was ordained in 1983 and entered Quarr Abbey on the Isle of Wight. However he could not stop doing mathematics and when he died he left a manuscript on the foundations of mathematics. He claims:-

The purpose of this investigation is to carry out the primary part of Hilbert's programme, i.e. to establish the consistency of set theory, abstract arithmetic and propositional logic and the method used is to construct a new and fundamental theory from which these theories can be deduced."

For a brief review of Temple's last work, see the note by Martin Hyland in "Fundamental Mathematical Theories," by George Temple, Philosophical Transactions of the Royal Society, A, Vol. 354, No. 1714 (Aug. 15, 1996), pp. 1941-1967.

The following remarks by Hyland are of more general interest—

"… one might crudely distinguish between philosophical and mathematical motivation. In the first case one tries to convince with a telling conceptual story; in the second one relies more on the elegance of some emergent mathematical structure. If there is a tradition in logic it favours the former, but I have a sneaking affection for the latter. Of course the distinction is not so clear cut. Elegant mathematics will of itself tell a tale, and one with the merit of simplicity. This may carry philosophical weight. But that cannot be guaranteed: in the end one cannot escape the need to form a judgement of significance."

— J. M. E. Hyland. "Proof Theory in the Abstract." (pdf)
Annals of Pure and Applied Logic 114, 2002, 43-78.

Here Hyland appears to be discussing semantic ("philosophical," or conceptual) and syntactic ("mathematical," or structural) approaches to proof theory. Some other remarks along these lines, from the late Gian-Carlo Rota

http://www.log24.com/log/pix10B/101202-RotaChXII-sm.jpg

    (Click to enlarge.)

See also "Galois Connections" at alpheccar.org and "The Galois Connection Between Syntax and Semantics" at logicmatters.net.

* Williams's novel says the letters of The Stone  are those of the Tetragrammaton— i.e., Yod, He, Vau, He  (cf. p. 26 of the 2001 Eerdmans edition). But the letters on the 2001 edition's cover Stone  include the three-pronged letter Shin , also found on the dreidel .  What esoteric religious meaning is implied by this, I do not know.

Wednesday, December 1, 2010

A Geometric Merkabah*

Filed under: Uncategorized — m759 @ 11:30 AM

For Hanukkah (which starts this evening)—

Part I — The Stella Octangula (see also Monday's ART WARS post)—

http://www.log24.com/log/pix10B/101201-McCroryStella.jpg

Part II — A different view of the Stella —

http://www.log24.com/log/pix10B/101130-StellaIllusion.jpg

Click images for some mathematical background.

For some philosophical background on illusion and reality, see Graham Priest in the Sunday, Nov. 28, New York Times  column "The Stone" and in a work of fiction he published in the Notre Dame Journal of Formal Logic  (Vol. 38, No. 4) in 1997.

* See Google Images for pictures that are less academically respectable.
  For some related religious lore, see Merkabah at Wikipedia.

Sunday, November 28, 2010

This Just In

Filed under: Uncategorized — m759 @ 9:48 PM

Leslie Nielsen Dies at Age 84

Readings that may or may not* be relevant —

Graham Priest, "The Stone" and The Jewel in the Lotus.

* See Priest in Notre Dame Journal of Formal Logic, Fall 1997 and see Block That Metaphor.

Saturday, November 27, 2010

Simplex Sigillum Veri

Filed under: Uncategorized — m759 @ 7:20 AM

An Adamantine View of "The [Philosophers'] Stone"

The New York Times  column "The Stone" on Sunday, Nov. 21 had this—

"Wittgenstein was formally presenting his Tractatus Logico-Philosophicus , an already well-known work he had written in 1921, as his doctoral thesis. Russell and Moore were respectfully suggesting that they didn’t quite understand proposition 5.4541 when they were abruptly cut off by the irritable Wittgenstein. 'I don’t expect you to understand!' (I am relying on local legend here….)"

Proposition 5.4541*—

http://www.log24.com/log/pix10B/101127-WittgensteinSimplex.jpg

Related material, found during a further search—

A commentary on "simplex sigillum veri" leads to the phrase "adamantine crystalline structure of logic"—

http://www.log24.com/log/pix10B/101127-LukasiewiczAdamantine.jpg

For related metaphors, see The Diamond Cube, Design Cube 2x2x2, and A Simple Reflection Group of Order 168.

Here Łukasiewicz's phrase "the hardest of materials" apparently suggested the commentators' adjective "adamantine." The word "diamond" in the links above refers of course not to a material, but to a geometric form, the equiangular rhombus. For a connection of this sort of geometry with logic, see The Diamond Theorem and The Geometry of Logic.

For more about God, a Stone, logic, and cubes, see Tale  (Nov. 23).

* 5.4541 in the German original—

  Die Lösungen der logischen Probleme müssen einfach sein,
  denn sie setzen den Standard der Einfachheit.
  Die Menschen haben immer geahnt, dass es
  ein Gebiet von Fragen geben müsse, deren Antworten—
  a priori—symmetrisch, und zu einem abgeschlossenen,
  regelmäßigen Gebilde vereint liegen.
  Ein Gebiet, in dem der Satz gilt: simplex sigillum veri.

  Here "einfach" means "simple," not "neat," and "Gebiet" means
  "area, region, field, realm," not (except metaphorically) "sphere."

Tuesday, November 23, 2010

Tale

Filed under: Uncategorized — Tags: , — m759 @ 8:00 PM

A reviewer says Steve Martin finds in his new novel An Object of Beauty  "a sardonic morality tale."

From this journal on the day The Cube  was published (see today's Art Object ) —

Monday February 20, 2006

m759 @ 12:00 AM

The Past Revisited

From Log24 a year ago on this date, a quote from Many Dimensions  (1931), by Charles Williams:

“Lord Arglay had a suspicion that the Stone would be purely logical.  Yes, he thought, but what, in that sense, were the rules of its pure logic?”

For the rest of the story, see the downloadable version at Project Gutenberg of Australia.

See also a post on Mathematics and Narrative from Nov. 14, 2009.

That post compares characters in Many Dimensions  to those in Logicomix

Whitehead and Russell, 'Logicomix' page 181

Monday, May 17, 2010

Rolling the Stone

Filed under: Uncategorized — m759 @ 10:12 PM

A new NY Times column:

http://www.log24.com/log/pix10A/100517-NYT-Stone.jpg

Today's New York Times
re-edited for philosophers:

http://www.log24.com/log/pix10A/100517-JonesClue.jpg

See also

Eightfold Symmetry,

John Baez's paper
Duality in Logic and Physics
(for a May 29 meeting at Oxford),

The Shining of May 29, and

Lubtchansky's Key, with its links
to Duelle (French, f. adj., dual)
and Art Wars for Trotsky's Birthday.

Sunday, November 15, 2009

The Dead Shepherd and…

Filed under: Uncategorized — m759 @ 8:48 AM

Chinese Boxes

Continued from “The  Dead Shepherd,” Jan. 24, 2007

Yesterday’s Washington Post:

“James R. Lilley, 81, a longtime CIA operative in Asia who served as ambassador to China during the Tiananmen Square crackdown… died Nov. 12.”

http://www.log24.com/log/pix09A/091115-JamesRLilley.jpg

James R. Lilley

From a page linked to here on the date of Lilley’s death:

“… the extraordinary set of nested Chinese boxes that we introduced earlier in this series….”

A seemingly unrelated item in today’s New York Times obituaries index:

http://www.log24.com/log/pix09A/091115-Pnueli.jpg

This suggests an article on temporal logic at IBM Developer Works, which contains a link to Time-Rover.com.

This in turn leads to…

http://www.log24.com/log/pix09A/091115-ManTakShing.jpg

Man-Tak Shing

Shing’s CV at the Naval Postgraduate School affirms the usefulness of temporal logic.

Those who prefer metaphysics may consult the novel Many Dimensions referred to in yesterday’s entries and in “Relativity Blues” (Feb. 20, 2005)–

From Many Dimensions:

“Lord Arglay had a suspicion that the Stone would be purely logical.  Yes, he thought, but what, in that sense, were the rules of its pure logic?”

Good question.

Monday, March 9, 2009

Monday March 9, 2009

Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

Humorism

'The Manchurian Candidate' campaign button

"Always with a
little humor."
Dr. Yen Lo  

Diamond diagram of the four humors, the four qualities, the four elements, the four seasons, and four colors

From Temperament: A Brief Survey

For other interpretations
of the above shape, see
The Illuminati Diamond.

from Jung's Aion:

"From the circle and quaternity motif is derived the symbol of the geometrically formed crystal and the wonder-working stone. From here analogy formation leads on to the city, castle, church, house, room, and vessel. Another variant is the wheel. The former motif emphasizes the ego’s containment in the greater dimension of the self; the latter emphasizes the rotation which also appears as a ritual circumambulation. Psychologically, it denotes concentration on and preoccupation with a centre…." –Jung, Collected Works, Vol. 9, Part II, paragraph 352

As for rotation, see the ambigrams in Dan Brown's Angels & Demons (to appear as a film May 15) and the following figures:

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison
 
Click on image
for a related puzzle.
For a solution, see
 The Diamond Theorem.

A related note on
"Angels & Demons"
director Ron Howard:

Director Ron Howard with illustration of the fictional discipline 'symbology'
 
Click image for details.

Tuesday, February 24, 2009

Tuesday February 24, 2009

Filed under: Uncategorized — Tags: — m759 @ 1:00 PM
 
Hollywood Nihilism
Meets
Pantheistic Solipsism

Tina Fey to Steve Martin
at the Oscars:
"Oh, Steve, no one wants
 to hear about our religion
… that we made up."

Tina Fey and Steve Martin at the 2009 Oscars

From Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 117:

… in 'The Pediment of Appearance,' a slight narrative poem in Transport to Summer

 A group of young men enter some woods 'Hunting for the great ornament, The pediment of appearance.' Though moving through the natural world, the young men seek the artificial, or pure form, believing that in discovering this pediment, this distillation of the real, they will also discover the 'savage transparence,' the rude source of human life. In Stevens's world, such a search is futile, since it is only through observing nature that one reaches beyond it to pure form. As if to demonstrate the degree to which the young men's search is misaligned, Stevens says of them that 'they go crying/The world is myself, life is myself,' believing that what surrounds them is immaterial. Such a proclamation is a cardinal violation of Stevens's principles of the imagination.


Superficially the young men's philosophy seems to resemble what Wikipedia calls "pantheistic solipsism"– noting, however, that "This article has multiple issues."

As, indeed, does pantheistic solipsism– a philosophy (properly called "eschatological pantheistic multiple-ego solipsism") devised, with tongue in cheek, by science-fiction writer Robert A. Heinlein.

Despite their preoccupation with solipsism, Heinlein and Stevens point, each in his own poetic way, to a highly non-solipsistic topic from pure mathematics that is, unlike the religion of Martin and Fey, not made up– namely, the properties of space.

Heinlein:

"Sharpie, we have condensed six dimensions into four, then we either work by analogy into six, or we have to use math that apparently nobody but Jake and my cousin Ed understands. Unless you can think of some way to project six dimensions into three– you seem to be smart at such projections."
    I closed my eyes and thought hard. "Zebbie, I don't think it can be done. Maybe Escher could have done it."

Stevens:

A discussion of Stevens's late poem "The Rock" (1954) in Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 120:

For Stevens, the poem "makes meanings of the rock." In the mind, "its barrenness becomes a thousand things/And so exists no more." In fact, in a peculiar irony that only a poet with Stevens's particular notion of the imagination's function could develop, the rock becomes the mind itself, shattered into such diamond-faceted brilliance that it encompasses all possibilities for human thought:

The rock is the gray particular of man's life,
The stone from which he rises, up—and—ho,
The step to the bleaker depths of his descents ...

The rock is the stern particular of the air,
The mirror of the planets, one by one,
But through man's eye, their silent rhapsodist,

Turquoise the rock, at odious evening bright
With redness that sticks fast to evil dreams;
The difficult rightness of half-risen day.

The rock is the habitation of the whole,
Its strength and measure, that which is near,
     point A
In a perspective that begins again

At B: the origin of the mango's rind.

                    (Collected Poems, 528)

Stevens's rock is associated with empty space, a concept that suggests "nothingness" to one literary critic:

B. J. Leggett, "Stevens's Late Poetry" in The Cambridge Companion to Wallace Stevens— On the poem "The Rock":

"… the barren rock of the title is Stevens's symbol for the nothingness that underlies all existence, 'That in which space itself is contained'….  Its subject is its speaker's sense of nothingness and his need to be cured of it."

This interpretation might appeal to Joan Didion, who, as author of the classic novel Play It As It Lays, is perhaps the world's leading expert on Hollywood nihilism.

More positively…

Space is, of course, also a topic
in pure mathematics…
For instance, the 6-dimensional
affine space
(or the corresponding
5-dimensional projective space)

The 4x4x4 cube

over the two-element Galois field
can be viewed as an illustration of
Stevens's metaphor in "The Rock."

Heinlein should perhaps have had in mind the Klein correspondence when he discussed "some way to project six dimensions into three." While such a projection is of course trivial for anyone who has taken an undergraduate course in linear algebra, the following remarks by Philippe Cara present a much more meaningful mapping, using the Klein correspondence, of structures in six (affine) dimensions to structures in three.

Cara:

Philippe Cara on the Klein correspondence
Here the 6-dimensional affine
space contains the 63 points
of PG(5, 2), plus the origin, and
the 3-dimensional affine
space contains as its 8 points
Conwell's eight "heptads," as in
Generating the Octad Generator.

Saturday, October 25, 2008

Saturday October 25, 2008

Filed under: Uncategorized — Tags: , — m759 @ 11:01 AM
Actual Being

The New York Times Book Review online today has a review by Sam Tanenhaus of a new John Updike book.

The title of the review (not the book) is "Mr. Wizard."

"John Updike is the great genial sorcerer of American letters. His output alone (60 books, almost 40 of them novels or story collections) has been supernatural. More wizardly still is the ingenuity of his prose. He has now written tens of thousands of sentences, many of them tiny miracles of transubstantiation whereby some hitherto overlooked datum of the human or natural world– from the anatomical to the zoological, the socio-economic to the spiritual– emerges, as if for the first time, in the complete­ness of its actual being."

Rolling Stone interview with Sting, February 7, 1991:

"'I was brought up in a very strong Catholic community,' Sting says. 'My parents were Catholic, and in the Fifties and Sixties, Catholicism was very strong. You know, they say, "Once a Catholic, always a Catholic." In a way I'm grateful for that background. There's a very rich imagery in Catholicism: blood, guilt, death, all that stuff.' He laughs."

http://www.log24.com/log/pix08A/081025-Sting.jpg

RS 597, Feb. 7, 1991

Last night's 12:00 AM
Log24 entry:

Midnight Bingo

From this date six years ago:


It All Adds Up.

From this morning's newspaper,
a religious meditation I had not
seen last night:

The image “http://www.log24.com/log/pix08A/081025-WizardOfIdSm.jpg” cannot be displayed, because it contains errors.

Related material:

Juneteenth through
Midsummer Night, 2007

and

Church of the Forbidden Planet

Friday, June 6, 2008

Friday June 6, 2008

Filed under: Uncategorized — Tags: — m759 @ 2:45 AM
The Dance of Chance

"Harvard seniors have
every right to demand a
    Harvard-calibre speaker."

— Adam Goldenberg in
The Harvard Crimson

"Look down now, Cotton Mather"

— Wallace Stevens,
Harvard College
Class of 1901

For Thursday, June 5, 2008,
commencement day for Harvard's
Class of 2008, here are the
Pennsylvania Lottery numbers:

Mid-day 025
Evening 761

Thanks to the late
Harvard professor
Willard Van Orman Quine,
the mid-day number 025
suggests the name
"Isaac Newton."

(For the logic of this suggestion,
see On Linguistic Creation
and Raiders of the Lost Matrix.)

Thanks to Google search, the
  name of Newton, combined with
  Thursday's evening number 761,
suggests the following essay:

Science 10 August 2007:
Vol. 317. no. 5839, pp. 761-762

PHILOSOPHY OF SCIENCE:
The Cha-Cha-Cha Theory
of Scientific Discovery

Daniel E. Koshland Jr.*

* D. E. Koshland Jr. passed away on 23 July 2007. He was a professor of biochemistry and molecular and cell biology at the University of California, Berkeley, since 1965. He served as Science's editor-in-chief from 1985 to 1995.
 


What can a non-scientist add?

Perhaps the Log24 entries for
the date of Koshland's death:

The Philosopher's Stone
and The Rock.

Or perhaps the following
observations:

On the figure of 25 parts
discussed in
"On Linguistic Creation"–

5x5 ultra super magic square

"The Moslems thought of the
central 1 as being symbolic
of the unity of Allah.
"

— Clifford Pickover  

"At the still point,
there the dance is.
"

— T. S. Eliot,
Harvard College
Class of 1910

Sunday, May 18, 2008

Sunday May 18, 2008

Filed under: Uncategorized — Tags: — m759 @ 2:02 PM

From the Grave

DENNIS OVERBYE

in yesterday's New York Times:

"From the grave, Albert Einstein
poured gasoline on the culture wars
between science and religion this week…."

An announcement of a
colloquium at Princeton:

Cartoon of Coxedter exhuming Geometry

Above: a cartoon,
"Coxeter exhuming Geometry,"
with the latter's tombstone inscribed

"GEOMETRY

  600 B.C. —
1900 A.D.
R.I.P."

Page from 'The Paradise of Childhood,' 1906 edition

The above is from
The Paradise of Childhood,
a work first published in 1869.

"I need a photo-opportunity,
I want a shot at redemption.
Don't want to end up a cartoon
In a cartoon graveyard."

— Paul Simon

Einstein on TIME cover as 'Man of the Century'

Albert Einstein,
1879-1955:

"It is quite clear to me that the religious paradise of youth, which was thus lost, was a first attempt to free myself from the chains of the 'merely-personal,' from an existence which is dominated by wishes, hopes and primitive feelings.  Out yonder there was this huge world, which exists independently of us human beings and which stands before us like a great, eternal riddle, at least partially accessible to our inspection and thinking.  The contemplation of this world beckoned like a liberation…."

Autobiographical Notes, 1949

Related material:

A commentary on Tom Wolfe's
"Sorry, but Your Soul Just Died"–

"The Neural Buddhists," by David Brooks,
 in the May 13 New York Times:

"The mind seems to have
the ability to transcend itself
and merge with a larger
presence that feels more real."

A New Yorker commentary on
a new translation of the Psalms:

"Suddenly, in a world without
Heaven, Hell, the soul, and
eternal salvation or redemption,
the theological stakes seem
more local and temporal:
'So teach us to number our days.'"

and a May 13 Log24 commentary
on Thomas Wolfe's
"Only the Dead Know Brooklyn"–

"… all good things — trout as well as
eternal salvation — come by grace
and grace comes by art
and art does not come easy."

A River Runs Through It

"Art isn't easy."
— Stephen Sondheim,
quoted in
Solomon's Cube.

For further religious remarks,
consult Indiana Jones and the
Kingdom of the Crystal Skull
and The Librarian:
Return to King Solomon's Mines.

Wednesday, April 23, 2008

Wednesday April 23, 2008

Filed under: Uncategorized — Tags: — m759 @ 9:00 AM

Upscale Realism

or, "Have some more
wine and cheese, Barack."

(See April 15, 5:01 AM)

  Allyn Jackson on Rebecca Goldstein
in the April 2006 AMS Notices (pdf)

"Rebecca Goldstein’s 1983 novel The Mind-Body Problem has been widely admired among mathematicians for its authentic depiction of academic life, as well as for its exploration of how philosophical issues impinge on everyday life. Her new book, Incompleteness: The Proof and Paradox of Kurt Gödel, is a volume in the 'Great Discoveries' series published by W. W. Norton….

In March 2005 the Mathematical Sciences Research Institute (MSRI) in Berkeley held a public event in which its special projects director, Robert Osserman, talked with Goldstein about her work. The conversation, which took place before an audience of about fifty people at the Commonwealth Club in San Francisco, was taped….

A member of the audience posed a question that has been on the minds of many of Goldstein’s readers: Is The Mind-Body Problem based on her own life? She did indeed study philosophy at Princeton, finishing her Ph.D. in 1976 with a thesis titled 'Reduction, Realism, and the Mind.' She said that while there are correlations between her life and the novel, the book is not autobiographical….

She… talked about the relationship between Gödel and his colleague at the Institute for Advanced Study, Albert Einstein. The two were very different: As Goldstein put it, 'Einstein was a real mensch, and Gödel was very neurotic.' Nevertheless, a friendship sprang up between the two. It was based in part, Goldstein speculated, on their both being exiles– exiles from Europe and intellectual exiles. Gödel's work was sometimes taken to mean that even mathematical truth is uncertain, she noted, while Einstein's theories of relativity were seen as implying the sweeping view that 'everything is relative.' These misinterpretations irked both men, said Goldstein. 'Einstein and Gödel were realists and did not like it when their work was put to the opposite purpose.'"


Related material:

From Log24 on
March 22 (Tuesday of
Passion Week), 2005:

 
"'What is this Stone?' Chloe asked…. 'It is told that, when the Merciful One made the worlds, first of all He created that Stone and gave it to the Divine One whom the Jews call Shekinah, and as she gazed upon it the universes arose and had being.'"

Many Dimensions,
by Charles Williams, 1931

For more on this theme
appropriate to Passion Week
Jews playing God — see

The image “http://www.log24.com/log/pix05/050322-Trio.jpg” cannot be displayed, because it contains errors.

Rebecca Goldstein
in conversation with
Bob Osserman
of the
Mathematical Sciences
Research Institute
at the
Commonwealth Club,
San Francisco,
Tuesday, March 22.

Wine and cheese
reception at 5:15 PM
(San Francisco time).

From
UPSCALE,
a website of the
physics department at
the University of Toronto:

Mirror Symmetry

Robert Fludd: Universe as mirror image of God

"The image [above]
is a depiction of
the universe as a
mirror image of God,
drawn by Robert Fludd
in the early 17th century.

The caption of the
upper triangle reads:

'That most divine and beautiful
counterpart visible below in the
flowing image of the universe.'

The caption of the
lower triangle is:

'A shadow, likeness, or
reflection of the insubstantial*
triangle visible in the image
of the universe.'"

* Sic. The original is incomprehensibilis, a technical theological term. See Dorothy Sayers on the Athanasian Creed and John 1:5.

For further iconology of the
above equilateral triangles,
see Star Wars (May 25, 2003),
Mani Padme (March 10, 2008),
Rite of Sping (March 14, 2008),
and
Art History: The Pope of Hope
(In honor of John Paul II
three days after his death
in April 2005).

Happy Shakespeare's Birthday.

Monday, April 7, 2008

Monday April 7, 2008

Filed under: Uncategorized — m759 @ 2:20 AM

“Lord Arglay had a suspicion that the Stone would be purely logical.  Yes, he thought, but what, in that sense, were the rules of its pure logic?”

— Charles Williams, Many Dimensions

Saturday, February 2, 2008

Saturday February 2, 2008

Filed under: Uncategorized — m759 @ 2:19 AM
Trevanian,
Incident at Twenty-Mile:

Matthew had a couple of hours on his hands before dinner with the Kanes, so he drifted up to the only grassy spot in Twenty-Mile, the triangular, up-tilted little meadow crossed by a rivulet running off from the cold spring that provided the town’s water. This meadow belonged to the livery stable, and half a dozen of its donkeys lazily nosed in the grass while, at the far end, a scrawny cow stood in the shade of the only tree in Twenty-Mile, a stunted skeleton whose leafless, wind-raked branches stretched imploringly to leeward, like bony fingers clawing the clouds. The meadow couldn’t be seen from any part of the town except the Livery, so Matthew felt comfortably secluded as he sauntered along, intending to investigate the burial ground that abutted the donkey meadow, but B. J. Stone called to him from the Livery, so he turned back and began the chore they had found for him to do: oiling tools.

LATER….

After they did the dishes, Matthew and Ruth Lillian walked down the Sunday-silent street, then turned up into the donkey meadow. He was careful to guide her away from the soggy patch beneath the tree, where the Bjorkvists had slaughtered that week’s beef. Lost in their own thoughts, they strolled across the meadow, the uneven ground causing their shoulders to brush occasionally, until they reached the fenced-in burying ground.

STILL LATER….

“Matthew?” she asked in an offhand tone.

“Hm-m-m?”

“What’s ‘the Other Place’?”

He turned and stared at her. “How do you know about that?”

“You told me.”

“I never!”

“Yes, you did. You were telling about your fight with the Benson boys, and you said you couldn’t feel their punches because you were in this ‘Other Place.’ I didn’t ask you about it then, ’cause you were all worked up.  But I’ve been curious about it ever since.”

“Oh, it’s just…” In a gesture that had something of embarrassment in it and something of imitation, he threw his stick as hard as he could, and it whop-whop-whop’d through the air, landing against the sagging fence that separated the burying ground from the donkey meadow.

“If you don’t want to tell me, forget it.  I just thought… Never mind.” She walked on.

“It’s not that I don’t want to tell you. But it’s… it’s hard to explain.”

She stopped and waited patiently.

“It’s just… well, when I was a little kid and I was scared– scared because Pa was shouting at Ma, or because I was going to have to fight some kid during recess– I’d fix my eyes on a crack in the floor or a ripple in a pane of glass– on anything, it didn’t matter what– and pretty soon I’d slip into this– this Other Place where everything was kind of hazy and echoey, and I was far away and safe. At first, I had to concentrate real hard to get to this safe place. But then, this one day a kid was picking on me, and just like that– without even trying– I was suddenly there, and I felt just as calm as calm, and not afraid of anything. I knew they were punching me, and I could hear the kids yelling names, but it didn’t hurt and I didn’t care, ’cause I was off in the Other Place.  And after that, any time I was scared, or if I was facing something that was just too bad, I’d suddenly find myself there. Safe and peaceful.” He searched here eyes. “Does that make any sense to you, Ruth Lillian?”

“Hm-m… sort of. It sounds kind of eerie.” And she added quickly, “But really interesting!”

“I’ve never told anybody about it. Not even my ma. I was afraid to because… This’ll sound funny, but I was afraid that if other people knew about the Other Place, it might heal up and go away, and I wouldn’t be able to get there when I really needed to. Crazy, huh?”

Related material:

The Meadow,

Logical Songs,

Plato, Pegasus, and
the Evening Star

Thursday, June 21, 2007

Thursday June 21, 2007

Filed under: Uncategorized — m759 @ 12:07 PM
Let No Man
Write My Epigraph

(See entries of June 19th.)

“His graceful accounts of the Bach Suites for Unaccompanied Cello illuminated the works’ structural logic as well as their inner spirituality.”

Allan Kozinn on Mstislav Rostropovich in The New York Times, quoted in Log24 on April 29, 2007

“At that instant he saw, in one blaze of light, an image of unutterable conviction…. the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”

— Thomas Wolfe, Of Time and the River, quoted in Log24 on June 9, 2005

“… the stabiliser of an octad preserves the affine space structure on its complement, and (from the construction) induces AGL(4,2) on it. (It induces A8 on the octad, the kernel of this action being the translation group of the affine space.)”

— Peter J. Cameron, “The Geometry of the Mathieu Groups” (pdf)

“… donc Dieu existe, réponse!

— Attributed, some say falsely,
to Leonhard Euler


“Only gradually did I discover
what the mandala really is:
‘Formation, Transformation,
Eternal Mind’s eternal recreation'”

(Faust, Part Two, as
quoted by Jung in
Memories, Dreams, Reflections)

Wolfgang Pauli as Mephistopheles

“Pauli as Mephistopheles
in a 1932 parody of
Goethe’s Faust at Niels Bohr’s
institute in Copenhagen.
The drawing is one of
many by George Gamow
illustrating the script.”
Physics Today

“Borja dropped the mutilated book on the floor with the others. He was looking at the nine engravings and at the circle, checking strange correspondences between them.

‘To meet someone’ was his enigmatic answer. ‘To search for the stone that the Great Architect rejected, the philosopher’s stone, the basis of the philosophical work. The stone of power. The devil likes metamorphoses, Corso.'”

The Club Dumas, basis for the Roman Polanski film “The Ninth Gate” (See 12/24/05.)

“Pauli linked this symbolism
with the concept of automorphism.”

The Innermost Kernel
 (previous entry)

And from
Symmetry in Mathematics
and Mathematics of Symmetry

(pdf), by Peter J. Cameron,
a paper presented at the
International Symmetry Conference,
Edinburgh, Jan. 14-17, 2007,
we have

The Epigraph–

Weyl on automorphisms
(Here “whatever” should
of course be “whenever.”)

Also from the
Cameron paper:

Local or global?

Among other (mostly more vague) definitions of symmetry, the dictionary will typically list two, something like this:

• exact correspondence of parts;
• remaining unchanged by transformation.

Mathematicians typically consider the second, global, notion, but what about the first, local, notion, and what is the relationship between them?  A structure M is homogeneous if every isomorphism between finite substructures of M can be extended to an automorphism of M; in other words, “any local symmetry is global.”

Some Log24 entries
related to the above politically
(women in mathematics)–

Global and Local:
One Small Step

and mathematically–

Structural Logic continued:
Structure and Logic
(4/30/07):

This entry cites
Alice Devillers of Brussels–

Alice Devillers

“The aim of this thesis
is to classify certain structures
which are, from a certain
point of view, as homogeneous
as possible, that is which have
  as many symmetries as possible.”

“There is such a thing
as a tesseract.”

Madeleine L’Engle 

Monday, April 16, 2007

Monday April 16, 2007

Filed under: Uncategorized — m759 @ 4:01 PM

The Abridgment of Hope

Part I: Framework

From Log24,
Here’s Your Sign,
Aug. 8, 2002–

“Paz also mentions the Christian concept of eternity as a realm outside time, and discusses what happened to modern thought after it abandoned the concept of eternity.

Naturally, many writers have dealt with the subject of time, but it seems particularly part of the Zeitgeist now, with a new Spielberg film about precognition.  My own small experience, from last night until today, may or may not have been precognitive.  I suspect it’s the sort of thing that many people often experience, a sort of ‘So that’s what that was about’ feeling.  Traditionally, such experience has been expressed in terms of a theological framework.”

Part II: Context

From Ann Copeland,
Faith and Fiction-Making:
The Catholic Context
“–

“Each of us is living out a once-only story which, unlike those mentioned here, has yet to reveal its ending. We live that story largely in the dark. From time to time we may try to plumb its implications, to decipher its latent design, or at least get a glimmer of how parts go together. Occasionally, a backward glance may suddenly reveal implications, an evolving pattern we had not discerned, couldn’t have when we were ‘in’ it. Ah, now I see what I was about, what I was after.”

Part III: Context Sensitivity

From Log24’s
Language Game,
Jan. 14, 2004–

Ludwig Wittgenstein,
Philosophical Investigations:

373. Grammar tells what kind of object anything is. (Theology as grammar.)

From Wikipedia

Another definition of context-sensitive grammars defines them as formal grammars where all productions are of the form

a yields b where the length of a is less than or equal to the length of b

Such a grammar is also called a monotonic or noncontracting grammar because none of the rules decreases the size of the string that is being rewritten.

If the possibility of adding the empty string to a language is added to the strings recognized by the noncontracting grammars (which can never include the empty string) then the languages in these two definitions are identical.

 Part IV: Abridgment

“Know the one about the Demiurge and the Abridgment of Hope?”

— Robert Stone, A Flag for Sunrise, Knopf, 1981, the final page, 439

Also from Stone’s novel, quoted by Ann Copeland in the above essay:

You after all? Inside, outside, round and about. Disappearing stranger, trickster. Christ, she thought, so far. Far from where?

But why always so far?

Por qué?” she asked. There was a guy yelling.

Always so far away. You. Always so hard on the kid here, making me be me right down the line. You old destiny. You of Jacob, you of Isaac, of Esau.

Let it be you after all. Whose after all I am. For whom I was nailed.

So she said to Campos: “Behold the handmaid of the Lord.” (416)

Tuesday, January 9, 2007

Tuesday January 9, 2007

Filed under: Uncategorized — m759 @ 12:00 PM
For Balanchine’s Birthday

(continued from
January 9, 2003)

George Balanchine

Encyclopædia Britannica Article

born January 22
[January 9, Old Style], 1904,
St. Petersburg, Russia
died April 30, 1983, New York,
New York, U.S.

Photograph:George Balanchine.
George Balanchine.
©1983 Martha Swope

original name 
Georgy Melitonovich Balanchivadze
most influential choreographer of classical ballet in the United States in the 20th century.  His works, characterized by a cool neoclassicism, include The Nutcracker (1954) and Don Quixote (1965), both pieces choreographed for the New York City Ballet, of which he was a founder (1948), the artistic director, and the…

Balanchine,  George… (75 of 1212 words)

“What on earth is
a concrete universal?”
— Robert M. Pirsig

Review:

From Wikipedia’s
“Upper Ontology”
and
Epiphany 2007:

“There is no neutral ground
that can serve as
a means of translating between
specialized (lower) ontologies.”

There is, however,
“the field of reason”–
the 3×3 grid:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

Click on grid
for details.

As Rosalind Krauss
has noted, some artists
regard the grid as
“a staircase to
  the Universal.”

Other artists regard
Epiphany itself as an
approach to
the Universal:

Epiphany signals the traversal
of the finite by the infinite,
of the particular by the universal,
of the mundane by the mystical,
of time by eternity.

Richard Kearney, 2005,
in The New Arcadia Review

The image “http://www.log24.com/log/pix07/070109-Kearney2.jpg” cannot be displayed, because it contains errors.

Kearney (right) with
Martin Scorsese (left)
and Gregory Peck
in 1997.

“… one of the things that worried me about traditional metaphysics, at least as I imbibed it in a very Scholastic manner at University College Dublin in the seventies, is that philosophy was realism and realism was truth. What disturbed me about that was that everything was already acquired; truth was always a systematic given and it was there to be learned from Creation onwards; it was spoken by Jesus Christ and then published by St. Thomas Aquinas: the system as perfect synthesis. Hence, my philosophy grew out of a hunger for the ‘possible’ and it was definitely a reaction to my own philosophical formation. Yet that wasn’t my only reaction. I was also reacting to what I considered to be the deep pessimism, and even at times ‘nihilism’ of the postmodern turn.”

— Richard Kearney, interview (pdf) in The Leuven Philosophy Newsletter, Vol. 14, 2005-2006

For more on “the possible,” see Kearney’s The God Who May Be, Diamonds Are Forever, and the conclusion of Mathematics and Narrative:

“We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes)).”

Keith Allen Korcz 

The image “http://www.log24.com/log/pix05B/050802-Stone.gif” cannot be displayed, because it contains errors.

“The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being….”

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity,
Christ Church College, Oxford
(the home of Lewis Carroll)

Friday, December 29, 2006

Friday December 29, 2006

Filed under: Uncategorized — m759 @ 11:01 AM
Tools
of Christ Church

“For every kind of vampire,
there is a kind of cross.”
— Thomas Pynchon

Cover of Thomas, by Shelley Mydans: Sword and its shadow, a cross

Click on picture for details.

Today is the feast
of St. Thomas Becket.

In his honor, a meditation
on tools and causation:

“Lewis Wolpert, an eminent developmental biologist at University College London, has just published Six Impossible Things Before Breakfast, a pleasant, though rambling, look at the biological basis of belief. While the book focuses on our ability to form causal beliefs about everyday matters (the wind moved the trees, for example), it spends considerable time on the origins of religious and moral beliefs. Wolpert defends the unusual idea that causal thinking is an adaptation required for tool-making. Religious beliefs can thus be seen as an odd extension of causal thinking about technology to more mysterious matters. Only a species that can reason causally could assert that ‘this storm was sent by God because we sinned.’ While Wolpert’s attitude toward religion is tolerant, he’s an atheist who seems to find religion more puzzling than absorbing.”

Review by H. Allen Orr in
The New York Review of Books,
Vol. 54, No. 1, January 11, 2007    


“An odd extension”–

Wolpert’s title is, of course,
from Lewis Carroll.

Related material:

“It’s a poor sort of memory
that only works backwards.”
Through the Looking-Glass

An event at the Kennedy Center
broadcast on
December 26, 2006
(St. Steven’s Day):

“Conductor John Williams, a 2004 Honoree, says, ‘Steven, sharing our 34-year collaboration has been a great privilege for me. It’s been an inspiration to watch you dream your dreams, nurture them and make them grow. And, in the process, entertain and edify billions of people around the world. Tonight we’d like to salute you, musically, with a piece that expresses that spirit beautifully … It was written by Leonard Bernstein, a 1980 Kennedy Center Honoree who was, incidentally, the first composer to be performed in this hall.’ Backed by The United States Army Chorus and The Choral Arts Society, soprano Harolyn Blackwell and tenor Gregory Turay sing the closing number for Spielberg’s tribute and the gala itself. It’s the finale to the opera ‘Candide,’ ‘Make Our Garden Grow,’ and Williams conducts.”

CBS press release

See also the following,
from the conclusion to

Mathematics and Narrative

(Log24, Aug. 22, 2005):

Diamond on cover of Narrative Form, by Suzanne Keen

“At times, bullshit can
only be countered
   with superior bullshit.”
Norman Mailer

Many Worlds and Possible Worlds in Literature and Art, in Wikipedia:

    “The concept of possible worlds dates back to at least Leibniz who in his Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds.  Voltaire satirized this view in his picaresque novel Candide….
    Borges’ seminal short story El jardín de senderos que se bifurcan (“The Garden of Forking Paths“) is an early example of many worlds in fiction.”

Il faut cultiver notre jardin.
— Voltaire

“We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes)).”

Keith Allen Korcz 

Diamond in a square

“The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being….”

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
 Regius Professor of Divinity,
  Christ Church College, Oxford
(the home of Lewis Carroll)

For further details,
click on the
Christ Church diamond.

Tuesday, October 10, 2006

Tuesday October 10, 2006

Filed under: Uncategorized — Tags: — m759 @ 8:00 PM
Mate in
Two Seconds


From Oct. 14 last year:

The image “http://www.log24.com/log/pix05B/051014-Tick.gif” cannot be displayed, because it contains errors.

From Oct. 13 last year
(Yom Kippur):

A Poem for Pinter

Oct. 13, 2005

The Guardian on Harold Pinter, winner of this year's Nobel Prize for Literature:

"Earlier this year, he announced his decision to retire from playwriting in favour of poetry,"

Michael Muskal in today's Los Angeles Times:

"Pinter, 75, is known for his sparse and thin style as well as his etched characters whose crystal patter cuts through the mood like diamond drill bits."

Robert Stone, A Flag for Sunrise (See Jan. 25):

"'That old Jew gave me this here.'  Egan looked at the diamond….  'It's worth a whole lot of money– you can tell that just by looking– but it means something, I think.  It's got a meaning, like.'

'Let's see,' Egan said, 'what would it mean?'  He took hold of Pablo's hand cupping the stone and held his own hand under it.  '"The jewel is in the lotus," perhaps that's what it means.  The eternal in the temporal….'"

Notes on Modal Logic:
 

"Modal logic was originally developed to investigate logic under the modes of necessary and possible truth.  The words 'necessary' and 'possible' are called modal connectives, or modalities.  A modality is a word that when applied to a statement indicates when, where, how, or under what circumstances the statement may be true.  In terms of notation, it is common to use a box [] for the modality 'necessary' and a diamond <> for the modality 'possible.'"

A Poem for Pinter

The image “http://www.log24.com/log/pix05B/051013-Waka.gif” cannot be displayed, because it contains errors.

Commentary:

"Waka" also means Japanese poem or Maori canoe.  (For instance, this Japanese poem and this Maori canoe.)

For a meditation on "bang splat," see Sept. 25-29.

For the meaning of "tick tick," see Emily Dickinson on "degreeless noon."

"Hash," of course, signifies "checkmate."  (See previous three entries.)

For language more suited to
the year's most holy day, see
this year's Yom Kippur entry,
from October 2.

That was also the day of the
Amish school killings in
Pennsylvania and the day that
mathematician Paul Halmos died.

For more on the former, see
Death in Two Seconds.

For more on the latter, see
The Halmos Tombstone.

4x9 black monolith
 

Monday, October 9, 2006

Monday October 9, 2006

Filed under: Uncategorized — m759 @ 9:00 AM
 
ART WARS:
To Apollo
 
The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

"This is the garden of Apollo,
the field of Reason…."
John Outram, architect

To Apollo (10/09/02)
Art Wars: Apollo and Dionysus
(10/09/02)
Balanchine's Birthday
(01/09/03)

Art Theory for Yom Kippur
(10/05/03)

A Form
(05/22/04)
Ineluctable
(05/27/04)

A Form, continued
(06/05/04)
Parallelisms
(06/06/04)
Ado
(06/25/04)

Deep Game
(06/26/04)
Gameplayers of Zen
(06/27/04)
And So To Bed
(06/29/04)
Translation Plane for Rosh Hashanah
(09/15/04)
Derrida Dead
(10/09/04)
The Nine
(11/09/04)
From Tate to Plato
(11/19/04)
Art History
(05/11/05)
A Miniature Rosetta Stone
(08/06/05)
High Concept
(8/23/05) 
High Concept, Continued
(8/24/05)
Analogical Train of Thought
(8/25/05)
Today's Sermon: Magical Thinking
(10/09/05)
Balance
(10/31/05)
Matrix
(11/01/05)
Seven is Heaven, Eight is a Gate
(11/12/05)
Nine is a Vine
(11/12/05)
Apollo and Christ
(12/02/05)
Hamilton's Whirligig
(01/05/06)
Cross
(01/06/06)
On Beauty
(01/26/06)
Sunday Morning
(01/29/06)
Centre
(01/29/06)
New Haven
(01/29/06) 
Washington Ballet
(02/05/06)
Catholic Schools Sermon
(02/05/06)
The Logic of Apollo
(02/05/06)
Game Boy
(08/06/06)
Art Wars Continued: The Krauss Cross
(09/13/06)
Art Wars Continued: Pandora's Box
(09/16/06)
The Pope in Plato's Cave
(09/16/06)
Today's Birthdays
(09/26/06)
Symbology 101
(09/26/06)

Wednesday, July 26, 2006

Wednesday July 26, 2006

Filed under: Uncategorized — m759 @ 1:44 PM
Partitions,
continued

“Mistakes are inevitable and may be either in missing a true signal or in thinking there is a signal when there is not. I am suggesting that believers in the paranormal (called ‘sheep’ in psychological parlance) are more likely to make the latter kind of error than are disbelievers (called ‘goats’).”

— “Psychic Experiences:
     Psychic Illusions,”
     by Susan Blackmore,
     Skeptical Inquirer, 1992

For Harvard mathematician
Frederick Mosteller,
dead on Sunday, July 23, 2006:
 
“… a drama built out of nothing
but numbers and imagination”

— Freeman Dyson, quoted in Log24
on the day Mosteller died

From Log24 on
Mosteller’s last birthday,
December 24, 2005:

The Club Dumas

by Arturo Perez-Reverte

One by one, he tore the engravings from the book, until he had all nine.  He looked at them closely.  “It’s a pity you can’t follow me where I’m going.  As the fourth engraving states, fate is not the same for all.”

“Where do you believe you’re going?”

Borja dropped the mutilated book on the floor with the others. He was looking at the nine engravings and at the circle, checking strange correspondences between them.

“To meet someone” was his enigmatic answer. “To search for the stone that the Great Architect rejected, the philosopher’s stone, the basis of the philosophical work. The stone of power. The devil likes metamorphoses, Corso.”

“Only gradually did I discover
what the mandala really is:
‘Formation, Transformation,
Eternal Mind’s eternal recreation'”
(Faust, Part Two)

Carl Gustav Jung,   

born on this date
Today’s other birthday:
Mick Jagger

Pleased to meet you,
hope you guess my name.”

Monday, February 20, 2006

Monday February 20, 2006

Filed under: Uncategorized — m759 @ 12:00 AM

The Past Revisited

From Log24 a year ago on this date, a quote from Many Dimensions (1931), by Charles Williams:

“Lord Arglay had a suspicion that the Stone would be purely logical.  Yes, he thought, but what, in that sense, were the rules of its pure logic?”

For the rest of the story, see the downloadable version at Project Gutenberg of Australia.

Monday, February 6, 2006

Monday February 6, 2006

Filed under: Uncategorized — m759 @ 10:00 AM
The Diamond Theory of Truth


“Legend says that when the stones
are brought together the diamonds
inside of them will glow.”

— Harrison Ford in
“Indiana Jones and the
Temple of Doom”

In today’s online New York Times:

(1) A review of pop-archaeology TV,
     “Digging for the Truth,”
(2) a Sunday news story,
     “Looking for the Lie,”
(3) and a profile,
     “Storyteller in the Family.”

From (1):
“The season premiere ‘Digging for the Truth: The Real Temple of Doom,’ showed Mr. Bernstein in South America, exploring tunnels….”
From (2):
“… scientists are building a cognitive theory of deception to show what lying looks like….”
From (3):
“I did feel one had to get not just the facts, but the emotional underpinnings.”

Related material:

Log24 on

Harrison Ford’s birthday
last July–

The image “http://www.log24.com/log/pix05A/050713-Ford.jpg” cannot be displayed, because it contains errors.

— and Mathematics and Narrative.

See also Saturday’s entry,
Raiders of the Lost Matrix,
for logic as an aid in
detecting lies.

Saturday, January 14, 2006

Saturday January 14, 2006

Filed under: Uncategorized — m759 @ 4:07 AM
Diamond Jubilance
(See previous entry.)

“A (very brief!) lit search reveals very little on the intersection between probability theory and modal logic…. probability and modality are such big topics one would think there’d be something on their intersection, and I don’t think the way I’ve framed the problem is entirely idiosyncratic.”

— Brian Weatherson, Associate Professor of Philosophy, Cornell University, May 11, 2004

Here, on the other hand, is a way of framing the problem that is entirely idiosyncratic:

On this date:

Probability:
In 1970, William Feller died.
Modality:
In 1978, Kurt Gödel died.
Intersection:
In 1898, the Rev. Deacon Charles Lutwidge Dodgson died.

Related material:
Log24, Jan. 14, 2003, and

The image “http://www.log24.com/log/pix05B/050802-Stone.gif” cannot be displayed, because it contains errors.

Modal Theology.

Saturday, December 24, 2005

Saturday December 24, 2005

Filed under: Uncategorized — m759 @ 9:00 PM
Nine is a Vine
(continued)

The image “http://www.log24.com/log/pix05B/051224-Stars.jpg” cannot be displayed, because it contains errors.

The figures are:
 
A symbol of Apollo from
Balanchine’s Birthday and
A Minature Rosetta Stone,

a symbol of pure reason from
Visible Mathematics and
Analogical Train of Thought,

a symbol of Venus from
Why Me?
and
To Graves at the Winter Solstice,

and, finally, a more
down-to-earth symbol,
adapted from a snowflake in

The image “http://www.log24.com/log/pix05B/051224-RebaCard2.jpg” cannot be displayed, because it contains errors.

an online Christmas card.

Those who prefer their
theological art on the scary side
may enjoy the
Christian Snowflake
link in the comments on
the “Logos” entry of
Orthodox Easter (May 1), 2005.

Wednesday, December 21, 2005

Wednesday December 21, 2005

Filed under: Uncategorized — m759 @ 4:07 PM
For the feast of
St. Francis Scott Key Fitzgerald

The Diamond
as Big as
the Monster

From Fitzgerald’s The Diamond as Big as the Ritz:

    “Now,” said John eagerly, “turn out your pocket and let’s see what jewels you brought along. If you made a good selection we three ought to live comfortably all the rest of our lives.”
     Obediently Kismine put her hand in her pocket and tossed two handfuls of glittering stones before him.
    “Not so bad,” cried John, enthusiastically. “They aren’t very big, but– Hello!” His expression changed as he held one of them up to the declining sun. “Why, these aren’t diamonds! There’s something the matter!”
    “By golly!” exclaimed Kismine, with a startled look. “What an idiot I am!”
    “Why, these are rhinestones!” cried John.

From The Hawkline Monster, by Richard Brautigan:
 
    “What are we going to do now?” Susan Hawkline said, surveying the lake that had once been their house.
    Cameron counted the diamonds in his hand.  There were thirty-five diamonds and they were all that was left of the Hawkline Monster.
    “We’ll think of something,” Cameron said.

Related material:

“A disciple of Ezra Pound, he adapts to the short story the ideogrammatic method of The Cantos, where a grammar of images, emblems, and symbols replaces that of logical sequence. This grammar allows for the grafting of particulars into a congeries of implied relation without subordination. In contrast to postmodernists, Davenport does not omit causal connection and linear narrative continuity for the sake of an aleatory play of signification but in order to intimate by combinational logic kinships and correspondences among eras, ideas and forces.”

When Novelists Become Cubists:
    The Prose Ideograms of Guy Davenport,
    by Andre Furlani

“T.S. Eliot’s experiments in ideogrammatic method are equally germane to Davenport, who shares with the poet an avant-garde aesthetic and a conservative temperament.  Davenport’s text reverberates with echoes of Four Quartets.”

Andre Furlani

“At the still point,
  there the dance is.”

—  T. S. Eliot, Four Quartets,
quoted in the epigraph to
the chapter on automorphism groups
in Parallelisms of Complete Designs,
by Peter J. Cameron,
published when Cameron was at
Merton College, Oxford.

“As Gatsby closed the door of
‘the Merton College Library’
I could have sworn I heard
the owl-eyed man
break into ghostly laughter.”

F. Scott Fitzgerald

Thursday, October 13, 2005

Thursday October 13, 2005

Filed under: Uncategorized — Tags: , — m759 @ 12:00 PM

A Poem for Pinter

The Guardian on Harold Pinter, winner of this year’s Nobel Prize for Literature:

“Earlier this year, he announced his decision to retire from playwriting in favour of poetry,”

Michael Muskal in today’s Los Angeles Times:

“Pinter, 75, is known for his sparse and thin style as well as his etched characters whose crystal patter cuts through the mood like diamond drill bits.”

Robert Stone, A Flag for Sunrise  (See Jan. 25):

“‘That old Jew gave me this here.’  Egan looked at the diamond….  ‘It’s worth a whole lot of money– you can tell that just by looking– but it means something, I think.  It’s got a meaning, like.’

‘Let’s see,’ Egan said, ‘what would it mean?’  He took hold of Pablo’s hand cupping the stone and held his own hand under it.  ‘”The jewel is in the lotus,” perhaps that’s what it means.  The eternal in the temporal….'”

Notes on Modal Logic:

“Modal logic was originally developed to investigate logic under the modes of necessary  and possible  truth.  The words ‘necessary’ and ‘possible’ are called modal connectives , or modalities .  A modality is a word that when applied to a statement indicates when, where, how, or under what circumstances the statement may be true.  In terms of notation, it is common to use a box [] for the modality ‘necessary’ and a diamond <> for the modality ‘possible.'”

A Poem for Pinter

The image “http://www.log24.com/log/pix05B/051013-Waka.gif” cannot be displayed, because it contains errors.

Commentary:

“Waka” also means Japanese poem or Maori canoe.

(For instance, this Japanese poem and this Maori canoe.)

For a meditation on “bang splat,” see Sept. 25-29.

For the meaning of “tick tick,” see Emily Dickinson on “degreeless noon.”

“Hash,” of course, signifies “checkmate.”  (See previous three entries.)

Monday, August 22, 2005

Monday August 22, 2005

Filed under: Uncategorized — m759 @ 4:07 PM
The Hole

Part I: Mathematics and Narrative

The image “http://www.log24.com/log/pix05B/050822-Narr.jpg” cannot be displayed, because it contains errors.

Apostolos Doxiadis on last month’s conference on “mathematics and narrative”–

Doxiadis is describing how talks by two noted mathematicians were related to

    “… a sense of a ‘general theory bubbling up’ at the meeting… a general theory of the deeper relationship of mathematics to narrative….

Doxiadis says both talks had “a big hole in the middle.”  

    “Both began by saying something like: ‘I believe there is an important connection between story and mathematical thinking. So, my talk has two parts.  [In one part] I’ll tell you a few things about proofs.  [And in the other part] I’ll tell you about stories.’ …. And in both talks it was in fact implied by a variation of the post hoc propter hoc, the principle of consecutiveness implying causality, that the two parts of the lectures were intimately related, the one somehow led directly to the other.”
  “And the hole?”
  This was exactly at the point of the link… [connecting math and narrative]… There is this very well-known Sidney Harris cartoon… where two huge arrays of formulas on a blackboard are connected by the sentence ‘THEN A MIRACLE OCCURS.’ And one of the two mathematicians standing before it points at this and tells the other: ‘I think you should be more explicit here at step two.’ Both… talks were one half fascinating expositions of lay narratology– in fact, I was exhilarated to hear the two most purely narratological talks at the meeting coming from number theorists!– and one half a discussion of a purely mathematical kind, the two parts separated by a conjunction roughly synonymous to ‘this is very similar to this.’  But the similarity was not clearly explained: the hole, you see, the ‘miracle.’  Of course, both [speakers]… are brilliant men, and honest too, and so they were very clear about the location of the hole, they did not try to fool us by saying that there was no hole where there was one.”

Part II: Possible Worlds

“At times, bullshit can only be countered with superior bullshit.”
Norman Mailer

Many Worlds and Possible Worlds in Literature and Art, in Wikipedia:

    “The concept of possible worlds dates back to a least Leibniz who in his Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds.  Voltaire satirized this view in his picaresque novel Candide….
    Borges’ seminal short story El jardín de senderos que se bifurcan (“The Garden of Forking Paths“) is an early example of many worlds in fiction.”

Il faut cultiver notre jardin.“– Voltaire 

Background:

Modal Logic in Wikipedia

Possible Worlds in Wikipedia

Possible-Worlds Theory, by Marie-Laure Ryan
(entry for The Routledge Encyclopedia of Narrative Theory)

The God-Shaped Hole
 

Part III: Modal Theology

  “‘What is this Stone?’ Chloe asked….
  ‘…It is told that, when the Merciful One made the worlds, first of all He created that Stone and gave it to the Divine One whom the Jews call Shekinah, and as she gazed upon it the universes arose and had being.'”

  — Many Dimensions, by Charles Williams, 1931 (Eerdmans paperback, April 1979, pp. 43-44)

“The lapis was thought of as a unity and therefore often stands for the prima materia in general.”

  — Aion, by C. G. Jung, 1951 (Princeton paperback, 1979, p. 236)

“Its discoverer was of the opinion that he had produced the equivalent of the primordial protomatter which exploded into the Universe.”

  — The Stars My Destination, by Alfred Bester, 1956 (Vintage hardcover, July 1996, p. 216)

“We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes)).

Keith Allen Korcz 

The image “http://www.log24.com/log/pix05B/050802-Stone.gif” cannot be displayed, because it contains errors.

“The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being….”

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)

Sunday, February 20, 2005

Sunday February 20, 2005

Filed under: Uncategorized — Tags: — m759 @ 2:20 PM

Relativity Blues

Today, February 20, is the 19th anniversary of my note The Relativity Problem in Finite Geometry.  Here is some related material.

In 1931, the Christian writer Charles Williams grappled with the theology of time, space, free will, and the many-worlds interpretation of quantum mechanics (anticipating by many years the discussion of this topic by physicists beginning in the 1950's).

(Some pure mathematics — untainted by physics or theology — that is nevertheless related, if only by poetic analogy, to Williams's 1931 novel, Many Dimensions, is discussed in the above-mentioned note and in a generalization, Solomon's Cube.)

On the back cover of Williams's 1931 novel, the current publisher, William B. Eerdmans Publishing Company of Grand Rapids, Michigan, makes the following statement:

"Replete with rich religious imagery, Many Dimensions explores the relation between predestination and free will as it depicts different human responses to redemptive transcendence."

One possible response to such statements was recently provided in some detail by a Princeton philosophy professor.  See On Bullshit, by Harry G. Frankfurt, Princeton University Press, 2005.

A more thoughtful response would take into account the following:

1. The arguments presented in favor of philosopher John Calvin, who discussed predestination, in The Death of Adam: Essays on Modern Thought, by Marilynne Robinson

2. The physics underlying Einstein's remarks on free will, God, and dice
 
3. The physics underlying Rebecca Goldstein's novel Properties of Light and Paul Preuss's novels  Secret Passages and Broken Symmetries

4. The physics underlying the recent so-called "free will theorem" of John Conway and Simon Kochen of Princeton University

5. The recent novel Gilead, by Marilynne Robinson, which deals not with philosophy, but with lives influenced by philosophy — indirectly, by the philosophy of the aforementioned John Calvin.

From a review of Gilead by Jane Vandenburgh:  

"In The Death of Adam, Robinson shows Jean Cauvin to be the foremost prophet of humanism whose Protestant teachings against the hierarchies of the Roman church set in motion the intellectual movements that promoted widespread literacy among the middle and lower classes, led to both the American and French revolutions, and not only freed African slaves in the United States but brought about suffrage for women. It's odd then that through our culture's reverse historicism, the term 'Calvinism' has come to mean 'moralistic repression.'"

For more on what the Calvinist publishing firm Eerdmans calls "redemptive transcendence," see various July 2003 Log24.net entries.  If these entries include a fair amount of what Princeton philosophers call bullshit, let the Princeton philosophers meditate on the summary of Harvard philosophy quoted here on November 5 of last year, as well as the remarks of November 5, 2003,  and those of November 5, 2002.

From Many Dimensions (Eerdmans paperback, 1963, page 53):

"Lord Arglay had a suspicion that the Stone would be purely logical.  Yes, he thought, but what, in that sense, were the rules of its pure logic?"

A recent answer:

Modal Theology

"We symbolize logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz,
(Log24.net, 1/25/05)

And what do we           
   symbolize by  The image “http://www.log24.com/theory/images/Modal-diamondbox.gif” cannot be displayed, because it contains errors. ?

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)

Thursday, February 17, 2005

Thursday February 17, 2005

Filed under: Uncategorized — m759 @ 1:00 PM
Modal Theology

“We symbolize logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes)).

Keith Allen Korcz,
(Log24.net, 1/25/05)

And what do we           
   symbolize by  The image “http://www.log24.com/theory/images/Modal-diamondbox.gif” cannot be displayed, because it contains errors. ?

On the Lapis Philosophorum,
the Philosophers’ Stone –

“‘What is this Stone?’ Chloe asked….
‘…It is told that, when the Merciful One
made the worlds, first of all He created
that Stone and gave it to the Divine One
whom the Jews call Shekinah,
and as she gazed upon it
the universes arose and had being.'”
Many Dimensions,
by Charles Williams, 1931
(Eerdmans paperback,
April 1979, pp. 43-44)

“The lapis was thought of as a unity
and therefore often stands for
the prima materia in general.”
Aion, by C. G. Jung, 1951
(Princeton paperback,
1979, p. 236)

“Its discoverer was of the opinion that
he had produced the equivalent of
the primordial protomatter
which exploded into the Universe.”
The Stars My Destination,
by Alfred Bester, 1956
(Vintage hardcover,
July 1996, p. 216)

“The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being….”

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)

See also
The Diamond Archetype.

For more on modal theology, see

Kurt Gödel’s Ontological Argument
and
 The Ontological Argument
 from Anselm to Gödel.

Tuesday, January 25, 2005

Tuesday January 25, 2005

Filed under: Uncategorized — m759 @ 12:00 PM

Diamonds Are Forever

 
The image “http://www.log24.com/theory/images/Modal-diamondinbox.gif” cannot be displayed, because it contains errors.

Robert Stone,
A Flag for Sunrise:

" 'That old Jew gave me this here.'  Egan looked at the diamond.  'I ain't giving this to you, understand?  The old man gave it to me for my boy.  It's worth a whole lot of money– you can tell that just by looking– but it means something, I think.  It's got a meaning, like.'

'Let's see,' Egan said, 'what would it mean?'  He took hold of Pablo's hand cupping the stone and held his own hand under it.  '"The jewel is in the lotus," perhaps that's what it means.  The eternal in the temporal.  The Boddhisattva declining nirvana out of compassion.   Contemplating the ignorance of you and me, eh?  That's a metaphor of our Buddhist friends.'

Pablo's eyes glazed over.  'Holy shit,' he said.  'Santa Maria.'  He stared at the diamond in his palm with passion.

'Hey,' he said to the priest, 'diamonds are forever!  You heard of that, right?  That means something, don't it?'

'I have heard it,' Egan said.  'Perhaps it has a religious meaning.' "
 


"We symbolize logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz


From

DIALECTIC AND EXISTENCE
IN KIERKEGAARD AND KANT

Nythamar Fernandes de Oliveira

Pontifical Catholic University
at Porto Alegre, Brazil

"Such is the paradoxical 'encounter' of the eternal with the temporal. Just like the Moment of the Incarnation, when the Eternal entered the temporal, Kierkegaard refers to the category of the Instant (Danish Ojeblikket, 'a glance of the eye, eyeblink,' German Augenblick) as the dialectical kernel of our existential consciousness:

If the instant is posited, so is the eternal –but also the future, which comes again like the past … The concept around which everything turns in Christianity, the concept which makes all things new, is the fullness of time, is the instant as eternity, and yet this eternity is at once the future and the past.

Although I cannot examine here the Kierkegaardian conception of time, the dialectical articulation of time and existence, as can be seen, underlies his entire philosophy of existence, just as the opposition between 'eternity' and 'temporality': the instant, as 'an atom of eternity,' serves to restructure the whole synthesis of selfhood into a spiritual one, in man’s 'ascent' toward its Other and the Unknown. In the last analysis, the Eternal transcends every synthesis between eternity and time, infinity and finiteness, preserving not only the Absolute Paradox in itself but above all the wholly otherness of God. It is only because of the Eternal, therefore, that humans can still hope to attain their ultimate vocation of becoming a Chistian. As Kierkegaard writes in Works of Love (1847),

The possibility of the good is more than possibility, for it is the eternal. This is the basis of the fact that one who hopes can never be deceived, for to hope is to expect the possibility of the good; but the possibility of the good is eternal. …But if there is less love in him, there is also less of the eternal in him; but if there is less of the eternal in him, there is also less possibility, less awareness of possibility (for possibility appears through the temporal movement of the eternal within the eternal in a human being)."

Thursday, December 16, 2004

Thursday December 16, 2004

Filed under: Uncategorized — Tags: — m759 @ 3:00 AM

Nothing Nothings
(Again)

Background: recent Log24 entries (beginning with Chorus from the Rock on Dec. 5, 2004) and Is Nothing Sacred? (quotations compiled on March 9, 2000).

From an obituary of Paul Edwards, a writer on philosophy, in this morning's New York Times:

"Heidegger's Confusions, a collection of Professor Edwards's scholarly articles, was published last month by Prometheus."

Edwards, born in Vienna in 1923 to Jewish parents, died on December 9.

Some sites I visited earlier this evening, before reading of Edwards's death:

  • " 'Nothingness itself nothings' — with these words, uttered by Martin Heidegger in the early 1930s, the incipient (and now-familiar) split between analytic and continental philosophy began tearing open. For Rudolf Carnap, a leader of the Vienna Circle [Wiener Kreis] of logical empiricists and a strident advocate of a new, scientific approach to philosophy, this Heideggerian proposition exemplified 'a metaphysical pseudo-sentence,' meaningless and unable to withstand any logical analysis. Heidegger countered that Carnap’s misplaced obsession with logic missed the point entirely."
    Review of A Parting of the Ways: Carnap, Cassirer, and Heidegger
  • "Death and Metaphysics," by Peter Kraus, pp. 98-111 in Death and Philosophy, ed. by Jeff Malpas and Robert Solomon.  Heidegger's famous phrase (misquoted by Quine in Gray Particular in Hartford) "Das Nichts selbst nichtet" is discussed on page 102.

Friday, September 17, 2004

Friday September 17, 2004

Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

God is in…
The Details

From an entry for Aug. 19, 2003 on
conciseness, simplicity, and objectivity:

Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale “block design” subtest.

Another Harvard psychiatrist, Armand Nicholi, is in the news lately with his book The Question of God: C.S. Lewis and Sigmund Freud Debate God, Love, Sex, and the Meaning of Life.

Pope

Nicholi

Old
Testament
Logos

New
Testament
Logos

For the meaning of the Old-Testament logos above, see the remarks of Plato on the immortality of the soul at

Cut-the-Knot.org.

For the meaning of the New-Testament logos above, see the remarks of R. P. Langlands at

The Institute for Advanced Study.

On Harvard and psychiatry: see

The Crimson Passion:
A Drama at Mardi Gras

(February 24, 2004)

This is a reductio ad absurdum of the Harvard philosophy so eloquently described by Alston Chase in his study of Harvard and the making of the Unabomber, Ted Kaczynski.  Kaczynski’s time at Harvard overlapped slightly with mine, so I probably saw him in Cambridge at some point.  Chase writes that at Harvard, the Unabomber “absorbed the message of positivism, which demanded value-neutral reasoning and preached that (as Kaczynski would later express it in his journal) ‘there is no logical justification for morality.'” I was less impressed by Harvard positivism, although I did benefit from a course in symbolic logic from Quine.  At that time– the early 60’s– little remained at Harvard of what Robert Stone has called “our secret culture,” that of the founding Puritans– exemplified by Cotton and Increase Mather.

From Robert Stone, A Flag for Sunrise:

“Our secret culture is as frivolous as a willow on a tombstone.  It’s a wonderful thing– or it was.  It was strong and dreadful, it was majestic and ruthless.  It was a stranger to pity.  And it’s not for sale, ladies and gentlemen.”

Some traces of that culture:

A web page
in Australia:

A contemporary
Boston author:

Click on pictures for details.

A more appealing view of faith was offered by PBS on Wednesday night, the beginning of this year’s High Holy Days:

Armand Nicholi: But how can you believe something that you don’t think is true, I mean, certainly, an intelligent person can’t embrace something that they don’t think is true — that there’s something about us that would object to that.

Jeremy Fraiberg: Well, the answer is, they probably do believe it’s true.

Armand Nicholi: But how do they get there? See, that’s why both Freud and Lewis was very interested in that one basic question. Is there an intelligence beyond the universe? And how do we answer that question? And how do we arrive at the answer of that question?

Michael Shermer: Well, in a way this is an empirical question, right? Either there is or there isn’t.

Armand Nicholi: Exactly.

Michael Shermer: And either we can figure it out or we can’t, and therefore, you just take the leap of faith or you don’t.

Armand Nicholi: Yeah, now how can we figure it out?

Winifred Gallagher: I think something that was perhaps not as common in their day as is common now — this idea that we’re acting as if belief and unbelief were two really radically black and white different things, and I think for most people, there’s a very — it’s a very fuzzy line, so that —

Margaret Klenck: It’s always a struggle.

Winifred Gallagher: Rather than — I think there’s some days I believe, and some days I don’t believe so much, or maybe some days I don’t believe at all.

Doug Holladay: Some hours.

Winifred Gallagher: It’s a, it’s a process. And I think for me the big developmental step in my spiritual life was that — in some way that I can’t understand or explain that God is right here right now all the time, everywhere.

Armand Nicholi: How do you experience that?

Winifred Gallagher: I experience it through a glass darkly, I experience it in little bursts. I think my understanding of it is that it’s, it’s always true, and sometimes I can see it and sometimes I can’t. Or sometimes I remember that it’s true, and then everything is in Technicolor. And then most of the time it’s not, and I have to go on faith until the next time I can perhaps see it again. I think of a divine reality, an ultimate reality, uh, would be my definition of God.

Winifred
Gallagher

Sangaku

Gallagher seemed to be the only participant in the PBS discussion that came close to the Montessori ideals of conciseness, simplicity, and objectivity.  Dr. Montessori intended these as ideals for teachers, but they seem also to be excellent religious values.  Just as the willow-tombstone seems suited to Geoffrey Hill‘s style, the Pythagorean sangaku pictured above seems appropriate to the admirable Gallagher.

Saturday, December 20, 2003

Saturday December 20, 2003

Filed under: Uncategorized — Tags: — m759 @ 5:00 PM

White, Geometric, and Eternal

This afternoon's surfing:

Prompted by Edward Rothstein's own Fides et Ratio encyclical in today's NY Times, I googled him.

At the New York Review of Books, I came across the following by Rothstein:

"… statements about TNT can be represented within TNT: the formal system can, in a precise way, 'talk' about itself."

This naturally prompted me to check what is on TNT on this, the feast day of St. Emil Artin.  At 5 PM this afternoon, we have Al Pacino in "The Devil's Advocate" — a perfect choice for the festival of an alleged saint.

Preparing for Al, I meditated on the mystical significance of the number 373, as explained in Zen and Language Games: the page number 373 in Robert Stone's theological classic A Flag for Sunrise conveys the metaphysical significance of the phrase "diamonds are forever" — "the eternal in the temporal," according to Stone's Catholic priest.  This suggests a check of another theological classic, Pynchon's Gravity's RainbowPage 373 there begins with the following description of prewar Berlin:

"white and geometric."

This suggests the following illustration of a white and geometric object related to yesterday's entry on Helmut Wielandt:

From antiquark.com

Figure 1

(This object, which illustrates the phrase "makin' the changes," also occurs in this morning's entry on the death of a jazz musician.)

A further search for books containing "white" and "geometric" at Amazon.com yields the following:

Figure 2

From Mosaics, by
Fassett, Bahouth, and Patterson:

"A risco fountain in Mexico city, begun circa 1740 and made up of Mexican pottery and Chinese porcelain, including Ming.

The delicate oriental patterns on so many different-sized plates and saucers [are] underlined by the bold blue and white geometric tiles at the base."

Note that the tiles are those of Diamond Theory; the geometric object in figure 1 above illustrates a group that plays a central role in that theory.

Finally, the word "risco" (from Casa del Risco) associated with figure 2 above leads us to a rather significant theological site associated with the holy city of Santiago de Compostela:

Figure 3

Vicente Risco's
Dedalus in Compostela.

Figure 3 shows James Joyce (alias Dedalus), whose daughter Lucia inspired the recent entry Jazz on St. Lucia's Day — which in turn is related, by last night's 2:45 entry and by Figure 1, to the mathematics of group theory so well expounded by the putative saint Emil Artin.

"His lectures are best described as
polished diamonds."
Fine Hall in its Golden Age,
by Gian-Carlo Rota

If Pynchon plays the role of devil's advocate suggested by his creation, in Gravity's Rainbow, of the character Emil Bummer, we may hope that Rota, no longer in time but now in eternity, can be persuaded to play the important role of saint's advocate for his Emil.
 

Update of 6:30 PM 12/20/03:

Riddled:

The Absolutist Faith
of The New York Times

White and Geometric, but not Eternal.

Tuesday, September 2, 2003

Tuesday September 2, 2003

Filed under: Uncategorized — m759 @ 1:11 PM

One Ring to Rule Them All

In memory of J. R. R. Tolkien, who died on this date, and in honor of Israel Gelfand, who was born on this date.

Leonard Gillman on his collaboration with Meyer Jerison and Melvin Henriksen in studying rings of continuous functions:

“The triple papers that Mel and I wrote deserve comment. Jerry had conjectured a characterization of beta X (the Stone-Cech compactification of X) and the three of us had proved that it was true. Then he dug up a 1939 paper by Gelfand and Kolmogoroff that Hewitt, in his big paper, had referred to but apparently not appreciated, and there we found Jerry’s characterization. The three of us sat around to decide what to do; we called it the ‘wake.’  Since the authors had not furnished a proof, we decided to publish ours. When the referee expressed himself strongly that a title should be informative, we came up with On a theorem of Gelfand and Kolmogoroff concerning maximal ideals in rings of continuous functions. (This proved to be my second-longest title, and a nuisance to refer to.) Kolmogoroff died many years ago, but Gelfand is still living, a vigorous octogenarian now at Rutgers. A year or so ago, I met him at a dinner party in Austin and mentioned the 1939 paper. He remembered it very well and proceeded to complain that the only contribution Kolmogoroff had made was to point out that a certain result was valid for the complex case as well. I was intrigued to see how the giants grouse about each other just as we do.”

Leonard Gillman: An Interview

This clears up a question I asked earlier in this journal….

Wednesday, May 14, 2003

Common Sense

On the mathematician Kolmogorov:

“It turns out that he DID prove one basic theorem that I take for granted, that a compact hausdorff space is determined by its ring of continuous functions (this ring being considered without any topology) — basic discoveries like this are the ones most likely to have their origins obscured, for they eventually come to be seen as mere common sense, and not even a theorem.”

Richard Cudney, Harvard ’03, writing at Xanga.com as rcudney on May 14, 2003

That this theorem is Kolmogorov’s is news to me.

See

The above references establish that Gelfand is usually cited as the source of the theorem Cudney discusses.  Gelfand was a student of Kolmogorov’s in the 1930’s, so who discovered what when may be a touchy question in this case.  A reference that seems relevant: I. M. Gelfand and A. Kolmogoroff, “On rings of continuous functions on topological spaces,” Doklady Akad. Nauk SSSR 22 (1939), 11-15.  This is cited by Gillman and Jerison in the classic Rings of Continuous Functions.

There ARE some references that indicate Kolmogorov may have done some work of his own in this area.  See here (“quite a few duality theorems… including those of Banaschewski, Morita, Gel’fand-Kolmogorov and Gel’fand-Naimark”) and here  (“the classical theorems of M. H. Stone, Gelfand & Kolmogorov”).

Any other references to Kolmogorov’s work in this area would be of interest.

Naturally, any discussion of this area should include a reference to the pioneering work of M. H. Stone.  I recommend the autobiographical article on Stone in McGraw-Hill Modern Men of Science, Volume II, 1968.

A response by Richard Cudney:

“In regard to your entry, it is largely correct.  The paper by Kolmogorov and Gelfand that you refer to is the one that I just read in his collected works.  So, I suppose my entry was unfair to Gelfand.  You’re right, the issue of credit is a bit touchy since Gelfand was his student.  In a somewhat recent essay, Arnol’d makes the claim that this whole thread of early work by Gelfand may have been properly due to Kolmogorov, however he has no concrete proof, having been but a child at the time, and makes this inference based only on his own later experience as Kolmogorov’s student.  At any rate, I had known about Gelfand’s representation theorem, but had not known that Kolmogorov had done any work of this sort, or that this theorem in particular was due to either of them. 

And to clarify-where I speak of the credit for this theorem being obscured, I speak of my own experience as an algebraic geometer and not a functional analyst.  In the textbooks on algebraic geometry, one sees no explanation of why we use Spec A to denote the scheme corresponding to a ring A.  That question was answered when I took functional analysis and learned about Gelfand’s theorem, but even there, Kolmogorov’s name did not come up.

This result is different from the Gelfand representation theorem that you mention-this result concerns algebras considered without any topology(or norm)-whereas his representation theorem is a result on Banach algebras.  In historical terms, this result precedes Gelfand’s theorem and is the foundation for it-he starts with a general commutative Banach algebra and reconstructs a space from it-thus establishing in what sense that the space to algebra correspondence is surjective, and hence by the aforementioned theorem, bi-unique.  That is to say, this whole vein of Gelfand’s work started in this joint paper.

Of course, to be even more fair, I should say that Stone was the very first to prove a theorem like this, a debt which Kolmogorov and Gelfand acknowledge.  Stone’s paper is the true starting point of these ideas, but this paper of Kolmogorov and Gelfand is the second landmark on the path that led to Grothendieck’s concept of a scheme(with Gelfand’s representation theorem probably as the third).

As an aside, this paper was not Kolmogorov’s first foray into topological algebra-earlier he conjectured the possibility of a classification of locally compact fields, a problem which was solved by Pontryagin.  The point of all this is that I had been making use of ideas due to Kolmogorov for many years without having had any inkling of it.”

Posted 5/14/2003 at 8:44 PM by rcudney

Wednesday, July 2, 2003

Wednesday July 2, 2003

Filed under: Uncategorized — m759 @ 7:00 PM

Three Days Late
and a Dollar Short

THE BOOK AGAINST GOD
By James Wood.
257 pp. New York:
Farrar, Straus & Giroux. $24. 

This is a book that attempts to recreate the myth of Saint Peter.

See the New York Times review of this book from today, July 2, 2003, three days late.  The Feast of St. Peter was on June 29.

The price, $24, also falls short of the theological glory reflected in the number 25, the common denominator of Christmas (12/25) and AntiChristmas (6/25), as well as the number of the heart of the Catholic church, the Bingo card

For all these issues, see my entries and links in memory of St. Peter, from June 29

The real “book against God,” a novel by Robert Stone, is cited there.  The legend of St. Peter is best described by Stone, not Wood.

Tuesday, July 1, 2003

Tuesday July 1, 2003

Filed under: Uncategorized — Tags: — m759 @ 5:37 PM

Jew’s on First

This entry is dedicated to those worshippers of Allah who have at one time or another cried
Itbah al-Yahud!” … Kill the Jew!
(See June 29 entries).

Dead at 78

Comedian Buddy Hackett died on Tuesday, July First, 2003, according to the New York Times.  According to Bloomberg.com, he died Sunday or Monday.

Associated Press

Buddy Hackett,
on the set of
“It’s a Mad, Mad,
Mad, Mad
World”
in 1962.

Whatever.  We may imagine he has now walked, leading a parade of many other stand-up saints, into a bar.


Hepburn at Chaillot

MIDRASH
for Buddy Hackett

From my May 25 entry,

Matrix of the Death God:

R. M. Abraham’s Diversions and Pastimes, published by Constable and Company, London, in 1933, has the following magic square:

The Matrix of Abraham

A summary of the religious import of the above from Princeton University Press:

“Moslems of the Middle Ages were fascinated by pandiagonal squares with 1 in the center…. The Moslems thought of the central 1 as being symbolic of the unity of Allah.  Indeed, they were so awed by that symbol that they often left blank the central cell on which the 1 should be positioned.”

— Clifford A. Pickover, The Zen of Magic Squares, Circles, and Stars, Princeton U. Press, 2002, pp. 71-72

Other appearances of this religious icon on the Web include:

On Linguistic Creation

Picasso’s Birthday

1991 Yearbook
Rolling Stone



Hackett

In the Picasso’s Birthday version, 22 of the 25 magic square cells are correlated with pictures on the “Class of ’91” cover of Rolling Stone magazine.  Number 7 is Rod Stewart.  In accordance with the theological rhyme “Seven is heaven, eight is a gate,” our site music for today is “Forever Young,” a tune made famous by Stewart.

Roderick, actually   the name of the hero in “Madwoman of Chaillot”

Saturday, June 14, 2003

Saturday June 14, 2003

Filed under: Uncategorized — m759 @ 5:00 PM

Indiana Jones
and the Hidden Coffer

In memory of Bernard Williams,

Oxford philosopher, who died Tuesday, June 10, 2003. 

“…in… Truth and Truthfulness [September, 2002], he sought to speak plainly, and took on the post-modern, politically correct notion that truth is merely relative…”

— Christopher Lehmann-Haupt

“People have always longed for truths about the world — not logical truths, for all their utility; or even probable truths, without which daily life would be impossible; but informative, certain truths, the only ‘truths’ strictly worthy of the name. Such truths I will call ‘diamonds’; they are highly desirable but hard to find….

A new epistemology is emerging to replace the Diamond Theory of truth. I will call it the ‘Story Theory’ of truth: There are no diamonds. People make up stories about what they experience. Stories that catch on are called ‘true.’ The Story Theory of truth is itself a story that is catching on. It is being told and retold, with increasing frequency, by thinkers of many stripes…. My own viewpoint is the Story Theory….”

— Richard J. Trudeau, The Non-Euclidean Revolution, Birkhauser Boston, 1987

Today is the feast day of Saint Jorge Luis Borges (b. Buenos Aires, August 24, 1899 – d. Geneva, June 14, 1986).

From Borges’s “The Aleph“:

“The Faithful who gather at the mosque of Amr, in Cairo, are acquainted with the fact that the entire universe lies inside one of the stone pillars that ring its central court…. The mosque dates from the seventh century; the pillars come from other temples of pre-Islamic religions…. Does this Aleph exist in the heart of a stone?”

(“Los fieles que concurren a la mezquita de Amr, en el Cairo, saben muy bien que el universo está en el interior de una de las columnas de piedra que rodean el patio central…. la mezquita data del siglo VII; las columnas proceden de otros templos de religiones anteislámicas…. ¿Existe ese Aleph en lo íntimo de una piedra?”)

From The Hunchback of Notre Dame:

Un cofre de gran riqueza
Hallaron dentro un pilar,
Dentro del, nuevas banderas
Con figuras de espantar.*

* A coffer of great richness
In a pillar’s heart they found,
Within it lay new banners,
With figures to astound.

See also the figures obtained by coloring and permuting parts of the above religious symbol.

Lena Olin and Harrison Ford
in “Hollywood Homicide

Tuesday, May 20, 2003

Tuesday May 20, 2003

Filed under: Uncategorized — m759 @ 8:23 PM

Mental Health Month:
The Lottery Covenant

Here are the evening lottery numbers for Pennsylvania, the Keystone state, drawn on Monday, May 19, 2003:

401 and 1993.

This, by the sort of logic beloved of theologians, suggests we find out the significance of the divine date 4/01/1993.

It turns out that April 1, 1993, was the date of the New York opening of the Stephen Sondheim retrospective “Putting It Together.”

For material related to puzzles, games, Sondheim, and Mental Health Month, see

Notes on
Literary and Philosophical Puzzles

The figures below illustrate some recurrent themes in these notes.

WAIS blocks


IZZI puzzle


Michael Douglas
in “The Game”


Putting It
Together

“Not games. Puzzles. Big difference. That’s a whole other matter. All art — symphonies, architecture, novels — it’s all puzzles. The fitting together of notes, the fitting together of words have by their very nature a puzzle aspect. It’s the creation of form out of chaos. And I believe in form.”

— Stephen Sondheim, in Stephen Schiff,
    “Deconstructing Sondheim,” 
    The New Yorker, March 8, 1993, p. 76
 

Wednesday, May 14, 2003

Wednesday May 14, 2003

Filed under: Uncategorized — m759 @ 2:00 PM

Common Sense

On the mathematician Kolmogorov:

“It turns out that he DID prove one basic theorem that I take for granted, that a compact hausdorff space is determined by its ring of continuous functions (this ring being considered without any topology) — basic discoveries like this are the ones most likely to have their origins obscured, for they eventually come to be seen as mere common sense, and not even a theorem.”

Richard Cudney, Harvard ’03, writing at Xanga.com as rcudney on May 14, 2003

That this theorem is Kolmogorov’s is news to me.

See

The above references establish that Gelfand is usually cited as the source of the theorem Cudney discusses.  Gelfand was a student of Kolmogorov’s in the 1930’s, so who discovered what when may be a touchy question in this case.  A reference that seems relevant: I. M. Gelfand and A. Kolmogoroff, “On rings of continuous functions on topological spaces,” Doklady Akad. Nauk SSSR 22 (1939), 11-15.  This is cited by Gillman and Jerison in the classic Rings of Continuous Functions.

There ARE some references that indicate Kolmogorov may have done some work of his own in this area.  See here (“quite a few duality theorems… including those of Banaschewski, Morita, Gel’fand-Kolmogorov and Gel’fand-Naimark”) and here  (“the classical theorems of M. H. Stone, Gelfand & Kolmogorov”).

Any other references to Kolmogorov’s work in this area would be of interest.

Naturally, any discussion of this area should include a reference to the pioneering work of M. H. Stone.  I recommend the autobiographical article on Stone in McGraw-Hill Modern Men of Science, Volume II, 1968.

Wednesday, November 27, 2002

Wednesday November 27, 2002

Filed under: Uncategorized — Tags: — m759 @ 11:30 PM

Waiting for Logos

Searching for background on the phrase "logos and logic" in yesterday's "Notes toward a Supreme Fact," I found this passage:

"…a theory of psychology based on the idea of the soul as the dialectical, self-contradictory syzygy of a) soul as anima and b) soul as animus. Jungian and archetypal psychology appear to have taken heed more or less of only one half of the whole syzygy, predominantly serving an anima cut loose from her own Other, the animus as logos and logic (whose first and most extreme phenomenological image is the killer of the anima, Bluebeard). Thus psychology tends to defend the virginal innocence of the anima and her imagination…"

— Wolfgang Giegerich, "Once More the Reality/Irreality Issue: A Reply to Hillman's Reply," website 

The anima and other Jungian concepts are used to analyze Wallace Stevens in an excellent essay by Michael Bryson, "The Quest for the Fiction of an Absolute." Part of Bryson's motivation in this essay is the conflict between the trendy leftist nominalism of postmodern critics and the conservative realism of more traditional critics:

"David Jarraway, in his Stevens and the Question of Belief, writes about a Stevens figured as a proto-deconstructionist, insisting on 'Steven's insistence on dismantling the logocentric models of belief' (311) in 'An Ordinary Evening in New Haven.' In opposition to these readings comes a work like Janet McCann's Wallace Stevens Revisited: 'The Celestial Possible', in which the claim is made (speaking of the post-1940 period of Stevens' life) that 'God preoccupied him for the rest of his career.'"

Here "logocentric" is a buzz word for "Christian." Stevens, unlike the postmodernists, was not anti-Christian. He did, however, see that the old structures of belief could not be maintained indefinitely, and pondered what could be found to replace them. "Notes toward a Supreme Fiction" deals with this problem. In his essay on Stevens' "Notes," Bryson emphasizes the "negative capability" of Keats as a contemplative technique:

"The willingness to exist in a state of negative capability, to accept that sometimes what we are seeking is not that which reason can impose…."

For some related material, see Simone Weil's remarks on Electra waiting for her brother Orestes. Simone Weil's brother was one of the greatest mathematicians of the past century, André Weil.

"Electra did not seek Orestes, she waited for him…"

— Simone Weil

"…at the end, she pulls it all together brilliantly in the story of Electra and Orestes, where the importance of waiting on God rather than seeking is brought home forcefully."

— Tom Hinkle, review of Waiting for God

Compare her remarks on waiting for Orestes with the following passage from Waiting for God:

"We do not obtain the most precious gifts by going in search of them but by waiting for them. Man cannot discover them by his own powers, and if he sets out to seek for them he will find in their place counterfeits of which he will be unable to discern falsity.

The solution of a geometry problem does not in itself constitute a precious gift, but the same law applies to it because it is the image of something precious. Being a little fragment of particular truth, it is a pure image of the unique, eternal, and living Truth, the very Truth that once in a human voice declared: "I am the Truth."

Every school exercise, thought of in this way, is like a sacrament.

In every school exercise there is a special way of waiting upon truth, setting our hearts upon it, yet not allowing ourselves to go out in search of it. There is a way of giving our attention to the data of a problem in geometry without trying to find the solution…."

— Simone Weil, "Reflections on the Right Use of School Studies with a View to the Love of  God"

Weil concludes the preceding essay with the following passage:

"Academic work is one of those fields containing a pearl so precious that it is worth while to sell all of our possessions, keeping nothing for ourselves, in order to be able to acquire it."

This biblical metaphor is also echoed in the work of Pascal, who combined in one person the theological talent of Simone Weil and the mathematical talent of her brother. After discussing how proofs should be written, Pascal says

"The method of not erring is sought by all the world. The logicians profess to guide to it, the geometricians alone attain it, and apart from their science, and the imitations of it, there are no true demonstrations. The whole art is included in the simple precepts that we have given; they alone are sufficient, they alone afford proofs; all other rules are useless or injurious. This I know by long experience of all kinds of books and persons.

And on this point I pass the same judgment as those who say that geometricians give them nothing new by these rules, because they possessed them in reality, but confounded with a multitude of others, either useless or false, from which they could not discriminate them, as those who, seeking a diamond of great price amidst a number of false ones, but from which they know not how to distinguish it, should boast, in holding them all together, of possessing the true one equally with him who without pausing at this mass of rubbish lays his hand upon the costly stone which they are seeking and for which they do not throw away the rest."

— Blaise Pascal, The Art of Persuasion

 

For more diamond metaphors and Jungian analysis, see

The Diamond Archetype.

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