Log24

Wednesday, November 30, 2005

Wednesday November 30, 2005

Filed under: General,Geometry — Tags: — m759 @ 8:20 pm

Hobgoblin?

Brian Davies is a professor of mathematics at King’s College London.  In the December Notices of the American Mathematical Society, he claims that arithmetic may, for all we know, be inconsistent:

“Gödel taught us that it is not possible to prove that Peano arithmetic is consistent, but everyone has taken it for granted that in fact it is indeed consistent.
    Platonistically-inclined mathematicians would deny the possibility that Peano arithmetic could be flawed.  From Kronecker onwards many consider that they have a direct insight into the natural numbers, which guarantees their existence. If the natural numbers exist and Peano’s axioms describe properties that they possess then, since the axioms can be instantiated, they must be consistent.”

“It is not possible to prove that Peano arithmetic is consistent”…?!

Where did Gödel say this?  Gödel proved, in fact, according to a well-known mathematician at Princeton, that (letting PA stand for Peano Arithmetic),

“If PA is consistent, the formula expressing ‘PA is consistent’ is unprovable in PA.”

— Edward Nelson,
   Mathematics and Faith (pdf)

Remarkably, even after he has stated correctly Gödel’s result, Nelson, like Davies, concludes that

“The consistency of PA cannot be concretely demonstrated.”

I prefer the argument that the existence of a model ensures the consistency of a theory.

For instance, the Toronto philosopher William Seager writes that

“Our judgement as to the consistency of some system is not dependent upon that system’s being able to prove its own consistency (i.e. generate a formula that states, e.g. ‘0=1’ is not provable). For if that was the sole basis, how could we trust it? If the system was inconsistent, it could generate this formula as well (see Smullyan, Gödel’s Incompleteness Theorems, (Oxford, 1992, p. 109)). Furthermore, [George] Boolos allows that we do know that certain systems, such as Peano Arithmetic, are consistent even though they cannot prove their own consistency. Presumably, we know this because we can see that a certain model satisfies the axioms of the system at issue, hence that they are true in that model and so must be consistent.”

— Yesterday’s Algorithm:
    Penrose and the Gödel Argument

The relationship between consistency and the existence of a model is brought home by the following weblog entry that neatly summarizes a fallacious argument offered in the AMS Notices by Davies:

The following is an interesting example that I came across in the article “Whither Mathematics?” by Brian Davies in the December issue of Notices of the American Mathematical Society.

Consider the following list A1 of axioms.

(1) There is a natural number 0.
(2) Every natural number a has a successor, denoted by S(a).
(3) There is no natural number whose successor is 0.
(4) Distinct natural numbers have distinct successors: a = b if and only if S(a) = S(b).
(5) If a property is possessed by 0 and also by the successor of every natural number which possesses it, then it is possessed by all the natural numbers.

Now consider the following list A2 of axioms.

(1) G is a set of elements and these elements obey the group axioms.
(2) G is finite but not isomorphic to any known list of finite simple groups.
(3) G is simple, in other words, if N is a subset of G satisfying certain properties then N=G.

We can roughly compare A2 with A1. The second axiom in A2 can be thought of as analogous to the third axiom of A1. Also the third axiom of A2 is analogous to the fifth axiom of A1, insofar as it refers to an unspecified set with cetain properties and concludes that it is equal to G.

Now, as is generally believed by most group theorists, the system A2 is internally inconsistent and the proof its inconsistency runs for more than 10000 pages.

So who is to deny that the system A1 is also probably internally inconsistent! Particularly since Godel proved that you can not prove it is consistent (staying inside the system). May be the shortest proof of its inconsistency is one hundred million pages long!

— Posted by Krishna,
   11/29/2005 11:46:00 PM,
   at his weblog,
  “Quasi-Coherent Ruminations”

An important difference between A1 (the set of axioms of Peano arithmetic) and A2 (a set of axioms that describe a new, unknown, finite simple group) is that A1 is known to have a model (the nonnegative integers) and A2 is not known to have a model.

Therefore, according to Seager’s argument, A1 is consistent and A2 may or may not be consistent.

The degree to which Seager’s argument invokes Platonic realism is debatable.  Less debatable is the quasireligious faith in nominalism proclaimed by Davies and Nelson.  Nelson’s own account of a religious experience in 1976 at Toronto is instructive.

I must relate how I lost my faith in Pythagorean numbers. One morning at the 1976 Summer Meeting of the American Mathematical Society in Toronto, I woke early. As I lay meditating about numbers, I felt the momentary overwhelming presence of one who convicted me of arrogance for my belief in the real existence of an infinite world of numbers, leaving me like an infant in a crib reduced to counting on my fingers. Now I live in a world in which there are no numbers save those that human beings on occasion construct.

— Edward Nelson,
   Mathematics and Faith (pdf)

Nelson’s “Mathematics and Faith” was written for the Jubilee for Men and Women from the World of Learning held at the Vatican, 23-24 May 2000.  It concludes with an invocation of St. Paul:

During my first stay in Rome I used to play chess with Ernesto Buonaiuti. In his writings and in his life, Buonaiuti with passionate eloquence opposed the reification of human abstractions. I close by quoting one sentence from his Pellegrino di Roma.  “For [St. Paul] abstract truth, absolute laws, do not exist, because all of our thinking is subordinated to the construction of this holy temple of the Spirit, whose manifestations are not abstract ideas, but fruits of goodness, of peace, of charity and forgiveness.”

— Edward Nelson,
   Mathematics and Faith (pdf)

Belief in the consistency of arithmetic may or may not be foolish, and therefore an Emersonian hobgoblin of little minds, but bullshit is bullshit, whether in London, in Princeton, in Toronto, or in Rome.

Wednesday November 30, 2005

Filed under: General,Geometry — Tags: , — m759 @ 1:00 am

For St. Andrew’s Day

“The miraculous enters…. When we investigate these problems, some fantastic things happen….”

— John H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, preface to first edition (1988)

The remarkable Mathieu group M24, a group of permutations on 24 elements, may be studied by picturing its action on three interchangeable 8-element “octads,” as in the “Miracle Octad Generator” of R. T. Curtis.

A picture of the Miracle Octad Generator, with my comments, is available online.


 Cartoon by S.Harris

Related material:
Mathematics and Narrative.

Tuesday, November 29, 2005

Tuesday November 29, 2005

Filed under: General — m759 @ 12:25 am
The Way of the Pilgrim,
Part III:
 
For the Birthday
of C. S. Lewis

The image “http://www.log24.com/log/pix05B/051129-Tao.jpg” cannot be displayed, because it contains errors.

The Tao, Chapter I

“The Chinese… speak of a great thing (the greatest thing) called the Tao. It is the reality beyond all predicates, the abyss that was before the Creator Himself. It is Nature, it is the Way, the Road. It is the Way in which the universe goes on, the Way in which things everlastingly emerge, stilly and tranquilly, into space and time. It is also the Way which every man should tread in imitation of that cosmic and supercosmic progression, conforming all activities to that great exemplar.”

— C. S. Lewis in The Abolition of Man

“In his preface to That Hideous Strength, Lewis says the novel has a serious point that he has tried to make in this little book, The Abolition of Man.  The novel is a work of fantasy or science fiction, while Abolition is a short philosophical work about moral education, but as we shall see the two go together; we will understand either book better by having read and thought about the other.”

— Dale Nelson, Notes on The Abolition of Man

“In Epiphany Term, 1942, C.S. Lewis delivered the Riddell Memorial Lectures… in….  the University of Durham….  He delivered three lectures entitled ‘Men without Chests,’ ‘The Way,’ and ‘The Abolition of Man.’  In them he set out to attack and confute what he saw as the errors of his age. He started by quoting some fashionable lunacy from an educationalists’ textbook, from which he developed a general attack on moral subjectivism.  In his second lecture he argued against various contemporary isms, which purported to replace traditional objective morality.  His final lecture, ‘The Abolition of Man,’ which also provided the title of the book published the following year, was a sustained attack on hard-line scientific anti-humanism. The intervening fifty years have largely vindicated Lewis.”

— J. R. Lucas, The Restoration of Man

Monday, November 28, 2005

Monday November 28, 2005

Filed under: General — Tags: — m759 @ 1:00 pm
The Way of the Pilgrim,
Part II:
 
Einstein’s Orgy

In a recent Edge article, “The Vagaries of Religious Experience,” a Harvard psychologist, Daniel Gilbert,  quotes Einstein on his own religious vagaries:

“(I had) a deep religiosity, which, however, found an abrupt ending at the age of 12. Through the reading of popular scientific books I soon reached the conviction that much in the stories of the Bible could not be true. The consequence was a positively fanatic orgy* of freethinking coupled with the impression that youth is intentionally being deceived by the state through lies. It was a crushing impression. Suspicion against every kind of authority grew out of this experience, a skeptical attitude towards the convictions which were alive in any specific social environment– an attitude which has never again left me.” (Autobiographical Notes, 1949)

Gilbert adds,

“Einstein’s orgy* of freethinking forever changed our understanding of space and time, and the phrase ‘Religion for Dummies’ became, in the view of many scientists, a redundancy.”

Here is another Einstein quotation, from the paragraph in Autobiographical Notes following the paragraph quoted by Gilbert:

“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…. The road to this paradise was not as comfortable and alluring as the road to the religious paradise; but it has proved itself as trustworthy, and I have never regretted having chosen it.”

Einstein describes “the road to the religious paradise” as “comfortable and alluring.”  He might therefore have profited by the book saluted in the previous entry… a book that might be described, to adapt Gilbert’s charming phrase, as “Religion for Dummies like Einstein.”

For an approach to the contemptible religion of Scientism that is more subtle than Gilbert’s, see “Einstein’s Third Paradise,” by Gerald Holton, another Harvard savant.

* In the original, the words “orgy of” appear in square brackets to indicate an interpolation by the editor, Paul A. Schilpp, a Methodist minister (pdf).  Einstein’s own words were “eine geradezu fanatische Freigeisterei.”  Gilbert’s omission of the brackets indicates both the moral slovenliness typical of those embracing Scientism and the current low standards of scholarship at Harvard.  (Related material: The Crimson Passion.)

Monday November 28, 2005

Filed under: General — m759 @ 4:00 am
The Way of the Pilgrim,
Part I:
 
For John Bunyan’s
Birthday
The image “http://www.log24.com/log/pix05B/051128-PilgrimsProgress12.jpg” cannot be displayed, because it contains errors.

Click on picture to enlarge.

“AS I walk’d through the wilderness of this world, I lighted on a certain place where was a Den, and I laid me down in that place to sleep; and as I slept, I dreamed a Dream. I dreamed, and behold I saw a Man cloathed with Rags, standing in a certain place, with his face from his own house, a Book in his hand, and a great Burden upon his back. I looked, and saw him open the Book, and read therein; and as he read, he wept and trembled; and not being able longer to contain, he brake out with a lamentable cry, saying What shall I do?“

— The Pilgrim’s Progress, by John Bunyan

Friday, November 25, 2005

Friday November 25, 2005

Filed under: General,Geometry — m759 @ 9:00 pm

Holy Geometry

What was “the holy geometry book” (“das heilige Geometrie-Büchlein,” p. 10 in the Schilpp book below) that so impressed the young Albert Einstein?

“At the age of 12 I experienced a second wonder of a totally different nature: in a little book dealing with Euclidian plane geometry, which came into my hands at the beginning of a schoolyear.  Here were assertions, as for example the intersection of the three altitudes of a triangle in one point, which– though by no means evident– could nevertheless be proved with such certainty that any doubt appeared to be out of the question.  This lucidity and certainty made an indescribable impression upon me.”

(“Im Alter von 12 Jahren erlebte ich ein zweites Wunder ganz verschiedener Art: An einem Büchlein über Euklidische Geometrie der Ebene, das ich am Anfang eines Schuljahres in die Hand bekam.  Da waren Aussagen wie z.B. das Sich-Schneiden der drei Höhen eines Dreieckes in einem Punkt, die– obwohl an sich keineswegs evident– doch mit solcher Sicherheit bewiesen werden konnten, dass ein Zweifel ausgeschlossen zu sein schien.  Diese Klarheit und Sicherheit machte einen unbeschreiblichen Eindruck auf mich.”)

— Albert Einstein, Autobiographical Notes, pages 8 and 9 in Albert Einstein: Philosopher-Scientist, ed. by Paul A. Schilpp

From a website by Hans-Josef Küpper:

“Today it cannot be said with certainty which book is Einstein’s ‘holy geometry book.’  There are three different titles that come into question:

Theodor Spieker, 1890
 Lehrbuch der ebenen Geometrie. Mit Übungsaufgaben für höhere Lehranstalten.

Heinrich Borchert Lübsen, 1870
 Ausführliches Lehrbuch der ebenen und sphärischen Trigonometrie. Zum Selbstunterricht. Mit Rücksicht auf die Zwecke des praktischen Lebens.

Adolf Sickenberger, 1888
 Leitfaden der elementaren Mathematik.

Young Albert Einstein owned all of these three books. The book by T. Spieker was given to him by Max Talmud (later: Talmey), a Jewish medic. The book by H. B. Lübsen was from the library of his uncle Jakob Einstein and the one of A. Sickenberger was from his parents.”

Küpper does not state clearly his source for the geometry-book information.

According to Banesh Hoffman and Helen Dukas in Albert Einstein, Creator and Rebel, the holy geometry book was Lehrbuch der Geometrie zum Gebrauch an höheren Lehranstalten, by Eduard Heis (Catholic astronomer and textbook writer) and Thomas Joseph Eschweiler.

An argument for Sickenberger from The Young Einstein: The Advent of Relativity (pdf), by Lewis Pyenson, published by Adam Hilger Ltd., 1985:

    “Throughout Einstein’s five and a half years at the Luitpold Gymnasium, he was taught mathematics from one or another edition of the separately published parts of Sickenberger’s Textbook of Elementary Mathematics.  When it first appeared in 1888 the book constituted a major contribution to reform pedagogy.  Sickenberger based his book on twenty years of experience that in his view necessarily took precedence over ‘theoretical doubts and systematic scruples.’  At the same time Sickenberger made much use of the recent pedagogical literature, especially that published in the pages of Immanuel Carl Volkmar Hoffmann’s Zeitschrift für mathematischen und naturwissenschaftlichen Unterricht, the leading pedagogical mathematics journal of the day.  Following in the tradition of the reform movement, he sought to present everything in the simplest, most intuitive way possible.  He opposed introducing scientific rigour and higher approaches in an elementary text.  He emphasised that he would follow neither the synthesis of Euclidean geometry nor the so-called analytical-genetic approach.  He opted for a great deal of freedom in the form of presentation because he believed that a textbook was no more than a crutch for oral instruction.  The spoken word, in Sickenberger’s view, could infuse life into the dead forms of the printed text.  Too often, he insisted in the preface to his text, mathematics was seen and valued ‘as the pure science of reason.’  In reality, he continued, mathematics was also ‘an essential tool for daily work.’  In view of the practical dimension of mathematics Sickenberger sought most of all to present basic propositions clearly rather than to arrive at formal conciseness.   Numerous examples took the place of long, complicated, and boring generalities.  In addition to the usual rules of arithmetic Sickenberger introduced diophantine equations.  To solve three linear, homogeneous, first-order equations with three unknowns he specified determinants and determinant algebra.  Then he went on to quadratic equations and logarithms.  In the second part of his book, Sickenberger treated plane geometry.
     According to a biography of Einstein written by his step-son-in-law, Rudolf Kayser– one that the theoretical physicist described as ‘duly accurate’– when he was twelve years old Einstein fell into possession of the ‘small geometry book’ used in the Luitpold Gymnasium before this subject was formally presented to him.  Einstein corroborated Kayser’s passage in autobiographical notes of 1949, when he described how at the age of twelve ‘a little book dealing with Euclidean plane geometry’ came into his hands ‘at the beginning of a school year.’  The ‘lucidity and certainty’ of plane geometry according to this ‘holy geometry booklet’ made, Einstein wrote, ‘an indescribable impression on me.’  Einstein saw here what he found in other texts that he enjoyed: it was ‘not too particular’ in logical rigour but ‘made up for this by permitting the main thoughts to stand out clearly and synoptically.’  Upon working his way through this text, Einstein was then presented with one of the many editions of Theodor Spieker’s geometry by Max Talmey, a medical student at the University of Munich who dined with the Einsteins and who was young Einstein’s friend when Einstein was between the ages of ten and fifteen.  We can only infer from Einstein’s retrospective judgment that the first geometry book exerted an impact greater than that produced by Spieker’s treatment, by the popular science expositions of Aaron Bernstein and Ludwig Büchner also given to him by Talmey, or by the texts of Heinrich Borchert Lübsen from which Einstein had by the age of fourteen taught himself differential and integral calculus.
     Which text constituted the ‘holy geometry booklet’?  In his will Einstein gave ‘all his books’ to his long-time secretary Helen Dukas.  Present in this collection are three bearing the signature ‘J Einstein’: a logarithmic and trigonometric handbook, a textbook on analysis, and an introduction to infinitesimal calculus.  The signature is that of Einstein’s father’s brother Jakob, a business partner and member of Einstein’s household in Ulm and Munich.  He presented the books to his nephew Albert.  A fourth book in Miss Dukas’s collection, which does not bear Jakob Einstein’s name, is the second part of a textbook on geometry, a work of astronomer Eduard Heis’s which was rewritten after his death by the Cologne schoolteacher Thomas Joseph Eschweiler.  Without offering reasons for his choice Banesh Hoffmann has recently identified Heis and Eschweiler’s text as the geometry book that made such an impression on Einstein.  Yet, assuming that Kayser’s unambiguous reporting is correct, it is far more likely that the geometrical part of Sickenberger’s text was what Einstein referred to in his autobiographical notes.  Sickenberger’s exposition was published seven years after that of Heis and Eschweiler, and unlike the latter it appeared with a Munich press.  Because it was used in the Luitpold Gymnasium, copies would have been readily available to Uncle Jakob or to whoever first acquainted Einstein with Euclidean geometry.”

What might be the modern version of a “holy geometry book”?

I suggest the following,
first published in 1940:

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

Click on picture for details.

Friday November 25, 2005

Filed under: General — m759 @ 3:48 pm

Rehearsing Hell

Art critic Michael Kimmelman
in today’s New York Times:

The Los Angeles veteran Mike Kelley’s latest show is a sprawling, scabrous spectacle of noisome installations and hilarious videos, occupying the whole of the cavernous Gagosian Gallery in Chelsea. Ingratiating Mr. Kelley’s work never has been, nor is it now. But serious it is, in its brainy, abrasive, black-humored way, and this is by far his most ambitious and perversely entertaining effort, an attempted Gesamtkunst-werk of satanic rituals and advertising jingles mingled with allusions to Godard, German Expressionist cinema and Stockhausen….
    A teenage girl dressed like a hillbilly recounts a nonsense parable in the manner of H. P. Lovecraft crossed with William Faulkner as part of a faux-reality show….
    Did I mention the church confirmation in which a plump female communicant morphs into a devil worshiper, and teenage boys dressed in Nazi outfits suddenly rap about sex with fat women?….
     … Mr. Kelley’s deep roots are in the performance tradition going back to the Vienna Actionists.

For descriptions of the Vienna Actionists, do a Google search.

From yesterday:

Angels
  Even devils too
  Wait to show
How far we come
To joy
— Chris Whitley, “To Joy    
(Revolution of the Innocents)” —
mp3 and lyrics.

It seems that Mike Kelley and Michael Kimmelman are among Chris Whitley’s “devils.”  Let us hope that they enjoy the company of General Augusto Pinochet (see previous entry) in the afterlife.

Related material: Art Wars and The Crimson Passion.

Friday November 25, 2005

Filed under: General — m759 @ 2:28 pm

Buckley and Pinochet

Yesterday, William F. Buckley, Jr., author of God and Man at Yale, turned 80.

Here is an entry from yesterday, postponed until today so it would not intervene between yesterday’s related entries “Crossroads” and “For Constantine’s Angel.”

Recommended reading
for William F. Buckley, Jr.

  1. Joyce and Aquinas (Yale Studies in English)
  2. God and Man in Twentieth-Century Fiction
  3. Modern Literature and the Sense of Time
  4. Three Young Men in Rebellion
  5. James Joyce: Unfacts, Fiction, and Facts
  6. Yeats and the Human Body
  7. Poetry and Prayer

These titles are from an Amazon.com search.  All seem to be by the same “William T. Noon,” a Jesuit priest.  Except for Joyce and Aquinas and Poetry and Prayer,  little of Noon’s work is now remembered.

Thought to accompany the above reading list:

“And now I was beginning to surmise:
Here was the library of Paradise.”

— Hermann Hesse, Magister Ludi

Before he attains to Paradise, Buckley’s reading list in Purgatory might include the complete weblog of Andrew Cusack, a young Christian Fascist at the University of St. Andrews.

A related item…

According to “Today in History,” by the Associated Press, for Nov. 25, 2005,

“Today’s Birthdays: Former Chilean dictator General Augusto Pinochet is 90….”

If, in fact, Hell also has a library, let us pray that it contains, for Pinochet’s future edification, the collected works of Pablo Neruda.

Thursday, November 24, 2005

Thursday November 24, 2005

Filed under: General — Tags: — m759 @ 3:33 pm
Crossroads

In memory of Diego Rivera,
who died on this date in 1957

"… the socialist muralist Diego Rivera, hired by Nelson Rockefeller to paint a fresco for the newly constructed Rockefeller Center in New York, inserted a likeness of Lenin's head into the fresco. Rockefeller insisted that the head be replaced or removed, and when Rivera refused the fresco was destroyed…. The event… is captured with great wit in E.B. White's poem…."

— Harvard Law Review

I Paint What I See
[A Ballad of Artistic Integrity]
by E.B. White
The New Yorker, 20 May 1933

"'What do you paint, when you paint on a wall?'
Said John D.'s grandson Nelson.
'Do you paint just anything there at all?
'Will there be any doves, or a tree in fall?
'Or a hunting scene, like an English hall?'

'I paint what I see,' said Rivera.

'What are the colors you use when you paint?'
Said John D.'s grandson Nelson.
'Do you use any red in the beard of a saint?
'If you do, is it terribly red, or faint?
'Do you use any blue? Is it Prussian?'

'I paint what I paint,' said Rivera.

'Whose is that head that I see on the wall?'
Said John D.'s grandson Nelson.
'Is it anyone's head whom we know, at all?
'A Rensselaer, or a Saltonstall?
'Is it Franklin D.? Is it Mordaunt Hall?
Or is it the head of a Russian?

'I paint what I think,' said Rivera.

'I paint what I paint, I paint what I see,
'I paint what I think,' said Rivera,
'And the thing that is dearest in life to me
'In a bourgeois hall is Integrity;
'However . . .
'I'll take out a couple of people drinkin'
'And put in a picture of Abraham Lincoln;
'I could even give you McCormick's reaper
'And still not make my art much cheaper.
'But the head of Lenin has got to stay
'Or my friends will give the bird today,
'The bird, the bird, forever.'

'It's not good taste in a man like me,'
Said John D.'s grandson Nelson,
'To question an artist's integrity
'Or mention a practical thing like a fee,
'But I know what I like to a large degree,
'Though art I hate to hamper;
'For twenty-one thousand conservative bucks
'You painted a radical. I say shucks,
'I never could rent the offices—–
'The capitalistic offices.
'For this, as you know, is a public hall
'And people want doves, or a tree in fall
'And though your art I dislike to hamper,
'I owe a little to God and Gramper,
'And after all,
'It's my wall . . .'

'We'll see if it is,' said Rivera.

Related material:

Pictures of the Rockefeller Center mural,
"Man at the Crossroads," and
Rivera's re-creation of the mural,
"Man, Controller of the Universe."

See also another treatment of the "Man at the Crossroads" theme–

The Concrete Gospel
of Donald E. Knuth:

In Hoc Signo

(from Feb. 18),
continued —

The image “http://www.log24.com/log/pix05/050219-Signo.gif” cannot be displayed, because it contains errors.

This holy icon
appeared at
N37°25.638'
W122°09.574'
on August 22, 2003,
at the Stanford campus.

— Log24, Feb. 19, 2005  

Thursday November 24, 2005

Filed under: General — m759 @ 2:12 pm
Recommended reading
for William F. Buckley, Jr.,
who is 80 today

“And now I was beginning to surmise:
Here was the library of Paradise.”

— Hermann Hesse, Magister Ludi


Joyce and Aquinas (Yale Studies in English)
by William T. Noon
God and Man in Twentieth-Century Fiction
by William T. Noon
Modern Literature and the Sense of Time
by William T. Noon
Three Young Men in Rebellion
by William T. Noon
James Joyce: Unfacts, Fiction, and Facts
by William T. Noon
Yeats and the Human Body
by William T. Noon
Poetry and Prayer
by William T. Noon

Thursday November 24, 2005

Filed under: General — m759 @ 4:00 am
For Constantine‘s Angel

The image “http://www.log24.com/log/pix05B/051124-Whitley2.jpg” cannot be displayed, because it contains errors.

Lyrics by Chris Whitley,
who died on Sunday,
November 20, 2005:

Angels
  Even devils too
  Wait to show
How far we come
To joy

— “To Joy    
(Revolution of the Innocents)” —
mp3 and lyrics.

Wednesday, November 23, 2005

Wednesday November 23, 2005

Filed under: General — m759 @ 12:00 pm

Also on Saint Cecilia’s Day
(Release date: 11/22/2005)…

Bright Music
Illustrated

The image “http://www.log24.com/log/pix05B/051123-Reba.jpg” cannot be displayed, because it contains errors.

 Reba #1’s
Reba McEntire
Album Length Compact Disc

For Reba,
a very bright star,
the symbol of Venus
always shines:

The image “http://www.log24.com/log/pix05B/051123-Star.jpg” cannot be displayed, because it contains errors.

Tuesday, November 22, 2005

Tuesday November 22, 2005

Filed under: General — Tags: , — m759 @ 3:09 pm

For St. Cecilia’s Day–
A flashback to June 8, 2004:

Dark Music
Illustrated
 
The image “http://www.log24.com/log/pix04A/040608-Klee.gif” cannot be displayed, because it contains errors.
Paul Klee

From today’s
Arts & Letters Daily:

 

Critics in Mozart’s age
threw up their hands
at the dark Don Giovanni,
calling it perverse, amoral.
These days, such qualities
turn us on… more»

The image “http://www.log24.com/log/pix04A/040608-Don.jpg” cannot be displayed, because it contains errors.
Paul Klee,
The Bavarian Don Giovanni,
1919, watercolor and ink
on paper

The image “http://www.log24.com/log/pix04A/040608-Spot.jpg” cannot be displayed, because it contains errors.

There’s a little black spot
on the sun today….

 

Tuesday November 22, 2005

Filed under: General — Tags: — m759 @ 4:23 am

Cartoon Graveyard
(continued)

From yesterday’s New York Post:

By LARRY CELONA, JOHN MAZOR and DAN MANGAN

November 21, 2005 — The former tour manager for superstars Paul Simon and Billy Joel was stabbed to death yesterday by his prostitute girlfriend on his 57th birthday less than a block from Gracie Mansion, cops said.

“It looked like a horror movie in there,” said an NYPD detective after seeing the blood-drenched bed in the couple’s sixth-floor studio at 530 East 89th St., where cops say music producer Danny Harrison was stabbed twice in the chest with a long butcher knife by his live-in lover just before 1 p.m.

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

Below: cartoonist Lou Myers,
who also died on Sunday, Nov. 20,
with a horse from yesterday’s entry.

The image “http://www.log24.com/log/pix05B/051121-Horse.jpg” cannot be displayed, because it contains errors.

“... and behold: a pale horse.
And his name, that sat on him,
was Death. And Hell
followed with him.”

— Johnny Cash

Related material:
Log24 entries of
Sept. 15, 2003.

 

Monday, November 21, 2005

Monday November 21, 2005

Filed under: General — m759 @ 12:00 pm
Picasso’s
Tragedy:

Detail by
 Lou Myers,
1915-2005

The image “http://www.log24.com/log/pix05B/051121-Myers7.gif” cannot be displayed, because it contains errors.

Myers died yesterday,
the 30th anniversary
of the death of
Francisco Franco.

For the source of
the above picture,
see ZAKS illustrators.

Original caption of cartoon
from which the above picture
was excerpted:

“Picasso’s tragedy was that
he was an artist who
ran out of new things
to paint.”

The image “http://www.log24.com/log/pix05B/051121-Franco1.gif” cannot be displayed, because it contains errors.

“… behold: a pale horse.
And his name,
that sat on him,
was Death. And Hell
followed with him.”

— Johnny Cash

Sunday, November 20, 2005

Sunday November 20, 2005

Filed under: General,Geometry — Tags: , — m759 @ 4:04 pm

An Exercise
of Power

Johnny Cash:
“And behold,
a white horse.”

The image “http://www.log24.com/log/pix05B/051120-SpringerLogo9.gif” cannot be displayed, because it contains errors.
Adapted from
illustration below:

The image “http://www.log24.com/log/pix05B/051120-NonEuclideanRev.jpg” cannot be displayed, because it contains errors.

“There is a pleasantly discursive treatment of Pontius Pilate’s unanswered question ‘What is truth?'”

— H. S. M. Coxeter, 1987, introduction to Richard J. Trudeau’s remarks on the “Story Theory” of truth as opposed to  the “Diamond Theory” of truth in The Non-Euclidean Revolution

“A 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*….”

— Richard J. Trudeau in
The Non-Euclidean Revolution

“‘Deniers’ of truth… insist that each of us is trapped in his own point of view; we make up stories about the world and, in an exercise of power, try to impose them on others.”

— Jim Holt in The New Yorker.

(Click on the box below.)

The image “http://www.log24.com/log/pix05B/050819-Critic4.jpg” cannot be displayed, because it contains errors.

Exercise of Power:

Show that a white horse–

A Singer 7-Cycle

a figure not unlike the
symbol of the mathematics
publisher Springer–
is traced, within a naturally
arranged rectangular array of
polynomials, by the powers of x
modulo a polynomial
irreducible over a Galois field.

This horse, or chess knight–
“Springer,” in German–
plays a role in “Diamond Theory”
(a phrase used in finite geometry
in 1976, some years before its use
by Trudeau in the above book).

Related material

On this date:

 In 1490, The White Knight
 (Tirant lo Blanc The image “http://www.log24.com/images/asterisk8.gif” cannot be displayed, because it contains errors. )–
a major influence on Cervantes–
was published, and in 1910

The image “http://www.log24.com/log/pix05B/051120-Caballo1.jpg” cannot be displayed, because it contains errors.

the Mexican Revolution began.

Illustration:
Zapata by Diego Rivera,
Museum of Modern Art,
New York

The image “http://www.log24.com/images/asterisk8.gif” cannot be displayed, because it contains errors. Description from Amazon.com—

“First published in the Catalan language in Valencia in 1490…. Reviewing the first modern Spanish translation in 1969 (Franco had ruthlessly suppressed the Catalan language and literature), Mario Vargas Llosa hailed the epic’s author as ‘the first of that lineage of God-supplanters– Fielding, Balzac, Dickens, Flaubert, Tolstoy, Joyce, Faulkner– who try to create in their novels an all-encompassing reality.'”

Friday, November 18, 2005

Friday November 18, 2005

Filed under: General — m759 @ 7:00 pm

x

Friday November 18, 2005

Filed under: General — m759 @ 2:56 am
It’s still the same old story,
a fight for love and…

Glory

Wikipedia on the tesseract:

“Glory Road (1963) included the foldbox, a hyperdimensional packing case that was bigger inside than outside.”

Robert A. Heinlein in Glory Road:

    “Rufo’s baggage turned out to be a little black box about the size and shape of a portable typewriter. He opened it.
    And opened it again.
    And kept on opening it– And kept right on unfolding its sides and letting them down until the durn thing was the size of a small moving van and even more packed….
    … Anyone who has studied math knows that the inside does not have to be smaller than the outside, in theory….  Rufo’s baggage just carried the principle further.”

Johnny Cash: “And behold, a white horse.”

On The Last Battle, a book in the Narnia series by C. S. Lewis:

“… there is much glory in this wonderfully written apocalypse.  Tirian, looking into the stable through the hole in the door, says, ‘The stable seen from within and the stable seen from without are two different places.’ Digory answers, ‘Its inside is bigger than its outside.’  It is the perceptive Lucy who voices the hope that is in us, ‘In our world, too, a stable once had something inside it that was bigger than our whole world.'”


Lewis said in “The Weight of Glory”—
 

“Do you think I am trying to weave a spell? Perhaps I am; but remember your fairy tales. Spells are used for breaking enchantments as well as for inducing them.”

On enchantments that need to be broken:

See the description of the Eater of Souls in Glory Road and of Scientism in

Friday November 18, 2005

Filed under: General — m759 @ 1:00 am
Crank Power!

One night in Bangkok
and the world’s your oyster…

Tonight’s Bangkok Post
on a new $100 laptop
from an MIT designer:

The image “http://www.log24.com/log/pix05B/051118-Laptop2.jpg” cannot be displayed, because it contains errors.

No logo for the initiative has yet been released, but designers could do worse than adopting as their symbol the bright yellow hand-crank that protrudes from the side of the laptop. This throwback to the days of the gramophone is designed to enable users to manually crank up electricity to run the laptop in places with irregular or non-existent access to the fixed electric power grid.

Details from Wired News
Kevin Poulsen, 12:58 PM Nov. 17, 2005 PT:

TUNIS, Tunisia — If tech luminary Nicholas Negroponte has his way, the pale light from rugged, hand-cranked $100 laptops will illuminate homes in villages and townships throughout the developing world, and give every child on the planet a computer of their own by 2010.

The MIT Media Lab and Wired magazine founder stood shoulder to shoulder with U.N. Secretary-General Kofi Annan to unveil the first working prototype of the “$100 laptop” — currently more like $110 — at the U.N. World Summit on the Information Society here Wednesday. The Linux-based machine instantly became the hit of the show, and Thursday saw diplomats and dignitaries, reporters and TV cameras perpetually crowded around the booth of One Laptop Per Child — Negroponte’s nonprofit — craning for a glimpse of the toy-like tote.

With its cheery green coloring and Tonka-tough shell, the laptop certainly looks cool. It boasts a 7-inch screen that swivels like a tablet PC, and an electricity-generating crank that provides 40 minutes of power from a minute of grinding.

Related material:
Certified Crank.

Thursday, November 17, 2005

Thursday November 17, 2005

Filed under: General — m759 @ 2:22 pm
All the King’s Men

(See also Time and
All the King’s Horses.)

LEAR:

Now you better do some thinkin’
    then you’ll find
You got the only daddy
    that’ll walk the line.

The image “http://www.log24.com/log/pix05B/051117-Ridin1.jpg” cannot be displayed, because it contains errors.

FOOL:

I’ve always been different
    with one foot over the line….
I’ve always been crazy
    but it’s kept me from going insane.

For related material, see

The Line: Notes on Iconology,

and last night’s winner of

The image “http://www.log24.com/log/pix05B/051117-Award2.jpg” cannot be displayed, because it contains errors.

the National Book Award
for nonfiction, i.e.,
“all hard facts, all reality, with
no illusions and no fantasy.”  

A Story That Works

  • “There is the dark, eternally silent, unknown universe;
  • there are the friend-enemy minds shouting and whispering their tales and always seeking the three miracles —
    • that minds should really touch, or
    • that the silent universe should speak, tell minds a story, or (perhaps the same thing)
    • that there should be a story that works, that is all hard facts, all reality, with no illusions and no fantasy;
  • and lastly, there is lonely, story-telling, wonder-questing, mortal me.”

    — Fritz Leiber in “The Button Molder“

Thursday November 17, 2005

Filed under: General — m759 @ 4:04 am
For a Man in Black

The image “http://www.log24.com/log/pix05B/051117-MIB.jpg” cannot be displayed, because it contains errors.

Related material:

Log24 Sept. 1-15, 2003

and

State of Morelos.

Wednesday, November 16, 2005

Wednesday November 16, 2005

Filed under: General — Tags: , — m759 @ 4:04 pm
Images

Adam Gopnik on C. S. Lewis in this week's New Yorker:
 
"Lewis began with a number of haunted images…."

"The best of the books are the ones… where the allegory is at a minimum and the images just flow."

"'Everything began with images,' Lewis wrote…."

"We go to the writing of the marvellous, and to children’s books, for stories, certainly, and for the epic possibilities of good and evil in confrontation, not yet so mixed as they are in life. But we go, above all, for imagery: it is the force of imagery that carries us forward. We have a longing for inexplicable sublime imagery…."

"The religious believer finds consolation, and relief, too, in the world of magic exactly because it is at odds with the necessarily straitened and punitive morality of organized worship, even if the believer is, like Lewis, reluctant to admit it. The irrational images– the street lamp in the snow and the silver chair and the speaking horse– are as much an escape for the Christian imagination as for the rationalist, and we sense a deeper joy in Lewis’s prose as it escapes from the demands of Christian belief into the darker realm of magic. As for faith, well, a handful of images is as good as an armful of arguments, as the old apostles always knew."

Related material:

The image “http://www.log24.com/log/pix05B/051116-Time.jpg” cannot be displayed, because it contains errors.

Click on pictures for details.

See also Windmills and
Verbum sat sapienti?
as well as

an essay

 at Calvin College
on Simone Weil,
Charles Williams,
Dante, and
"the way of images."

Tuesday, November 15, 2005

Tuesday November 15, 2005

Filed under: General,Geometry — m759 @ 11:07 am
Windmills
 
The image “http://www.log24.com/log/pix05B/051115-StarRocks1.jpg” cannot be displayed, because it contains errors.

Upper part of above picture–

From today’s New York Times,
Seeing Mountains in
Starry Clouds of Creation.

Lower part of above picture–
Pilgrimage to Spider Rock:

“This magical place, according to Navajo Legend, was the home of Spider Woman, who gave the gift of weaving to the Dineh’ People.  Today’s Navajos trace the excellence of their finest textiles to this time of legends, when their patron, Changing Woman, met Spider Woman, the first Weaver.”

Vine Deloria Jr.,
 
Evolution, Creationism,
and Other Modern Myths:

“The continuing struggle between evolutionists and creationists, a hot political topic for the past four decades, took a new turn in the summer of 1999 when the Kansas Board of Education voted to omit the mention of evolution in its newly approved curriculum, setting off outraged cries of foul by the scientific establishment.  Don Quixotes on both sides mounted their chargers and went searching for windmills.”

Related material–

A figure from
last night’s entry,
Spider Woman:

Fritz Leiber's 'Spider' symbol

From Sunday, the day
of Vine Deloria’s death,
a picture that might be
called Changing Woman:

  

Kaleidoscope turning…
Shifting pattern
within unalterable structure…
— Roger Zelazny, Eye of Cat     

See also the windmill figure

The image “http://www.log24.com/theory/images/Whirl3.gif” cannot be displayed, because it contains errors.

in Time and Eternity
(Log 24, Feb. 1, 2003)

and

a review
of Fritz Leiber’s
The Big Time,

The image “http://www.log24.com/log/pix05B/051115-BigTimePic.jpg” cannot be displayed, because it contains errors.

“a story that works.”

Tuesday November 15, 2005

Filed under: General,Geometry — m759 @ 2:56 am
Spider Woman

    “Time traveling, which is not quite the good clean boyish fun it’s cracked up to be, started for me when this woman with the sigil on her forehead looked in on me from the open doorway of the hotel bedroom where I’d hidden myself and the bottles and asked me, ‘Look, Buster, do you want to live?’….
    Her right arm was raised and bent, the elbow touching the door frame, the hand brushing back the very dark bangs from her forehead to show me the sigil, as if that had a bearing on her question.

Fritz Leiber's 'Spider' symbol

Bordered version
of the sigil

The sigil was an eight-limbed asterisk made of fine dark lines and about as big as a silver dollar.  An X superimposed on a plus sign.  It looked permanent.”

— Fritz Leiber, “Damnation Morning“

For Vine Deloria Jr., who died at 72 on Sunday, Nov. 13, 2005:

        Things forgotten are shadows.
        The shadows will be as real
        as wind and rain and song and light,
        there in the old place.
        Spider Woman atop your rock,
        I would greet you,
        but I am going the other way.
        Only a fool would pursue a Navajo
        into the Canyon of Death.

— Roger Zelazny, Eye of Cat

Related material:
from a Log24 entry
on the morning of
Deloria’s death–

Kaleidoscope turning…
Shifting pattern
within unalterable structure…

— Roger Zelazny, Eye of Cat

  

Monday, November 14, 2005

Monday November 14, 2005

Filed under: General — m759 @ 3:09 am

Culture Wars

‘Chicken Little’ Lays Golden Egg
(Dean Goodman, Reuters)

‘Bee Season’ Anxiety
(Leonard Klady, Movie City News):

The mixed bag of limited release preems was highlighted by an excellent response to the concert film Sarah Silverman: Jesus is Magic. The film recorded a $19,000 plus per engagement average from seven outings for a $130,000 gross. The family drama Bee Season had a comparable gross but on three times as many screens that translated into anxiety about the Richard Gere film’s expansion prospects.

Weekend Estimates
Nov. 11-13, 2005

Title
Gross (average)
Theaters
Cume
Chicken Little
32.7   (  8,950)
3658
81.5 
Sarah Silverman:
Jesus is Magic
0.13 (19,210)
7
0.13
Bee Season
0.13 (  6,280)
21
0.13

Sunday, November 13, 2005

Sunday November 13, 2005

Filed under: General — m759 @ 10:48 am
Reunion:
An Introduction
to Multispeech

From Log24, Oct. 31, 2005:

“They don’t understand
what it is to be awake,
To be living
on several planes at once
Though one cannot speak
with several voices at once.”

— T. S. Eliot,
The Family Reunion

From Finnegans Wake:

“And even if Humpty shell fall frumpty times as awkward again in the beardsboosoloom of all our grand remonstrancers there’ll be iggs for the brekkers come to mournhim, sunny side up with care….”

From Urban Legends Reference Pages:

The image “http://www.log24.com/log/pix05B/051113-Reunion.jpg” cannot be displayed, because it contains errors.

See also
the previous two entries,
Ten is a Hen and Structure,
about a mother and child.

Sunday November 13, 2005

Filed under: General,Geometry — m759 @ 6:40 am
Structure

“Sunrise–
Hast thou a Flag for me?”
— Emily Dickinson

From a
Beethoven’s Birthday entry:

  

Kaleidoscope turning…
Shifting pattern
within unalterable structure…
— Roger Zelazny, Eye of Cat

Related material:

Blue
(below),

The image “http://www.log24.com/log/pix05B/051113-Blue.jpg” cannot be displayed, because it contains errors.

Bee Season
(below),

The image “http://www.log24.com/log/pix05B/051113-Scope1.jpg” cannot be displayed, because it contains errors.

Halloween Meditations,
Aquarius Jazz,
We Are the Key,
and
Jazz on St. Lucia’s Day.

“Y’know, I never imagined
the competition version involved
so many tricky permutations.”

— David Brin, Glory Season

Saturday, November 12, 2005

Saturday November 12, 2005

Filed under: General — m759 @ 10:00 pm
Ten is a Hen

“Follow the spiritual journey
that is BEE SEASON.“

The image “http://www.log24.com/log/pix05B/051112-Tikkun1.jpg” cannot be displayed, because it contains errors.

“‘Tikkun Olam,
the fixing of the world,’
she whispers.  ‘I’ve been
gathering up the broken vessels
to make things whole again.'”

   — Miriam in Bee Season

“Tikkun Olam, the gathering
of the divine fragments,
is a religious activity….
How do we work for
the repair of the world?
If we live in a
humpty dumpty world,
how do we get it all
put back together again?”

The Rev. Dr. Joshua Snyder,
October 5, 2003

“… the tikkun can’t start until
everyone asks what happened–
not just the Jews but everybody.
The strange thing is that
  Christ evidently saw this.”

— Martha Cooley, The Archivist 

“She understands that Bloom asked for breakfast in bed. Since we were present when Bloom fell asleep and he had not asked for breakfast in bed before he fell asleep, Molly may have misunderstood his sleepy murmurs about the Roc’s egg.”

Jorn Barger on Finnegans Wake:

“Acknowledging the dream as sexually harrowing, we’re offered relief in a view of ALP as a hen scratching up battle-relics from a midden heap after the fall/Flood.

And even if Humpty shell fall frumpty times as awkward again in the beardsboosoloom of all our grand remonstrancers there’ll be iggs for the brekkers come to mournhim, sunny side up with care….”

Saturday November 12, 2005

Filed under: General — m759 @ 9:00 pm
Nine is a Vine

The image “http://www.log24.com/theory/images/quat-1.jpg” cannot be displayed, because it contains errors.

Representation
of a quaternion

Related material:

“Oh, I wasn’t about to hole up
in a monastery.  I still wanted–
  What did I want?
      I wanted a Roc’s egg….”

— Robert A. Heinlein
  Glory Road

   And So To Bed.

(Log24, St. Peter’s Day, 2004)

Saturday November 12, 2005

Filed under: General — Tags: — m759 @ 8:00 pm
Seven is Heaven,
Eight is a Gate

(continued)

A Singer 7-Cycle

“… problems are the poetry of chess.
They demand from the composer
 the same virtues that characterize
all worthwhile art:
originality, invention,
harmony, conciseness,
complexity, and
splendid insincerity.”

— Vladimir Nabokov

Saturday November 12, 2005

Filed under: General — m759 @ 7:00 pm

State of Grace
On this date in 1929,
Grace Kelly was born.

 Enough —
    the first Abode
On the familiar Road
Galloped in Dreams —

— Emily Dickinson

 

“Nonbeing must in some sense be, otherwise what is it that there is not? This tangled doctrine might be nicknamed Plato’s beard; historically it has proved tough, frequently dulling the edge of Occam’s razor…. I have dwelt at length on the inconvenience of putting up with it. It is time to think about taking steps.”

— Willard Van Orman Quine, 1948, “On What There Is,” reprinted in From a Logical Point of View, Harvard University Press, 1980

“Item: Friar Guillaume’s razor
ne’er shaved the barber,
it is much too dull.”

— Robert A. Heinlein
  Glory Road

Related material:
Plato, Pegasus, and
the Evening Star

Saturday November 12, 2005

Filed under: General,Geometry — Tags: , — m759 @ 1:28 pm
Glory Season

"…his eyes ranged the Consul's books disposed quite neatly… on high shelves around the walls: Dogme et Ritual de la Haute Magie, Serpent and Siva Worship in Central America, there were two long shelves of this, together with the rusty leather bindings and frayed edges of the numerous cabbalistic and alchemical books, though some of them looked fairly new, like the Goetia of the Lemegaton of Solomon the King, probably they were treasures, but the rest were a heterogeneous collection…."

— Malcolm Lowry, Under the Volcano, Chapter VI

"… when Saul does reach for a slim leather-bound volume Eliza cannot help but feel that something momentous is about to happen.  There is care in the way he carries the book on the short journey from its shelf, as if it were constructed not of leather and parchment but of flesh and blood….
    "Otzar Eden HaGanuz," Saul says.  "The Hidden Eden.  In this book, Abulafia describes the process of permutation…. Once you have mastered it, you will have mastered words, and once you have mastered words, you will be ready to receive shefa."

— Bee Season: A Novel

"In the Inner Game, we call the Game Dhum Welur, the Mind of God."

— The Gameplayers of Zan, a novel featuring games based on cellular automata

"Regarding cellular automata, I'm trying to think in what SF books I've seen them mentioned. Off the top of my head, only three come to mind:

The Gameplayers of Zan M.A. Foster
Permutation City Greg Egan
Glory Season David Brin"

— Jonathan L. Cunningham, Usenet

    "If all that 'matters' are fundamentally mathematical relationships, then there ceases to be any important difference between the actual and the possible. (Even if you aren't a mathematical Platonist, you can always find some collection of particles of dust to fit any required pattern. In Permutation City this is called the 'logic of the dust' theory.)….
    … Paul Durham is convinced by the 'logic of the dust' theory mentioned above, and plans to run, just for a few minutes, a complex cellular automaton (Permutation City) started in a 'Garden of Eden' configuration — one which isn't reachable from any other, and which therefore must have been the starting point of a simulation….  I didn't understand the need for this elaborate set-up, but I guess it makes for a better story than 'well, all possible worlds exist, and I'm going to tell you about one of them.'"

— Danny Yee, review of Permutation City

"Y'know, I never imagined the competition version involved so many tricky permutations."

— David Brin, Glory Season, 1994 Spectra paperback, p. 408
 

Related material:
 
The image “http://www.log24.com/log/pix05B/051112-EdenFigs.jpg” cannot be displayed, because it contains errors.

Figure 2

 

 

"… matter is consciousness expressed in the intermixing of force and form, but so heavily structured and constrained by form that its behaviour becomes describable using the regular and simple laws of  physics. This is shown in Figure 2.
    The glyph in Figure 2 is the basis for a kabbalistic diagram called the Etz Chaiim, or Tree of Life. The first principle of being or consciousness is called Keter, which means Crown. The raw energy of consciousness is called Chokhmah or Wisdom, and the capacity to give form to the energy of consciousness is called Binah, which is sometimes translated as Understanding, and sometimes as Intelligence. The outcome of the interaction of force and form, the physical world, is called Malkhut or Kingdom.  This is shown… in Figure 3."

Figure 3

"This quaternary is a Kabbalistic representation of God-the-Knowable, in the sense that it the most abstract representation of God we are capable of comprehending….
    God-the-Knowable has four aspects, two male and two female: Keter and Chokhmah are both represented as male, and Binah and Malkhut are represented as female. One of the titles of Chokhmah is Abba, which means Father, and one of the titles of Binah is Imma, which means Mother, so you can think of Chokhmah as God-the-Father, and Binah as God-the-Mother. Malkhut is the daughter, the female spirit of God-as-Matter, and it would not be wildly wrong to think of her as Mother Earth. And what of God-the-Son? Is there also a God-the-Son in Kabbalah? There is…."

— A Depth of Beginning: Notes on Kabbalah by Colin Low (pdf)

See also
Cognitive Blending and the Two Cultures,
Mathematics and Narrative,
Deep Game,
and the previous entry.

Friday, November 11, 2005

Friday November 11, 2005

Filed under: General,Geometry — Tags: , — m759 @ 3:26 pm
720 in the Book
(continued)

From today's
New York Times:

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

The image “http://www.log24.com/log/pix05B/051111-BeeSeason.jpg” cannot be displayed, because it contains errors.

Phil Bray

Transcendence through spelling:
Richard Gere and Flora Cross
as father and daughter
in "Bee Season."

Words Made Flesh: Code, Culture, Imagination—

The earliest known foundation of the Kabbalah is the Sefer Yetzirah (Book of Creation) whose origin and history is unknown….

… letters create things by the virtue of an algorithm…

    "From two letters or forms He composed two dwellings; from three, six; from four, twenty-four; from five, one hundred and twenty; from six, seven hundred and twenty…."
— Sefer Yetzirah    

Foucault's Pendulum—

Mystic logic, letters whirling in infinite change, is the world of bliss, it is the music of thought, but see that you proceed slowly, and with caution, because your machine may bring you delirium instead of ecstasy. Many of Abulafia's disciples were unable to walk the fine line between contemplation of the names of God and the practice of magic.

Bee Season—

"The exercises we've been doing are Abulafia's. His methods are primarily a kind of Jewish yoga, a way to relax. For most, what Abulafia describes as shefa, the influx of the Divine, is a historical curiosity to be discussed and interpreted. Because, while anyone can follow Abulafia's instructions for permutation and chanting, very few can use them to achieve transcendence….

Spelling is a sign, Elly. When you win the national bee, we'll know that you are ready to follow in Abulafia's footsteps. Once you're able to let the letters guide you through any word you are given, you will be ready to receive shefa."

In the quiet of the room, the sound of Eliza and her father breathing is everything.

"Do you mean," Eliza whispers, "that I'll be able to talk to God?"

Related material:

Log24, Sept. 3, 2002,

Diamond Theory notes
of Feb. 4, 1986,
of April 26, 1986, and
 of May 26, 1986,

  Sacerdotal Jargon
(Log24, Dec. 5, 2002),

and 720 in the Book
(Log24, Epiphany 2004).

Thursday, November 10, 2005

Thursday November 10, 2005

Filed under: General — m759 @ 4:00 pm
The Rhetoric of
Scientism

Kansas, Where “Ignorant”
is the New “Educated”:

“… the Board of Education went as far as to redefine what science is: it’s no longer just a search for natural explanations for natural phenomena. Now it’s a search for… well, that’s a bit hard to say. Any sort of explanation, apparently. Pixies, ghosts, telekinesis, auras, ancient astronauts, excesses of choleric humor, they all seem to be fair game in the interest of ‘academic freedom.'”

— John Rennie, editor in chief of
  Scientific American, Nov. 8, 2005

The shocking redefinition
(with changes highlighted):
Kansas Definition of Science
Adopted Feb. 14, 2001

“Science is the human activity of seeking natural explanations for what we observe in the world around us.  Science does so through the use of observation, experimentation, and logical argument while maintaining strict empirical standards and healthy skepticism. Scientific explanations are built on observations, hypotheses, and theories. A hypothesis is a testable statement about the natural world that can be used to build more complex inferences and explanations. A theory is a well-substantiated explanation of some aspect of the natural world that can incorporate observations, inferences, and tested hypotheses

 Kansas Definition of Science
Approved Nov. 8, 2005

“Science is a systematic method of continuing investigation that uses observations, hypothesis testing, measurement, experimentation, logical argument and theory building to lead to more adequate explanations of natural phenomena. Science does so while maintaining strict empirical standards and healthy skepticism. Scientific explanations are built on observations, hypotheses, and theories. A hypothesis is a testable statement about the natural world that can be used to build more complex inferences and explanations. A theory is a well-substantiated explanation of some aspect of the natural world that can incorporate observations, inferences, and tested hypotheses.
Scientific explanations must meet certain criteria. Scientific explanations are consistent with experimental and/or observational data and testable by scientists through additional experimentation and/or observation. Scientific explanation must meet criteria that govern the repeatability of observations and experiments. The effect of these criteria is to insure that scientific explanations about the world are open to criticism and that they will be modified or abandoned in favor of new explanations if empirical evidence so warrants. Because all scientific explanations depend on observational and experimental confirmation, all scientific knowledge is, in principle, subject to change as new evidence becomes available. The core theories of science have been subjected to a wide variety of confirmations and have a high degree of reliability within the limits to which they have been tested. In areas where data or understanding are incomplete, new data may lead to changes in current theories or resolve current conflicts. In situations where information is still fragmentary, it is normal for scientific ideas to be incomplete, but this is also where the opportunity for making advances may be greatest. Science has flourished in different regions during different time periods, and in history, diverse cultures have contributed scientific knowledge and technological inventions. Changes in scientific knowledge usually occur as gradual modifications, but the scientific enterprise also experiences periods of rapid advancement. The daily work of science and technology results in incremental advances in our understanding of the world about us.” Scientific explanations must meet certain criteria. Scientific explanations are consistent with experimental and/or observational data and testable by scientists through additional experimentation and/or observation. Scientific explanation must meet criteria that govern the repeatability of observations and experiments. The effect of these criteria is to insure that scientific explanations about the world are open to criticism and that they will be modified or abandoned in favor of new explanations if empirical evidence so warrants. Because all scientific explanations depend on observational and experimental confirmation, all scientific knowledge is, in principle, subject to change as new evidence becomes available. The core theories of science have been subjected to a wide variety of confirmations and have a high degree of reliability within the limits to which they have been tested. In areas where data or understanding is incomplete, new data may lead to changes in current theories or resolve current conflicts. In situations where information is still fragmentary, it is normal for scientific ideas to be incomplete, but this is also where the opportunity for making advances may be greatest. Science has flourished in different regions during different time periods, and in history, diverse cultures have contributed scientific knowledge and technological inventions. Changes in scientific knowledge usually occur as gradual modifications, but the scientific enterprise also experiences periods of rapid advancement. The daily work of science and technology results in incremental advances in understanding the world.”

From both old (2001) and
new (2005) Kansas standards:

Teaching With Tolerance and Respect

“A teacher is an important role model for  demonstrating respect, sensitivity, and civility. Teachers should not ridicule, belittle or embarrass a student for expressing an alternative view or belief.”

It’s a very ancient saying,
But a true and honest thought,
That if you become a teacher,
By your pupils you’ll be taught.

— Oscar Hammerstein,
“Getting to Know You”

Scientism and Civility:

A Google blog search for
fucking kansas evolution standards -fuck
yields “about 47” entries.

A search for
fuck kansas evolution standards -fucking
yields  “about 34” entries.

A search for
fuck fucking kansas evolution standards
yields “about 42” entries.

Wednesday, November 9, 2005

Wednesday November 9, 2005

Filed under: General — m759 @ 7:59 pm
Butterfly Effect

From today’s
online New York Times:
The image “http://www.log24.com/log/pix05B/051109-EvolNYT1.jpg” cannot be displayed, because it contains errors.

John Fowles on two of his novels:

“I wanted to show the seeds of an intense future evolution in a particular period.”

Ray Bradbury, “A Sound of Thunder” (1952), on the death of a butterfly:

“It fell to the floor, an exquisite thing, a small thing that could upset balances and knock down a line of small dominoes and then big dominoes and then gigantic dominoes, all down the years across Time.”

Zhuangzi:

“Once Zhuang Zhou dreamt he was a butterfly, a butterfly flitting and fluttering around, happy with himself and doing as he pleased.  He didn’t know he was Zhuang Zhou.  Suddenly he woke up and there he was, solid and unmistakable Zhuang Zhou.  But he didn’t know if he was Zhuang Zhou who had dreamt he was a butterfly, or a butterfly dreaming he was Zhuang Zhou.  Between Zhuang Zhou and a butterfly there must be some distinction!  This is called the Transformation of Things.”

Related material:

Wednesday November 9, 2005

Filed under: General,Geometry — Tags: , — m759 @ 3:09 pm
In honor of the 120th anniversary
of the birth of Hermann Weyl:

Tuesday, November 8, 2005

Tuesday November 8, 2005

Filed under: General — Tags: — m759 @ 7:59 am

Review:
 
A Constant Idea and
A Constant Idea: 759.

Monday, November 7, 2005

Monday November 7, 2005

Filed under: General — m759 @ 9:00 pm
Butterfly and Wheel

The illustration for the previous entry,

The image “http://www.log24.com/log/pix05B/051107-Aristos2.jpg” cannot be displayed, because it contains errors.

taken from fowlesbooks.com,
suggests more links:

1. To Butterflies and Wheels* (banner below),

The image “http://www.log24.com/log/pix05B/051107-Butt.jpg” cannot be displayed, because it contains errors.

a site that attacks Mary Midgley, and

2. To an AAAS site offering Midgley’s

Evolution as a Religion:
A Comparison of Prophecies

I personally prefer Midgley,
an Oxford-trained philosopher
also known as
Mary, Mary, Quite Contrary.

Related material:
a meditation on the phrase
“crucified on the wheel of time.”

* “Who breaks a Butterfly upon a Wheel?”
— Alexander Pope

Monday November 7, 2005

Filed under: General — m759 @ 2:02 pm
Tick Tick Hash

On Saturday, November 5, 2005,
author John Fowles died.
 

The image “http://www.log24.com/log/pix05B/051107-Aristos.jpg” cannot be displayed, because it contains errors.
From Log24
on the date of
Fowles’ death: 
Coincidence
and Design

Related material:
The Collector and
Speak, Memory

From Log24
on the date of
Fowles’ death:
Contrapuntal
Themes
in a Shadowland

Related material:
The Aristos

“Two years after The Collector had brought him international recognition and a year before he published The Magus, John Fowles set out his ideas on life in The Aristos.  The chief inspiration behind them was the fifth century BC philosopher Heraclitus.  In the world he posited of constant and chaotic flux the supreme good was the Aristos, ‘of a person or thing, the best or most excellent of its kind.'”

— Random House Australia

Monday November 7, 2005

Filed under: General — m759 @ 1:20 am

But seriously…

The image “http://www.log24.com/log/pix05B/051107-Keen.jpg” cannot be displayed, because it contains errors. “Sir Frederick Gray, Minister of Defence, is a dignified, upper-class gentleman who is well respected in intelligence circles. However for most of his appearances, Gray is a strict by-the-book person who plays it seriously at all times. Consequently he despises Bond’s playful attitude towards life and his disregard to take his missions seriously.”

— jamesbondmm.co.uk

Geoffrey Keen, who played Sir Frederick Gray in six James Bond films, died on November 3, 2005.

Related material:

The Log24 entry of 11:07 AM on the date of Keen’s death, and the five Log24 entries ending on January 20, 2005.

Sunday, November 6, 2005

Sunday November 6, 2005

Filed under: General — m759 @ 10:00 pm

x

Sunday November 6, 2005

Filed under: General — m759 @ 10:30 am

For Mike Nichols,
whose birthday is today:

Angels in Arabia

Yesterday’s entries discussed an angel and a fugue; this suggests Clive Barker’s classic tale Weaveworld, which in turn suggests the following links:

1.  the Log24 archive,
     Aug. 1-6, 2005, and

2.  C. S. Lewis, George Orwell, and
     the Corruption of Language,

an essay at the website of
St. Christopher’s Cathedral
in Bahrain, Arabia.

Nichols, who is Jewish, may of course prefer the following remark of comedian Sarah Silverman:

“I wear this St. Christopher medal sometimes because– I’m Jewish, but my boyfriend is Catholic– it was cute the way he gave it to me. He said if it doesn’t burn through my skin it will protect me.”

Saturday, November 5, 2005

Saturday November 5, 2005

Filed under: General,Geometry — Tags: , , — m759 @ 4:24 pm

Contrapuntal Themes
in a Shadowland
 
(See previous entry.)

Douglas Hofstadter on his magnum opus:

"… I realized that to me, Gödel and Escher and Bach were only shadows cast in different directions by some central solid essence. I tried to reconstruct the central object, and came up with this book."

The image “http://www.log24.com/theory/images/GEBcover.jpg” cannot be displayed, because it contains errors.
Hofstadter's cover

Here are three patterns,
"shadows" of a sort,
derived from a different
"central object":

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

For details, see
Solomon's Cube.

Related material:
The reference to a
"permutation fugue"
(pdf) in an article on
Gödel, Escher, Bach.

Saturday November 5, 2005

Filed under: General — m759 @ 12:06 pm
Coincidence
and Design

Headline from a local newspaper this morning:

Area Catholics Receive
St. Thomas Aquinas Awards
 

Headline from today’s New York Times:

Closing Arguments Made
in Trial on Intelligent Design 

Taken together, these headlines suggest that the following link (pdf) may be appropriate for today:

Neutral Evolution
and Aesthetics:
Vladimir Nabokov
and Insect Mimicry.

Related material
on Nabokov and theology:

A Contrapuntal Theme

Today’s birthday:

The image “http://www.log24.com/log/pix05B/051105-Swinton2.jpg” cannot be displayed, because it contains errors.

Tilda Swinton,
angel in
“Constantine.”

“Gnostic also is the preposterous stage-direction at the end of Elizabeth Barrett Browning’s Drama of Exile…

The stars shine on brightly while ADAM and EVE pursue their way into the far wilderness. There is a sound through the silence, as of the falling tears of an angel.

‘How much noise,’ inquires G. K. Chesterton with brutal common sense, ‘is made by an angel’s tears? Is it a sound of emptied buckets, or of mountain cataracts?'”

— Dorothy Sayers,
   The Mind of the Maker, Chapter 10

For the answer, see

A Contrapuntal Theme.

Thursday, November 3, 2005

Thursday November 3, 2005

Filed under: General — m759 @ 11:07 am

Bond

USA Today on last night’s White House dinner:

“In his toast, Bush said the royal visit was ‘a reminder of the unique and enduring bond’ between the two countries.”

From Log24, July 18, 2003:

The use of the word “idea” in my entries’ headlines yesterday was not accidental.  It is related to an occurrence of the word in Understanding: On Death and Truth, a set of journal entries from May 9-12.  The relevant passage on “ideas” is quoted there, within commentary by an Oberlin professor:

“That the truth we understand must be a truth we stand under is brought out nicely in C. S. Lewis’ That Hideous Strength when Mark Studdock gradually learns what an ‘Idea’ is. While Frost attempts to give Mark a ‘training in objectivity’ that will destroy in him any natural moral sense, and while Mark tries desperately to find a way out of the moral void into which he is being drawn, he discovers what it means to under-stand.

‘He had never before known what an Idea meant: he had always thought till now that they were things inside one’s own head. But now, when his head was continually attacked and often completely filled with the clinging corruption of the training, this Idea towered up above him-something which obviously existed quite independently of himself and had hard rock surfaces which would not give, surfaces he could cling to.’

This too, I fear, is seldom communicated in the classroom, where opinion reigns supreme. But it has important implications for the way we understand argument.”

— “On Bringing One’s Life to a Point,” by Gilbert Meilaender, First Things, November 1994

The old philosophical conflict between realism and nominalism can, it seems, have life-and-death consequences.  I prefer Plato’s realism, with its “ideas,” such as the idea of seven-ness.  A reductio ad absurdum of nominalism may be found in the Stanford Encyclopedia of Philosophy under Realism:

“A certain kind of nominalist rejects the existence claim which the platonic realist makes: there are no abstract objects, so sentences such as ‘7 is prime’ are false….”

The claim that 7 is not prime is, regardless of its motives, dangerously stupid.

The New York Lottery evening number
for All Souls’ Day, Nov. 2, 2005, was

007.

Related material:

Entries for Nov. 1, 2005 and
the song Planned Obsolescence
by the 10,000 Maniacs

(Hope Chest:
The Fredonia Recordings)

Wednesday, November 2, 2005

Wednesday November 2, 2005

Filed under: General — Tags: — m759 @ 3:24 pm

To Serve Man

The image “http://www.log24.com/log/pix05B/051102-Remains2.jpg” cannot be displayed, because it contains errors.

Starring
Sir Anthony Hopkins
as Smithers
(See previous entry.)

In memory of Lloyd Bochner,
who died on Oct. 29, 2005:

"In his most memorable television role, Mr. Bochner starred as Michael Chambers in the famous 1962 'Twilight Zone' episode 'To Serve Man.' Chambers and his assistant are decoding experts in charge of translating a book given to Earth by visiting extraterrestrials. The assistant learns that it is a cookbook, but is too late to save Mr. Bochner's character from boarding a spaceship and heading toward becoming an alien meal."

— Monica Potts in today's New York Times

Wednesday November 2, 2005

Filed under: General — m759 @ 1:00 pm

All Souls’ Day

Malcolm Lowry, Under the Volcano:

“… Let me see, he was only praelector in my time….”
   “He was still praelector in mine.”
   (In my time?… But what, exactly, does that mean?….)
….
   “He was beginning to get the wines and the first editions slightly mixed up in my day.”….
   “Bring me a bottle of the very best John Donne, will you, Smithers?… You know, some of the genuine old 1611.”
   “God how funny… Or isn’t it?….”

In memory of Malcolm Lowry, a quotation from Donne, 1611:

And, Oh, it can no more be questioned,
That beauties best, proportion, is dead,
Since euen griefe it selfe, which now alone
Is left vs, is without proportion.
Shee by whose lines proportion should bee
Examin’d measure of all Symmetree,
Whom had the Ancient seene, who thought soules made
Of Harmony, he would at next haue said
That Harmony was shee, and thence infer.
That soules were but Resultances from her,

Here is a link to a later Cambridge praelector, Robert Alexander Rankin.  Rankin, a purveyor of pure mathematics, may help to counteract the pernicious influence on souls of Sir Michael Atiyah (see previous two entries and Plato, Pegasus, and the Evening Star).

Tuesday, November 1, 2005

Tuesday November 1, 2005

Filed under: General,Geometry — Tags: , , — m759 @ 9:00 pm
The image “http://www.log24.com/log/pix05B/051101-Seal.gif” cannot be displayed, because it contains errors.

 

The above seal is from an ad (pdf) for an Oct. 21 lecture, "The Nature of Space," by Sir Michael Atiyah, sponsored by the American Mathematical Society.

The picture in the seal is of Plato's Academy.

"The great philosopher Plato excluded from his Academy anyone who had not studied geometry.  He would have been delighted to admit Sir Michael Atiyah, who was for a time Savilian Professor of Geometry at Oxford…"


Would he?

Sir Michael Atiyah's
Anti-Platonism

"Mathematics is an evolution from the human brain, which is responding to outside influences, creating the machinery with which it then attacks the outside world. It is our way of trying to reduce complexity into simplicity, beauty and elegance….

I tend to think that science and mathematics are ways the human mind looks and experiences– you cannot divorce the human mind from it. Mathematics is part of the human mind. The question whether there is a reality independent of the human mind, has no meaning– at least, we cannot answer it."

— Sir Michael Atiyah, interview in Oslo, May 2004

"For Plato, the Forms represent truth, or reality…. these Forms are independent of the mind: they are eternal, unchanging and perfect."

—  Roy Jackson (pdf)

Atiyah's denial of a reality independent of the human mind may have something to do with religion:

"Socrates and Plato were considered 'Christians before Christ'; they paved the way for the coming of Christianity by providing it with philosophical and theoretical foundations that would be acceptable to the western mind.
    In the analogy of the cave, the sun represents the Form of the Good. In the same way that the sun is the source of all things and gives light to them, the Form of the Good is over and above the other Forms, giving them light and allowing us to perceive them. Therefore, when you have awareness of the Form of the Good you have achieved true enlightenment. In Christianity, the Form of the Good becomes God: the source of all things."

— Roy Jackson, The God of Philosophy (pdf)

See also the previous entry.

Tuesday November 1, 2005

Filed under: General — Tags: , , — m759 @ 12:00 pm

Antidote to Atiyah

In a recent talk, "The Nature of Space," Sir Michael Atiyah gave a misleading description of Plato's doctrine of "ideas," or "idealism."  Atiyah said that according to Plato, ideas reside in  "an imaginary world–  the world of the mind," and that what we see in the external world is "some pale reflection" of ideas in the mind.

An antidote to Atiyah's nonsense may be found in the Catholic Encyclopedia:

"So it came to pass that the word idea in various languages took on more and more the meaning of 'representation,' 'mental image,' and the like. Hence too, there was gradually introduced the terminology which we find in the writings of Berkeley, and according to which idealism is the doctrine that ascribes reality to our ideas, i.e. our representations, but denies the reality of the physical world. This sort of idealism is just the reverse of that which was held by the philosophers of antiquity and their Christian successors; it does away with the reality of ideal principles by confining them exclusively to the thinking subject; it is a spurious idealism…."

Atiyah contrasts his mistaken view of Plato with what he calls the "realism" of Hume.  He does not mention that Plato's doctrine of ideas is also known as "realism."  For details, see, again, the Catholic Encyclopedia:

"The conciliation of the one and the many, the changing and the permanent, was a favourite problem with the Greeks; it leads to the problem of universals. The typical affirmation of Exaggerated Realism, the most outspoken ever made, appears in Plato's philosophy; the real must possess the attributes of necessity, universality, unity, and immutability which are found in our intellectual representations. And as the sensible world contains only the contingent, the particular, the unstable, it follows that the real exists outside and above the sensible world. Plato calls it eîdos, idea. The idea is absolutely stable and exists by itself (ontos on; auta kath' auta), isolated from the phenomenal world, distinct from the Divine and human intellect…. The exaggerated Realism of Plato… is the principal doctrine of his metaphysics."
 
Atiyah's misleading remarks may appeal to believers in the contemptible religion of Scientism, but they have little to do with either historical reality or authentic philosophy.

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