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. 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.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" 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. 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:-- Edward Nelson, Mathematics and Faith (pdf) 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. Posted 11/30/2005 at 8:20 PM |
For St. Andrew's Day
"The miraculous enters....
When we investigate these problems, some fantastic things happen...." A picture of the Miracle Octad Generator, with my comments, is available online. Related material: Posted 11/30/2005 at 1:00 AM |
"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." "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." Posted 11/29/2005 at 12:25 AM |
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.) Posted 11/28/2005 at 1:00 PM |
The Way of the Pilgrim, Part I: For John Bunyan's Birthday 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 Posted 11/28/2005 at 4:00 AM |
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
Heinrich Borchert
Lübsen, 1870
Adolf Sickenberger,
1888
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. What might be the modern version of a "holy geometry book"?
I suggest the following,
first published in 1940:
Posted 11/25/2005 at 9:00 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 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. Posted 11/25/2005 at 3:48 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.
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.
A related item...Thought to accompany the above reading list: "And now I was beginning to surmise: -- 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.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.Posted 11/25/2005 at 2:28 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
|
"And now I was beginning to surmise: -- Hermann Hesse, Magister Ludi
Posted 11/24/2005 at 2:12 PM |
Lyrics by Chris Whitley, who died on Sunday, November 20, 2005: Angels Even devils too Wait to show How far we come To joy Posted 11/24/2005 at 4:00 AM |
Also on Saint Cecilia's Day (Release date: 11/22/2005)... Bright Music Illustrated Reba #1's Reba McEntire Album Length Compact Disc For Reba, a very bright star, the symbol of Venus always shines: Posted 11/23/2005 at 12:00 PM |
For St. Cecilia's Day-- A flashback to June 8, 2004: Dark Music
Illustrated Paul Klee From today's
Critics in Mozart’s age |
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 who also died on Sunday, Nov. 20, with a horse from yesterday's entry.
And his name, that sat on him, was Death. And Hell followed with him." -- Johnny Cash Related material: Log24 entries of Sept. 15, 2003. Posted 11/22/2005 at 4:23 AM |
Picasso's Tragedy: Detail by Lou Myers, 1915-2005 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." "... behold: a pale horse. And his name, that sat on him, was Death. And Hell followed with him." -- Johnny Cash Posted 11/21/2005 at 12:00 PM |
"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
"'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.)
Exercise of Power: Show that a white horse--
a figure not unlike the This horse, or chess knight-- Related material On this date: In 1490, The White Knight the Mexican Revolution began. Illustration: "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.'" Posted 11/20/2005 at 4:04 PM |
x Posted 11/18/2005 at 7:00 PM |
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
Posted 11/18/2005 at 2:56 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: 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.Posted 11/18/2005 at 1:00 AM |
All the King's Men (See also Time and All the King's Horses.) LEAR: Now you better do some thinkin' FOOL: I've always been different For related material, see and last night's winner of the National Book Award
Posted 11/17/2005 at 2:22 PM |
Posted 11/17/2005 at 4:04 AM |
Images "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:
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." Posted 11/16/2005 at 4:04 PM |
Windmills
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:
Kaleidoscope turning... See also the windmill figure in Time and Eternity (Log 24, Feb. 1, 2003) and a review of Fritz Leiber's The Big Time, "a story that works." Posted 11/15/2005 at 11:07 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?'....
Bordered version -- 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 Posted 11/15/2005 at 2:56 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
Posted 11/14/2005 at 3:09 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: See also the previous two entries, Ten is a Hen and Structure, about a mother and child. Posted 11/13/2005 at 10:48 AM |
Structure "Sunrise-- Hast thou a Flag for me?" -- Emily Dickinson From a
Kaleidoscope turning... Related material: Blue Bee Season Halloween Meditations,
"Y'know, I never imagined Posted 11/13/2005 at 6:40 AM |
Ten is a Hen "Follow the spiritual journey that is BEE SEASON." "'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...." Posted 11/12/2005 at 10:00 PM |
Nine is a Vine 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) Posted 11/12/2005 at 9:00 PM |
Seven is Heaven, Eight is a Gate (continued) "... 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 Posted 11/12/2005 at 8:00 PM |
State of Grace
"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 Posted 11/12/2005 at 7:00 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:
See also Cognitive Blending and the Two Cultures, Mathematics and Narrative, Deep Game, and the previous entry. Posted 11/12/2005 at 1:28 PM |
720 in the Book (continued) 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). Posted 11/11/2005 at 3:26 PM |
"... 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.'" The shocking redefinition
(with changes highlighted):
From both old (2001) and
new (2005) Kansas standards: Teaching With Tolerance and Respect 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. Posted 11/10/2005 at 4:00 PM |
Butterfly Effect
From today's online New York Times: John Fowles on two of his novels: "I wanted to show the seeds of an intense future evolution in a particular period." "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:
Posted 11/9/2005 at 7:59 PM |
Posted 11/9/2005 at 3:09 PM |
Review: A Constant Idea and A Constant Idea: 759. Posted 11/8/2005 at 7:59 AM |
Butterfly and Wheel
The illustration for the previous entry, taken from fowlesbooks.com, suggests more links: 1. To Butterflies and Wheels* (banner below), a site that attacks Mary Midgley, and 2. To an AAAS site offering Midgley's
I personally prefer Midgley, Related material: * "Who breaks a Butterfly upon a Wheel?" Posted 11/7/2005 at 9:00 PM |
"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.'" Posted 11/7/2005 at 2:02 PM |
But seriously...
"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." 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. Posted 11/7/2005 at 1:20 AM |
x Posted 11/6/2005 at 10:00 PM |
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." Posted 11/6/2005 at 10:30 AM |
Douglas Hofstadter on his magnum opus: "... I realized that to me, Gödel and Escher and Bach were only shadows cast in different directions by some central solid essence. I tried to reconstruct the central object, and came up with this book." Hofstadter's cover
Here are three patterns,
"shadows" of a sort, derived from a different "central object": For details, see Solomon's Cube. Related material: The reference to a "permutation fugue" (pdf) in an article on Gödel, Escher, Bach. Posted 11/5/2005 at 4:24 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 Related material Today's birthday: Tilda Swinton, "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 Posted 11/5/2005 at 12:06 PM |
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."
The New York Lottery evening number 007. Related material: Entries for Nov. 1, 2005 and (Hope Chest: Posted 11/3/2005 at 11:07 AM |
To Serve Man 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 Posted 11/2/2005 at 3:24 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). Posted 11/2/2005 at 1:00 PM |
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. 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 -- 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. Posted 11/1/2005 at 9:00 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. Posted 11/1/2005 at 12:00 PM |