Wednesday, November 30, 2005 8:20 PM
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
that Peano arithmetic could be flawed. From Kronecker onwards
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"...?!
did Gödel say this? Gödel proved, in fact, according to a
mathematician at Princeton, that (letting PA stand for Peano
"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
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:
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:
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.
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
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
(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
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
-- Posted by Krishna,
11/29/2005 11:46:00 PM,
at his weblog,
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
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)
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)
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 1:00 AM
miraculous enters.... When we investigate these problems, some
fantastic things happen...."
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.
-- John H. Conway and N. J. A. Sloane, Sphere Packings, Lattices
and Groups, preface to first edition (1988)
A picture of the
Miracle Octad Generator, with my comments, is available online.
Tuesday, November 29, 2005 12:25 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
-- 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
Epiphany Term, 1942, C.S. Lewis delivered the Riddell Memorial
Lectures... in.... the University of Durham.... He
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
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
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 1:00 PM
The Way of the Pilgrim,
In a recent Edge article, "The Vagaries of Religious Experience," a Harvard
psychologist, Daniel Gilbert, quotes Einstein on his own
"(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)
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:
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
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
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."
describes "the road to the religious paradise" as "comfortable and
alluring." He might therefore have profited by the book saluted
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
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
Monday, November 28, 2005 4:00 AM
The Way of the Pilgrim,
For John Bunyan's
Click on picture to enlarge.
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?"
Pilgrim's Progress, by John Bunyan
Friday, November 25, 2005 9:00 PM
What was "the holy geometry book" ("das heilige Geometrie-Büchlein," p.
10 in the Schilpp book below) that so impressed the young Albert
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."
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
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
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:
it cannot be said with certainty which book is Einstein’s 'holy
geometry book.' There are three different titles that come into
Theodor Spieker, 1890
der ebenen Geometrie. Mit Übungsaufgaben für höhere Lehranstalten.
Heinrich Borchert Lübsen,
Lehrbuch der ebenen und sphärischen Trigonometrie. Zum
Selbstunterricht. Mit Rücksicht auf die Zwecke des praktischen Lebens.
Adolf Sickenberger, 1888
der elementaren Mathematik.
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
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:
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
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
the tradition of the reform movement, he sought to present everything
in the simplest, most intuitive way possible. He opposed
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
great deal of freedom in the form of presentation because he believed
that a textbook was no more than a crutch for oral instruction.
spoken word, in Sickenberger's view, could infuse life into the dead
forms of the printed text. Too often, he insisted in the preface
his text, mathematics was seen and valued 'as the pure science of
reason.' In reality, he continued, mathematics was also 'an
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
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
homogeneous, first-order equations with three unknowns he specified
determinants and determinant algebra. Then he went on to
equations and logarithms. In the second part of his book,
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.'
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
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
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
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
is that of Einstein's father's brother Jakob, a business partner and
member of Einstein's household in Ulm and Munich. He presented
books to his nephew Albert. A fourth book in Miss Dukas's
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
has recently identified Heis and Eschweiler's text as the geometry book
that made such an impression on Einstein. Yet, assuming that
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
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
Click on picture for details.
Friday, November 25, 2005 3:48 PM
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
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....
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.
Even devils too
Wait to show
How far we come
-- 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
Augusto Pinochet (see previous entry) in the afterlife.
Related material: Art Wars and The Crimson
Friday, November 25, 2005 2:28 PM
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
for William F. Buckley, Jr.
- Joyce and
Aquinas (Yale Studies in English)
- God and Man in
- Modern Literature and the Sense
- Three Young Men in Rebellion
- James Joyce: Unfacts, Fiction, and
- Yeats and the Human Body
- 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.
A related item...
Thought to accompany the above reading list:
"And now I was beginning to surmise:
Here was the library of Paradise."
-- Hermann Hesse, Magister
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,
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 3:33 PM
In memory of Diego
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.
Pictures of the Rockefeller Center mural,
"Man at the
Rivera's re-creation of the mural,
Controller of the Universe."
See also another treatment of the "Man at the Crossroads" theme--
Thursday, November 24, 2005 4:00 AM
-- "To Joy
(Revolution of the Innocents)" --
mp3 and lyrics.
Wednesday, November 23, 2005 12:00 PM
Also on Saint Cecilia's Day
(Release date: 11/22/2005)...
Album Length Compact Disc
a very bright star,
the symbol of Venus
Tuesday, November 22, 2005 3:09 PM
For St. Cecilia's Day--
A flashback to June 8, 2004:
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 Bavarian Don
1919, watercolor and ink
There's a little black spot
on the sun today....
Tuesday, November 22, 2005 4:23 AM
From yesterday's New
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
Below: cartoonist Lou Myers,
I want a shot at redemption
Don't want to end up a cartoon
In a cartoon graveyard
-- Paul Simon
who also died on Sunday, Nov. 20,
with a horse from yesterday's entry.
"... and behold: a pale horse.
And his name, that sat on him,
was Death. And Hell
followed with him."
-- Johnny Cash
Log24 entries of
Sept. 15, 2003.
Monday, November 21, 2005 12:00 PM
Myers died yesterday,
the 30th anniversary
of the death of
For the source of
the above picture,
Original caption of cartoon
from which the above picture
"Picasso's tragedy was that
he was an artist who
ran out of new things
"... behold: a pale horse.
And his name,
that sat on him,
was Death. And Hell
followed with him."
-- Johnny Cash
Sunday, November 20, 2005 4:04 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
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
(Click on the box
Exercise of Power:
Show that a white horse--
a figure not unlike the
symbol of the mathematics
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).
On this date:
In 1490, The White Knight
(Tirant lo Blanc )--
a major influence on Cervantes--
was published, and in 1910
Zapata by Diego Rivera,
Museum of Modern Art,
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
Friday, November 18, 2005 2:56 AM
still the same old story,
a fight for love and...
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
On The Last Battle, a
book in the Narnia series by C. S. Lewis:
there is much glory in this wonderfully written apocalypse.
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.'
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"--
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
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 1:00 AM
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.
Thursday, November 17, 2005 2:22 PM
Thursday, November 17, 2005 4:04 AM
Wednesday, November 16, 2005 4:04 PM
"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...."
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."