"Don't solicit for your sister, it's not nice . . ." — The late Tom Lehrer.
"The pleasure comes from the illusion"
— André Weil in 1940, quoted here on the dies natalis of Elizabeth II.
"Don't solicit for your sister, it's not nice . . ." — The late Tom Lehrer.
"The pleasure comes from the illusion"
— André Weil in 1940, quoted here on the dies natalis of Elizabeth II.
The phrase "Herald of the Apocalypse" from a New York Times
opinion piece of May 15 suggests a flashback . . .
Wednesday, April 23, 2014
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* A reference to song lyrics cited in a Bluesky post.
From the previous post, "The Large Language Model,"
a passage from Wikipedia —
"… sometimes large models undergo a 'discontinuous phase shift'
where the model suddenly acquires substantial abilities not seen
in smaller models. These are known as 'emergent abilities,' and
have been the subject of substantial study." — Wikipedia
Compare and contrast
this with the change undergone by a "small space model,"
that of the finite affine 4-space A with 16 points (a Galois tesseract ),
when it is augmented by an eight-point "octad." The 30 eight-point
hyperplanes of A then have a natural extension within the new
24-point set to 759 eight-point octads, and the 322,560 affine
automorphisms of the space expand to the 244,823,040 Mathieu
automorphisms of the 759-octad set — a (5, 8, 24) Steiner system.
For a visual analogue of the enlarged 24-point space and some remarks
on analogy by Simone Weil's brother, a mathematician, see this journal
on September 8 and 9, 2022.
From a post of October 25, 2002 —
"A work of art has an author and yet,
when it is perfect, it has something
which is essentially anonymous about it."
— Simone Weil, Gravity and Grace
This flashback was suggested by a quotation
in today's previous post —
"Go back to the darkest roots of civilisation
and you will find them knotted round
some sacred stone or encircling
some sacred well."
— G. K. Chesterton, Orthodoxy , Ch. 5 —
"The Flag of the World."
A post of May 26, 2005, displays, if not the sword,
a place for it —
"The beautiful in mathematics resides in contradiction.
Incommensurability, logoi alogoi, was the first splendor
in mathematics." — Simone Weil, Oeuvres Choisies,
éd. Quarto , Gallimard, 1999, p. 100
Logos Alogos by S. H. Cullinane
"To a mathematician, mathematical entities have their own existence,
they habitate spaces created by their intention. They do things,
things happen to them, they relate to one another. We can imagine
on their behalf all sorts of stories, providing they don't contradict
what we know of them. The drama of the diagonal, of the square…"
— Dennis Guedj, abstract of "The Drama of Mathematics," a talk
to be given this July at the Mykonos conference on mathematics and
narrative. For the drama of the diagonal of the square, see
In Memoriam:
See also, from posts now tagged Abyssus, a quote from Simone Weil —
"Adam and Eve sought for divinity in vital energy —
in a tree, a fruit. But it is prepared for us on some
dead wood, geometrically squared, upon which
hangs a corpse."
A Web search for "diamond pivot bright" yields . . .
An "irrational image" from Log24 (Nov. 26, 2002) —
"The beautiful in mathematics resides in contradiction.
Incommensurability, logoi alogoi , was the first splendor
in mathematics."
— Simone Weil, Oeuvres Choisies ,
éd. Quarto, Gallimard, 1999, p. 100
"Simone Weil said that morality
was a matter of attention not of will.
We need a new vocabulary of attention."
— Iris Murdoch, "Against Dryness"
… A Scottish Play suggested by …
"The Hegel action is applied to understand creative processes
in two classical compositions — Beethoven’s Hammerklavier
Sonata op. 106, and Liszt’s Mephisto Walzer — but also to
the creation of a small model composition."
— From the abstract of "Hegel’s Conceptual
Group Action on Creative Dynamics in Music," by
Guerino Mazzola and Maria Mannone
http://toomuchhorrorfiction.blogspot.com/
2014/04/go-waltzing-mephisto-with-me.html
Wednesday, April 23, 2014
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Illustration —

In memory of Peter Drummond-Murray, two readings:
The Beauty that Saves and The Trials of Device.
Drummond-Murray reportedly died at 84 on April 13,
Palm Sunday. The Telegraph describes him:
“A big, grim-faced man with a dour wit,
Drummond-Murray resembled some rugged
Jacobite from a novel by Sir Walter Scott.”
Or Sydney Greenstreet.
“The stuff that dreams are made of.” — The Maltese Falcon
Yesterday's 11 AM post Mad Day concluded
with a link to a 2001 American Mathematical Society
article by Pierre Cartier that sums up the religion and
politics of many mathematicians…
"Here ends the infancy narrative of the gospel…."
"… while Simone Weil's Catholicism was violently
anti-Semitic (in 1942!), Grothendieck's Buddhism
bears a strong resemblance to the practices of
his Hasidic ancestors."
See also Simone Weil in this journal.
Note esp. a post of April 6, 2004 that provides
a different way of viewing Derrida's notion of
inscription .
A meditation suggested by the April 20 post Complex Reflection
and by the life and April 20 death of a scientist who worked
at Los Alamos (home of the Monte Carlo method) and at
the Santa Fe Institute (home of complexity theory).

A search for 286 in this journal yields "Yet Another Cartoon Graveyard."
That June 1, 2008, post linked to poem 286 in a 1919 anthology.
Here is that poem, together with poem 823.
Together, these poems may be regarded as a meditation on
Simone Weil and her brother André Weil or,
more abstractly, on Love and Death.
Happy birthday to Al Pacino.
"My work is motivated by a hope that there may be a way to recapture the ancient and medieval vision of both Beauty and purpose in a way which is relevant to our own century. I even dare to hope that the two ideas may be related, that Beauty is actually part of the meaning and purpose of life."
"The Reverend T. P. Kirkman knew in 1862 that there exists a group of degree 16 and order 322560 with a normal, elementary abelian, subgroup of order 16 [1, p. 108]. Frobenius identified this group in 1904 as a subgroup of the Mathieu group M24 [4, p. 570]…."
1. Biggs N.L., "T. P. Kirkman, Mathematician," Bulletin of the London Mathematical Society 13, 97–120 (1981).
4. Frobenius G., "Über die Charaktere der mehrfach transitiven Gruppen," Sitzungsber. Königl. Preuss. Akad. Wiss. zu Berlin, 558–571 (1904). Reprinted in Frobenius, Gesammelte Abhandlungen III (J.-P. Serre, editor), pp. 335–348. Springer, Berlin (1968).
Olli Pottonen, "Classification of Steiner Quadruple Systems" (Master's thesis, Helsinki, 2005)–
"The concept of group actions is very useful in the study of isomorphisms of combinatorial structures."
"Simplify, simplify."
— Thoreau
"Beauty is bound up
with symmetry."
— Weyl
Pottonen's thesis is
dated Nov. 16, 2005.
For some remarks on
images and theology,
see Log24 on that date.
Click on the above image
for some further details.
The conclusion of yesterday’s commentary on the May 30-31 Pennsylvania Lottery numbers:
Thomas Pynchon, Gravity’s Rainbow:
“The fear balloons again inside his brain. It will not be kept down with a simple Fuck You…. A smell, a forbidden room, at the bottom edge of his memory. He can’t see it, can’t make it out. Doesn’t want to. It is allied with the Worst Thing.
He knows what the smell has to be: though according to these papers it would have been too early for it, though he has never come across any of the stuff among the daytime coordinates of his life, still, down here, back here in the warm dark, among early shapes where the clocks and calendars don’t mean too much, he knows that’s what haunting him now will prove to be the smell of Imipolex G.
Then there’s this recent dream he is afraid of having again. He was in his old room, back home. A summer afternoon of lilacs and bees and
286”
What are we to make of this enigmatic 286? (No fair peeking at page 287.)
One possible meaning, given The Archivist‘s claim that “existence is infinitely cross-referenced”–
Page 286 of Ernest G. Schachtel, Metamorphosis: On the Conflict of Human Development and the Psychology of Creativity (first published in 1959), Hillsdale NJ and London, The Analytic Press, 2001 (chapter– “On Memory and Childhood Amnesia”):
“Both Freud and Proust speak of the autobiographical [my italics] memory, and it is only with regard to this memory that the striking phenomenon of childhood amnesia and the less obvious difficulty of recovering any past experience may be observed.”
The concluding “summer afternoon of lilacs and bees” suggests that 286 may also be a chance allusion to the golden afternoon of Disney’s Alice in Wonderland. (Cf. St. Sarah’s Day, 2008)
Some may find the Disney afternoon charming; others may see it as yet another of Paul Simon’s dreaded cartoon graveyards.
More tastefully, there is poem 286 in the 1919 Oxford Book of English Verse– “Love.”
For a midrash on this poem, see Simone Weil, who became acquainted with the poem by chance:
“I always prefer saying chance rather than Providence.”
— Simone Weil, letter of about May 15, 1942
Weil’s brother André might prefer Providence (source of the Bulletin of the American Mathematical Society.)
(Photo from Providence)

For more on the mathematical significance of this figure, see (for instance) Happy Birthday, Hassler Whitney, and Combinatorics of Coxeter Groups, by Anders Björner and Francesco Brenti, Graduate Texts in Mathematics, vol. 231, Springer, New York, 2005.
This book is reviewed in the current issue (July 2008) of the above-mentioned Providence Bulletin.
The review in the Bulletin discusses reflection groups in continuous spaces.
Something Anonymous
Nineteenth-century quilt design:
Related material:

Happy birthday, George:

Sources:
Salute to Anthony Hopkins,
May 3, May 4, May 5
Today’s Wizard of Id
Judeo-Christian Heritage:
The Wiener Kreis
André Weil As I Knew Him,
by Goro Shimura (pdf)
Related material:
Born on this date
100 years ago:
André Weil
“… just as God defeats the devil:
this bridge exists….”
— André Weil
“… I always prefer saying chance
rather than Providence….”
— Simone Weil
"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."
Click on pictures for details.
See also Windmills and
Verbum sat sapienti?
as well as
at Calvin College
on Simone Weil,
Charles Williams,
Dante, and
"the way of images."
— Billy Graham Evangelistic Association,
according to messiahpage.com
"… just as God defeats the devil:
this bridge exists;
it is the theory of the field
of algebraic functions over
a finite field of constants
(that is to say, a finite number
of elements: also said to be a Galois
field, or earlier 'Galois imaginaries'
because Galois first defined them
and studied them….)"
— André Weil, 1940 letter to his sister,
Simone Weil, alias Simone Galois
(see previous entry)
Related material:
Billy Graham and the City:
A Later Look at His Words
— New York Times, June 24, 2005
Logos Alogos
by S. H. Cullinane
"To a mathematician, mathematical entities have their own existence, they habitate spaces created by their intention. They do things, things happen to them, they relate to one another. We can imagine on their behalf all sorts of stories, providing they don't contradict what we know of them. The drama of the diagonal, of the square…"
— Dennis Guedj, abstract of "The Drama of Mathematics," a talk to be given this July at the Mykonos conference on mathematics and narrative.
For the drama of the diagonal of the square, see
Ideas and Art, Part III
The first idea was not our own. Adam
In Eden was the father of Descartes…
— Wallace Stevens, from
Notes Toward a Supreme Fiction
"Quaedam ex his tanquam rerum imagines sunt, quibus solis proprie convenit ideae nomen: ut cùm hominem, vel Chimaeram, vel Coelum, vel Angelum, vel Deum cogito."
— Descartes, Meditationes III, 5
"Of my thoughts some are, as it were, images of things, and to these alone properly belongs the name idea; as when I think [represent to my mind] a man, a chimera, the sky, an angel or God."
— Descartes, Meditations III, 5
Begin, ephebe, by perceiving the idea
Of this invention, this invented world,
The inconceivable idea of the sun.
You must become an ignorant man again
And see the sun again with an ignorant eye
And see it clearly in the idea of it.
— Wallace Stevens, from
Notes Toward a Supreme Fiction
"… Quinimo in multis saepe magnum discrimen videor deprehendisse: ut, exempli causâ, duas diversas solis ideas apud me invenio, unam tanquam a sensibus haustam, & quae maxime inter illas quas adventitias existimo est recensenda, per quam mihi valde parvus apparet, aliam verò ex rationibus Astronomiae desumptam, hoc est ex notionibus quibusdam mihi innatis elicitam, vel quocumque alio modo a me factam, per quam aliquoties major quàm terra exhibetur; utraque profecto similis eidem soli extra me existenti esse non potest, & ratio persuadet illam ei maxime esse dissimilem, quae quàm proxime ab ipso videtur emanasse."
— Descartes, Meditationes III, 11
"… I have observed, in a number of instances, that there was a great difference between the object and its idea. Thus, for example, I find in my mind two wholly diverse ideas of the sun; the one, by which it appears to me extremely small draws its origin from the senses, and should be placed in the class of adventitious ideas; the other, by which it seems to be many times larger than the whole earth, is taken up on astronomical grounds, that is, elicited from certain notions born with me, or is framed by myself in some other manner. These two ideas cannot certainly both resemble the same sun; and reason teaches me that the one which seems to have immediately emanated from it is the most unlike."
— Descartes, Meditations III, 11
"Et quamvis forte una idea ex aliâ nasci possit, non tamen hîc datur progressus in infinitum, sed tandem ad aliquam primam debet deveniri, cujus causa sit in star archetypi, in quo omnis realitas formaliter contineatur, quae est in ideâ tantùm objective."
— Descartes, Meditationes III, 15
"And although an idea may give rise to another idea, this regress cannot, nevertheless, be infinite; we must in the end reach a first idea, the cause of which is, as it were, the archetype in which all the reality [or perfection] that is found objectively [or by representation] in these ideas is contained formally [and in act]."
— Descartes, Meditations III, 15
Michael Bryson in an essay on Stevens's "Notes Toward a Supreme Fiction,"
The Quest for the Fiction of the Absolute:
"Canto nine considers the movement of the poem between the particular and the general, the immanent and the transcendent: "The poem goes from the poet's gibberish to / The gibberish of the vulgate and back again. / Does it move to and fro or is it of both / At once?" The poet, the creator-figure, the shadowy god-figure, is elided, evading us, "as in a senseless element." The poet seeks to find the transcendent in the immanent, the general in the particular, trying "by a peculiar speech to speak / The peculiar potency of the general." In playing on the senses of "peculiar" as particular and strange or uncanny, these lines play on the mystical relation of one and many, of concrete and abstract."
Brian Cronin in Foundations of Philosophy:
"The insight is constituted precisely by 'seeing' the idea in the image, the intelligible in the sensible, the universal in the particular, the abstract in the concrete. We pivot back and forth between images and ideas as we search for the correct insight."
— From Ch. 2, Identifying Direct Insights
Michael Bryson in an essay on Stevens's "Notes Toward a Supreme Fiction":
"The fourth canto returns to the theme of opposites. 'Two things of opposite natures seem to depend / On one another . . . . / This is the origin of change.' Change resulting from a meeting of opposities is at the root of Taoism: 'Tao produced the One. / The One produced the two. / The two produced the three. / And the three produced the ten thousand things' (Tao Te Ching 42) …."
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From an entry of March 7, 2004:
From the web page
Introduction to the I Ching– "He who has perceived the meaning of change fixes his attention no longer on transitory individual things but on the immutable, eternal law at work in all change. This law is the tao of Lao-tse, the course of things, the principle of the one in the many. That it may become manifest, a decision, a postulate, is necessary. This fundamental postulate is the 'great primal beginning' of all that exists, t'ai chi — in its original meaning, the 'ridgepole.' Later Chinese philosophers devoted much thought to this idea of a primal beginning. A still earlier beginning, wu chi, was represented by the symbol of a circle. Under this conception, t'ai chi was represented by the circle divided into the light and the dark, yang and yin,
This symbol has also played a significant part in India and Europe. However, speculations of a gnostic-dualistic character are foreign to the original thought of the I Ching; what it posits is simply the ridgepole, the line. With this line, which in itself represents oneness, duality comes into the world, for the line at the same time posits an above and a below, a right and left, front and back-in a word, the world of the opposites." The t'ai chi symbol is also illustrated on the web page Cognitive Iconology, which says that
"W.J.T. Mitchell calls 'iconology' A variation on the t'ai chi symbol appears in a log24.net entry for March 5:
The Line, See too my web page Logos and Logic, which has the following:
Logos Alogos, In the conclusion of Section 3, Canto X, of "Notes," Stevens says
This is the logoi alogoi of Simone Weil. |
In "Notes toward a Supreme Fiction,"
Wallace Stevens lists three criteria
for a work of the imagination:
It Must Be Abstract

The Line,
by S.H. Cullinane
It Must Change
It Must Give Pleasure
Related material:
Ridgepole
CBS News Sunday Morning today had a ridgepole ceremony for a house that was moved from China to Salem, Massachusetts.
From the web page
Introduction to the I Ching–
By Richard Wilhelm:
"He who has perceived the meaning of change fixes his attention no longer on transitory individual things but on the immutable, eternal law at work in all change. This law is the tao of Lao-tse, the course of things, the principle of the one in the many. That it may become manifest, a decision, a postulate, is necessary. This fundamental postulate is the 'great primal beginning' of all that exists, t'ai chi — in its original meaning, the 'ridgepole.' Later Chinese philosophers devoted much thought to this idea of a primal beginning. A still earlier beginning, wu chi, was represented by the symbol of a circle. Under this conception, t'ai chi was represented by the circle divided into the light and the dark, yang and yin,
.
This symbol has also played a significant part in India and Europe. However, speculations of a gnostic-dualistic character are foreign to the original thought of the I Ching; what it posits is simply the ridgepole, the line. With this line, which in itself represents oneness, duality comes into the world, for the line at the same time posits an above and a below, a right and left, front and back-in a word, the world of the opposites."
The t'ai chi symbol is also illustrated on the web page Cognitive Iconology, which says that
"W.J.T. Mitchell calls 'iconology' a study of the 'logos' (the words, ideas, discourse, or 'science') of 'icons' (images, pictures, or likenesses). It is thus a 'rhetoric of images' (Iconology: Image, Text, Ideology, p. 1)."
A variation on the t'ai chi symbol appears in a log24.net entry for March 5:
The Line,
by S. H. Cullinane
See too my web page Logos and Logic, which has the following:
"The beautiful in mathematics resides in contradiction. Incommensurability, logoi alogoi, was the first splendor in mathematics."
— Simone Weil, Oeuvres Choisies, éd. Quarto, Gallimard, 1999, p. 100
Logos Alogos,
by S. H. Cullinane
In the conclusion of Section 3, Canto X, of "Notes," Stevens says
"They will get it straight one day
at the Sorbonne.
We shall return at twilight
from the lecture
Pleased that
the irrational is rational…."
This is the logoi alogoi of Simone Weil.
Postmodern
Postmortem
“I had a lot of fun with this audacious and exasperating book. … [which] looks more than a little like Greil Marcus’s Lipstick Traces, a ‘secret history’ tracing punk rock through May 1968….”
— Michael Harris, Institut de Mathématiques de Jussieu, Université Paris 7, review of Mathematics and the Roots of Postmodern Thought, by Vladimir Tasic, Notices of the American Mathematical Society, August 2003
For some observations on the transgressive predecessors of punk rock, see my entry Funeral March of July 26, 2003 (the last conscious day in the life of actress Marie Trintignant — see below), which contains the following:
“Sky is high and so am I,
If you’re a viper — a vi-paah.”
— The Day of the Locust,
by Nathanael West (1939)
As I noted in another another July 26 entry, the disease of postmodernism has, it seems, now infected mathematics. For some recent outbreaks of infection in physics, see the works referred to below.
“Postmodern Fields of Physics: In his book The Dreams of Reason, H. R. Pagels focuses on the science of complexity as the most outstanding new discipline emerging in recent years….”
— “The Semiotics of ‘Postmodern’ Physics,” by Hans J. Pirner, in Symbol and Physical Knowledge: The Conceptual Structure of Physics, ed. by M. Ferrari and I.-O. Stamatescu, Springer Verlag, August 2001
For a critical look at Pagels’s work, see Midsummer Eve’s Dream. For a less critical look, see The Marriage of Science and Mysticism. Pagels’s book on the so-called “science of complexity” was published in June 1988. For more recent bullshit on complexity, see
The Critical Idiom of Postmodernity and Its Contributions to an Understanding of Complexity, by Matthew Abraham, 2000,
which describes a book on complexity theory that, besides pronouncements about physics, also provides what “could very well be called a ‘postmodern ethic.’ “
The book reviewed is Paul Cilliers’s Complexity and Postmodernism: Understanding Complex Systems.
A search for related material on Cilliers yields the following:
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Janis Joplin, Postmodernist ” …’all’ is ‘one,’ … the time is ‘now’ and … ‘tomorrow never happens,’ …. as Janis Joplin says, ‘it’s all the same fucking day.’ It appears that ‘time,’ … the linear, independent notion of ‘time’ that our culture embraces, is an artifact of our abstract thinking … The problem is that ‘tomorrow never happens’ …. Aboriginal traditionalists are well aware of this topological paradox and so was Janis Joplin. Her use of the expletive in this context is therefore easy to understand … love is never having to say ‘tomorrow.’ “ |
“That’s the dumbest thing I ever heard.”
— Ryan O’Neal in “What’s Up, Doc?”
A more realistic look at postmodernism in action is provided by the following news story:
| Brutal Death of an Actress Is France’s Summertime Drama
By JOHN TAGLIABUE The actress, Marie Trintignant, died Friday [Aug. 1, 2003] in a Paris hospital, with severe head and face injuries. Her rock star companion, Bertrand Cantat, is confined to a prison hospital…. According to news reports, Ms. Trintignant and Mr. Cantat argued violently in their hotel room in Vilnius in the early hours of [Sunday] July 27 at the end of a night spent eating and drinking…. In coming months, two films starring Ms. Trintignant are scheduled to debut, including “Janis and John” by the director Samuel Benchetrit, her estranged husband and the father of two of her four children. In it, Ms. Trintignant plays Janis Joplin. |
” ‘…as a matter of fact, as we discover all the time, tomorrow never happens, man. It’s all the same f…n’ day, man!’ –Janis Joplin, at live performance in Calgary on 4th July 1970 – exactly four months before her death. (apologies for censoring her exact words which can be heard on the ‘Janis Joplin in Concert’ CD)”
— Janis Joplin at FamousTexans.com
All of the above fits in rather nicely with the view of science and scientists in the C. S. Lewis classic That Hideous Strength, which I strongly recommend.
For those few who both abhor postmodernism and regard the American Mathematical Society Notices

as a sort of “holy place” of Platonism, I recommend a biblical reading–
Matthew 24:15, CEV:
“Someday you will see that Horrible Thing in the holy place….”
See also Logos and Logic for more sophisticated religious remarks, by Simone Weil, whose brother, mathematician André Weil, died five years ago today.
Symmetries…. May 15, 1998
The following journal note, from the day after Sinatra died, was written before I heard of his death. Note particularly the quote from Rilke. Other material was suggested, in part, by Alasdair Gray's Glasgow novel 1982 Janine. The "Sein Feld" heading is a reference to the Seinfeld final episode, which aired May 14, 1998. The first column contains a reference to angels — apparently Hell's Angels — and the second column provides a somewhat more serious look at this theological topic.
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Sein Feld
1984 Janine
"But Angels love their own
"Logos means above all relation."
"Gesang ist Dasein…. |
Geometry and Theology
PA lottery May 14, 1998: |
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Tape purchased 12/23/97:
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"In the middle of 1982 Janine there are pages in which Jock McLeish is fighting with drugs and alcohol, attempting to either die or come through and get free of his fantasies. In his delirium, he hears the voice of God, which enters in small print, pushing against the larger type of his ravings. Something God says is repeated on the first and last pages of Unlikely Stories, Mostly, complete with illustration and the words 'Scotland 1984' beside it. God's statement is 'Work as if you were in the early days of a better nation.' It is the inherent optimism in that statement that perhaps best captures the strength of Aladair Gray's fiction, its straightforwardness and exuberance." |
For another look at angels, see "Winging It," by Christopher R. Miller, The New York Times Book Review Bookend page for Sunday, May 24, 1998. May 24 is the feast day of Sara (also known by the Hindu name Kali), patron saint of Gypsies.
For another, later (July 16, 1998) reply to Dyson, from a source better known than myself, see Why Religion Matters, by Huston Smith, Harper Collins, 2001, page 66.
Homer
“No matter how it’s done, you won’t like it.”
— Robert Redford to Robert M. Pirsig in Lila
“The evening before Harriet injures Roy,
she asks him, in a restaurant car,
whether he has read Homer.”
— Oxford website on the film of The Natural
“Brush Up Your Shakespeare”
— Cole Porter lyric for a show that opened
on December 30, 1948
Judy Davis as Harriet Bird
Thine eyes I love…
Shakespeare, Sonnet 132
“Roy’s Guenevere-like lover is named Memo Paris,
presumably the face that launched a thousand strikes.”
— Oxford website on the film of The Natural
Nicole Kidman
as Memo Paris
“Iris is someone to watch over Roy.”
— Oxford website on the film of The Natural
Kate Winslet as young Iris Murdoch
From the second-draft screenplay
for The Sting,
with Robert Redford as Hooker:
HOOKER
(shuffling a little)
I, ah…thought you might wanna come out for a while. Maybe have a drink or somethin’.
LORETTA
You move right along, don’t ya.
HOOKER
(with more innocence than confidence)
I don’t mean nothin’ by it. I just don’t know many regular girls, that’s all.
LORETTA
And you expect me to come over, just like that.
HOOKER
If I expected somethin’, I wouldn’t be still standin’ out here in the hall.
Loretta looks at him carefully. She knows it’s not a line.
LORETTA
(with less resistance now)
I don’t even know you.
HOOKER
(slowly)
You know me. I’m just like you…
It’s two in the morning and I don’t know nobody.
The two just stand there in silence a second. There’s nothing more to say. She stands back and lets him in.
Iris Murdoch on Plato’s Form of the Good,
by Joseph Malikail:
“For Murdoch as for Plato, the Good belongs to Plato’s Realm of Being not the Realm of Becoming…. However, Murdoch does not read Plato as declaring his faith in a divine being when he says that the Good is
the universal author of all things beautiful and right, parent of light and the lord of light in the visible world, and the immediate source of reason and truth in the intellectual; and that this is the power upon which [one who] would act rationally either in public or private life must have his eyes fixed (Republic…).
Though she acknowledges the influence of Simone Weil in her reading of Plato, her understanding of Plato on Good and God is not Weil’s (1952, ch.7)*. For Murdoch,
Plato never identified his Form of the Good with God (the use of theos in the Republic… is a façon de parler), and this separation is for him an essential one. Religion is above the level of the ‘gods.’ There are no gods and no God either. Neo-Platonic thinkers made the identification (of God with good) possible; and the Judaeo-Christian tradition has made it easy and natural for us to gather together the aesthetic and consoling impression of Good as a person (1992, 38)**.
As she understands Plato:
The Form of the Good as creative power is not a Book of Genesis creator ex nihilo … Plato does not set up the Form of the Good as God, this would be absolutely un-Platonic, nor does he anywhere give the sign of missing or needing a real God to assist his explanations. On the contrary, Good is above the level of the gods or God (ibid., 475)**.
Mary Warnock, her friend and fellow-philosopher, sums up Murdoch’s metaphysical view of the Vision of the Good:
She [Murdoch] holds that goodness has a real though abstract existence in the world. The actual existence of goodness is, in her view, the way it is now possible to understand the idea of God.
Or as Murdoch herself puts it, ‘Good represents the reality of which God is the dream.’ (1992, 496)**”
*Weil, Simone. 1952. Intimations of Christianity Among The Ancient Greeks. Ark Paperbacks, 1987/1952.
**Murdoch, Iris. 1992. Metaphysics As A Guide To Morals. London: Chatto and Windus.
From the conclusion of Lila,
by Robert M. Pirsig:
“Good is a noun. That was it. That was what Phaedrus had been looking for. That was the homer over the fence that ended the ballgame.”
A Logocentric Archetype
Today we examine the relativist, nominalist, leftist, nihilist, despairing, depressing, absurd, and abominable work of Samuel Beckett, darling of the postmodernists.
One lens through which to view Beckett is an essay by Jennifer Martin, "Beckettian Drama as Protest: A Postmodern Examination of the 'Delogocentering' of Language." Martin begins her essay with two quotations: one from the contemptible French twerp Jacques Derrida, and one from Beckett's masterpiece of stupidity, Molloy. For a logocentric deconstruction of Derrida, see my note, "The Shining of May 29," which demonstrates how Derrida attempts to convert a rather important mathematical result to his brand of nauseating and pretentious nonsense, and of course gets it wrong. For a logocentric deconstruction of Molloy, consider the following passage:
"I took advantage of being at the seaside to lay in a store of sucking-stones. They were pebbles but I call them stones…. I distributed them equally among my four pockets, and sucked them turn and turn about. This raised a problem which I first solved in the following way. I had say sixteen stones, four in each of my four pockets these being the two pockets of my trousers and the two pockets of my greatcoat. Taking a stone from the right pocket of my greatcoat, and putting it in my mouth, I replaced it in the right pocket of my greatcoat by a stone from the right pocket of my trousers, which I replaced by a stone from the left pocket of my trousers, which I replaced by a stone from the left pocket of my greatcoat, which I replaced by the stone which was in my mouth, as soon as I had finished sucking it. Thus there were still four stones in each of my four pockets, but not quite the same stones….But this solution did not satisfy me fully. For it did not escape me that, by an extraordinary hazard, the four stones circulating thus might always be the same four."
Beckett is describing, in great detail, how a damned moron might approach the extraordinarily beautiful mathematical discipline known as group theory, founded by the French anticleric and leftist Evariste Galois. Disciples of Derrida may play at mimicking the politics of Galois, but will never come close to imitating his genius. For a worthwhile discussion of permutation groups acting on a set of 16 elements, see R. D. Carmichael's masterly work, Introduction to the Theory of Groups of Finite Order, Ginn, Boston, 1937, reprinted by Dover, New York, 1956.
There are at least two ways of approaching permutations on 16 elements in what Pascal calls "l'esprit géométrique." My website Diamond Theory discusses the action of the affine group in a four-dimensional finite geometry of 16 points. For a four-dimensional euclidean hypercube, or tesseract, with 16 vertices, see the highly logocentric movable illustration by Harry J. Smith. The concept of a tesseract was made famous, though seen through a glass darkly, by the Christian writer Madeleine L'Engle in her novel for children and young adults, A Wrinkle in Tme.
This tesseract may serve as an archetype for what Pascal, Simone Weil (see my earlier notes), Harry J. Smith, and Madeleine L'Engle might, borrowing their enemies' language, call their "logocentric" philosophy.
For a more literary antidote to postmodernist nihilism, see Archetypal Theory and Criticism, by Glen R. Gill.
For a discussion of the full range of meaning of the word "logos," which has rational as well as religious connotations, click here.
Waiting for Logos
Searching for background on the phrase "logos and logic" in yesterday's "Notes toward a Supreme Fact," I found this passage:
"…a theory of psychology based on the idea of the soul as the dialectical, self-contradictory syzygy of a) soul as anima and b) soul as animus. Jungian and archetypal psychology appear to have taken heed more or less of only one half of the whole syzygy, predominantly serving an anima cut loose from her own Other, the animus as logos and logic (whose first and most extreme phenomenological image is the killer of the anima, Bluebeard). Thus psychology tends to defend the virginal innocence of the anima and her imagination…"
— Wolfgang Giegerich, "Once More the Reality/Irreality Issue: A Reply to Hillman's Reply," website
The anima and other Jungian concepts are used to analyze Wallace Stevens in an excellent essay by Michael Bryson, "The Quest for the Fiction of an Absolute." Part of Bryson's motivation in this essay is the conflict between the trendy leftist nominalism of postmodern critics and the conservative realism of more traditional critics:
"David Jarraway, in his Stevens and the Question of Belief, writes about a Stevens figured as a proto-deconstructionist, insisting on 'Steven's insistence on dismantling the logocentric models of belief' (311) in 'An Ordinary Evening in New Haven.' In opposition to these readings comes a work like Janet McCann's Wallace Stevens Revisited: 'The Celestial Possible', in which the claim is made (speaking of the post-1940 period of Stevens' life) that 'God preoccupied him for the rest of his career.'"
Here "logocentric" is a buzz word for "Christian." Stevens, unlike the postmodernists, was not anti-Christian. He did, however, see that the old structures of belief could not be maintained indefinitely, and pondered what could be found to replace them. "Notes toward a Supreme Fiction" deals with this problem. In his essay on Stevens' "Notes," Bryson emphasizes the "negative capability" of Keats as a contemplative technique:
"The willingness to exist in a state of negative capability, to accept that sometimes what we are seeking is not that which reason can impose…."
For some related material, see Simone Weil's remarks on Electra waiting for her brother Orestes. Simone Weil's brother was one of the greatest mathematicians of the past century, André Weil.
"Electra did not seek Orestes, she waited for him…"
— Simone Weil
"…at the end, she pulls it all together brilliantly in the story of Electra and Orestes, where the importance of waiting on God rather than seeking is brought home forcefully."
— Tom Hinkle, review of Waiting for God
Compare her remarks on waiting for Orestes with the following passage from Waiting for God:
"We do not obtain the most precious gifts by going in search of them but by waiting for them. Man cannot discover them by his own powers, and if he sets out to seek for them he will find in their place counterfeits of which he will be unable to discern falsity.
The solution of a geometry problem does not in itself constitute a precious gift, but the same law applies to it because it is the image of something precious. Being a little fragment of particular truth, it is a pure image of the unique, eternal, and living Truth, the very Truth that once in a human voice declared: "I am the Truth."
Every school exercise, thought of in this way, is like a sacrament.
In every school exercise there is a special way of waiting upon truth, setting our hearts upon it, yet not allowing ourselves to go out in search of it. There is a way of giving our attention to the data of a problem in geometry without trying to find the solution…."
— Simone Weil, "Reflections on the Right Use of School Studies with a View to the Love of God"
Weil concludes the preceding essay with the following passage:
"Academic work is one of those fields containing a pearl so precious that it is worth while to sell all of our possessions, keeping nothing for ourselves, in order to be able to acquire it."
This biblical metaphor is also echoed in the work of Pascal, who combined in one person the theological talent of Simone Weil and the mathematical talent of her brother. After discussing how proofs should be written, Pascal says
"The method of not erring is sought by all the world. The logicians profess to guide to it, the geometricians alone attain it, and apart from their science, and the imitations of it, there are no true demonstrations. The whole art is included in the simple precepts that we have given; they alone are sufficient, they alone afford proofs; all other rules are useless or injurious. This I know by long experience of all kinds of books and persons.
And on this point I pass the same judgment as those who say that geometricians give them nothing new by these rules, because they possessed them in reality, but confounded with a multitude of others, either useless or false, from which they could not discriminate them, as those who, seeking a diamond of great price amidst a number of false ones, but from which they know not how to distinguish it, should boast, in holding them all together, of possessing the true one equally with him who without pausing at this mass of rubbish lays his hand upon the costly stone which they are seeking and for which they do not throw away the rest."
— Blaise Pascal, The Art of Persuasion
Notes toward a Supreme Fact
In "Notes toward a Supreme Fiction," Wallace Stevens lists criteria for a work of the imagination:
For a work that seems to satisfy these criteria, see the movable images at my diamond theory website. Central to these images is the interplay of rational sides and irrational diagonals in square subimages.
"Logos and logic, crystal hypothesis,
Incipit and a form to speak the word
And every latent double in the word…."— "Notes toward a Supreme Fiction," Section 1, Canto VIII
Recall that "logos" in Greek means "ratio," as well as (human or divine) "word." Thus when I read the following words of Simone Weil today, I thought of Stevens.
"The beautiful in mathematics resides in contradiction. Incommensurability, logoi alogoi , was the first splendor in mathematics."
— Simone Weil, Oeuvres Choisies , éd. Quarto, Gallimard, 1999, p. 100
In the conclusion of Section 3, Canto X, of "Notes," Stevens says
"They will get it straight one day at the Sorbonne.
We shall return at twilight from the lecture
Pleased that the irrational is rational…."
This is the logoi alogoi of Simone Weil.
Dancing about Architecture
The title’s origin is obscure, but its immediate source is a weblog entry and ensuing comments: “Writing about music is like dancing about architecture.”
A related quote:
“At the still point, there the dance is.”
— T. S. Eliot, “Burnt Norton” in Four Quartets
“Eliot by his own admission took ‘the still point of the turning world’ in ‘Burnt Norton’ from the Fool in Williams’s The Greater Trumps.”
— Humphrey Carpenter, The Inklings (1978), Ballantine Books, 1981, page 106. Carpenter cites an “unpublished journal of Mary Trevelyan (in possession of the author).”
The following was written this morning as a comment on a weblog entry, but may stand on its own as a partial description of Eliot’s and Williams’s “dance.”
Three sermons on the Fool card, each related to Charles Williams’s novel The Greater Trumps:
To Play the Fool,
Games “Not Unlike Chesse,” and
Charles Williams and Inklings Links.
“Here is the Church,
Here is the steeple,
Open the door and see all the People.”
For some architecture that may or may not be worth dancing about, see the illustrations to Simone Weil’s remarks in my note of November 25, 2002, “The Artist’s Signature.”
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