A death on May 29, from The Fresno Bee —
See as well "La Diadema de la Muerte."
A death on May 29, from The Fresno Bee —
See as well "La Diadema de la Muerte."
(Continued from May 29, 2002)
May 29, 1832—
Évariste Galois, Lettre de Galois à M. Auguste Chevalier—
Après cela, il se trouvera, j'espère, des gens qui trouveront leur profit à déchiffrer tout ce gâchis.
(Later there will be, I hope, some people who will find it to their advantage to decipher all this mess.)
Martin Gardner on the above letter—
"Galois had written several articles on group theory, and was merely annotating and correcting those earlier published papers."
– The Last Recreations , by Martin Gardner, published by Springer in 2007, page 156.
Commentary from Dec. 2011 on Gardner's word "published" —
Review in Variety , August 13, 2021, by Jay Weissberg —
" Audiences heading for the doors during the final credits
will miss this crucial coda in which Hawke says he didn’t
really understand the script and then goes on to spout
innocuous platitudes about death, life and the start of
a new day, ending it all with 'yes, this is part of the film.' ”
This, on the other hand, is presumably not part of the film —
See "The Shining of May 29" in this journal.
"The purpose of mathematics cannot be derived from an activity
inferior to it but from a higher sphere of human activity, namely,
religion."
— Igor Shafarevitch, 1973 remark published as above in 1982.
"Perhaps."
— Steven H. Cullinane, February 13, 2019
From Log24 on Good Friday, April 18, 2003 — . . . What, indeed, is truth? I doubt that the best answer can be learned from either the Communist sympathizers of MIT or the “Red Mass” leftists of Georgetown. For a better starting point than either of these institutions, see my note of April 6, 2001, Wag the Dogma. See, too, In Principio Erat Verbum , which notes that “numbers go to heaven who know no more of God on earth than, as it were, of sun in forest gloom.” Since today is the anniversary of the death of MIT mathematics professor Gian-Carlo Rota, an example of “sun in forest gloom” seems the best answer to Pilate’s question on this holy day. See
“Examples are the stained glass windows Motto of Plato’s Academy † The Exorcist, 1973 |
Detail from an image linked to in the above footnote —
"And the darkness comprehended it not."
Id est :
A Good Friday, 2003, article by
a student of Shafarevitch —
"… there are 25 planes in W . . . . Of course,
replacing {a,b,c} by the complementary set
does not change the plane. . . ."
Of course.
See. however, Six-Set Geometry in this journal.
Hexagram 29,
The Abyss (Water)
This post was suggested by an August 6, 2010, post by the designer
(in summer or fall, 2010) of the Stack Exchange math logo (see
the previous Log24 post, Art Space Illustrated) —
In that post, the designer quotes the Wilhelm/Baynes I Ching to explain
his choice of Hexagram 63, Water Over Fire, as a personal icon —
"When water in a kettle hangs over fire, the two elements
stand in relation and thus generate energy (cf. the
production of steam). But the resulting tension demands
caution. If the water boils over, the fire is extinguished
and its energy is lost. If the heat is too great, the water
evaporates into the air. These elements here brought in
to relation and thus generating energy are by nature
hostile to each other. Only the most extreme caution
can prevent damage."
See also this journal on Walpurgisnacht (April 30), 2010 —
Hexagram 29:
|
Hexagram 30: |
A thought from another German-speaking philosopher —
"Die Philosophie ist ein Kampf gegen die Verhexung
unsres Verstandes durch die Mittel unserer Sprache."
See also The Crimson 's abyss in today's 4:35 AM post Art Space, Continued.
From a 2002 note, "The Shining of May 29" —
Related material: The remarks in this journal on April 1, 2013.
"Philosophy is a battle against the bewitchment [Verhexung ]
of our intelligence by means of our language."
— Wittgenstein, Philosophical Investigations , Section 109
"The philosophy of logic speaks of sentences and words
in exactly the sense in which we speak of them in ordinary life
when we say e.g. 'Here is a Chinese sentence,' or 'No, that only
looks like writing; it is actually just an ornament' and so on."
— Wittgenstein, Philosophical Investigations , Section 108
Monday, June 30, 2014
High Concept
|
For the title, see a post of Nov. 4, 2007.
Related material:
Hexagram 29, Water, and a pattern resembling
the symbol for Aquarius:
For some backstory about the former,
see the June 21 post Hallmark.
For some backstory about the latter,
see today’s post Toward Evening.
Tom Wolfe has supplied some scaffolding*
to support the concept.
A suitable hallmark for
the previous post, Logical Death:
Hexagram 29: "K'an represents…
the principle of light inclosed in the dark."
— The Richard Wilhelm I Ching
A related page from Stanford:
Some mathematical background for yesterday's
remarks "For the Bregnans" and "Lost in Translation"—
"Matching Theory: A Sampler, from Dénes König
to the Present," by Michael D. Plummer, 1991.
See also Matching Theory by Plummer and Lovász.
Translation by Barbara Johnson:
"The minimum number of rows— lines or columns—
that contain all the zeros in a matrix is equal to
the maximum number of zeros
located in any individual line or column ."
In the original:
"situés sur des lignes ou des colonnes distinctes "
Update of 11:30 PM ET May 29, 2014:
Derrida in 1972 was quoting Philippe Sollers, Nombres
(Paris: Éditions du Seuil , 1968). Sollers in turn was
perhaps quoting A. Kaufmann, Méthodes et Modèles
de la Recherche Opérationnelle , Paris, Dunod , 1964,
L'Économie d'Entreprise 10 , vol. 2, page 305:
"Le nombre minimal de rangées
(lignes et/ou colonnes) contenant
tous les zéros d'une matrice, est égal
au nombre maximal de zéros
situés sur des lignes et des colonnes distinctes."
The Shining of May 29…
The original note and references to it here.
* As opposed to the Monicans . See previous post.
See January 4th, 2012.
(This link resulted from an application of Heidegger's
philosophy of "the opening" and "the shining" (Die Lichtung ).)
See also The Shining of May 29.
Update of 12:19 AM Feb. 3, 2012—
The undated (but cached by Google on January 4th, 2012)
unsigned post from a deleted weblog linked to above as
"an application" is also available in a version that is signed
(but still undated).
A Meditation on the NY Lottery of May 29
Yesterday's NY Lottery— Midday 981, Evening 275.
As noted in yesterday morning's linked-to post,
The Shining of May 29…
"By groping toward the light we are made to realize
how deep the darkness is around us."
— Arthur Koestler, The Call Girls: A Tragi-Comedy ,
Random House, 1973, page 118
One interpretation of the mystic numbers revealed by the Lottery yesterday—
981 as the final page* of David Foster Wallace's famed novel Infinite Jest …
275 as a page in Wallace's non-fiction book about infinity Everything and More …
Gregory Chaitin points out that this is nonsense …
As noted elsewhere in this journal, I have a different concept of "math's absolute
Prince of Darkness"— and, indeed, of a "quest for Omega." (See posts of May 2010.)
Yesterday's numbers indicate a different struggle between darkness and light—
Light —
Darkness —
* From infinitesummer.org/archives/168 — "A note about editions:
As it turns out, all (physical) editions of Infinite Jest have 981 pages:
the one from 1996, the one from 2004, the paperback, the hardcover, etc.
A big thank you to the men and women in the publishing industry who
were kind and/or lazy enough to keep things consistent."
"You think you've seen the sun but you ain't seen it shine."
— "The Best Is Yet to Come," lyrics by Carolyn Leigh, music by Cy Coleman
Related material— The Shining of May 29.
A new NY Times column:
Today's New York Times
re-edited for philosophers:
See also
John Baez's paper
Duality in Logic and Physics
(for a May 29 meeting at Oxford),
Lubtchansky's Key, with its links
to Duelle (French, f. adj., dual)
and Art Wars for Trotsky's Birthday.
A Penny for My Thoughts? by Maureen Dowd “If an online newspaper in Pasadena, Calif., can outsource coverage to India, I wonder how long can it be before some guy in Bangalore is writing my column….” — New York Times teaser for a column of Sunday, November 30, 2008 (St. Andrew’s Day) |
DH News Service, Bangalore, Tuesday, Dec. 2, 2008:
“Monday evening had a pleasant surprise in store for sky-watchers as the night sky sported a smiley, in the form of a crescent moon flanked by two bright planets Jupiter and Venus…” |
Meanwhile, at National Geographic:
Jupiter, Venus, Moon Make “Frown”
A Midrash for Maureen:
Related material on Pasadena:
Happy birthday, R. P. Dilworth.
Related material on India:
The Shining of May 29 (2002) and
A Well-Known Theorem (2005).
— Barry Mazur in 2000 as quoted today at the University of St. Andrews
"Numbers go to heaven
who know no more
of God on earth than,
as it were,
of sun in forest gloom."
— Meister Eckhart,
In Principio Erat Verbum
Related material:
yesterday's entry, and
Hour of the Wolf
Today is Schicksalstag, the “day of fate” in German history.
This entry’s time slot, 3:00 AM ET– which some say is the beginning of “the hour of the wolf*”– was reserved earlier for some entry appropriate to the day. (Actual time of this entry: about 12:48 PM ET).
Markus Wolf, East German Spymaster, Dies at 83 By THE ASSOCIATED PRESS Published: Thursday, Nov. 9, 2006 Filed at 11:16 a.m. ET BERLIN (AP) — Markus Wolf, the ”man without a face” who outwitted the West as communist East Germany’s long-serving spymaster, died Thursday [Nov. 9, 2006]. He was 83. Wolf died in his apartment in Berlin, his stepdaughter Claudia Wall said in a statement. The cause of his death, on the 17th anniversary of the fall of the Berlin Wall, was not released. |
Game Boy
Click on picture for details.
“Nine is a very
powerful Nordic number.” — Katherine Neville
|
* “Wolf” — See the etymological notes
in The Shining of May 29.
“When he was taken to church
he amused himself by factorizing
the numbers of the hymns.”
— C. P. Snow, foreword to
A Mathematician’s Apology,
by G. H. Hardy
An application of
lottery hermeneutics:
420 –> 4/20 –>
Hall of Shame,
Easter Sunday,
April 20, 2003;
145 –> 5*29 –> 5/29 –>
The Rev. Wright may also
be interested in the following
Related material:
“Shem was a sham….”
(FW I.7, 170 and Log24 Oct. 13),
and The Hebrew Word Shem:
This word occurs, notably, in Psalm (or “hymn”) 145.
See http://scripturetext.com/psalms/145-1.htm:
thy name
shem (shame)
an appellation, as a mark or memorial of individuality; by implication honor, authority, character — + base, (in-)fame(-ous), named(-d), renown, report.
Related material:
The Crimson Passion
Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance, Part III:
“The wave of crystallization rolled ahead. He was seeing two worlds, simultaneously. On the intellectual side, the square side, he saw now that Quality was a cleavage term. What every intellectual analyst looks for. You take your analytic knife, put the point directly on the term Quality and just tap, not hard, gently, and the whole world splits, cleaves, right in two…
hip and square, classic and romantic, technological and humanistic…and the split is clean. There’s no mess. No slop. No little items that could be one way or the other. Not just a skilled break but a very lucky break. Sometimes the best analysts, working with the most obvious lines of cleavage, can tap and get nothing but a pile of trash. And yet here was Quality; a tiny, almost unnoticeable fault line; a line of illogic in our concept of the universe; and you tapped it, and the whole universe came apart, so neatly it was almost unbelievable. He wished Kant were alive. Kant would have appreciated it. That master diamond cutter. He would see. Hold Quality undefined. That was the secret.”
See also the discussion of
subjective and objective
by Robert M. Pirsig in
Zen and the Art of
Motorcycle Maintenance,
Part III,
followed by this dialogue:
Are We There Yet?
Chris shouts, “When are we
going to get to the top?”
“Probably quite a way yet,”
I reply.
“Will we see a lot?”
“I think so. Look for blue sky
between the trees. As long as we
can’t see sky we know it’s a way yet.
The light will come through the trees
when we round the top.”
Related material:
The Boys from Uruguay,
Lichtung!,
The Shining of May 29,
A Guiding Philosophy,
Ticket Home.
The philosophy of Heidegger
discussed and illustrated
in the above entries may
be regarded as honoring
today’s 100th anniversary
of the birth of Heidegger’s
girlfriend, Hannah Arendt.
See also
Yesterday’s Pennsylvania
Mid-day 266
Evening 529
Related material:
The 266-Day Method
and
The Shining of May 29
(Wednesday, May 29, 2002) Commentary on Hexagram 29: — Richard Wilhelm, “How do we explain — Rhetorical question |
Happy birthday, Robert M. Pirsig.
Readings for the hour of the wolf:
Yesterday was Arthur Koestler’s birthday.
“By groping toward the light
we are made to realize
how deep the darkness is
around us.”
— Arthur Koestler,
The Call Girls: A Tragi-Comedy,
Random House, 1973, page 118
For John F. Kennedy's birthday:
See The Shining of May 29
from 2002
and the references to
the marriage theorem
in Dharwadker's Alleged Proof
from 2005.
"By groping toward the light
we are made to realize
how deep the darkness is
around us."
— Arthur Koestler,
The Call Girls: A Tragi-Comedy,
Random House, 1973, page 118
For related material on
academic darkness, see
Mathematics and Narrative.
“In The Painted Word, a rumination on the state of American painting in the 1970s, Tom Wolfe described an epiphany….”
— Peter Berkowitz, “Literature in Theory”
“I had an epiphany.”
— Apostolos Doxiadis, organizer of last summer’s conference on mathematics and narrative. See the Log24 entry of 1:06 PM last August 23 and the four entries that preceded it.
“… das Durchleuchten des ewigen Glanzes des ‘Einen’ durch die materielle Erscheinung“
— A definition of beauty from Plotinus, via Werner Heisenberg
“By groping toward the light we are made to realize how deep the darkness is around us.”
— Arthur Koestler, The Call Girls: A Tragi-Comedy, Random House, 1973, page 118, quoted in The Shining of May 29
“Perhaps we are meant to see the story as a cubist retelling of the crucifixion….”
— Adam White Scoville, quoted in Cubist Crucifixion, on Iain Pears’s novel, An Instance of the Fingerpost
Part I: The Light
The Shining of May 29
and
Diamond Theory
Part II: The Darkness
The Shining of Apollo
"Plato's most significant passage may be found in Phaedrus 265b: 'And we made four divisions of the divine madness, ascribing them to four gods, saying that prophecy was inspired by Apollo, the mystic madness by Dionysos, the poetic by the Muses, and the madness of love […] by Aphrodite and Eros' (trans. by H.N. Fowler, in the Loeb Classical Library)."
— Saverio Marchignoli, note on section 20, paragraphs 115-119, of the Discourse on the Dignity of Man (Oratio de hominis dignitate) (1486) by Pico della Mirandola, considered the "Manifesto of the Renaissance."
Related material:
A Mass for Lucero,
The Shining of May 29,
Shining Forth,
Sermon for St. Patrick's Day, and the phrase
Diamond Struck by the Sun.
Make a Différance
From Frida Saal's
Lacan Derrida:
"Différance is that which all signs have, what constitutes them as signs, as signs are not that to which they refer: i) they differ, and hence open a space from that which they represent, and ii) they defer, and hence open up a temporal chain, or, participate in temporality. As well, following de Sassure's famous argument, signs 'mean' by differing from other signs. The coined word 'différance' refers to at once the differing and the deferring of signs. Taken to the ontological level†, the differing and deferring of signs from what they mean, means that every sign repeats the creation of space and time; and ultimately, that différance is the ultimate phenomenon in the universe, an operation that is not an operation, both active and passive, that which enables and results from Being itself."
22. Without using the Pythagorean Theorem prove that the hypotenuse of an isosceles right triangle will have the length if the equal legs have the length 1. Suggestion: Consider the similar triangles in Fig. 39. 23. The ancient Greeks regarded the Pythagorean Theorem as involving areas, and they proved it by means of areas. We cannot do so now because we have not yet considered the idea of area. Assuming for the moment, however, the idea of the area of a square, use this idea instead of similar triangles and proportion in Ex. 22 above to show that x = .
— Page 98 of Basic Geometry, by George David Birkhoff, Professor of Mathematics at Harvard University, and Ralph Beatley, Associate Professor of Education at Harvard University (Scott, Foresman 1941) |
The above is from October 1999.
See also Naturalized Epistemology,
from Women's History Month, 2001.
Readings for
St. Patrick's Day
Time of this entry: 12:00:36 PM.
Hence,
"Here the climax of the darkening is reached. The dark power at first held so high a place that it could wound all who were on the side of good and of the light. But in the end it perishes of its own darkness, for evil must itself fall at the very moment when it has wholly overcome the good, and thus consumed the energy to which it owed its duration."
Narrativity: Theory and Practice, by Philip John Moore Sturgess
Sturgess's book deals with the narrative logic of the above novels by Koestler and Conrad, as well as some Irish material:
Narrativity: Theory and Practice | |||||||||||||||||||||||||||||||||||||||||||||||||||
|
These readings are in opposition to the works of Barbara Johnson published by Harvard University Press.
For some background, see The Shining of May 29 (JFK's birthday).
Discussion question:
In the previous entry, who represents the
Hexagram 36 "dark power"
Literary Archaeology
“Mrs. Who’s spectacles shone out
at them triumphantly,
‘And the light shineth in darkness;
and the darkness
comprehended it not.’ ”
— A Wrinkle in Time
See, too,
Shining Forth and
Realism in Literature:
Under the Volcano
Mexican Volcano Blast
|
Here are 3 webcam views of the volcano. Nothing to see at the moment.
Literary background:
Malcolm Lowry’s Under the Volcano,
Plato, Pegasus, and the Evening Star,
and, as background for today’s earlier entry on Platonism and Derrida,
For more on Plato and Christian theology, consult the highly emotional site Further Into the Depths of Satan: “…in The Last Battle on page 170 [C. S.] Lewis has Digory saying, ‘It’s all in Plato, all in Plato.’ Now, Lewis calls Plato ‘an overwhelming theological genius’ (Reflections on the Psalms, p. 80)….” The title “Further Into the Depths of Satan,” along with the volcano readings above, suggests a reading from a related site: Gollum and the Mystery of Evil: “Gollum here clearly represents Frodo’s hidden self. It is ‘as if we are witnessing the darkest night of the soul and one side attempting to master the other’ (Jane Chance 102). Then Frodo, whose finger has been bitten off, cries out, and Gollum holds the Ring aloft, shrieking: ‘Precious, precious, precious! My Precious! O my Precious!’ (RK, VI, 249). At this point, stepping too near the edge, he falls into the volcano, taking the Ring with him. With this, the mountain |
In the above two-step vignette, the part of Gollum is played by the author of “Further Into the Depths of Satan,” who called C. S. Lewis a fool† “that was and is extremely useful to his father the devil.”
† See Matthew 5:22: “…whosoever shall say, Thou fool, shall be in danger of hell fire.”
To the Society of Jesus (also known as the Jesuits):
Have a Good Friday, Traitors
†
Prompted by Pilate’s question “What is truth?” and by my March 24 attack on Noam Chomsky, I decided this afternoon to further investigate what various people have written about Chomsky’s posing of what he calls “Plato’s problem” and “Orwell’s problem.” The former concerns linguistics, the latter, politics. As my March 24 entry indicates, I have nothing but contempt for both Chomsky’s linguistics and Chomsky’s politics. What I discovered this afternoon is that Georgetown University, a Jesuit institution, in 2001 appointed a Chomskyite, David W. Lightfoot, as Dean of the Graduate School of Arts and Sciences.
“Why do we know so much more than we have evidence for in certain areas, and so much less in others? In tackling these questions — Plato’s and Orwell’s problem — Chomsky again demonstrates his unequalled capacity to integrate vast amounts of material.” — David W. Lightfoot, review of Chomsky’s Knowledge of Language
What, indeed, is truth? I doubt that the best answer can be learned from either the Communist sympathizers of MIT or the “Red Mass” leftists of Georgetown. For a better starting point than either of these institutions, see my note of April 6, 2001, Wag the Dogma.
See, too, In Principio Erat Verbum, which notes that “numbers go to heaven who know no more of God on earth than, as it were, of sun in forest gloom.”
Since today is the anniversary of the death of MIT mathematics professor Gian-Carlo Rota, an example of “sun in forest gloom” seems the best answer to Pilate’s question on this holy day. See
“Examples are the stained glass windows of knowledge.” — Vladimir Nabokov
Motto of Plato’s Academy
† The Exorcist, 1973
For Otto Preminger's birthday:
Lichtung!
Today's symbol-mongering (see my Sept. 7, 2002, note The Boys from Uruguay) involves two illustrations from the website of the Deutsche Schule Montevideo, in Uruguay. The first, a follow-up to Wallace Stevens's remarks on poetry and painting in my note "Sacerdotal Jargon" of earlier today, is a poem, "Lichtung," by Ernst Jandl, with an illustration by Lucia Spangenberg.
manche meinen |
|
by Ernst Jandl |
The second, from the same school, illustrates the meaning of "Lichtung" explained in my note The Shining of May 29:
"We acknowledge a theorem's beauty when we see how the theorem 'fits' in its place, how it sheds light around itself, like a Lichtung, a clearing in the woods."
— Gian-Carlo Rota, page 132 of Indiscrete Thoughts, Birkhauser Boston, 1997
From the Deutsche Schule Montevideo mathematics page, an illustration of the Pythagorean theorem:
Braucht´s noch Text? |
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.
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