Log24

Monday, July 19, 2021

Big Sur

Filed under: General — Tags: — m759 @ 2:18 am

A Log24 post from 2020 —

An Instagram story from yesterday —

Tuesday, January 2, 2024

Mathematics Made Absurd:  Domain and Range

Filed under: General — Tags: , — m759 @ 7:54 am

" the dominant discourse limits the range
     of discussion in each domain…."

https://americanaffairsjournal.org/2023/11/
the-stagnant-science-mainstream-economics-in-america/

See as well Boole vs. Galois and

Tuesday, October 10, 2023

Religious Art:  Resurrecting the Scarecrow

Filed under: General — Tags: , — m759 @ 9:08 pm

Click or tap to enlarge.

Monday, August 7, 2023

Treasure of the Sierra Madre: Huichol Swordfish

Filed under: General — Tags: — m759 @ 6:13 pm

This suggests some art that reflects aspects of
my own teen space, which was many years ago . . .

Update for fans of Nevermore Academy:

Teen-related art from loisvb —

Wednesday, February 24, 2021

Saturday, August 19, 2023

Annals of Magical Thinking: The Shuttering

Filed under: General — Tags: , — m759 @ 9:17 am

"Death Valley and Joshua Tree national parks announced campgrounds
closures from noon Saturday through at least Tuesday and preemptively
shuttered several roadways." — Los Angeles Times  yesterday

Friday, June 30, 2023

Indiana Jones and S/Z

Filed under: General — Tags: — m759 @ 12:48 am

"Indiana Jones and the Dial of Destiny 
had its world premiere at Cannes 
on May 18, 2023, and is scheduled to
be released in the United States on
June 30, 2023." — Data from Wikipedia

From this  journal on May 18, 2023 —

In memory of Mr. Zell, some notes suggested by his initials . . .

S/Z  in Wikipedia and . . .

Related amusements from the above publication date —
August 1, 2017 — "Biff's Pleasure Detailing."

Tuesday, June 20, 2023

Menu Secreto

Filed under: General — Tags: , , — m759 @ 2:45 pm

Sunday, April 30, 2023

For Harlan Kane: The Walpurgisnacht Hallucination

Note that if the "compact Riemann surface" is a torus formed by
joining opposite edges of a 4×4 square array, and the phrase
"vector bundle" is replaced by "projective line," and so forth,
the above ChatGPT hallucination is not completely unrelated to
the following illustration from the webpage "galois.space" —

See as well the Cullinane  diamond theorem.

Friday, February 24, 2023

Red Lines: ChatGPT vs. ChatGPS

Filed under: General — Tags: , , — m759 @ 8:48 am

"Recently, several leading academic journals and publishers
updated their submission guidelines to explicitly ban researchers
from listing ChatGPT as a co-author, or using text copied from a
ChatGPT response. Some professors have criticized these bans
as shortsightedly resistant to an inevitable technological change.
We shouldn’t be surprised at the disagreement. This is a new
ethical space that only roughly follows the outlines of our existing
agreements on plagiarism, authorship criteria, and fraud.
Precisely where to draw red lines is not clear."

— Ben Chrisinger, Feb. 22, 2023, in The Chronicle of Higher Education

Flashback to Log24 on Dec. 11, 2022

Compare and Contrast:


Digitally-Assisted Art from … 
 

Chat 'N' Chill ®
 

The Source:

A perhaps more interesting digital assistant
now offers Netflix 'N' Chill —


See as well "red line overload" in the previous post.

Thursday, September 8, 2022

Analogy in Mathematics: Chevron Variations

André Weil in 1940 on analogy in mathematics —

. "Once it is possible to translate any particular proof from one theory to another, then the analogy has ceased to be productive for this purpose; it would cease to be at all productive if at one point we had a meaningful and natural way of deriving both theories from a single one. In this sense, around 1820, mathematicians (Gauss, Abel, Galois, Jacobi) permitted themselves, with anguish and delight, to be guided by the analogy between the division of the circle (Gauss’s problem) and the division of elliptic functions. Today, we can easily show that both problems have a place in the theory of abelian equations; we have the theory (I am speaking of a purely algebraic theory, so it is not a matter of number theory in this case) of abelian extensions. Gone is the analogy: gone are the two theories, their conflicts and their delicious reciprocal reflections, their furtive caresses, their inexplicable quarrels; alas, all is just one theory, whose majestic beauty can no longer excite us. Nothing is more fecund than these slightly adulterous relationships; nothing gives greater pleasure to the connoisseur, whether he participates in it, or even if he is an historian contemplating it retrospectively, accompanied, nevertheless, by a touch of melancholy. The pleasure comes from the illusion and the far from clear meaning; once the illusion is dissipated, and knowledge obtained, one becomes indifferent at the same time; at least in the Gitâ there is a slew of prayers (slokas) on the subject, each one more final than the previous ones."

"The pleasure comes from the illusion" . . .

Exercise:

Compare and contrast the following structure with the three
"bricks" of the R. T. Curtis Miracle Octad Generator (MOG).

http://www.log24.com/log/pix11B/110805-The24.jpg

Note that the 4-row-2-column "brick" at left is quite 
different from the other two bricks, which together
show chevron variations within a Galois tesseract —

Tuesday, August 23, 2022

Pasaje:  Raiders of the Lost Chord

Filed under: General — m759 @ 1:17 pm

Season 1 of "The Resort" will end as "The Lord of the Rings:
The Rings of Power
" begins.

For seekers of the Pasaje — "The Room Outside of Time" —

"The Vision is of what the transliteration of their collaborative
Great Music into a material reality would be like. They are
shown that the Music has a point, has a result and effect
beyond its composition and singing: it amounts to no less
than a highly detailed template commensurate with the entire
history – beginning to end – of a material, 'physical' Universe
that could exist inside 'time'." 

— https://lotr.fandom.com/wiki/Ainulindal%C3%AB

Friday, July 15, 2022

The Cubes  continues.

Filed under: General — Tags: — m759 @ 1:36 pm

From a Toronto Star  video on the Langlands program —

From a review of the 2017 film "Justice League" —

"Now all they need is to resurrect Superman (Henry Cavill),
stop Steppenwolf from reuniting his three Mother Cubes
(sure, whatever) and wrap things up in under two cinematic
hours (God bless)."

See also the 2018 film "Avengers of Justice: Farce Wars."

Wednesday, June 29, 2022

Techie Wordplay: “Lynx”

Filed under: General — Tags: , , , — m759 @ 2:38 pm

On the  Lynx  web browser

"As of 2022, it is the oldest web browser still being maintained,,,,"

"The speed benefits of text-only browsing are most apparent
when using low bandwidth internet connections, or older computer
hardware that may be slow to render image-heavy content."
— Wikipedia [“Older” link added.]

And then there is . . .

See as well the LYNX of Oslo artist Josefine Lyche.

Update of June 30, 2022 —

Lyche, whose art often incorporates mathematical notions,
has not yet, as far as I know, explored the Borromean  link
(three rings, linked mutually but not pairwise) in her art.

Remarks by a different math fan, Evelyn Lamb

"I have had a thing for the Borromean rings for years now.
There’s something so poetic about them. The three rings
are strong together, but they fall apart if any one of them
is removed. Alternatively, the three rings are trapped together
until one of them leaves and sets the others free. I’m kind of
surprised there isn’t a Wisława Szymborska poem or 
Tom Stoppard play that explores the metaphorical possibilities
in the Borromean rings." — Scientific American , Sept. 30, 2016.

See also the Lamb date Sept. 30, 2016, as well as work 
by Lyche, in Log24 posts tagged Star Cube.

Related material — The Log24 post Borromean Generators.

Saturday, March 26, 2022

Box Geometry: Space, Group, Art  (Work in Progress)

Filed under: General — Tags: — m759 @ 2:06 am

Many structures of finite geometry can be modeled by
rectangular or cubical arrays ("boxes") —
of subsquares or subcubes (also "boxes").

Here is a draft for a table of related material, arranged
as internet URL labels.

Finite Geometry Notes — Summary Chart
 

Name Tag .Space .Group .Art
Box4

2×2 square representing the four-point finite affine geometry AG(2,2).

(Box4.space)

S4 = AGL(2,2)

(Box4.group)

 

(Box4.art)

Box6 3×2 (3-row, 2-column) rectangular array
representing the elements of an arbitrary 6-set.
S6  
Box8 2x2x2 cube or  4×2 (4-row, 2-column) array. S8 or Aor  AGL(3,2) of order 1344, or  GL(3,2) of order 168  
Box9 The 3×3 square. AGL(2,3) or  GL(2,3)  
Box12 The 12 edges of a cube, or  a 4×3  array for picturing the actions of the Mathieu group M12. Symmetries of the cube or  elements of the group M12  
Box13 The 13 symmetry axes of the cube. Symmetries of the cube.  
Box15 The 15 points of PG(3,2), the projective geometry
of 3 dimensions over the 2-element Galois field.
Collineations of PG(3,2)  
Box16 The 16 points of AG(4,2), the affine geometry
of 4 dimensions over the 2-element Galois field.

AGL(4,2), the affine group of 
322,560 permutations of the parts
of a 4×4 array (a Galois tesseract)

 
Box20 The configuration representing Desargues's theorem.    
Box21 The 21 points and 21 lines of PG(2,4).    
Box24 The 24 points of the Steiner system S(5, 8, 24).    
Box25 A 5×5 array representing PG(2,5).    
Box27 The 3-dimensional Galois affine space over the
3-element Galois field GF(3).
   
Box28 The 28 bitangents of a plane quartic curve.    
Box32 Pair of 4×4 arrays representing orthogonal 
Latin squares.
Used to represent
elements of AGL(4,2)
 
Box35 A 5-row-by-7-column array representing the 35
lines in the finite projective space PG(3,2)
PGL(3,2), order 20,160  
Box36 Eurler's 36-officer problem.    
Box45 The 45 Pascal points of the Pascal configuration.    
Box48 The 48 elements of the group  AGL(2,3). AGL(2,3).  
Box56

The 56 three-sets within an 8-set or
56 triangles in a model of Klein's quartic surface or
the 56 spreads in PG(3,2).

   
Box60 The Klein configuration.    
Box64 Solomon's cube.    

— Steven H. Cullinane, March 26-27, 2022

Wednesday, March 23, 2022

Watchmen Squid Game: Pronoun Trouble

Filed under: General — Tags: — m759 @ 8:05 am

"… Wade’s entire life is built around the squid attack. In the episode’s opening, we see that 34 years ago, young Wade was at a carnival in Hoboken, New Jersey, proselytizing as a Jehovah’s Witness when the squid emitted a psychic blast that killed three million people in the New York area. Just before the attack, a girl led him into a house of mirrors, feigning interest in hooking up with him in order to steal his clothes, leaving him naked and humiliated in the fairground attraction. But the cruel prank also saved his life, as mirrors can apparently repel the squid's psychic blast."

Related literary remarks —

"It may have been by chance, and it may have had the side effect of being easy to read, but this way of putting a novel together offered a bridge between the miniaturist in Doerr and the seeker of world-spanning connections. He could focus on the details of every piece in the narrative, but there was pleasure, too, in placing them against each other. Sometimes he would lay out all these micro chapters on the floor so he could see them and discover the resonances between characters across space and time.

'That’s the real joy,' Doerr said, 'the visceral pleasure that comes from taking these stories, these lives, and intersecting them, braiding them.'"

— "A version of this article appears in print on Sept. 20, 2021, Section C, Page 4 of the New York edition with the headline: Bringing His Readers To Higher Ground." 

Tuesday, November 2, 2021

Personal Experience:  Superimposed Figures

Filed under: General — m759 @ 10:21 am

From a post at midnight on the night of Jan. 7-8, 2018:

"The resulting figures look rather unimpressive
until they are superimposed, but then they yield
a variety of surprisingly orderly figures."

Context: See the tag The Overnight Case .

See as well a search in this journal for "Double Day."

Wednesday, October 20, 2021

A Treasure Hunt

Filed under: General — m759 @ 11:36 am

Clue:

The clue leads to . . .

The above Spratt date leads to . . .

The above snark from this  journal leads to . . .

… as well as …

 

Thursday, September 9, 2021

Enlarging the Spielraum… Continues.

Filed under: General — m759 @ 12:30 pm

Click the chessboard for some Chinese hermeneutics.

Friday, September 20, 2019

Das Humankapital , or:  The Jews and Linz*

Filed under: General — m759 @ 8:42 am

From the above aldaily.com link —

https://www.nybooks.com/articles/2019/10/10/
jia-tolentino-song-my-self-care/

From a review of

Trick Mirror:  Reflections on Self-Delusion 
by Jia Tolentino
Random House, 303 pp., $27.00

… as she grew up in Texas. In a way, she was primed for the illimitable expanse of the Internet by her Christian upbringing, which teaches its followers that everyone on earth is being watched by God. It gave her a flight of optimism, before this same system slowly but surely “metastasize[d] into a wreck”: “this feverish, electric, unlivable hell.” While the Internet was meant to allow you to reach out to any- and everyone without a hint of the cruel discriminations that blight our world, it turned into the opposite, a forum where individuals are less speaking to other people than preening and listening to themselves—turning themselves into desirable objects to be coveted by all. It became, that is, the perfect embodiment of consumer capitalism, where everything can be touted in the marketplace.

How, Tolentino asks, did the idea take hold that “ordinary personhood would seamlessly adjust itself around whatever within it would sell”? How did our basic humanity come to be “reframed as an exploitable viral asset”? 

Related course — "History and Human Capital" at Harvard, a course
taught last spring by professors Claudia Goldin and Lawrence Katz —

Related reading — "Human Capital," by Claudia Goldin:

The above material suggested this post's title, "Das Humankapital ."

The same phrase is also the title of a perceptive website from Linz, Austria.

* For the alternative title, see a Wikipedia article on The Jew of Linz .

Monday, January 11, 2016

Surreal Midrash

Filed under: General — m759 @ 6:25 am

The time of the previous post, 3:10 (AM), suggests, in a
surreal manner that the spirit of the late David Bowie might
find amusing, a review of Log24 posts last year on 3/10 —

An Obit for Dooley and The Big Screw.

As for the time, 6:25, of this  post, see Apocatastasis.

Wednesday, October 10, 2012

Melancholia, Depression, Ambiguity

Filed under: General,Geometry — Tags: , — m759 @ 11:00 pm

Occurrences of the phrase "magic square" in Lowe-Porter's translation of the Thomas Mann novel Doctor Faustus

"On the wall above the  piano was an arithmetical diagram fastened with drawing-pins, something he had found in a second-hand shop: a so-called magic square, such as appears also in Dürer's Melancolia , along with the hour-glass, the circle, the scale, the polyhedron, and other symbols. Here as there, the figure was divided into sixteen Arabic-numbered fields, in such a way that number one was in the right-hand lower corner, sixteen in the upper left; and the magic, or the oddity, simply consisted in the fact that the sum of these numerals, however you added them, straight down, crosswise, or diagonally, always came to thirty-four. What the principle was upon which this magic uniformity rested I never made out, but by virtue of the prominent place Adrian had given it over the piano, it always attracted the eye, and I believe I never visited his room without giving a quick glance, slanting up or straight down and testing once more the invariable, incredible result."

….

"Adrian kept without changing during the whole four and a half years he spent in Leipzig his two-room quarters in Peterstrasse near the Collegium Beatae Virginis, where he had again pinned the magic square above his cottage piano."

….

" 'The decisive factor is that every note, without exception, has significance and function according to its place in the basic series or its derivatives. That would guarantee what I call the indifference to harmony and melody.' 

'A magic square,' I said. 'But do you hope to have people hear all that?' "

….

" 'Extraordinarily Dürerish. You love it. First "how will I shiver after the sun"; and then the houre-glasse of the Melancolia .  Is the magic square coming too?' "

….

"Here I will remind the reader of a conversation I had with Adrian on a long-ago day, the day of his sister's wedding at Buchel, as we walked round the Cow Trough. He developed for me— under pressure of a headache— his idea of the 'strict style,' derived from the way in which, as in the lied 'O lieb Madel, wie schlecht bist du ' melody and harmony are determined by the permutation of a fundamental five-note motif, the symbolic letters h, e, a, e, e-flat. He showed me the 'magic square' of a style of technique which yet developed the extreme of variety out of identical material and in which there is no longer anything unthematic, anything that could not prove itself to be a variation of an ever constant element. This style, this technique, he said, admitted no note, not one, which did not fulfil its thematic function in the whole structure— there was no longer any free note."

Review of related material— 

Last night's midnight post (disambiguation), the followup 1 AM post (ambiguation), today's noon post (ambiguity), and Dürer in this journal.

The tesseracts of the noon post are related to the Dürer magic square by a well-known adjacency property.

"… the once stable 'father's depression' has been transmuted into a shifting reality that shimmered in a multiplicity of facets."

Haim Omer, Tel-Aviv University, on Milanese ambiguation  therapy,
     p. 321 in "Three Styles of Constructive Therapy,"
     Constructive Therapies, Vol. 2 , pp. 319-333, 
     ed. by Michael F. Hoyt (Guilford Press paperback, 1998)

Monday, June 18, 2012

Surface

Filed under: General,Geometry — Tags: , , , — m759 @ 11:00 pm

"Poetry is an illumination of a surface…."

— Wallace Stevens

IMAGE- NY Times online front page, June 18, 2012- New Microsoft 'Surface' computer

Some poetic remarks related to a different surface, Klein's Quartic

This link between the Klein map κ and the Mathieu group M24
is a source of great delight to the author. Both objects were
found in the 1870s, but no connection between them was
known. Indeed, the class of maximal subgroups of M24
isomorphic to the simple group of order 168 (often known,
especially to geometers, as the Klein group; see Baker [8])
remained undiscovered until the 1960s. That generators for
the group can be read off so easily from the map is
immensely pleasing.

— R. T. Curtis, Symmetric Generation of Groups ,
     Cambridge University Press, 2007, page 39

Other poetic remarks related to the simple group of order 168—

Wednesday, March 9, 2011

Ash Wednesday Surprise

Filed under: General — m759 @ 11:07 am

IMAGE- Errol Morris- 'The Ashtray'- at The New York Times

 Part 3 of 5  (See also Part 1 and Part 2) begins as follows…

"Incommensurable. It is a strange word. I wondered, why  did Kuhn choose it? What was the attraction? 

Here’s one clue. At the very end of 'The Road Since Structure,' a compendium of essays on Kuhn’s work, there is an interview with three Greek philosophers of science, Aristides Baltas, Kostas Gavroglu and Vassiliki Kindi. Kuhn provides a brief account of the historical origins of his idea. Here is the relevant segment of the interview.

T. KUHN: Look, 'incommensurability' is easy.

V. KINDI: You mean in mathematics?

T. KUHN: …When I was a bright high school mathematician and beginning to learn Calculus, somebody gave me—or maybe I asked for it because I’d heard about it—there was sort of a big two-volume Calculus book by, I can’t remember whom. And then I never really read it. I read the early parts of it. And early on it gives the proof of the irrationality of the square root of 2. And I thought it was beautiful. That was terribly exciting, and I learned what incommensurability was then and there. So, it was all ready for me, I mean, it was a metaphor but it got at nicely what I was after. So, that’s where I got it.

'It was all ready for me.' I thought, 'Wow.' The language was suggestive. I imagined √2 provocatively dressed, its lips rouged. But there was an unexpected surprise. The idea didn’t come from the physical sciences or philosophy or linguistics, but from mathematics ."

A footnote from Morris (no. 29)—

"Those who are familiar with the proof [of irrationality] certainly don’t want me to explain it here; likewise, those who are unfamiliar with it don’t want me to explain it here, either. There are many simple proofs in many histories of mathematics — E.T. Bell, Sir Thomas Heath, Morris Kline, etc., etc. Barry Mazur offers a proof in his book, 'Imagining Numbers (particularly the square root of minus fifteen),' New York, NY: Farrar, Straus and Giroux. 2003, 26ff. And there are two proofs in his essay, 'How Did Theaetetus Prove His Theorem?', available on Mazur’s Harvard Web site."

There may, actually, be a few who do  want the proof. They may consult the sources Morris gives, or the excellent  description by G.H. Hardy in A Mathematician's Apology , or, perhaps best of all for present purposes, the proof as described in a "sort of a big two-volume Calculus book" (perhaps the one Kuhn mentioned)…  See page 6 and page 7 of  Volume One  of Richard Courant's classic Differential and Integral Calculus  (second edition, 1937, reprinted many times through 1970, and again in a Wiley Classics Library Edition in 1988).

Monday, June 14, 2010

Theory of Ambiguity

Filed under: General,Geometry — m759 @ 5:01 pm

Théorie de l'Ambiguité

According to a 2008 paper by Yves André of the École Normale Supérieure  of Paris—

"Ambiguity theory was the name which Galois used
 when he referred to his own theory and its future developments."

The phrase "the theory of ambiguity" occurs in the testamentary letter Galois wrote to a friend, Auguste Chevalier, on the night before Galois was shot in a duel.

Hermann Weyl in Symmetry, Princeton University Press, 1952—

"This letter, if judged by the novelty and profundity of ideas it contains, is perhaps
  the most substantial piece of writing in the whole literature of mankind."

Conclusion of the Galois testamentary letter, according to
the 1897 Paris edition of Galois's collected works—

Image-- Galois on his theory of ambiguity, from Collected Works, Paris, 1897

The original—

Image-- Concluding paragraphs, Galois's 'last testament' letter to Chevalier, May 29, 1832

A transcription—

Évariste GALOIS, Lettre-testament, adressée à Auguste Chevalier—

Tu sais mon cher Auguste, que ces sujets ne sont pas les seuls que j'aie
explorés. Mes principales méditations, depuis quelques temps,
étaient dirigées sur l'application à l'analyse transcendante de la théorie de
l'ambiguité. Il s'agissait de voir a priori, dans une relation entre des quantités
ou fonctions transcendantes, quels échanges on pouvait faire, quelles
quantités on pouvait substituer aux quantités données, sans que la relation
put cesser d'avoir lieu. Cela fait reconnaitre de suite l'impossibilité de beaucoup
d'expressions que l'on pourrait chercher. Mais je n'ai pas le temps, et mes idées
ne sont pas encore bien développées sur ce terrain, qui est
immense.

Tu feras imprimer cette lettre dans la Revue encyclopédique.

Je me suis souvent hasardé dans ma vie à avancer des propositions dont je n'étais
pas sûr. Mais tout ce que j'ai écrit là est depuis bientôt un an dans ma
tête, et il est trop de mon intérêt de ne pas me tromper pour qu'on
me soupconne d'avoir énoncé des théorèmes dont je n'aurais pas la démonstration
complète.

Tu prieras publiquement Jacobi et Gauss de donner leur avis,
non sur la vérité, mais sur l'importance des théorèmes.

Après cela, il y aura, j'espère, des gens qui trouveront leur profit
à déchiffrer tout ce gachis.

Je t'embrasse avec effusion.

                                               E. Galois   Le 29 Mai 1832

A translation by Dr. Louis Weisner, Hunter College of the City of New York, from A Source Book in Mathematics, by David Eugene Smith, Dover Publications, 1959–

You know, my dear Auguste, that these subjects are not the only ones I have explored. My reflections, for some time, have been directed principally to the application of the theory of ambiguity to transcendental analysis. It is desired see a priori  in a relation among quantities or transcendental functions, what transformations one may make, what quantities one may substitute for the given quantities, without the relation ceasing to be valid. This enables us to recognize at once the impossibility of many expressions which we might seek. But I have no time, and my ideas are not developed in this field, which is immense.

Print this letter in the Revue Encyclopédique.

I have often in my life ventured to advance propositions of which I was uncertain; but all that I have written here has been in my head nearly a year, and it is too much to my interest not to deceive myself that I have been suspected of announcing theorems of which I had not the complete demonstration.

Ask Jacobi or Gauss publicly to give their opinion, not as to the truth, but as to the importance of the theorems.

Subsequently there will be, I hope, some people who will find it to their profit to decipher all this mess.

J t'embrasse avec effusion.
                        
                                                     E. Galois.   May 29, 1832.

Translation, in part, in The Unravelers: Mathematical Snapshots, by Jean Francois Dars, Annick Lesne, and Anne Papillaut (A.K. Peters, 2008)–

"You know, dear Auguste, that these subjects are not the only ones I have explored. For some time my main meditations have been directed on the application to transcendental analysis of the theory of ambiguity. The aim was to see in a relation between quantities or transcendental functions, what exchanges we could make, what quantities could be substituted to the given quantities without the relation ceasing to take place. In that way we see immediately that many expressions that we might look for are impossible. But I don't have the time and my ideas are not yet developed enough in this vast field."

Another translation, by James Dolan at the n-Category Café

"My principal meditations for some time have been directed towards the application of the theory of ambiguity to transcendental analysis. It was a question of seeing a priori in a relation between quantities or transcendent functions, what exchanges one could make, which quantities one could substitute for the given quantities without the original relation ceasing to hold. That immediately made clear the impossibility of finding many expressions that one could look for. But I do not have time and my ideas are not yet well developed on this ground which is immense."

Related material

"Renormalisation et Ambiguité Galoisienne," by Alain Connes, 2004

"La Théorie de l’Ambiguïté : De Galois aux Systèmes Dynamiques," by Jean-Pierre Ramis, 2006

"Ambiguity Theory, Old and New," preprint by Yves André, May 16, 2008,

"Ambiguity Theory," post by David Corfield at the n-Category Café, May 19, 2008

"Measuring Ambiguity," inaugural lecture at Utrecht University by Gunther Cornelissen, Jan. 16, 2009

Monday, July 19, 2021

Seeking the Source

Filed under: General — Tags: , , , , — m759 @ 7:19 pm

A post from January 21, 2003, now also tagged Big Sur,
suggested a search for the source of that post's
Shih Te poem. The result of the search —

Related Fredonia material, from posts tagged Church and Temple

Update, from six minutes later, on related entertainment —

 

Update of 12:38 PM ET on the next day — July 20, 2021 —

**********************************************************************

Crystal Poem by Shide (Shih Te, etc.)

at https://terebess.hu/zen/chang/shide.html

from "Comparative List of Shide's Poems" —

Traditional Chinese:

無去無來本湛然,
不居內外及中間。
一顆水精絕瑕翳,
光明透滿出人天。

Simplified Chinese:

无去无来本湛然,
不居内外及中间。
一颗水精绝瑕翳,
光明透满出人天。

Romanization:

wú qù wú lái běn zhàn rán ,
bù jū nèi wài jí zhōng jiān 。
yī kē shuǐ jīng jué xiá yì ,
guāng míng tòu mǎn chū rén tiān 。

English Translation by Paul Rouzer:

No goings, no comings, originally tranquil;
No dwelling within or without, or at the point between.
A single crystal of purity without flaw or crack;
Its light penetrates and fills up the worlds of men and gods.

English Translation by Red Pine:

Not waxing or waning essentially still
not inside or outside and nowhere between
a single flawless crystal
whose light shines through to gods and men

*******************************************************************

Tuesday, January 21, 2003

Tuesday January 21, 2003

Filed under: General — Tags: , , — m759 @ 5:09 pm

Diablo Ballet

Thanks to Meghan for the following:

not going, not coming,
rooted, deep and still
not reaching out, not reaching in
just resting, at the center
a single jewel, the flawless crystal drop
in the blaze of its brilliance
the way beyond.

— Shih Te (c. 730)

It turns out that Shih Te ("Foundling") was the sidekick of Han Shan ("Cold Mountain").  Here are some relevant links:

Thoughts of Robert Frost (see past two days' entries) lead to "Two Tramps in Mud Time," which in turn leads to Jack Kerouac and Gary Snyder splitting wood in The Dharma Bums.

This in turn leads, via a search on "Kerouac" and "axe," to the sentence

"There's the grace of an axe handle 
 as good as an Eglevsky ballet,"

in Big Sur

Kerouac taught me when I was 16 and he is still teaching me now that I am 60.

Searching for "Eglevsky ballet" leads to this site on André Eglevsky, his work, his life, and his children.  A further search leads to his daughter Marina Eglevsky, who stages dance for the Diablo Ballet.

Born to Dance

Marina Eglevsky and
the Diablo Ballet —
a rare and gifted
pas de deux

Those who feel the above is too "arty" for them may nevertheless appreciate the movie by the same name: "Born to Dance" (1936), starring Eleanor Powell and James Stewart.

In the larger metaphorical sense, of course, Powell and Eglevsky are both part of the same dance… at the "still point" described so well by Shih Te. 

"just resting, at the center
a single jewel…"

"At the still point,
there the dance is."
— T. S. Eliot

From Marshall's Jewelers, Tucson —

A Diamond-Cutter Sutra:

The ideal cut is a mathematical formula for cutting diamonds to precise angles and proportions to maximize the reflection and refraction of light. In addition to these ideal proportions, the polish and symmetry of the diamond is done to the highest standards also. Only then does it qualify to receive the American Gem Society (AGS) "triple zero" rating. A "zero" rating is the most perfect rating that the AGS gives evaluating the cut, polish, and symmetry of the diamond.

When a diamond receives the "zero" rating for each of these areas, (cut, polish, and symmetry), it gets three "zeros," hence the "triple zero" rating. Because of this attention to detail, it takes up to four times longer to cut a diamond to these standards than an "average" diamond.

You may choose to compromise on color or clarity but to ensure the most brilliant diamond you should not compromise on cut….

The "triple zero" ideal cut guarantees you a magnificent balance of brilliance, sparkle, and fire.

Postscript of 1/25/03:

See also the obituary of Irene Diamond, ballet patron, for whom the New York City Ballet's "Diamond Project" is named.  Diamond died on January 21, 2003, the date of the above weblog entry.

 

Monday, January 20, 2003

Monday January 20, 2003

Filed under: General — Tags: — m759 @ 5:00 pm

Shine On, Robinson Jeffers

"…be in nothing so moderate as in love of man, 
      a clever servant, insufferable master.
There is the trap that catches noblest spirits,
     that caught — they say — God, when he walked on earth."
Shine, Perishing Republic, by Robinson Jeffers

Robinson Jeffers died at Big Sur, California, on January 20, 1962 — a year to the day after Robert Frost spoke at the Kennedy inauguration.

"The poetry of Robinson Jeffers shines with a diamond's brilliance when he depicts Nature's beauty and magnificence.   His verse also flashes with a diamond's hardness when he portrays human pain and folly."
Gary Suttle  

"Praise Him, He hath conferred aesthetic distance
Upon our appetites, and on the bloody
Mess of our birthright, our unseemly need,
Imposed significant form. Through Him the brutes
Enter the pure Euclidean kingdom of number…."
— Howard Nemerov, 
   Grace To Be Said at the Supermarket 

"Across my foundering deck shone 
A beacon, an eternal beam. | Flesh fade, and mortal trash 
Fáll to the resíduary worm; | world's wildfire, leave but ash: 
In a flash, at a trumpet crash, 
I am all at once what Christ is |, since he was what I am, and 
Thís Jack, jóke, poor pótsherd, | patch, matchwood,
    immortal diamond, 
Is immortal diamond."
— Gerard Manley Hopkins,
    That Nature is a Heraclitean Fire and of the Comfort of the Resurrection

"In the last two weeks, I've been returning to Hopkins.  Even in the 'world's wildfire,' he asserts that 'this Jack, joke, poor potsherd, patch, matchwood, immortal diamond,/Is immortal diamond.' A comfort."
— Michael Gerson, head White House speechwriter,
    in Vanity Fair, May 2002, page 162

"There's none but truth can stead you.  Christ is truth."
— Gerard Manley Hopkins

"The rock cannot be broken.  It is the truth."
— Wallace Stevens 

"My ghost you needn't look for; it is probably
Here, but a dark one, deep in the granite…."
— Robinson Jeffers, Tor House

On this date in 1993, the inauguration day of William Jefferson Clinton, Audrey Hepburn died.

"…today, the Rock cries out to us, clearly, forcefully…."
Maya Angelou, January 20, 1993

"So, purposing each moment to retire,
She linger'd still. Meantime, across the moors,
Had come young Porphyro, with heart on fire"
— John Keats, The Eve of St. Agnes (January 20), IX

Top view of
ordinary
diamond

Top view of
Hearts On Fire
diamond

Advertising Copy:

What you see with a Hearts On Fire diamond is an unequalled marriage of math and physics, resulting in the world's most perfectly cut diamond.

 

"Eightpointed symmetrical signs are ancient symbols for the Venus goddess or the planet Venus as either the Morning star or the Evening star."
Symbols.com

"Set me as a seal upon your heart, as a seal upon your arm; for love is strong as death, passion fierce as the grave.  Its flashes are flashes of fire, a raging flame."
Song of Solomon

"The last words from the people in the towers and on the planes, over and over again, were 'I love you.'  Over and over again, the message was the same, 'I love you.' …. Perhaps this is the loudest chorus from The Rock:  we are learning just how powerful love really is, even in the face of death."
The Rev. Kenneth E. Kovacs

"Then I'll get on my knees and pray
We don't get fooled again."
The Who 

See also my note, "Bright Star," of October 23, 2002.

 

Friday, October 13, 2023

Turn, Turn, Turn

Filed under: General — Tags: , , — m759 @ 3:06 am

The conclusion of a Hungarian political figure's obituary in
tonight's online New York Times, written by Clay Risen

"A quietly religious man, he spent his last years translating
works dealing with Roman Catholic canon law."

This  journal on the Hungarian's date of death, October 8,
a Sunday, dealt in part with the submission to Wikipedia of
the following brief article . . . and its prompt rejection.

The Cullinane diamond theorem is a theorem
about the Galois geometry underlying
the Miracle Octad Generator of R. T. Curtis.[1]

The theorem also explains symmetry properties of the
sort of chevron or diamond designs often found on quilts.

Reference

1. Cullinane diamond theorem at
the Encyclopedia of Mathematics

Some quotations I prefer to Catholic canon law —

Ludwig Wittgenstein,
Philosophical Investigations  (1953)

97. Thought is surrounded by a halo.
—Its essence, logic, presents an order,
in fact the a priori order of the world:
that is, the order of possibilities * ,
which must be common to both world and thought.
But this order, it seems, must be
utterly simple . It is prior  to all experience,
must run through all experience;
no empirical cloudiness or uncertainty can be
allowed to affect it ——It must rather be of
the purest crystal. But this crystal does not appear
as an abstraction; but as something concrete,
indeed, as the most concrete,
as it were the hardest  thing there is.

* See the post Wittgenstein's Diamond.

Related language in Łukasiewicz (1937)—

http://www.log24.com/log/pix10B/101127-LukasiewiczAdamantine.jpg

See as well Diamond Theory in 1937.

Thursday, February 2, 2023

“Here I Come Again”

Filed under: General — Tags: — m759 @ 1:09 am

From tonight's previous post

"here I come again . . . the square root of minus one,
having terminated my humanities" — 

Samuel Beckett, Stories and Texts for Nothing
(New York: Grove, 1967), 128.

From The French Mathematician
by Tom Petsinis (Nov. 30, 1998) —

0

I had foreseen it all in precise detail.
One step led inevitably to the next,
like the proof of a shining theorem,
down to the conclusive shot that still echoes
through time and space. 
Facedown in the damp pine needles,
I embraced that fatal sphere
with my whole body. Dreams, memories,
even the mathematics I had cherished
and set down in my last will and testament–
all receded. I am reduced to
a singular point; in an instant
I am transformed to .

i = an imaginary being

Here, on this complex space,
i  am no longer the impetuous youth
who wanted to change the world
first with a formula and then with a flame.
Having learned the meaning of infinite patience,
i  now rise to the text whenever anyone reads 
about Evariste Galois, preferring to remain 
just below the surface, 
like a goldfish nibbling the fringe of a floating leaf.
Ink is more mythical than blood
(unless some ancient poet slit his 
vein and wrote an epic in red):
The text is a two-way mirror 
that allows me to look into
the life and times of the reader. 
Who knows, someday i  may rise
to a text that will compel me 
to push through to the other side.
Do you want proof that i  exist? Where am ?
Beneath every word, behind each letter, 
on the side of a period that will never see the light.

Related reading . . .

See also "William Lawvere, Category Theory, Hegel, Mao, and Code."

( https://www.reddit.com/r/socialistprogrammers/comments/m1oe88/
william_lawvere_category_theory_hegel_mao_and_code/ )

Also relating category theory and computation —
the interests of Lawvere and those of Davis — is
an article at something called The Topos Institute (topos.site) —

"Computation and Category Theory," by Joshua Meyers,
Wednesday, 10 Aug., 2022.

Meyers on Davis —

Wednesday, March 16, 2022

Midnight Memorial

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

"On a crisp Fall morning…." — The late Maureen Howard, writer of fiction.

Non-fiction: Feb. 19, 2022, 
https://news.yahoo.com/frances-haugen-
on-meta-headquarters-122958675.html
 —

FRANCES HAUGEN: To give you a sense of how absurd the space is,
so Facebook is obsessed with 15 and 30-minute meetings. It's like they're
very efficient, everyone's– they're obsessed with the word crisp, like are
your documents crisp, is your explanation crisp? The space is so large that
I would regularly walk 15 minutes, 10, 15 minutes to go to a 30-minute meeting. 

And again, fiction . . .

Monday, October 18, 2021

Get Star

Filed under: General — Tags: , — m759 @ 4:13 pm

From Log24 on July 19, 2021

Screenshots today from a social media site I joined last night —

The star in the previous post, "Logo," I drew last night for tchop use —

Saturday, October 2, 2021

Woodstock Hat Check

Filed under: General — Tags: — m759 @ 11:49 am

♫  The way you wear your hat . . .
   The way your smile just beams . . .

Later . . .

Richie Havens performed onstage at
the Woodstock Music and Arts Fair
in Bethel, New York, August 15, 1969.

Havens in Rolling Stone

I thought, "Oh, God, they're going to kill me. I'm not going out there first. What, are you crazy?" It was about 2:30 or 3 p.m. on Friday afternoon, and the concert was already almost three hours late. I was supposed to be fifth on the bill, but the other entertainers were still at the hotel, seven miles away. I thought, "Jeez, they're gonna throw beer cans at me because the concert's late." So I did a little fast talking, a little rap, and then I did a nearly three-hour set, until some of the others finally showed up. My bass player, Eric Oxendine, had gotten caught in the traffic on the New York State Thruway. He abandoned his car 30 miles away and walked, and he arrived just as we got offstage. When we left the festival, there wasn't another car on the thruway except ours. For 75 miles cars were parked five deep. That was the most surrealistic thing I've ever seen in my life. My fondest memory was realizing that I was seeing something I never thought I'd ever see in my lifetime — an assemblage of such numbers of people who had the same spirit and consciousness. And believe me, you wouldn't want to be in a place with that many people if they weren't like-minded! It was the first expression of the first global-minded generation born on the planet. Live Aid was a baby Woodstock, a child of Woodstock, which I call Globalstock. The history of the be-in is interesting. Originally it wasn't just about music. It was: "Let's go out to the park and throw Frisbees and be with each other." It went from that to the Monterey Pop Festival, which was a nonprofit concert in 1967, and from that came the hint: "Let's try to do one of these things, but let's try to make some money." That's where their heads were at, but that didn't happen. It turned into the world's largest be-in, which I call the Cosmic Accident. It was totally unexpected. The organizers thought that if it were like Monterey Pop — which drew 50 to 60,000 people — they'd make off like bandits. However, there were about 400,000 people the first afternoon, and it was free before it started. The only people who made off like bandits was Warner Bros., who got the movie rights. So the merits of Woodstock being love, peace, and harmony still stand on pillars of "Let's make money." That's what it was in the beginning. The consciousness was realized afterward. The movie chronicled that consciousness. It didn't make a big deal out of the music. You saw some of the musicians playing a song or two, but it was less than half the musicians who performed. So it wasn't a true depiction of what happened onstage, but you did see members of the older generation, like the police chief, saying, "Leave the kids alone, the kids are great, they're not bothering anybody." That was much more influential than the music on the people who went to see it. Woodstock wasn't just sex, drugs and rock & roll. Thank God for the movie, because the people who saw it got a touch of the Woodstock spirit, the spirit of people just being people.

A version of this story was originally published in the August 24th, 1989 print edition of Rolling Stone.

Wednesday, February 17, 2021

Raiders of the Lost Coordinates . . .

Continues.

From other posts tagged Tetrahedron vs. Square —

"There is  such a thing as a 4-set."
— Saying adapted from a 1962 young-adult novel.

Illustration (central detail  a  from the above tetrahedral figure) —

A Harvard Variation
from Timothy Leary —

The topics of Harvard and Leary suggest some other cultural
history, from The Coasters"Poison Ivy" and "Yakety Yak."

Monday, November 30, 2020

Space Exploration

Filed under: General — Tags: , , — m759 @ 2:52 pm

http://www.log24.com/log/pix18/180810-Huston-chessboard-post-100710.jpg

A sequel suggested by Jaime King’s Instagram yesterday

IMAGE- 'Right through hell there is a path.'

And they swam and they swam all over the dam.

Wednesday, November 11, 2020

The Work of a Comedian

Filed under: General — Tags: , — m759 @ 10:57 am

Flashback to Sept. 7, 2008

Change for Washington:

'The Laws of Change: I Ching and the Philosophy of Life,' by Jack M. Balkin

For the details, see yale.edu/lawweb:

“As important to Chinese civilization as the Bible is to Western culture,
the I Ching  or Book of Changes  is one of the oldest treasures of
world literature. Yet despite many commentaries written over the years,
it is still not well understood in the English-speaking world. In this
masterful [sic ] new interpretation, Jack Balkin returns the I Ching  to
its rightful place….

Jack M. Balkin

Jack M. Balkin

Jack M. Balkin is Knight Professor of Constitutional Law
and the First Amendment at Yale Law School, and
the founder and director of Yale’s Information Society Project.
His books and articles range over many different fields….”

Wallace Stevens on 'the work of a comedian'

Tuesday, November 10, 2020

The Lost Girls of 1983

Filed under: General — Tags: — m759 @ 3:45 am

Or:  The Doily Man Meets Roger Vadim

Tuesday, October 20, 2020

The Browning Methods

Filed under: General — Tags: , — m759 @ 6:00 am

The Ballad of Goo Ballou —
the Sequel to . . .

Let me count  the ways” is an appropriate request
for students of the discrete ,  as opposed to the
continuous , which instead requires measurement .

Related academic material —

Raymond Cattell on crystallized  vs. fluid  intelligence.
For a more literary approach, see Crystal and Dragon
and For Trevanian.

This post was inspired in part by
the American Sequel Society and . . .

Monday, September 14, 2020

Classics Illustrated

Filed under: General — m759 @ 6:28 pm

“You’re reading me,” she murmurs.

“Particularly and surprisingly well-preserved;
tight, bright, clean and especially sharp-cornered.”

Update of 7 PM ET Sept. 14, 2020 —

A sequel to Creamy and Sweaty

“Stop loading this page.” . . . “Too late.”

Monday, May 25, 2020

Cyberface

Filed under: General — Tags: , — m759 @ 3:45 pm

(A sequel to D8ing the Joystick)

Adam Gopnik today in The New Yorker

“In remote therapy sessions, with the loss of familiarly structured
therapeutic spaces, a kind of staring contest takes place.”

This  journal on the above YouTube date — May 28, 2011 —

“Two things of opposite natures seem to depend
On one another, as a man depends
On a woman, day on night, the imagined
On the real. This is the origin of change.
Winter and spring, cold copulars, embrace
And forth the particulars of rapture come.”

— Wallace Stevens,
“Notes Toward a Supreme Fiction,”
Canto IV of “It Must Change”

Update of 5:45  PM ET —

The  above May 28, 2011, Stevens quotation is from a post
titled “Savage Detectives.” A related image starring Sean Young —

Friday, May 15, 2020

Review

Filed under: General — Tags: , , , — m759 @ 5:24 pm

Charles Taylor,
“Epiphanies of Modernism,”
Chapter 24 of Sources of the Self
(Cambridge U. Press, 1989, p. 477) —

“… the object sets up
a kind of frame or space or field
within which there can be epiphany.”

See also Talking of Michelangelo.

Related material for comedians —

BOX: Binary Object Extension

Literature ad absurdum

Friday, April 17, 2020

Introduction to Quantum Woo

Filed under: General — Tags: — m759 @ 1:07 am

“In his big book, Gravity  [sic ], Wheeler puts our space
into what he calls superspace, and speculates on the
most basic physical laws which operate on superspace.
He comes to the (to me) surprising conclusion that the
rock-bottom laws are the laws of the propositional calculus!”

— Martin Gardner, letter to Donald E. Knuth, 8 January 1976,
on cover of Notices of the American Mathematical Society ,
March 2011 issue.

Fact check —

Related reading —

Sunday, March 24, 2019

Espacement: Geometry of the Interstice in Literary Theory

Filed under: General — Tags: , , , , — m759 @ 3:28 am

"You said something about the significance of spaces between
elements being repeated. Not only the element itself being repeated,
but the space between. I'm very interested in the space between.
That is where we come together." — Peter Eisenman, 1982

https://www.parrhesiajournal.org/
parrhesia03/parrhesia03_blackburne.pdf

Parrhesia  No. 3 • 2007 • 22–32

(Up) Against the (In) Between: Interstitial Spatiality
in Genet and Derrida

by Clare Blackburne

Blackburne — www.parrhesiajournal.org 24 —

"The excessive notion of espacement  as the resurgent spatiality of that which is supposedly ‘without space’ (most notably, writing), alerts us to the highly dynamic nature of the interstice – a movement whose discontinuous and ‘aberrant’ nature requires further analysis."

Blackburne — www.parrhesiajournal.org 25 —

"Espacement  also evokes the ambiguous figure of the interstice, and is related to the equally complex derridean notions of chora , différance , the trace and the supplement. Derrida’s reading of the Platonic chora  in Chora L Works  (a series of discussions with the architect Peter Eisenman) as something which defies the logics of non-contradiction and binarity, implies the internal heterogeneity and instability of all structures, neither ‘sensible’ nor ‘intelligible’ but a third genus which escapes conceptual capture.25 Crucially, chora , spacing, dissemination and différance  are highly dynamic concepts, involving hybridity, an ongoing ‘corruption’ of categories, and a ‘bastard reasoning.’26 Derrida identification of différance  in Margins of  Philosophy , as an ‘unappropriable excess’ that operates through spacing as ‘the becoming-space of time or the becoming-time of space,’27 chimes with his description of chora  as an ‘unidentifiable excess’ that is ‘the spacing which is the condition for everything to take place,’ opening up the interval as the plurivocity of writing in defiance of ‘origin’ and ‘essence.’28  In this unfolding of différance , spacing  ‘insinuates  into  presence an  interval,’29 again alerting us to the crucial role of the interstice in deconstruction, and, as Derrida observes  in Positions ,  its  impact  as  ‘a movement,  a  displacement  that  indicates  an  irreducible alterity’: ‘Spacing is the impossibility for an identity to be closed on itself, on the inside of its proper interiority, or on its coincidence with itself. The irreducibility of spacing is the irreducibility of the other.’30"

25. Quoted in Jeffrey Kipnis and Thomas Leeser, eds., 
Chora L Works. Jacques Derrida and Peter Eisenman  
(New York: The Monacelli Press, 1997), 15.

26. Ibid, 25.

27. Derrida, Margins of Philosophy.
(Brighton: The Harvester Press, 1982), 6 and 13.

28. Derrida, Chora L Works , 19 and 10.

29. Ibid, 203.

30. Derrida, Positions , 94.

Saturday, May 5, 2018

Galois Imaginary

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

" Lying at the axis of everything, zero is both real and imaginary. Lovelace was fascinated by zero; as was Gottfried Leibniz, for whom, like mathematics itself, it had a spiritual dimension. It was this that let him to imagine the binary numbers that now lie at the heart of computers: 'the creation of all things out of nothing through God's omnipotence, it might be said that nothing is a better analogy to, or even demonstration of such creation than the origin of numbers as here represented, using only unity and zero or nothing.' He also wrote, 'The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and nonbeing.' "

— A footnote from page 229 of Sydney Padua's
    April 21, 2015, book on Lovelace and Babbage

A related passage —

From The French Mathematician
by Tom Petsinis (Nov. 30, 1998) —

0

I had foreseen it all in precise detail.
One step led inevitably to the next,
like the proof of a shining theorem,
down to the conclusive shot that still echoes
through time and space. 
Facedown in the damp pine needles,
I embraced that fatal sphere
with my whole body. Dreams, memories,
even the mathematics I had cherished
and set down in my last will and testament–
all receded. I am reduced to
a singular point; in an instant
I am transformed to .

i = an imaginary being

Here, on this complex space,
i  am no longer the impetuous youth
who wanted to change the world
first with a formula and then with a flame.
Having learned the meaning of infinite patience,
i  now rise to the text whenever anyone reads 
about Evariste Galois, preferring to remain 
just below the surface, 
like a goldfish nibbling the fringe of a floating leaf.
Ink is more mythical than blood
(unless some ancient poet slit his 
vein and wrote an epic in red):
The text is a two-way mirror 
that allows me to look into
the life and times of the reader. 
Who knows, someday i  may rise
to a text that will compel me 
to push through to the other side.
Do you want proof that i  exist? Where am ?
Beneath every word, behind each letter, 
on the side of a period that will never see the light.

Sunday, April 29, 2018

Amusement

Filed under: General,Geometry — Tags: , — m759 @ 7:00 pm

From the online New York Times  this afternoon:

Disney now holds nine of the top 10
domestic openings of all time —
six of which are part of the Marvel
Cinematic Universe. “The result is
a reflection of 10 years of work:
of developing this universe, creating
stakes as big as they were, characters
that matter and stories and worlds that
people have come to love,” Dave Hollis,
Disney’s president of distribution, said
in a phone interview.

From this  journal this morning:

"But she felt there must be more to this
than just the sensation of folding space
over on itself. Surely the Centaurs hadn't
spent ten years telling humanity how to 
make a fancy amusement-park ride
.
There had to be more—"

Factoring Humanity , by Robert J. Sawyer,
Tom Doherty Associates, 2004 Orb edition,
page 168

"The sensation of folding space . . . ."

Or unfolding:

Click the above unfolded space for some background.

Wednesday, February 28, 2018

A Girl’s Guide to Chaos

Filed under: General — Tags: — m759 @ 9:55 am

The title is that of a play mentioned last night in
a New York Times  obituary .

Related recent film lines —

  • Thor:  How do I escape?
  • Heimdall:  You're on a planet surrounded by doorways.
    Go through one.
  • Thor:  Which one?
  • Heimdall:  The big one!

Related material from this  journal on Jan. 20, 2018 —

The Chaos Symbol of Dan Brown.

Sunday, March 5, 2017

A Hitch in Hell

Filed under: General — m759 @ 5:55 pm

The New York Times  today on a Feb. 24 death —

"Mr. Tenney was released when Japan surrendered
in August 1945, days after America dropped atomic
bombs on Hiroshima and on Nagasaki, a city across
the bay from the prison camp where he was held.
. . . .

Mr. Tenney recounted his wartime experiences in
a memoir, My Hitch in Hell , published in 1995."

Related material —

Box office report for opening weekend of Wolverine's X-Men spinoff 'Logan'

Zen ideal —

"… and Hell followed with him.

Friday, March 18, 2016

Weimar, Baby!*

Filed under: General — m759 @ 2:42 pm

Happy birthday to composer John Kander, who turns 89 today.

NPR MUSIC INTERVIEWS

Broadway Composer John Kander Reflects On
A Career Of 'Hidden Treasures'

TERRY GROSS, HOST:

This is FRESH AIR. I'm Terry Gross. My guest, composer John Kander, along with his longtime lyricist, the late Fred Ebb, wrote the songs for the Broadway shows "Cabaret," "Chicago," "Flora The Red Menace," "Kiss Of The Spider Woman" and "The Scottsboro Boys," as well as the songs for Martin Scorsese's 1977 film "New York, New York." The title song was a big hit for Frank Sinatra.

GROSS: …. John Kander, what impact did writing the songs for "Cabaret" have on you as a secular Jew because it's— you know, it's set in Germany as the Nazis are coming to power.

KANDER: I don't think I ever thought about that. I think I thought about it [as] a piece of theater. So

* See Noonan Weimar in this journal.

Monday, December 14, 2015

Dirac and Geometry

Filed under: General,Geometry — Tags: , — m759 @ 10:30 am

(Continued)

See a post by Peter Woit from Sept. 24, 2005 — Dirac's Hidden Geometry.

The connection, if any, with recent Log24 posts on Dirac and Geometry
is not immediately apparent.  Some related remarks from a novel —

From Broken Symmetries by Paul Preuss
(first published by Simon and Schuster in 1983) —

"He pondered the source of her fascination with the occult, which sooner or later seemed to entangle a lot of thoughtful people who were not already mired in establishmentarian science or religion. It was  the religious impulse, at base. Even reason itself could function as a religion, he supposed— but only for those of severely limited imagination. 

He’d toyed with 'psi' himself, written a couple of papers now much quoted by crackpots, to his chagrin. The reason he and so many other theoretical physicists were suckers for the stuff was easy to understand— for two-thirds of a century an enigma had rested at the heart of theoretical physics, a contradiction, a hard kernel of paradox. Quantum theory was inextricable from the uncertainty relations. 

The classical fox knows many things, but the quantum-mechanical hedgehog knows only one big thing— at a time. 'Complementarity,' Bohr had called it, a rubbery notion the great professor had stretched to include numerous pairs of opposites. Peter Slater was willing to call it absurdity, and unlike some of his older colleagues who, following in Einstein’s footsteps, demanded causal explanations for everything (at least in principle), Peter had never thirsted after 'hidden variables' to explain what could not be pictured. Mathematical relationships were enough to satisfy him, mere formal relationships which existed at all times, everywhere, at once. It was a thin nectar, but he was convinced it was the nectar of the gods. 

The psychic investigators, on the other hand, demanded to know how  the mind and the psychical world were related. Through ectoplasm, perhaps? Some fifth force of nature? Extra dimensions of spacetime? All these naive explanations were on a par with the assumption that psi is propagated by a species of nonlocal hidden variables, the favored explanation of sophisticates; ignotum per ignotius

'In this connection one should particularly remember that the human language permits the construction of sentences which do not involve any consequences and which therefore have no content at all…' The words were Heisenberg’s, lecturing in 1929 on the irreducible ambiguity of the uncertainty relations. They reminded Peter of Evan Harris Walker’s ingenious theory of the psi force, a theory that assigned psi both positive and negative values in such a way that the mere presence of a skeptic in the near vicinity of a sensitive psychic investigation could force null results. Neat, Dr. Walker, thought Peter Slater— neat, and totally without content. 

One had to be willing to tolerate ambiguity; one had to be willing to be crazy. Heisenberg himself was only human— he’d persuasively woven ambiguity into the fabric of the universe itself, but in that same set of 1929 lectures he’d rejected Dirac’s then-new wave equations with the remark, 'Here spontaneous transitions may occur to the states of negative energy; as these have never been observed, the theory is certainly wrong.' It was a reasonable conclusion, and that was its fault, for Dirac’s equations suggested the existence of antimatter: the first antiparticles, whose existence might never have been suspected without Dirac’s crazy results, were found less than three years later. 

Those so-called crazy psychics were too sane, that was their problem— they were too stubborn to admit that the universe was already more bizarre than anything they could imagine in their wildest dreams of wizardry."

Particularly relevant

"Mathematical relationships were enough to satisfy him,
mere formal relationships which existed at all times,
everywhere, at once."

Some related pure  mathematics

Anticommuting Dirac matrices as spreads of projective lines

Sunday, November 1, 2015

Transitions

Filed under: General — m759 @ 5:48 pm

Two transitions from last Monday, Oct. 26, 2015,
according to the online New York Times  today —

Leo P. Kadanoff, a physicist who provided critical insights into the transformations of matter from one state to another, died last Monday in Chicago. He was 78.

The cause was respiratory failure, said the University of Chicago, where he was a professor from 1978 until his retirement in 2003.

A member of the National Academy of Sciences and a fellow of the American Academy of Arts and Sciences, he received the National Medal of Science in 1999.

“He won basically every prize except the Nobel Prize, and many people thought he should have won the Nobel,” said Emil Martinec, a physics professor at the University of Chicago who directs the university’s Kadanoff Center for Theoretical Physics.

Dr. Kadanoff’s biggest scientific contribution came in the 1960s as scientists were trying to understand phase transitions, when matter changes from one form to another.

A Cornell chemist, Benjamin Widom, had come up with mathematical relationships that described behavior associated with second-order phase transitions, which include the boiling of water to steam at a particular temperature and pressure. But Dr. Widom did not have an underlying physical explanation for why these relationships existed.

Willis Carto, a reclusive behind-the-scenes wizard of the far-right fringe of American politics who used lobbying and publishing to denigrate Jews and other minorities and galvanize the movement to deny the Holocaust, died last Monday at his home in Virginia. He was 89.

His death was announced by The American Free Press, a newspaper he helped found.

Mr. Carto raised funds to finance a right-wing military dictatorship in the United States, campaigned to persuade blacks to voluntarily return to Africa and, most influentially, started newsletters, a journal and conferences of academics and others to deny the scale, and even the existence, of the Holocaust.

The Anti-Defamation League called him “one of the most influential American anti-Semitic propagandists” and “the mastermind of the hate network.”

His associates included neo-Nazis, Christian vigilantes, John Birch Society members and Ku Klux Klansmen, and his extreme views alienated mainstream conservatives. After William F. Buckley sued Mr. Carto for libel and won in 1985, Mr. Buckley said Mr. Carto epitomized “the fever swamps of the crazed right.’’

Related remarks:

Posts tagged "Steam," the post "On Ice-Breaking" from Oct. 27,
the post "Expanding the Seagram Spielraum" from Oct. 26, and
a 2008 article on the subject of the obituary at right above.

"Integrity, Craftsmanship, Tradition"

Monday, October 12, 2015

Space, Time, Matter (continued)

Filed under: General — m759 @ 5:08 pm

Cool Mystery:

http://www.log24.com/log/pix11C/111005-PlancksCafe-CruzEnters.jpg

Detective Cruz enters Planck's Constant Café in "The Big Bang."

The above images are from a Log24 post of October 5, 2011.

Related material for fans of recreational math and Manil Suri

A book that Amazon.com says was published on that same date —
October 5, 2011 —

Space, Time and Matter 

by Ashay Dharwadker (Author), Vinay Dharwadker  (Author)

Product Details

  • Paperback: 98 pages
  • Publisher: CreateSpace Independent Publishing
                       Platform (October 5, 2011)
  • Language: English
  • Amazon Best Sellers Rank: #7,605,448 in Books 

See as well

Con Vocation  (Log24, Sept. 2, 2014).

Monday, September 28, 2015

Cracker Jack Prize

Filed under: General,Geometry — Tags: — m759 @ 11:00 pm

From a post of July 24, 2011

Mira Sorvino in 'The Last Templar'

A review —

“The story, involving the Knights Templar, the Vatican, sunken treasure,
the fate of Christianity and a decoding device that looks as if it came out of 
a really big box of medieval Cracker Jack, is the latest attempt to combine
Indiana Jones derring-do with ‘Da Vinci Code’ mysticism.”

— The New York Times

A feeble attempt at a purely mathematical "decoding device"
from this journal earlier this month

Image that may or may not be related to the extended binary Golay code and the large Witt design

For some background, see a question by John Baez at Math Overflow
on Aug. 20, 2015.

The nonexistence of a 24-cycle in the large Mathieu group
might discourage anyone hoping for deep new insights from
the above figure.

See Marston Conder's "Symmetric Genus of the Mathieu Groups" —

Saturday, January 24, 2015

Now We Are Six (continued)

Filed under: General — Tags: — m759 @ 11:01 am

Wikipedia on a 1953 novel by Theodore Sturgeon:

"The novel concerns the coming together of
six extraordinary people with strange powers…."

Review of the novel by Ted Gioia at Conceptual Fiction :

"If there is a flaw to More Than Human , it comes from
the writer’s desire to achieve more than fiction. If you 
think that sci-fi books don’t pay attention to deep
inner meanings, you will be surprised by the conclusion
to this work, in which Sturgeon reaches for something
bigger than a story of this scale can deliver."

Background: Sturgeon's novella Baby is Three  (1952).

See also  6!  in this journal.

Monday, November 3, 2014

Wisconsin Death Trip*

Filed under: General — Tags: — m759 @ 8:59 pm

Courtesy of Mira Sorvino.

Enter Madison :

From “Intruders,” BBC America, Season 1, Episode 2, at 1:07 of 43:31.

You sure know how to show a girl a good time.

* The title is a reference to a Wisconsin-related Halloween post.

Thursday, August 14, 2014

MIT Mystery

Filed under: General — m759 @ 11:00 am

Robin Williams and the Stages of Grief

A weblog post from Jan. 25, 2014 (click image to enlarge)—

Clues for a Mystery   (Click links for more details)—

Clue 1:  A June 11,* 2014, math death.

Clue 2:  The answer is a surname.

Midrash for Will Hunting:

See Nanavira Thera at Wikipedia and space notes from September 2012.

* According to a (perhaps inaccurate) math department.
June 10, according to other sources cited by the department.

Saturday, July 26, 2014

OOPs

Filed under: General — Tags: — m759 @ 2:01 pm

Or:  Two Rivets Short of a Paradigm

Detail from an author photo:

IMAGE- 'House of Cards,' book on Bear Stearns, author photo, with two missing rivets

From rivet-rivet.net:

The philosopher Graham Harman is invested in re-thinking the autonomy of objects and is part of a movement called Object-Oriented-Philosophy (OOP). Harman wants to question the authority of the human being at the center of philosophy to allow the insertion of the inanimate into the equation. With the aim of proposing a philosophy of objects themselves, Harman puts the philosophies of Bruno Latour and Martin Heidegger in dialogue. Along these lines, Harman proposes an unconventional reading of the tool-being analysis made by Heidegger. For Harman, the term tool does not refer only to human-invented tools such as hammers or screwdrivers, but to any kind of being or thing such as a stone, dog or even a human. Further, he uses the terms objects, beings, tools and things, interchangeably, placing all on the same ontological footing. In short, there is no “outside world.”

Harman distinguishes two characteristics of the tool-being: invisibility and totality. Invisibility means that an object is not simply used but is: “[an object] form(s) a cosmic infrastructure of artificial and natural and perhaps supernatural forces, power by which our last action is besieged.” For instance, nails, wooden boards and plumbing tubes do their work to keep a house “running” silently (invisibly) without being viewed or noticed. Totality means that objects do not operate alone but always in relation to other objects–the smallest nail can, for example, not be disconnected from wooden boards, the plumbing tubes or from the cement. Depending on the point of view of each entity (nail, tube, etc.) a different reality will emerge within the house. For Harman, “to refer to an object as a tool-being is not to say that it is brutally exploited as a means to an end, but only that it is torn apart by the universal duel between the silent execution of an object’s reality and the glistening aura of its tangible surface.”

— From "The Action of Things," an M.A. thesis at the Center for Curatorial Studies, Bard College, by Manuela Moscoso, May 2011, edited by Sarah Demeuse

From Wikipedia, a programming paradigm:

See also posts tagged Turing's Cathedral, and Alley  Oop (Feb. 11, 2003).

Sunday, April 27, 2014

Sunday School

Filed under: General,Geometry — Tags: , — m759 @ 9:00 am

Galois and Abel vs. Rubik

(Continued)

“Abel was done to death by poverty, Galois by stupidity.
In all the history of science there is no completer example
of the triumph of crass stupidity….”

— Eric Temple Bell,  Men of Mathematics

Gray Space  (Continued)

… For The Church of Plan 9.

Saturday, March 22, 2014

Two Types of Symmetry

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

Mathematical

IMAGE- Weber hexads in 'Kummer's Quartic Surface'

IMAGE- Ohashi on the 192 Weber hexads

Literary (also from May 18, 2010)

IMAGE- Heraclitus, 'Immortals mortal, mortals immortal'- 'athanatoi thnetoi, thnetoi athanatoi'

Friday, March 7, 2014

Field Dream

Filed under: General — m759 @ 7:11 pm

A field in China —

IMAGE- Chinese field from opening of TV series 'Resurrection'

The following link was suggested by today’s previous post
and by the ABC TV series “Resurrection” scheduled to start
at 9 PM ET Sunday, March 9, 2014 —

Field Dream

Thursday, December 5, 2013

Blackboard Jungle

Filed under: General,Geometry — Tags: , , — m759 @ 11:07 am

Continued from Field of Dreams, Jan. 20, 2013.

IMAGE- Richard Kiley in 'Blackboard Jungle,' with grids and broken records

That post mentioned the March 2011 AMS Notices ,
an issue on mathematics education.

In that issue was an interview with Abel Prize winner
John Tate done in Oslo on May 25, 2010, the day
he was awarded the prize. From the interview—

Research Contributions

Raussen and Skau: This brings us to the next
topic: Your Ph.D. thesis from 1950, when you were
twenty-five years old. It has been extensively cited
in the literature under the sobriquet “Tate’s thesis”.
Several mathematicians have described your thesis
as unsurpassable in conciseness and lucidity and as
representing a watershed in the study of number
fields. Could you tell us what was so novel and fruitful
in your thesis?

Tate: Well, first of all, it was not a new result, except
perhaps for some local aspects. The big global
theorem had been proved around 1920 by the
great German mathematician Erich Hecke, namely
​the fact that all L -functions of number fields,
abelian -functions, generalizations of Dirichlet’s
L -functions, have an analytic continuation
throughout the plane with a functional equation
of the expected type. In the course of proving
it Hecke saw that his proof even applied to a new
kind of L -function, the so-called L -functions with
Grössencharacter. Artin suggested to me that one
might prove Hecke’s theorem using abstract
harmonic analysis on what is now called the adele
ring, treating all places of the field equally, instead
of using classical Fourier analysis at the archimedian 
places and finite Fourier analysis with congruences 
at the p -adic places as Hecke had done. I think I did
a good job —it might even have been lucid and
concise!—but in a way it was just a wonderful 
exercise to carry out this idea. And it was also in the
air. So often there is a time in mathematics for 
something to be done. My thesis is an example. 
Iwasawa would have done it had I not.

[For a different perspective on the highlighted areas of
mathematics, see recent remarks by Edward Frenkel.]

"So often there is a time in mathematics for something to be done."

— John Tate in Oslo on May 25, 2010.

See also this journal on May 25, 2010, as well as
Galois Groups and Harmonic Analysis on Nov. 24, 2013.

Wednesday, July 31, 2013

The Question

Filed under: General — Tags: — m759 @ 8:00 am

Maya Alexandri on September 7, 2009

… Blixen herself may have cut closer to the truth
in her final story in Winter's Tales , "A Consolatory Tale" [1942].

In it, a character explains,

What exactly [the imposter to the Prince] has told
the people I cannot report, partly because his sayings
seem to be deep and twofold, so that those who have
heard them do not remember them, and partly because
he really does not say much.  But the impression which
he has made is sure to be very profound.

Later, the imposter utters the following enigma: "Life and Death
are two locked caskets, each of which contains the key to the other."  
In other words, this imposter bore a striking resemblance to
Kahlil Gibran (or his modern day incarnate, Paulo Coelho).

Stylist or fraud, that's the question.

Stylist or fraud?

Saturday, May 11, 2013

Core

Promotional description of a new book:

“Like Gödel, Escher, Bach  before it, Surfaces and Essences  will profoundly enrich our understanding of our own minds. By plunging the reader into an extraordinary variety of colorful situations involving language, thought, and memory, by revealing bit by bit the constantly churning cognitive mechanisms normally completely hidden from view, and by discovering in them one central, invariant core— the incessant, unconscious quest for strong analogical links to past experiences— this book puts forth a radical and deeply surprising new vision of the act of thinking.”

“Like Gödel, Escher, Bach  before it….”

Or like Metamagical Themas .

Rubik core:

Swarthmore Cube Project, 2008

Non- Rubik cores:

Of the odd  nxnxn cube:

Of the even  nxnxn cube:

The image “http://www.log24.com/theory/images/cube2x2x2.gif” cannot be displayed, because it contains errors.

Related material: The Eightfold Cube and

“A core component in the construction
is a 3-dimensional vector space  over F.”

—  Page 29 of “A twist in the M24 moonshine story,”
by Anne Taormina and Katrin Wendland.
(Submitted to the arXiv on 13 Mar 2013.)

Tuesday, April 30, 2013

Logline

Filed under: General,Geometry — Tags: , , — m759 @ 9:29 am

Found this morning in a search:

logline  is a one-sentence summary of your script.
www.scriptologist.com/Magazine/Tips/Logline/logline.html
It's the short blurb in TV guides that tells you what a movie
is about and helps you decide if you're interested 

The search was suggested by a screenwriting weblog post,
"Loglines: WHAT are you doing?".

What is your story about?
No, seriously, WHAT are you writing about?
Who are the characters? What happens to them?
Where does it take place? What’s the theme?
What’s the style? There are nearly a million
little questions to answer when you set out
to tell a story. But it all starts with one
super, overarching question.
What are you writing about? This is the first
big idea that we pull out of the ether, sometimes
before we even have any characters.
What is your story about?

The screenwriting post was found in an earlier search for
the highlighted phrase.

The screenwriting post was dated December 15, 2009.

What I am doing now  is checking for synchronicity.

This  weblog on December 15, 2009, had a post
titled A Christmas Carol. That post referred to my 1976
monograph titled Diamond Theory .

I guess the script I'm summarizing right now is about
the heart of that theory, a group of 322,560 permutations
that preserve the symmetry of a family of graphic designs.

For that group in action, see the Diamond 16 Puzzle.

The "super overarching" phrase was used to describe
this same group in a different context:

IMAGE- Anne Taormina on 'Mathieu Moonshine' and the 'super overarching symmetry group'

This is from "Mathieu Moonshine," a webpage by Anne Taormina.

A logline summarizing my  approach to that group:

Finite projective geometry explains
the surprising symmetry properties
of some simple graphic designs—
found, for instance, in quilts.

The story thus summarized is perhaps not destined for movie greatness.

Monday, April 1, 2013

Desargues via Rosenhain

Filed under: General,Geometry — Tags: , , — m759 @ 6:00 pm

Background: Rosenhain and Göpel Tetrads in PG(3,2)

Introduction:

The Large Desargues Configuration

Added by Steven H. Cullinane on Friday, April 19, 2013

Desargues' theorem according to a standard textbook:

"If two triangles are perspective from a point
they are perspective from a line."

The converse, from the same book:

"If two triangles are perspective from a line
they are perspective from a point."

Desargues' theorem according to Wikipedia 
combines the above statements:

"Two triangles are in perspective axially  [i.e., from a line]
if and only if they are in perspective centrally  [i.e., from a point]."

A figure often used to illustrate the theorem, 
the Desargues configuration , has 10 points and 10 lines,
with 3 points on each line and 3 lines on each point.

A discussion of the "if and only if" version of the theorem
in light of Galois geometry requires a larger configuration—
15 points and 20 lines, with 3 points on each line 
and 4 lines on each point.

This large  Desargues configuration involves a third triangle,
needed for the proof   (though not the statement ) of the 
"if and only if" version of the theorem. Labeled simply
"Desargues' Theorem," the large  configuration is the
frontispiece to Volume I (Foundations)  of Baker's 6-volume
Principles of Geometry .

Point-line incidence in this larger configuration is,
as noted in the post of April 1 that follows
this introduction, described concisely 
by 20 Rosenhain tetrads  (defined in 1905 by
R. W. H. T. Hudson in Kummer's Quartic Surface ).

The third triangle, within the larger configuration,
is pictured below.

IMAGE- The proof of the converse of Desargues' theorem involves a third triangle.

 

 

 

A connection discovered today (April 1, 2013)—

(Click to enlarge the image below.)

Update of April 18, 2013

Note that  Baker's Desargues-theorem figure has three triangles,
ABC, A'B'C', A"B"C", instead of the two triangles that occur in
the statement of the theorem. The third triangle appears in the
course of proving, not just stating, the theorem (or, more precisely,
its converse). See, for instance, a note on a standard textbook for 
further details.

(End of April 18, 2013 update.)

Update of April 14, 2013

See Baker's Proof (Edited for the Web) for a detailed explanation 
of the above picture of Baker's Desargues-theorem frontispiece.

(End of April 14, 2013 update.)

Update of April 12, 2013

A different figure, from a site at National Tsing Hua University,
shows the three triangles of Baker's figure more clearly:

IMAGE- Desargues' theorem with three triangles, and Galois-geometry version

(End of update of April 12, 2013)

Update of April 13, 2013

Another in a series of figures illustrating
Desargues's theorem in light of Galois geometry:
IMAGE- Veblen and Young 1910 Desargues illustration, with 2013 Galois-geometry version

See also the original Veblen-Young figure in context.

(End of update of April 13, 2013)

Rota's remarks, while perhaps not completely accurate, provide some context
for the above Desargues-Rosenhain connection.  For some other context,
see the interplay in this journal between classical and finite geometry, i.e.
between Euclid and Galois.

For the recent  context of the above finite-geometry version of Baker's Vol. I
frontispiece, see Sunday evening's finite-geometry version of Baker's Vol. IV
frontispiece, featuring the Göpel, rather than the Rosenhain, tetrads.

For a 1986 illustration of Göpel and Rosenhain tetrads (though not under
those names), see Picturing the Smallest Projective 3-Space.

In summary… the following classical-geometry figures
are closely related to the Galois geometry PG(3,2):

Volume I of Baker's Principles  
has a cover closely related to 
the Rosenhain tetrads in PG(3,2)
Volume IV of Baker's Principles 
has a cover closely related to
the Göpel tetrads in PG(3,2) 
Foundations
(click to enlarge)

 

 

 

 

Higher Geometry
(click to enlarge)

 

 

 

 

 

Sunday, March 10, 2013

Galois Space

Filed under: General,Geometry — Tags: — m759 @ 5:30 pm

(Continued)

The 16-point affine Galois space:

Further properties of this space:

In Configurations and Squares, see the
discusssion of the Kummer 166 configuration.

Some closely related material:

  • Wolfgang Kühnel,
    "Minimal Triangulations of Kummer Varieties,"
    Abh. Math. Sem. Univ. Hamburg 57, 7-20 (1986).

    For the first two pages, click here.

  • Jonathan Spreer and Wolfgang Kühnel,
    "Combinatorial Properties of the 3 Surface:
    Simplicial Blowups and Slicings,"
    preprint, 26 pages. (2009/10) (pdf).
    (Published in Experimental Math. 20,
    issue 2, 201–216 (2011).)

Saturday, January 19, 2013

Executioner’s Song

Filed under: General — m759 @ 12:24 pm

For Terry Gilliam

IMAGE- Ace of Spades in Disney's version of 'Aquarela do Brasil,' uploaded Aug. 13, 2011

See also, from the the above uploading date, Taylor Made,
with its linked-to passage from a book by Charles Taylor.

For some more recent background, see

Sunday, December 9, 2012

Deep Structure

Filed under: General,Geometry — Tags: , — m759 @ 10:18 am

The concept of "deep structure," once a popular meme,
has long been abandoned by Chomskians.

It still applies, however, to the 1976 mathematics, diamond theory  ,
underlying the formal patterns discussed in a Royal Society paper
this year.

A review of deep structure, from the Wikipedia article Cartesian linguistics

[Numbers in parentheses refer to pages in the original 1966 Harper edition of Chomsky's book Cartesian Linguistics .]

Deep structure vs. surface structure

"Pursuing the fundamental distinction between body and mind, Cartesian linguistics characteristically assumes that language has two aspects" (32). These are namely the sound/character of a linguistic sign and its significance (32). Semantic interpretation or phonetic interpretation may not be identical in Cartesian linguistics (32). Deep structures are often only represented in the mind (a mirror of thought), as opposed to surface structures, which are not.

Deep structures vary less between languages than surface structures. For instance, the transformational operations to derive surface forms of Latin and French may obscure common features of their deep structures (39). Chomsky proposes, "In many respects, it seems to me quite accurate, then, to regard the theory of transformational generative grammar, as it is developing in current work, as essentially a modern and more explicit version of the Port-Royal theory" (39).

Summary of Port Royal Grammar

The Port Royal Grammar is an often cited reference in Cartesian Linguistics  and is considered by Chomsky to be a more than suitable example of Cartesian linguistic philosophy. "A sentence has an inner mental aspect (a deep structure that conveys its meaning) and an outer, physical aspect as a sound sequence"***** This theory of deep and surface structures, developed in Port Royal linguistics, meets the formal requirements of language theory. Chomsky describes it in modern terms as "a base system that generates deep structures and a transformational system that maps these into surface structures", essentially a form of transformational grammar akin to modern studies (42).

The corresponding concepts from diamond theory are

"Deep structure"— The line diagrams indicating the underlying
structure of varying patterns

"A base system that generates deep structures"—
Group actions on square arrays for instance, on the 4×4 square

"A transformational system"— The decomposition theorem 
that maps deep structure into surface structure (and vice-versa)

Monday, November 19, 2012

Poetry and Truth

From today's noon post

"In all his poems with all their enchantments
for the poet himself, there is the final enchantment
that they are true. The significance of the poetic act
then is that it is evidence. It is instance and illustration.
It is an illumination of a surface,
the movement of a self in the rock.
Above all it is a new engagement with life.
It is that miracle to which the true faith of the poet
attaches itself."

— Wallace Stevens at Bard College, March 30, 1951

Stevens also said at Bard that

"When Joan of Arc said: 

Have no fear: what I do, I do by command.
My brothers of Paradise tell me what I have to do.

these words were the words of an hallucination.
No matter what her brothers of Paradise drove her to do,
what she did was never a poetic act of faith in reality
because it could not be."

There are those who would dispute this.

Some related material:

"Ageometretos me eisito."—
"Let no one ignorant of geometry enter."—
Said to be a saying of Plato, part of the
seal of the American Mathematical Society—

A poetic approach to geometry—

"A surface" and "the rock," from All Saints' Day, 2012

Spaces as Hypercubes

— and from 1981—

http://www.log24.com/log/pix09/090217-SolidSymmetry.jpg

Some mathematical background for poets in Purgatory—

"… the Klein correspondence underlies Conwell's discussion 
of eight heptads. These play an important role in another
correspondence, illustrated in the Miracle Octad Generator
of R. T. Curtis, that may be used to picture actions
of the large Mathieu group M24."

Saturday, October 27, 2012

Behind the Green Door

Filed under: General — Tags: , — m759 @ 10:00 pm

It's 10 PM .

Backstory—

Posts of October 24th—
Love Ghost and Versions
and a version of Plan 9— 

Favicon 9

http://www.log24.com/log/pix11/110408-HopkinsAsExorcist.jpg

Related religious meditation—

Irresistible Grace, illustrated by The Girl in the Yellow Dress.

Thursday, September 27, 2012

Kummer and the Cube

Filed under: General,Geometry — Tags: , , — m759 @ 7:11 pm

Denote the d-dimensional hypercube by  γd .

"… after coloring the sixty-four vertices of  γ6
alternately red and blue, we can say that
the sixteen pairs of opposite red vertices represent
the sixteen nodes of Kummer's surface, while
the sixteen pairs of opposite blue vertices
represent the sixteen tropes."

— From "Kummer's 16," section 12 of Coxeter's 1950
    "Self-dual Configurations and Regular Graphs"

Just as the 4×4 square represents the 4-dimensional
hypercube  γ4  over the two-element Galois field GF(2),
so the 4x4x4 cube represents the 6-dimensional
hypercube  γ6  over GF(2).

For religious interpretations, see
Nanavira Thera (Indian) and
I Ching  geometry (Chinese).

See also two professors in The New York Times
discussing images of the sacred in an op-ed piece
dated Sept. 26 (Yom Kippur).

Wednesday, September 19, 2012

For Odin’s Day*

Filed under: General — m759 @ 12:00 pm

(Mathematics and Narrative, continued)

"My dad has a great expression,"
Steve Sabol told USA TODAY Sports
last year. "He always says, 'Tell me
a fact, and I'll learn. Tell me the truth,
and I believe. But tell me a story,
and it will live in my heart forever.' "

Fact—

Sabol died yesterday.

Truth—

An art gallery in Oslo is exhibiting a tesseract.

Story—

The Jewel of Odin's Treasure Room

(Click to enlarge.)

* I.e., Wednesday. For some apt Nordic spirit,
   see Odin's Day 2012 Trailer.

Monday, September 17, 2012

Pattern Conception

Filed under: General,Geometry — Tags: , , , , — m759 @ 10:00 am

( Continued from yesterday's post FLT )

Context Part I —

"In 1957, George Miller initiated a research programme at Harvard University to investigate rule-learning, in situations where participants are exposed to stimuli generated by rules, but are not told about those rules. The research program was designed to understand how, given exposure to some finite subset of stimuli, a participant could 'induce' a set of rules that would allow them to recognize novel members of the broader set. The stimuli in question could be meaningless strings of letters, spoken syllables or other sounds, or structured images. Conceived broadly, the project was a seminal first attempt to understand how observers, exposed to a set of stimuli, could come up with a set of principles, patterns, rules or hypotheses that generalized over their observations. Such abstract principles, patterns, rules or hypotheses then allow the observer to recognize not just the previously seen stimuli, but a wide range of other stimuli consistent with them. Miller termed this approach 'pattern conception ' (as opposed to 'pattern perception'), because the abstract patterns in question were too abstract to be 'truly perceptual.'….

…. the 'grammatical rules' in such a system are drawn from the discipline of formal language theory  (FLT)…."

— W. Tecumseh Fitch, Angela D. Friederici, and Peter Hagoort, "Pattern Perception and Computational Complexity: Introduction to the Special Issue," Phil. Trans. R. Soc. B  (2012) 367, 1925-1932 

Context Part II —

IMAGE- Wikipedia article 'Formal language'

Context Part III —

A four-color theorem describes the mathematics of
general  structures, not just symbol-strings, formed from
four kinds of things— for instance, from the four elements
of the finite Galois field GF(4), or the four bases of DNA.

Context Part IV —

A quotation from William P. Thurston, a mathematician
who died on Aug. 21, 2012—

"It may sound almost circular to say that
what mathematicians are accomplishing
is to advance human understanding of mathematics.
I will not try to resolve this
by discussing what mathematics is,
because it would take us far afield.
Mathematicians generally feel that they know
what mathematics is, but find it difficult
to give a good direct definition.
It is interesting to try. For me,
'the theory of formal patterns'
has come the closest, but to discuss this
would be a whole essay in itself."

Related material from a literate source—

"So we moved, and they, in a formal pattern"

Formal Patterns—

Not formal language theory  but rather
finite projective geometry  provides a graphic grammar
of abstract design

IMAGE- Harvard Crimson ad, Easter Sunday, 2008: 'Finite projective geometry as a graphic grammar of abstract design'

See also, elsewhere in this journal,
Crimson Easter Egg and Formal Pattern.

Thursday, September 6, 2012

Decomp Revisited

Filed under: General — m759 @ 1:11 pm

Frogs:

"Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time."

— Freeman Dyson (See July 22, 2011)

A Rhetorical Question:

Robert Osserman in 2004

"The past decade has been an exciting one in the world of mathematics and a fabulous one (in the literal sense) for mathematicians, who saw themselves transformed from the frogs of fairy tales— regarded with a who-would-want-to-kiss-that aversion, when they were noticed at all— into fascinating royalty, portrayed on stage and screen….

Who bestowed the magic kiss on the mathematical frog?"

A Rhetorical Answer:

http://www.log24.com/log/pix11C/111130-SunshineCleaning.jpg

Above: Amy Adams in "Sunshine Cleaning"

Related material:

Thursday, July 26, 2012

Solomon’s Seal

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

(Mathematics and Narrative, continued)

Narrative—

The Ring and The Stone from yesterday’s post, and…

“In Medieval Jewish, Christian and Islamic legends,
the Seal of Solomon was a magical signet ring
said to have been possessed by King Solomon….”

— Wikipedia article, Seal of Solomon

Mathematics—

IMAGE- Eric Temple Bell on the mathematics of 'Solomon's Seal' (in his 'Development of Mathematics')

A fact related to the mathematical
“Solomon’s seal” described above by Bell:

IMAGE- J.W.P. Hirschfeld on the mathematics of 'Solomon's Seal', with reference to Edge on the same topic

The reference to Edge is as follows—

[3] Edge, W. L., Quadrics over GF(2) and
their relevance for the cubic surface group
,
Canadian J. Maths. 11 (1959) ….

(This reference relates Hirschfeld’s remarks
quoted above to the 64-point affine space
illustrated below (via the associated
63-point projective  space PG (5, 2)).

As for the narrative’s Stone… 

See Solomon’s Cube.

IMAGE- 'Solomon's Cube'

Sunday, July 1, 2012

Shining Night*

Filed under: General — m759 @ 11:59 pm
 

This evening's online New York Times

Doris Sams, Pro Baseball Star, Dies at 85

By RICHARD GOLDSTEIN

Published: July 1, 2012

Doris Sams, who pitched a perfect game and set a single-season home run record in the women’s professional baseball world of the 1940s and 50s that inspired the movie “A League of Their Own,” died Thursday in Knoxville, Tenn. She was 85. more>>

"High summer holds the earth." 

James Agee, quoted in a post by University Diaries
linked to here on Thursday.

See also For Taylor and Country Strong.

* A phrase from the quoted Agee poem

Friday, June 22, 2012

Bowling in Diagon Alley

Filed under: General,Geometry — Tags: , — m759 @ 8:28 am

IMAGE- Josefine Lyche bowling, from her Facebook page

Josefine Lyche bowling (Facebook, June 12, 2012)

"Where Does Math Come From?"

A professor of philosophy in 1984 on Socrates's geometric proof in Plato's Meno  dialogue—

"These recondite issues matter because theories about mathematics have had a big place in Western philosophy. All kinds of outlandish doctrines have tried to explain the nature of mathematical knowledge. Socrates set the ball rolling…."

— Ian Hacking in The New York Review of Books , Feb. 16, 1984

The same professor introducing a new edition of Kuhn's Structure of Scientific Revolutions

"Paradigms Regained" (Los Angeles Review of Books , April 18, 2012)—

"That is the structure of scientific revolutions: normal science with a paradigm and a dedication to solving puzzles; followed by serious anomalies, which lead to a crisis; and finally resolution of the crisis by a new paradigm. Another famous word does not occur in the section titles: incommensurability. This is the idea that, in the course of a revolution and paradigm shift, the new ideas and assertions cannot be strictly compared to the old ones."

The Meno  proof involves inscribing diagonals  in squares. It is therefore related, albeit indirectly, to the classic Greek discovery that the diagonals of a square are incommensurable  with its sides. Hence the following discussion of incommensurability seems relevant.

IMAGE- Von Fritz in 1945 on incommensurability and the tetractys (10 as a triangular number)

See also von Fritz and incommensurability in The New York Times  (March 8, 2011).

For mathematical remarks related to the 10-dot triangular array of von Fritz, diagonals, and bowling, see this  journal on Nov. 8, 2011— "Stoned."

Tuesday, June 19, 2012

Design

Filed under: General — m759 @ 12:00 pm

The New York Times online front page last night

"Microsoft introduced its own tablet computer,
called Surface, illustrating the pressure
Apple's success has put on it to marry
software and hardware more tightly."

Commentary—

IMAGE- The Marriage of Heaven and Hell-- Swedenborg Chapel and the Harvard Graduate School of Design

Google Maps image

Related material

"Was ist Raum, wie können wir ihn
 erfassen und gestalten?"

Walter Gropius,

The Theory and
Organization of the
Bauhaus
  (1923)

Update of Feb. 3, 2013:
See also The Perception of Doors in this journal.

Thursday, May 24, 2012

Dark, Dark, Dark

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

Damnation Morning

From her left arm hung a black handbag that closed with a drawstring and from which protruded the tip of a silvery object about which I found myself apprehensively curious.

Her right arm was raised and bent, the elbow touching the door frame, the hand brushing back the very dark bangs from her forehead to show me the sigil, as if that had a bearing on her question.

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


IMAGE- 'Eight-limbed asterisk' of Fritz Leiber (square version)

Except for the bangs she wore her hair pinned up. Her ears were flat, thin-edged, and nicely shaped, with the long lobes that in Chinese art mark the philosopher. Small square silver flats with rounded corners ornamented them.

Her face might have been painted by Toulouse-Lautrec or Degas. The skin was webbed with very fine lines; the eyes were darkly shadowed and there was a touch of green on the lids (Egyptian?—I asked myself); her mouth was wide, tolerant, but realistic. Yes, beyond all else, she seemed realistic.

Mary Karr

You’re not afraid to show yourself at your lowest ebb. In Lit, you stop breast-feeding because you’ve started drinking again. You describe yourself hiding in a closet with a bottle of whiskey, a bottle of Listerine, and a spit bowl.

It’s not a proud moment. The temptation in Lit was to either make myself seedy or show some glamour. But there wasn’t any. It was just dark, dark, dark for days. Ugly.

Were you surprised by how deeply people related to this dark stuff?

If I’m doing my job then I’m able to make the strange seem familiar. Bad memoirs try to make the strange stranger, to provide something for people to gawk at. I try to create an experience where no matter how bizarre something is, it seems normal. I don’t want readers to balk, I want them to be in the experience. My goal isn’t for people to go, “Oh, poor little Mary Karr,” but rather to have the reader go, “I can be an asshole too,” or just to have enthusiasm for the possibility for change.

Tuesday, May 15, 2012

Midnight in Paris

Filed under: General — m759 @ 6:00 pm

Six PM EDT is midnight in Paris.

Así Que Pasen Cinco Años

Theater review from The Guardian

" 'Impossible' was how the Spanish playwright
Lorca described his own 1931 'legend of time
in three acts and five scenes,' which draws
strongly on the surrealist influences and experiments
of his close friends Salvador Dali and Luis Buñuel."

Related material—

This afternoon's previous post Murió Fuentes  and,
from this date five years ago…

A Flag for Sunrise and Jerry Falwell Dies.

Friday, March 23, 2012

Embedding the Stone

Filed under: General,Geometry — Tags: — m759 @ 8:00 am

"Imbedding the God character in a holy book's very detailed narrative
and building an entire culture around this narrative
seems by itself to confer a kind of existence on Him."

John Allen Paulos in the philosophy column "The Stone,"
     New York Times  online, Oct. 24, 2010

A related post from Log24 later that year—

Sunday, November 28, 2010

The Embedding

 — m759 @ 6:00 AM

The New York Times Magazine  this morning on a seminar on film theory at Columbia University—

"When the seminar reconvened after the break, Schamus said, 'Let’s dive into the Meno,' a dialogue in which Plato and Socrates consider virtue. 'The heart of it is the mathematical proof.' He rose from his seat and went to the whiteboard, where he drew figures and scribbled numbers as he worked through the geometry. 'You can only get the proof visually,' he concluded, stepping back and gazing at it. Plato may be skeptical about the category of the visual, he said, but 'you are confronted with a visual proof that gets you back to the idea embedded in visuality.'"

The Meno Embedding

Plato's Diamond embedded in The Matrix

See also Plato's Code and
 Plato Thanks the Academy.

 

 

"Next come the crown of thorns and Jesus' agonized crawl across the stage,
bearing the weight of his own crucifix. And at last, after making
yet another entrance, Mr. Nolan strikes the pose immortalized
in centuries of art, clad in a demure loincloth, arms held out to his sides,
one leg artfully bent in front of the other, head hanging down
in tortured exhaustion. Gently spotlighted, he rises from the stage
as if by magic, while a giant cross, pulsing with hot gold lights,
descends from above to meet him. Mr. Lloyd Webber's churning guitar rock
hits a climactic note, and the audience erupts in excited applause."

— Charles Isherwood, review of "Jesus Christ Superstar" in today's  New York Times

Other remarks on embedding —

Part I

Review of a new book on linguistics, embedding, and a South American tribe—

"Imagine a linguist from Mars lands on Earth to survey the planet's languages…."
Chronicle of Higher Education , March 20, 2012

Part II

The Embedding , by Ian Watson (Review of a 1973 novel from Shakespeare's birthday, 2006)

Tuesday, March 20, 2012

Field (continued)

Filed under: General — Tags: — m759 @ 11:11 pm

In memory of director Ulu Grosbard (continued from yesterday)

From  http://scripturetext.com/matthew/13-44.htm —

Again the kingdom of heaven is like unto treasure hid in a field
the which when a man hath found he hideth and for joy thereof
goeth and selleth all that he hath and buyeth that field

ΚΑΤΑ ΜΑΤΘΑΙΟΝ 13:44 Greek NT: Byzantine/Majority Text (2000)
παλιν ομοια εστιν η βασιλεια των ουρανων θησαυρω κεκρυμμενω εν τω αγρω

LEXICON  


παλιν  adverb


palin  pal'-in:  (adverbially) anew, i.e. (of place) back, (of time) once more, or (conjunctionally) furthermore or on the other hand — again.


ομοια  adjective – nominative singular feminine


homoios  hom'-oy-os:  similar (in appearance or character) — like, + manner.


εστιν  verb – present indicative – third person singular 


esti  es-tee':  he (she or it) is; also (with neuter plural) they are


η  definite article – nominative singular feminine


ho  ho:  the definite article; the (sometimes to be supplied, at others omitted, in English idiom) — the, this, that, one, he, she, it, etc.


βασιλεια  noun – nominative singular feminine


basileia  bas-il-i'-ah:  royalty, i.e. (abstractly) rule, or (concretely) a realm — kingdom, + reign.


των  definite article – genitive plural masculine


ho  ho:  the definite article; the (sometimes to be supplied, at others omitted, in English idiom) — the, this, that, one, he, she, it, etc.


ουρανων  noun – genitive plural masculine


ouranos  oo-ran-os':  the sky; by extension, heaven (as the abode of God); by implication, happiness, power, eternity; specially, the Gospel (Christianity) — air, heaven(-ly), sky.


θησαυρω  noun – dative singular masculine


thesauros  thay-sow-ros':  a deposit, i.e. wealth — treasure.


κεκρυμμενω  verb – perfect passive participle – dative singular masculine 


krupto  kroop'-to:  to conceal (properly, by covering) — hide (self), keep secret, secret(-ly).


εν  preposition


en  en:  in, at, (up-)on, by, etc.


τω  definite article – dative singular masculine


ho  ho:  the definite article; the (sometimes to be supplied, at others omitted, in English idiom) — the, this, that, one, he, she, it, etc.


αγρω  noun – dative singular masculine


agros  ag-ros':  a field (as a drive for cattle); genitive case, the country; specially, a farm, i.e. hamlet — country, farm, piece of ground, land.

Wednesday, February 1, 2012

Disturbing Archimedes

Filed under: General — Tags: — m759 @ 2:01 pm

Princeton University Press on a book it will publish in March—

Circles Disturbed: The Interplay of
Mathematics and Narrative

"… brings together important thinkers in mathematics,
history, and philosophy to explore the relationship
between mathematics and narrative.
  The book's title recalls the last words of the great
Greek mathematician Archimedes before he was
slain by a Roman soldier— 'Don't disturb my circles' …."

Related material—

Archimedes's Vicious Circle

IMAGE- Archimedes's measurement of the area of a circle (by sharply pointed triangles)

IMAGE- The Mouth of Truth in 'Roman Holiday'

Friday, January 27, 2012

Mathematics and Narrative (continued)

Filed under: General,Geometry — Tags: — m759 @ 1:44 am

Princeton University Press on a book it will publish in March—

Circles Disturbed: The Interplay of Mathematics and Narrative

"Circles Disturbed  brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier— 'Don't disturb my circles'— words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds–stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities."

Timeline of the Marvel Cinematic Universe — Norway, March 1942

"The Red Skull finds the Tesseract, a cube of strange power,
said to be the jewel of Odin’s treasure room, in Tonsberg Norway.
 (Captain America: The First Avenger)"

Tesseracts Disturbed — (Click to enlarge)

Detail of Tesseracts Disturbed —

Narrative of the detail—

See Tesseract in this journal and Norway, May 2010

The Oslo Version and Annals of Conceptual Art.

"Oh, what a tangled web we weave…"

Saturday, November 12, 2011

Professor Dodge

Filed under: General,Geometry — m759 @ 11:30 pm

From today's previous post, a fragmentary thought—

"Professor Dodge and the underground artists
whose work he helped save are the subjects of a book…"

Jim Dodge, Stone Junction

(a novel first published in 1989)

From pages 206-208, Kindle Edition

`Have you seen it?'

Volta hesitated. `Well, I've dreamed  it.'

Daniel shook his head. `I'm getting lost. You want me to vanish into your dreams?'

`Good Lord, no,' Volta blanched. `That's exactly what I don't  want you to do.'

`So, what is it exactly you do  want me to do?'

`Steal the diamond.'

`So, it's a diamond?'

`Yes, though it's a bit like saying the ocean is water. The diamond is perfectly spherical,* perfectly clear— though it seems to glow— and it's about two-thirds the size of a bowling ball. I think of it as the Diamond. Capital D.'

`Who owns it?'

`No one. The United States government has it at the moment. We want it. And to be honest with you, Daniel, I particularly want it, want it dearly. I want to look at it, into it, hold it in my hands. I had a vision involving a spherical diamond, a vision that changed my life, and I want to confirm that it was a vision of something real, the spirit embodied, the circuit complete.'

Daniel was smiling. `You're going to love this. That dream I wanted to talk to you about, my first since the explosion? It just happened to feature a raven with a spherical diamond in its beak. Obviously, it wasn't as big as a bowling ball, and there was a thin spiral flame running edge to edge through its center, which made it seem more coldly brilliant than warmly glowing, but it sounds like the same basic diamond to me.'

`And what do you think it is?'

`I think it's beautiful.'

Volta gave him a thin smile. `If I were more perverse than I already lamentably am, I would say it is the Eye of the Beholder. In fact, I don't know what it is.'

`It might be a dream,' Daniel said.

`Very possibly,' Volta agreed, `but I don't think so. I think— feel , to be exact— that the Diamond is an interior force given exterior density, the transfigured metaphor of the prima materia , the primordial mass, the Spiritus Mundi . I'm assuming you're familiar with the widely held supposition that the entire universe was created from a tiny ball of dense matter which exploded, sending pieces hurtling into space, expanding from the center. The spherical diamond is the memory, the echo, the ghost of that generative cataclysm; the emblematic point of origin. Or if, as some astrophysicists believe, the universe will reach some entropic point in its expansion and begin to collapse back into itself, in that case the Diamond may be a homing point, the seed crystal, to which it will all come hurtling back together— and perhaps through itself, into another dimension entirely. Or it might be the literal Philosopher's Stone we alchemists speak of so fondly. Or I might be completely wrong. That's why I want to see it. If I could actually stand in its presence, I'm convinced I'd know what it is. I would even venture to say, at the risk of rabid projection, that it wants  to be seen and known.'

`But you're not even sure it exists,' Daniel said. `Right? And hey, it's tough to steal something that doesn't  exist, even if you can be invisible. The more I think about this the less sense it makes.'

* Here Dodge's mystical vision seems akin to that of Anthony Judge in "Embodying the Sphere of Change" (St. Stephen's Day, 2001). Actually, the cube, not the sphere, is the best embodiment of Judge's vision.

See also Tuesday's "Stoned" and the 47 references
to the term "bowling" in the Kindle Stone Junction .

Furthermore… Live from New York, it's Saturday Night!

Wednesday, October 26, 2011

Possibly Related

Filed under: General — m759 @ 11:22 am
 
New York Lottery, October 25, 2011, as reported by The New York Times

Peter Woit, phrase from a weblog post on October 25th, 2011—

"In possibly related news…."

For 779, see post 779 in this  weblog.

For 8974, see Hollywood Endings.

For 082, see page  82 of Culture and Value , ed. G.H. von Wright, tr. Peter Winch (Oxford 1980) (as quoted by M. Jamie Ferreira in "The Point Outside the World: Kierkegaard and Wittgenstein on Nonsense, Paradox and Religion," Religious Studies , Vol. 30, March 1994, pp. 29-44, reprinted in Wittgenstein Studies  (1997))—

Wittgenstein: “God’s essence is supposed to guarantee his existence— but what this really means is that what is here at issue is not the existence of something.”

For 0372, see page  372 in Essays of Three Decades , by Thomas Mann, translated by H. T. Lowe-Porter, Alfred A. Knopf, 1947 ("Schopenhauer," 1938, pp. 372-410)—

THE PLEASURE we take in a metaphysical system, the gratification purveyed by the intellectual organization of the world into a closely reasoned, complete, and balanced structure of thought, is always of a pre-eminently aesthetic kind. It flows from the same source as the joy, the high and ever happy satisfaction we get from art, with its power to shape and order its material, to sort out life's manifold confusions so as to give us a clear and general view.

Truth and beauty must always be referred the one to the other. Each by itself, without the support given by the other, remains a very fluctuating value. Beauty that has not truth on its side and cannot have reference to it, does not live in it and through it, would be an empty chimera— and "What is truth?"

Wednesday, October 5, 2011

Hermenautics

Filed under: General — m759 @ 10:30 pm

University Diaries  today

"Educated people— with some exceptions, like Nader— like to explore the senses, and indeed many of your humanities courses (like the one UD ‘s teaching right now about beauty, in which we just read Susan Sontag’s “Against Interpretation,” with its famous concluding lines: In place of a hermeneutics, we need an erotics of art ) feature artworks and ideas that celebrate sensuality."

This suggests a review lecture on the unorthodox concept of lottery hermeneutics .

Today's New York Lottery—

http://www.log24.com/log/pix11C/111005-NYlottery-500w.jpg

A quote suggested by the UD  post

"Sainte-Beuve's Volupté  (1834) introduced the idea of idler as hero (and seeking pleasurable new sensations as the highest good), so Baudelaire indulged himself in sex and drugs."

Article on Baudelaire by Joshua Glenn in the journal Hermenaut

Some reflections suggested by Hermenaut  and by the NY evening numbers, 674 and 1834—

(Click images to enlarge.)

http://www.log24.com/log/pix11C/111005-Sainte-Beuve-P674-300w.jpg

http://www.log24.com/log/pix11C/111005-Sainte-Beuve-1834-300w.jpg

http://www.log24.com/log/pix11C/111005-Sainte-Beuve-CoolMystery-300w.jpg

Cool Mystery:

http://www.log24.com/log/pix11C/111005-PlancksCafe-CruzEnters.jpg

Detective Cruz enters Planck's Constant Café in "The Big Bang."

As for the midday numbers—

For 412, see 4/12, and for 1030, see 10/30, Devil's Night (2005).

For further background, consult Monday's Realism in Plato's Cave.

Wednesday, September 21, 2011

Symmetric Generation

Suggested by yesterday's Relativity Problem Revisited and by Cassirer on Objectivity

From Symmetric Generation of Groups , by R.T. Curtis (Cambridge U. Press, 2007)—

"… we are saying much more than that G M 24 is generated by
some set of seven involutions, which would be a very weak
requirement. We are asserting that M 24 is generated by a set
of seven involutions which possesses all the symmetries of L3(2)
acting on the points of the 7-point projective plane…."
Symmetric Generation , p. 41

"It turns out that this approach is particularly revealing and that
many simple groups, both sporadic and classical, have surprisingly
simple definitions of this type."
Symmetric Generation , p. 42

See also (click to enlarge)—

http://www.log24.com/log/pix11B/110921-CassirerOnObjectivity-400w.jpg

Cassirer's remarks connect the concept of objectivity  with that of object .

The above quotations perhaps indicate how the Mathieu group M 24 may be viewed as an object.

"This is the moment which I call epiphany. First we recognise that the object is one  integral thing, then we recognise that it is an organised composite structure, a thing  in fact: finally, when the relation of the parts is exquisite, when the parts are adjusted to the special point, we recognise that it is that  thing which it is. Its soul, its whatness, leaps to us from the vestment of its appearance. The soul of the commonest object, the structure of which is so adjusted, seems to us radiant. The object achieves its epiphany."

— James Joyce, Stephen Hero

For a simpler object "which possesses all the symmetries of L3(2) acting on the points of the 7-point projective plane…." see The Eightfold Cube.

For symmetric generation of L3(2) on that cube, see A Simple Reflection Group of Order 168.

Friday, September 16, 2011

Art, Jung, Toronto

Filed under: General,Geometry — Tags: — m759 @ 9:29 am

http://www.log24.com/log/pix11B/110916-ArtJungToronto-NYT.jpg

Related art—

Midnight's Icons,

http://www.log24.com/log/pix11B/110915-Jung-FourDiamonds.gif

Faust in Toronto,

http://www.log24.com/log/pix11B/110916-NYT-Faust.jpg

and…

McLuhan 'tetrad' figure with four diamonds surrounding a fifth, the medium

McLuhan and the Four Diamonds

(Wikipedia figure)

"Visually, a tetrad can be depicted as
 four diamonds forming an X…."

" X never, ever, marks the spot."

Monday, September 12, 2011

Key Paper Now Online

Filed under: General — m759 @ 11:07 pm

The 3-Space PG(3,2) and Its Group

by George M. Conwell, Annals of Mathematics ,
Second Series, Vol. 11, No. 2 (Jan., 1910), pp. 60-76

Article Stable URL: http://www.jstor.org/stable/1967582

At least for now, this paper may be downloaded without
signing in or making a payment. Click the "View PDF" link.

Update of Sept. 13— From Library Journal  on Sept. 7—

The JSTOR journal archive announced today that it is making nearly 500,000 public domain journal articles from more than 220 journals—or about six percent of JSTOR's total content—freely available for use by "anyone, without registration and regardless of institutional affiliation."

The material, entitled Early Journal Content, will be rolled out in batches starting today over the course of one week. It includes content published in the United States before 1923 and international content published before 1870, which ensures that all the content is firmly in the public domain. JSTOR, in an announcement, said that the move was "a first step in a larger effort to provide more access options" to JSTOR content for independent scholars and others unaffiliated with universities.

Thursday, September 8, 2011

Starring the Diamond

Filed under: General,Geometry — m759 @ 2:02 pm

"In any geometry satisfying Pappus's Theorem,
the four pairs of opposite points of 83
are joined by four concurrent lines.
"
— H. S. M. Coxeter (see below)

Continued from Tuesday, Sept. 6

The Diamond Star

http://www.log24.com/log/pix11B/110905-StellaOctangulaView.jpg

The above is a version of a figure from Configurations and Squares.

Yesterday's post related the the Pappus configuration to this figure.

Coxeter, in "Self-Dual Configurations and Regular Graphs," also relates Pappus to the figure.

Some excerpts from Coxeter—

http://www.log24.com/log/pix11B/110908-Coxeter83.jpg

The relabeling uses the 8 superscripts
from the first picture above (plus 0).
The order of the superscripts is from
an 8-cycle in the Galois field GF(9).

The relabeled configuration is used in a discussion of Pappus—

http://www.log24.com/log/pix11B/110908-Coxeter83part2.jpg

(Update of Sept. 10, 2011—
Coxeter here has a note referring to page 335 of
G. A. Miller, H. F. Blichfeldt, and L. E. Dickson,
Theory and Applications of Finite Groups , New York, 1916.)

Coxeter later uses the the 3×3 array (with center omitted) again to illustrate the Desargues  configuration—

http://www.log24.com/log/pix11B/110908-Coxeter103.jpg

The Desargues configuration is discussed by Gian-Carlo Rota on pp. 145-146 of Indiscrete Thoughts

"The value  of Desargues' theorem and the reason  why the statement of this theorem has survived through the centuries, while other equally striking geometrical theorems have been forgotten, is in the realization that Desargues' theorem opened a horizon of possibilities  that relate geometry and algebra in unexpected ways."

Sunday, July 24, 2011

Sunday School

Filed under: General — m759 @ 8:00 am

Venus and Mars Realigned (continued from July 20) …

Mira Sorvino in 'The Last Templar'

A review —

“The story, involving the Knights Templar, the Vatican, sunken treasure,
the fate of Christianity and a decoding device that looks as if it came out of
a really big box of medieval Cracker Jack, is the latest attempt to combine
Indiana Jones derring-do with ‘Da Vinci Code’ mysticism.”

The New York Times

A related Google image search yields more Cracker Jack prizes.

Wednesday, July 20, 2011

Cover Art

Filed under: General — Tags: , , — m759 @ 8:00 am

The Misalignment of Mars and Venus

A death in Sarasota on Sunday leads to a weblog post from Tuesday
that suggests a review of Dan Brown's graphic philosophy—

From The Da Vinci Code :

Langdon pulled a pen from his pocket.  “Sophie are you familiar with the modern icons for male and female?”  He drew the common male symbol ♂ and female symbol ♀.

“Of course,” she said.

“These,” he said quietly, are not the original symbols for male and female.  Many people incorrectly assume the male symbol is derived from a shield and spear, while the female represents a mirror reflecting beauty.  In fact, the symbols originated as ancient astronomical symbols for the planet-god Mars and the planet-goddess Venus.  The original symbols are far simpler.”  Langdon drew another icon on the paper.

 

 

 

“This symbol is the original icon for male ,” he told her.  “A rudimentary phallus.”

“Quite to the point,” Sophie said.

“As it were,” Teabing added.

Langdon went on.  “This icon is formally known as the blade , and it represents aggression and manhood.  In fact, this exact phallus symbol is still used today on modern military uniforms to denote rank.”

“Indeed.”  Teabing grinned.  “The more penises you have, the higher your rank.  Boys will be boys.”

Langdon winced.  “Moving on, the female symbol, as you might imagine, is the exact opposite.”  He drew another symbol on the page.  “This is called the chalice .”

 

 

Sophie glanced up, looking surprised.

Langdon could see she had made the connection.  “The chalice,” he said, “resembles a cup or vessel, and more important, it resembles the shape of a woman’s womb.  This symbol communicates femininity, womanhood, and fertility.”

Langdon's simplified symbols, in disguised form, illustrate
a musical meditation on the misalignment of Mars and Venus—

http://www.log24.com/log/pix11B/110720-Misaligned.jpg

This was adapted from an album cover by "Meyers/Monogram"—

http://www.log24.com/log/pix11B/110720-BladeAndChalice-RomeoAndJuliet-500w.jpg

  See also Secret History and The Story of N.

Sunday, July 10, 2011

Wittgenstein’s Diamond

Filed under: General,Geometry — Tags: , — m759 @ 9:29 am

Philosophical Investigations  (1953)

97. Thought is surrounded by a halo.
—Its essence, logic, presents an order,
in fact the a priori order of the world:
that is, the order of possibilities * ,
which must be common to both world and thought.
But this order, it seems, must be
utterly simple . It is prior  to all experience,
must run through all experience;
no empirical cloudiness or uncertainty can be allowed to affect it
——It must rather be of the purest crystal.
But this crystal does not appear as an abstraction;
but as something concrete, indeed, as the most concrete,
as it were the hardest  thing there is
(Tractatus Logico-Philosophicus  No. 5.5563).

— Translation by G.E.M. Anscombe

5.5563

All propositions of our colloquial language
are actually, just as they are, logically completely in order.
That simple thing which we ought to give here is not
a model of the truth but the complete truth itself.

(Our problems are not abstract but perhaps
the most concrete that there are.)

97. Das Denken ist mit einem Nimbus umgeben.
—Sein Wesen, die Logik, stellt eine Ordnung dar,
und zwar die Ordnung a priori der Welt,
d.i. die Ordnung der Möglichkeiten ,
die Welt und Denken gemeinsam sein muß.
Diese Ordnung aber, scheint es, muß
höchst einfach  sein. Sie ist vor  aller Erfahrung;
muß sich durch die ganze Erfahrung hindurchziehen;
ihr selbst darf keine erfahrungsmäßige Trübe oder Unsicherheit anhaften.
——Sie muß vielmehr vom reinsten Kristall sein.
Dieser Kristall aber erscheint nicht als eine Abstraktion;
sondern als etwas Konkretes, ja als das Konkreteste,
gleichsam Härteste . (Log. Phil. Abh.  No. 5.5563.)

See also

Related language in Łukasiewicz (1937)—

http://www.log24.com/log/pix10B/101127-LukasiewiczAdamantine.jpg

* Updates of 9:29 PM ET July 10, 2011—

A  mnemonic  from a course titled “Galois Connections and Modal Logics“—

“Traditionally, there are two modalities, namely, possibility and necessity.
The basic modal operators are usually written box (square) for necessarily
and diamond (diamond) for possibly. Then, for example, diamondP  can be read as
‘it is possibly the case that P .'”

See also Intensional Semantics , lecture notes by Kai von Fintel and Irene Heim, MIT, Spring 2007 edition—

“The diamond symbol for possibility is due to C.I. Lewis, first introduced in Lewis & Langford (1932), but he made no use of a symbol for the dual combination ¬¬. The dual symbol was later devised by F.B. Fitch and first appeared in print in 1946 in a paper by his doctoral student Barcan (1946). See footnote 425 of Hughes & Cresswell (1968). Another notation one finds is L for necessity and M for possibility, the latter from the German möglich  ‘possible.’”

Barcan, Ruth C.: 1946. “A Functional Calculus of First Order Based on Strict Implication.” Journal of Symbolic Logic, 11(1): 1–16. URL http://www.jstor.org/pss/2269159.

Hughes, G.E. & Cresswell, M.J.: 1968. An Introduction to Modal Logic. London: Methuen.

Lewis, Clarence Irving & Langford, Cooper Harold: 1932. Symbolic Logic. New York: Century.

Friday, June 3, 2011

MIT Day

Filed under: General — m759 @ 7:59 am

Today is Commencement Day at MIT.

“To measure the changes
     of time and space
the smartest are nothing.”

— Shing-Tung Yau,
 The Emperor of Math
and Harvard philosopher

To measure the changes:

The image “http://www.log24.com/log/pix06A/061017-Yellowbook3.jpg” cannot be displayed, because it contains errors.

The smartest are nothing:

The image “http://www.log24.com/log/pix06A/061017-Gump2A.jpg” cannot be displayed, because it contains errors.

Well, perhaps not quite nothing.

The above pictures were posted here on the day the following book was published—

http://www.log24.com/log/pix11A/110603-NineLives.jpg

The lives of the nine Jews in the above book amount to more than Yau's "nothing."

Note, however, that claims by Jews (see Jill Abramson yesterday
that their secular publications constitute a substitute for religion
and contain only "absolute truth" should be viewed with at least one
raised eyebrow.

Abramson's remark yesterday that her promotion to New York Times  executive editor
was like "ascending to Valhalla" had a religious flavor worthy of yesterday's
Feast of the Ascension.

In related news from yesterday's Times

IMAGE- 'Fearless Ascent, as a God or a Jet' -NYT

See also a symbol related to Apollo, to nine, and to "nothing"

A minimalist 3×3 matrix favicon—

http://www.log24.com/log/pix11A/110518-3x3FaviconURL.jpg

This may, if one likes, be viewed as the "nothing"
present at the Creation.  See Jim Holt on physics.

Monday, May 16, 2011

Luck

Filed under: General — m759 @ 10:00 pm

From the Guardian  yesterday—

Stephen Hawking: 'There is no heaven; it's a fairy story'

In an exclusive interview with the Guardian, the cosmologist shares
his thoughts on death, M-theory, human purpose and our chance existence

http://www.log24.com/log/pix11A/110516-Hawking.jpg

Stephen Hawking dismisses belief in God in an exclusive interview with the Guardian.
Photograph: Solar & Heliospheric Observatory/Discovery Channel

What is the value in knowing "Why are we here?"

The universe is governed by science. But science tells us that we can't solve the equations, directly in the abstract. We need to use the effective theory of Darwinian natural selection of those societies most likely to survive. We assign them higher value.

You've said there is no reason to invoke God to light the blue touchpaper. Is our existence all down to luck?

Science predicts that many different kinds of universe will be spontaneously created out of nothing. It is a matter of chance which we are in.

So here we are….

New York Lottery today, May 16… Midday 374, Evening 430.

See also the Turner Classic Movies film now playing.

    Sunday, May 8, 2011

    Matrix

    Filed under: General,Geometry — m759 @ 7:59 am

    For Mother's Day

    http://www.log24.com/log/pix10/100121-Trigrams.jpg

    http://www.log24.com/log/pix11A/110508-Trigrams.jpg

    From Thomas Mann, "Schopenhauer," 1938, in Essays of Three Decades , translated by H. T. Lowe-Porter, Alfred A. Knopf, 1947, pp. 372-410—

    Page 372: THE PLEASURE we take in a metaphysical system, the gratification purveyed by the intellectual organization of the world into a closely reasoned, complete, and balanced structure of thought, is always of a pre-eminently aesthetic kind. It flows from the same source as the joy, the high and ever happy satisfaction we get from art, with its power to shape and order its material, to sort out life's manifold confusions so as to give us a clear and general view.

    Truth and beauty must always be referred the one to the other. Each by itself, without the support given by the other, remains a very fluctuating value. Beauty that has not truth on its side and cannot have reference to it, does not live in it and through it, would be an empty chimera— and "What is truth?"

    Wednesday, May 4, 2011

    Unity and Multiplicity

    Filed under: General — Tags: — m759 @ 9:00 am

    Continued from Crimson Walpurgisnacht.

    EpigraphsTwo quotations from  
    Shakespeare's Birthday last year

    Rebecca Goldstein
       on first encountering Plato
     

    "I was reading Durant's section on Plato, struggling to understand his theory of the ideal Forms that lay in inviolable perfection out beyond the phantasmagoria. (That was the first, and I think the last, time that I encountered that word.)"

    Screenwriter Joan Didion

    "We tell ourselves stories in order to live….

    We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the 'ideas' with which we have learned to freeze the shifting phantasmagoria which is our actual experience."

    From Thomas Mann, "Schopenhauer," 1938, in Essays of Three Decades , translated by H. T. Lowe-Porter, Alfred A. Knopf, 1947, pp. 372-410—

    Page 372: THE PLEASURE we take in a metaphysical system, the gratification purveyed by the intellectual organization of the world into a closely reasoned, complete, and balanced structure of thought, is always of a pre-eminently aesthetic kind. It flows from the same source as the joy, the high and ever happy satisfaction we get from art, with its power to shape and order its material, to sort out life's manifold confusions so as to give us a clear and general view.

    Truth and beauty must always be referred the one to the other. Each by itself, without the support given by the other, remains a very fluctuating value. Beauty that has not truth on its side and cannot have reference to it, does not live in it and through it, would be an empty chimera— and "What is truth?"

    ….

    Page 376: … the life of Plato was a very great event in the history of the human spirit; and first of all it was a scientific and a moral event. Everyone feels that something profoundly moral attaches to this elevation of the ideal as the only actual, above the ephemeralness and multiplicity of the phenomenal, this devaluation  of the senses to the advantage of the spirit, of the temporal to the advantage of the eternal— quite in the spirit of the Christianity that came after it. For in a way the transitory phenomenon, and the sensual attaching to it, are put thereby into a state of sin: he alone finds truth and salvation who turns his face to the eternal. From this point of view Plato's philosophy exhibits the connection between science and ascetic morality.

    But it exhibits another relationship: that with the world of art. According to such a philosophy time itself is merely the partial and piecemeal view which an individual holds of ideas— the latter, being outside time, are thus eternal. "Time"— so runs a beautiful phrase of Plato— "is the moving image of eternity." And so this pre-Christian, already Christian doctrine, with all its ascetic wisdom, possesses on the other hand extraordinary charm of a sensuous and creative kind; for a conception of the world as a colourful and moving phantasmagoria of pictures, which are transparencies for the ideal and the spiritual, eminently savours of the world of art, and through it the artist, as it were, first comes into his own.

    From last night's online NY Times  obituaries index—

    http://www.log24.com/log/pix11A/110503-NYTobits.jpg

    "How much story do you want?" — George Balanchine

    Tuesday, April 12, 2011

    Unique Figure

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

    http://www.log24.com/log/pix11/110412-BlackPlank.jpg

    National Gallery of Art

    In the landscape of minimalism, John McCracken cuts a unique figure. He is often grouped with the “light and space” artists who formed the West Coast branch of the movement. Indeed, he shares interests in vivid color, new materials, and polished surfaces with fellow Californians enamored of the Kustom Kar culture. On the other hand, his signature works, the “planks” that he invented in 1966 and still makes today, have the tough simplicity and aggressive presence of New York minimalism….

    “They kind of screw up a space because they lean,” McCracken has said of the planks. Their tilting, reflective surfaces activate the room, leaving the viewer uncertain of traditional boundaries. He notes that the planks bridge sculpture (identified with the floor) and painting (identified with the wall)….

    His ultimate goal, as with all mystics, is unity— not just of painting and sculpture, but of substance and illusion, of matter and spirit, of art and life. Such ideas recall the utopian aspirations of early modernists like Piet Mondrian and Wassily Kandinsky.

    Related Art —

    http://www.log24.com/log/pix11/110412-32x192plusmargin6.bmp

    Unity

    Roman numeral I
    as well as capital I

    For a related figure, see a  film review by A. O. Scott at The New York Times  (September 21, 2010)—

    “You Will Meet a Tall Dark Stranger” begins with an unseen narrator— Zak Orth, sounding a lot like Woody Allen— paraphrasing Shakespeare. You may remember the quotation from high school English, about how life is a tale told by an idiot, full of sound and fury, signifying nothing. The observation is attributed to the playwright himself (“Shakespeare once said”), rather than to Macbeth, whose grim experience led him to such nihilism, but never mind. In context, it amounts to a perfectly superfluous statement of the obvious.

    If life signifies nothing, perhaps the tall dark figure above signifies something . Discuss.

    Related Art Criticism —

    For more on light and space, see this journal on the date of McCracken’s death

    http://www.log24.com/log/pix11/110412-April8Lowry.jpg

    Note planks.

    Tuesday, April 5, 2011

    ART WARS continued

    Filed under: General — m759 @ 9:29 pm

    Escape from Kitsch Mountain

    "Why you gotta be so mean?" — Taylor Swift (see last night)

    This song includes, as part of the hook, the recurring phrase

    "Someday I'll be livin' in a big ol' city."

    From a big ol' city

    Rituals

    A Return to Kitsch Mountain

    By AUSTIN CONSIDINE

    Published in The New York Times  on January 16, 2009

    As my girlfriend, Larissa, and I approached Gatlinburg, Tenn., this fall, I did my best to prepare her. She hadn’t been to Gatlinburg before, but I had. I understood the town’s complicated reputation both as a gateway to some of the most beautiful country in the United States— the Great Smoky Mountains National Park— and as a flamboyant capital of kitsch….

    … It turned out that by 8 or 9 p.m., it was way too late to find a dinner show. The next morning, we had the opposite problem. By the time we woke up and wandered into Gatlinburg, it was noon. All the pancake houses were closed, and I was desolate. I had been thinking about those pancakes since the night before. So we did a little more sightseeing on foot.

    Looking at Gatlinburg’s strip with adult eyes, I wondered how much self-awareness was at work there. It would be easy for a city slicker to assume this place misses its own punch lines. In truth, I decided, it merely embraces that special brand of conscious kitsch that forms its own American kind of authenticity. With all its absurdities, Gatlinburg knows what it is and proclaims it loudly, from one flashing signboard to the next….

    From Gatlinburg—

    (Click to enlarge.)

    http://www.log24.com/log/pix11/110405-GatlinburgNews500w.jpg

    Friday, March 11, 2011

    Now Lens

    Filed under: General — m759 @ 10:00 am

    A Story in Pictures

    Errol Morris in The New York Times  on March 9

    "If everything is incommensurable, then everything is seen through the lens of the present, the lens of now ."

    "Borges concluded by quoting Chesterton, 'there is nothing more frightening than a labyrinth that has no center.' [72]"

    Now Lens

    http://www.log24.com/log/pix11/110311-NowLens.jpg

    Uncertified Copy

    http://www.log24.com/log/pix11/110311-UncertifiedCopy.jpg

    Del Toro

    http://www.log24.com/log/pix11/110311-delToro.jpg

    Plato's Diamond

    http://www.log24.com/log/pix11/110311-LychePlatosDiamond256w.jpg

    Portrait of an Artist

    http://www.log24.com/log/pix11/110311-JosefineLyche.jpg

    Meanwhile, back at the Times

    http://www.log24.com/log/pix11/110311-CertifiedCopy.jpg

    Thursday, March 10, 2011

    Paradigms Lost

    Filed under: General,Geometry — Tags: — m759 @ 5:48 pm

    (Continued from February 19)

    The cover of the April 1, 1970 second edition of The Structure of Scientific Revolutions , by Thomas S. Kuhn—

    http://www.log24.com/log/pix11/110310-KuhnCover.jpg

    This journal on January 19, 2011

    IMAGE- A Galois cube: model of the 27-point affine 3-space

    If Galois geometry is thought of as a paradigm shift from Euclidean geometry,
    both images above— the Kuhn cover and the nine-point affine plane—
    may be viewed, taken together, as illustrating the shift. The nine subcubes
    of the Euclidean  3x3x3 cube on the Kuhn cover do not  form an affine plane
    in the coordinate system of the Galois  cube in the second image, but they
    at least suggest  such a plane. Similarly, transformations of a
    non-mathematical object, the 1974 Rubik  cube, are not Galois  transformations,
    but they at least suggest  such transformations.

    See also today's online Harvard Crimson  illustration of problems of translation
    not unrelated to the problems of commensurability  discussed by Kuhn.

    http://www.log24.com/log/pix11/110310-CrimsonSm.jpg

    Monday, March 7, 2011

    Point Taken

    Filed under: General,Geometry — m759 @ 4:00 pm

    Recommended— An essay (part 1 of 5 parts) in today's New York TImes—

    THE ULTIMATUM

    I don’t want to die in
    a language I can’t understand.
    — Jorge Luis Borges

    Comment 71

    "I agree with one of the earlier commenters that this is a piece of fine literary work. And in response to some of those who have wondered 'WHAT IS THE POINT?!' of this essay, I would like to say: Must literature always answer that question for us (and as quickly and efficiently as possible)?"

    For an excellent survey of the essay's historical context, see The Stanford Encyclopedia of Philosophy article

    "The Incommensurability of Scientific Theories,"
    First published Wed., Feb. 25, 2009,
    by Eric Oberheim and Paul Hoyningen-Huene.

    Related material from this journal—

    Paradigms, Paradigms Lost, and a search for "mere geometry." This last includes remarks contrasting Euclid's definition of a point ("that which has no parts") with a later notion useful in finite geometry.

    See also (in the spirit of The Abacus Conundrum )…

    The Monolith Epiphany

    http://www.log24.com/log/pix11/110307-Monolith.jpg

    (Note the Borges epigraph above.)

    Tuesday, March 1, 2011

    Women’s History Month

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

    Susanne for Suzanne

    From pages 7-8 of William York Tindall’s Literary Symbolism  (Columbia U. Press, 1955)—

                                         ... According to Cassirer's Essay 
    on Man, as we have seen, art is a symbolic form, parallel in respect 
    of this to religion or science. Each of these forms builds up a universe 
    that enables man to interpret and organize his experience; and each 
    is a discovery, because a creation, of reality. Although similar in func- 
    tion, the forms differ in the kind of reality built. Whereas science
    builds it of facts, art builds it of feelings, intuitions of quality, and 
    the other distractions of our inner life— and in their degrees so do 
    myth and religion. What art, myth, and religion are, Cassirer con- 
    fesses, cannot be expressed by a logical definition. 
    
    Nevertheless, let us see what Clive Bell says about art. He calls 
    it "significant form," but what that is he is unable to say. Having 
    no quarrel with art as form, we may, however, question its signifi- 
    cance. By significant he cannot mean important in the sense of 
    having import, nor can he mean having the function of a sign; 
    for to him art, lacking reference to nature, is insignificant. Since, 
    however, he tells us that a work of art "expresses" the emotion of 
    its creator and "provokes" an emotion in its contemplator,he seems 
    to imply that his significant means expressive and provocative. The 
    emotion expressed and provoked is an "aesthetic emotion," contem- 
    plative, detached from all concerns of utility and from all reference. 
    
    Attempting to explain Bell's significant form, Roger Fry, equally 
    devoted to Whistler and art for art's sake, says that Flaubert's "ex- 
    pression of the idea" is as near as he can get to it, but neither Flaubert 
    nor Fry tells what is meant by idea. To "evoke" it, however, the artist 
    creates an "expressive design" or "symbolic form," by which the 
    spirit "communicates its most secret and indefinable impulses." 
    
    Susanne Langer,who occupies a place somewhere between Fry 
    and Cassirer, though nearer the latter, once said in a seminar that a 
    work of art is an "unassigned syntactical symbol." Since this defini- 
    
    End of page 7 
    
    tion does not appear in her latest book, she may have rejected it, but 
    it seems far more precise than Fry's attempt. By unassigned she prob- 
    ably intends insignificant in the sense of lacking sign value or fixed 
    reference; syntactical implies a form composed of parts in relation- 
    ship to one another; and a symbol, according to Feeling and Form, 
    is "any device whereby we are enabled to make an abstraction." Too 
    austere for my taste, this account of symbol seems to need elaboration, 
    which, to be sure, her book provides. For the present, however, taking 
    symbol to mean an outward device for presenting an inward state, 
    and taking unassigned and syntactical as I think she uses them, let 
    us tentatively admire her definition of the work of art.

    http://www.log24.com/log/pix11/110301-VegaSongsSm.jpg

    http://www.log24.com/log/pix11/110301-Diamond-RedOnGray.bmp

    Oh, the red leaf looks to the hard gray stone
    To each other, they know what they mean

    — Suzanne Vega, “Song in Red and Gray

    Sunday, December 5, 2010

    Hanukkah Continues —

    Filed under: General,Geometry — m759 @ 9:29 am

    Dan Brown Meets
    The Exorcist
    in…

    The 973 Code

    http://www.log24.com/log/pix10B/101205-PendantSm.jpg

    Baphomet with Ouroboros Pendant

    $140  Code: 973

    ____________________________________

    Meanwhile, our hero…

    http://www.log24.com/log/pix10B/101205-IndependenceDay.jpg

    goes to the movies.

    In this production, Jeff Goldblum is played by
    David Ben-Zvi of the University of Texas at Austin
    Geometry Research Group

    http://www.log24.com/log/pix10B/101205-Ben-Zvi.jpg

    Click Ben-Zvi for further narrative.

    Wednesday, November 3, 2010

    Consolation Prizes

    Filed under: General — m759 @ 10:25 am

    For Tom Hanks

    http://www.log24.com/log/pix10B/101102-NYlotteryHead.jpg

    and Kristin Davis

    http://www.log24.com/log/pix10B/101102-NYlottery.jpg

    __________________________________________

    Interpretations

    7/23/09 — Artistic Vision

    http://www.log24.com/log/pix10B/101103-ArtisticVision.jpg

    7/21/09 — The Lotus

    http://www.log24.com/log/pix10B/101102-MirrorBall-McLachlan.jpg

    "And the lotos rose, quietly, quietly,
    The surface glittered out of heart of light"

    __________________________________________

    Background

    Sunday night, Tuesday morning and afternoon

    Saturday, October 23, 2010

    Paranormal Jackass

    Filed under: General — Tags: , — m759 @ 8:28 pm

    From MTV.com this afternoon

    The follow-up to last year's runaway horror hit, "Paranormal Activity 2," kicked off its first weekend in theaters with a major haul. The creepy tale… pulled in $20.1 million on Friday.

    Trailing behind "Paranormal" is last week's box-office busting debut "Jackass 3D. " The prank-fest, which landed about $50 million its first weekend in theaters, slipped to the second-place slot….

    The Clint Eastwood-helmed ensemble drama "Hereafter" landed in fourth place. Exploring the lives of three people who are dealing with death and the afterlife in several ways, including the story of a psychic played by Matt Damon, the screen legend's latest turn in the director's chair made approximately $4.1 million on Friday.

    Related material—

    IMAGE-- Matt Damon stands where a door opens in 'Hereafter'

    Margaret Atwood on Lewis Hyde's Trickster Makes This World: Mischief, Myth, and Art

    "Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)

    What is "the next world"? It might be the Underworld….

    The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254)  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.

    The Paranormal Trickster Blog

    George P. Hansen on Martin Gardner and the paranormal.

    Friday, October 22, 2010

    But Seriously…

    Filed under: General — Tags: — m759 @ 3:19 pm

    Happy Birthday, Jean Simmons …  Jan. 31, 2008

    Elmer Gantry … Hollywood's view of the Foursquare Church

    Resurrection … An August 2003 post inspired by KHYI, then broadcasting from Plano, Texas

    For what it's worth, some free advice for Matt Damon…

    GET QUOTES

    IMAGE- NY Times market news and ad for 'Hereafter,' Oct. 22, 2010

    Thursday, October 21, 2010

    St. Ursula’s Day

    Filed under: General,Geometry — Tags: , — m759 @ 4:07 pm

    Mathematics and Narrative continued

    A search for Ursula in this journal yields a story…

    “The main character is a slave woman who discovers new patterns in the mosaics.”

    Other such stories: Plato’s Meno  and Changing Woman

    Changing Woman:

    “Kaleidoscope turning…

    Juliette Binoche in 'Blue'  The 24 2x2 Cullinane Kaleidoscope animated images

    Shifting pattern within
    unalterable structure…”

    — Roger Zelazny, Eye of Cat  

    Philosophical postscript—

    “That Lévi-Strauss should have been able to transmute the romantic passion of Tristes Tropiques  into the hypermodern intellectualism of La Pensée Sauvage  is surely a startling achievement. But there remain the questions one cannot help but ask. Is this transmutation science or alchemy? Is the ‘very simple transformation’ which produced a general theory out of a personal disappointment real or a sleight of hand? Is it a genuine demolition of the walls which seem to separate mind from mind by showing that the walls are surface structures only, or is it an elaborately disguised evasion necessitated by a failure to breach them when they were directly encountered? Is Lévi-Strauss writing, as he seems to be claiming in the confident pages of La Pensée Sauvage,  a prolegomenon to all future anthropology? Or is he, like some uprooted neolithic intelligence cast away on a reservation, shuffling the debris of old traditions in a vain attempt to revivify a primitive faith whose moral beauty is still apparent but from which both relevance and credibility have long since departed?”

    — Clifford Geertz, conclusion of “The Cerebral Savage: On the Work of Claude Lévi-Strauss

    Saturday, October 16, 2010

    The Mandelbrot Numbers

    Filed under: General — m759 @ 11:36 am
     

    Benoît Mandelbrot died on Oct. 14.
     

    NY Lottery Thursday, Oct. 14, 2010-- Midday 109, Evening 060

    — New York Lottery on Thursday, Oct. 14, 2010

    Related material on 109: See 1/09, 2009.
    Related material on 060: See Hexagram 60 of the I Ching  and…

    IMAGE-- Matt Damon stands where a door opens in 'Hereafter'

    Margaret Atwood on Lewis Hyde's Trickster Makes This World: Mischief, Myth, and Art

    "Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)

    What is "the next world"? It might be the Underworld….

    The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254)  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.

    Sunday, September 5, 2010

    M Theory

    Filed under: General — m759 @ 5:24 pm

    http://www.log24.com/log/pix10B/100905-MmusicmagSm.jpg

    "It's going to be accomplished in steps, this establishment
    of the Talented in the scheme of things."
    — Anne McCaffrey

    From this journal on August 23,
    a look at Resurrection Road  in M magazine—

    http://www.log24.com/log/pix10B/100823-ResurrectionRoadSm.jpg

    Notes for an unfinished novel, The Last Tycoon, by F. Scott Fitzgerald

    "There is a place for a hint somewhere
      of a big agent to complete the picture."

    Sunday, August 8, 2010

    Owl

    Filed under: General — m759 @ 7:15 pm

    See Susan Howe on Wallace Stevens and Henry Church.

    "    … Only the thought of those dark three
    Is dark, thought of the forms of dark desire."

    — "The Owl in the Sarcophagus"

    For one approach to such forms, see

    Sunday, July 11, 2010

    Philosophers’ Keystone

    Filed under: General — Tags: , — m759 @ 2:02 am

    (Background— Yesterday's Quarter to Three,
    A Manifold Showing, Class of 64, and Child's Play.)

    Image-- Notes on Lowry's arrival in Mexico on the ship 'Pennsylvania'

    Image-- PA Lottery Saturday, July 10, 2010-- Midday 017, Evening 673

    Hermeneutics

    Fans of Gregory Chaitin and Harry Potter
    may consult Writings for Yom Kippur
    for the meaning of yesterday's evening 673.

    (See also Lowry and Cabbala.)

    Fans of Elizabeth Taylor, Ava Gardner,
    and the Dark Lady may consult Prime Suspect
    for the meaning of yesterday's midday 17.

    For some more serious background, see Dante—

    "….mirando il punto 
    a cui tutti li tempi son presenti
    "

    – Dante, Paradiso, XVII, 17-18

    The symbol    is used throughout the entire book
    in place of such phrases as ‘Q.E.D.’  or
    ‘This completes the proof of the theorem’
    to signal the end of a proof.”

    Measure Theory, by Paul R. Halmos, Van Nostrand, 1950      

               
    Halmos died on the date of Yom Kippur —  
    October 2, 2006.            

    Tuesday, July 6, 2010

    What “As” Is

    Filed under: General,Geometry — Tags: , , , , — m759 @ 8:00 pm

    or:  Combinatorics (Rota) as Philosophy (Heidegger) as Geometry (Me)

    “Dasein’s full existential structure is constituted by
    the ‘as-structure’ or ‘well-joined structure’ of the rift-design*…”

    — Gary Williams, post of January 22, 2010

    Background—

    Gian-Carlo Rota on Heidegger…

    “… The universal as  is given various names in Heidegger’s writings….

    The discovery of the universal as  is Heidegger’s contribution to philosophy….

    The universal ‘as‘ is the surgence of sense in Man, the shepherd of Being.

    The disclosure of the primordial as  is the end of a search that began with Plato….
    This search comes to its conclusion with Heidegger.”

    — “Three Senses of ‘A is B’ in Heideggger,” Ch. 17 in Indiscrete Thoughts

    … and projective points as separating rifts

    Image-- The Three-Point Line: A Finite Projective Space

        Click image for details.

    * rift-design— Definition by Deborah Levitt

    Rift.  The stroke or rending by which a world worlds, opening both the ‘old’ world and the self-concealing earth to the possibility of a new world. As well as being this stroke, the rift is the site— the furrow or crack— created by the stroke. As the ‘rift design‘ it is the particular characteristics or traits of this furrow.”

    — “Heidegger and the Theater of Truth,” in Tympanum: A Journal of Comparative Literary Studies, Vol. 1, 1998

    Wednesday, June 23, 2010

    Group Theory and Philosophy

    Filed under: General,Geometry — Tags: , — m759 @ 5:01 pm

    Excerpts from "The Concept of Group and the Theory of Perception,"
    by Ernst Cassirer, Philosophy and Phenomenological Research,
    Volume V, Number 1, September, 1944.
    (Published in French in the Journal de Psychologie, 1938, pp. 368-414.)

    The group-theoretical interpretation of the fundaments of geometry is,
    from the standpoint of pure logic, of great importance, since it enables us to
    state the problem of the "universality" of mathematical concepts in simple
    and precise form and thus to disentangle it from the difficulties and ambigui-
    ties with which it is beset in its usual formulation. Since the times of the
    great controversies about the status of universals in the Middle Ages, logic
    and psychology have always been troubled with these ambiguities….

    Our foregoing reflections on the concept of group  permit us to define more
    precisely what is involved in, and meant by, that "rule" which renders both
    geometrical and perceptual concepts universal. The rule may, in simple
    and exact terms, be defined as that group of transformations  with regard to
    which the variation of the particular image is considered. We have seen
    above that this conception operates as the constitutive principle in the con-
    struction of the universe of mathematical concepts….

                                                                  …Within Euclidean geometry,
    a "triangle" is conceived of as a pure geometrical "essence," and this
    essence is regarded as invariant with respect to that "principal group" of
    spatial transformations to which Euclidean geometry refers, viz., displace-
    ments, transformations by similarity. But it must always be possible to
    exhibit any particular figure, chosen from this infinite class, as a concrete
    and intuitively representable object. Greek mathematics could not
    dispense with this requirement which is rooted in a fundamental principle
    of Greek philosophy, the principle of the correlatedness of "logos" and
    "eidos." It is, however, characteristic of the modern development of
    mathematics, that this bond between "logos" and "eidos," which was indis-
    soluble for Greek thought, has been loosened more and more, to be, in the
    end, completely broken….

                                                                …This process has come to its logical
    conclusion and systematic completion in the development of modern group-
    theory. Geometrical figures  are no longer regarded as fundamental, as
    date of perception or immediate intuition. The "nature" or "essence" of a
    figure is defined in terms of the operations  which may be said to
    generate the figure.
    The operations in question are, in turn, subject to
    certain group conditions….

                                                                                                        …What we
    find in both cases are invariances with respect to variations undergone by
    the primitive elements out of which a form is constructed. The peculiar
    kind of "identity" that is attributed to apparently altogether heterogen-
    eous figures in virtue of their being transformable into one another by means
    of certain operations defining a group, is thus seen to exist also in the
    domain of perception. This identity permits us not only to single out ele-
    ments but also to grasp "structures" in perception. To the mathematical
    concept of "transformability" there corresponds, in the domain of per-
    ception, the concept of "transposability." The theory  of the latter con-
    cept has been worked out step by step and its development has gone through
    various stages….
                                                                                     …By the acceptance of
    "form" as a primitive concept, psychological theory has freed it from the
    character of contingency  which it possessed for its first founders. The inter-
    pretation of perception as a mere mosaic of sensations, a "bundle" of simple
    sense-impressions has proved untenable…. 

                                 …In the domain of mathematics this state of affairs mani-
    fests itself in the impossibility of searching for invariant properties of a
    figure except with reference to a group. As long as there existed but one
    form of geometry, i.e., as long as Euclidean geometry was considered as the
    geometry kat' exochen  this fact was somehow concealed. It was possible
    to assume implicitly  the principal group of spatial transformations that lies
    at the basis of Euclidean geometry. With the advent of non-Euclidean
    geometries, however, it became indispensable to have a complete and sys-
    tematic survey of the different "geometries," i.e., the different theories of
    invariancy that result from the choice of certain groups of transformation.
    This is the task which F. Klein set to himself and which he brought to a
    certain logical fulfillment in his Vergleichende Untersuchungen ueber neuere
    geometrische Forschungen
    ….

                                                              …Without discrimination between the
    accidental and the substantial, the transitory and the permanent, there
    would be no constitution of an objective reality.

    This process, unceasingly operative in perception and, so to speak, ex-
    pressing the inner dynamics of the latter, seems to have come to final per-
    fection, when we go beyond perception to enter into the domain of pure
    thought. For the logical advantage and peculiar privilege of the pure con –
    cept seems to consist in the replacement of fluctuating perception by some-
    thing precise and exactly determined. The pure concept does not lose
    itself in the flux of appearances; it tends from "becoming" toward "being,"
    from dynamics toward statics. In this achievement philosophers have
    ever seen the genuine meaning and value of geometry. When Plato re-
    gards geometry as the prerequisite to philosophical knowledge, it is because
    geometry alone renders accessible the realm of things eternal; tou gar aei
    ontos he geometrike gnosis estin
    . Can there be degrees or levels of objec-
    tive knowledge in this realm of eternal being, or does not rather knowledge
    attain here an absolute maximum? Ancient geometry cannot but answer
    in the affirmative to this question. For ancient geometry, in the classical
    form it received from Euclid, there was such a maximum, a non plus ultra.
    But modern group theory thinking has brought about a remarkable change
    In this matter. Group theory is far from challenging the truth of Euclidean
    metrical geometry, but it does challenge its claim to definitiveness. Each
    geometry is considered as a theory of invariants of a certain group; the
    groups themselves may be classified in the order of increasing generality.
    The "principal group" of transformations which underlies Euclidean geome-
    try permits us to establish a number of properties that are invariant with
    respect to the transformations in question. But when we pass from this
    "principal group" to another, by including, for example, affinitive and pro-
    jective transformations, all that we had established thus far and which,
    from the point of view of Euclidean geometry, looked like a definitive result
    and a consolidated achievement, becomes fluctuating again. With every
    extension of the principal group, some of the properties that we had taken
    for invariant are lost. We come to other properties that may be hierar-
    chically arranged. Many differences that are considered as essential
    within ordinary metrical geometry, may now prove "accidental." With
    reference to the new group-principle they appear as "unessential" modifica-
    tions….

                     … From the point of view of modern geometrical systematization,
    geometrical judgments, however "true" in themselves, are nevertheless not
    all of them equally "essential" and necessary. Modern geometry
    endeavors to attain progressively to more and more fundamental strata of
    spatial determination. The depth of these strata depends upon the com-
    prehensiveness of the concept of group; it is proportional to the strictness of
    the conditions that must be satisfied by the invariance that is a universal
    postulate with respect to geometrical entities. Thus the objective truth
    and structure of space cannot be apprehended at a single glance, but have to
    be progressively  discovered and established. If geometrical thought is to
    achieve this discovery, the conceptual means that it employs must become
    more and more universal….

    Friday, March 26, 2010

    ART WARS: Hooligan

    Filed under: General — m759 @ 7:11 am

    You Can't Make This Stuff Up

    (continued)

    Art review by Holland Cotter in The New York Times this morning–

    "Although Confucius initially escaped severe censure by Mao, in the early 1970s he became 'No. 1 hooligan,' the embodiment of the hated 'four olds' (old culture, old ideology, old customs and old habits), a symbol of ruling-class oppression."

    For another hooligan fond of old customs, see yesterday's post and Sterling Hayden in "The Asphalt Jungle"–

    James Whitmore and Sterling Hayden in 1950-- Year of the Hooligan

    Related material:

    China's Cultural Revolution portrayed Confucius as the 'number one hooligan' (Yale U. Press, 2001)

    Sunday, March 14, 2010

    Joplin at the Lapin Blanc

    Filed under: General — m759 @ 10:00 pm

    For Alyssa

    From Google News this evening–

    Now Showing- “Alice in Wonderland”

    Red and Black – Michael Prochaska
    Tim Burton receives praise for his imaginative constructions
    (“Nightmare Before Christmas” was inspired by a dream),
    but if you analyze his work on adaptations of classic
    children-oriented escapism, whimsical surrealism bears
    a ball and chain.

    http://www.log24.com/log/pix10/100314-LapinBlancSm.gif

    A serenade for Einstein's birthday–

    Ball and Chain– Janis Joplin

    If you got it today you don't want it tomorrow, man,
    'cause you don't need it, 'cause as a matter of fact,
    as we discovered in the train,
    tomorrow never happens, man.
    It's all the same fucking day, man.

    Saturday, February 27, 2010

    Enchanted

    Filed under: General — m759 @ 10:31 am
                  Tell me about yourself, Linda.
                  What do you want to know?
                  Anything. I'd just like to know about you.
                  Well, basically...
                  Yes?
                  ...I'm an actress.
                  That's wonderful.
                  I like drama. I study.
                  Yes? Where's that?
                  Paul DeLucca. Have you ever heard of him?
                  Paul DeLucca? No, but then I wouldn't.
                  He's really well-known. He's a genius.
                  I'm sure.
                  He says he thinks I'm going to make it big.
                  I know you will.
                  Maybe you've seen some of my movies.
                  It's possible.
                  Did you ever see The Enchanted Pussy?
                  Not yet. But I... I... it's on my list.
                  They're videotaped, so you could rent it.
                  
                  -- Mighty Aphrodite
    

                       See also Fish Story.

    Friday, February 26, 2010

    Household Name

    Filed under: General — m759 @ 9:00 pm

    Detail from yesterday's post

    Surrealistic Alarm Clock

    'Pussy-Footer' alarm clock, LIFE Magazine, Oct. 10, 1949, page 122
    _________________________________________________________

    THE SEQUEL:

    Crawdaddy article on 'Surrealistic Pillow,' the classic 1967 album by Jefferson Airplane

    "…and Surrealistic Pillow  became
    a household name
    in the house of rock ‘n’ roll."

    Denise Sullivan in Crawdaddy,
    October 8, 2009

    Related material:

    "Which Dreamed It?"
    — Title of final chapter,
    Through the Looking Glass

    "Go ask Alice…
    I think she'll know."
    — Grace Slick, 1967   

    The Crawdaddy  date Oct. 8, 2009
    leads to the Log24 post
    Graphic Austerity.

    Ninefold square with shades of gray in chessboard pattern

    Clicking on those words
      in that post will lead you to…
    The Logic of Dreams.

    Thursday, February 25, 2010

    Through the Blackboard

    Filed under: General — Tags: — m759 @ 12:07 pm

    Or: "Gopnik Meets Oppenheimer in Heaven"

    (Or, for those less philosophically minded, "Raiders of the Lost Pussy")

    Midrash on "A Serious Man"
    by Steven Menashi at
    The American Scene

    "A Serious Man kicks off with a Yiddish-language frame story that takes place in a 19th-century Eastern European shtetl, where a married couple has an enigmatic encounter with an old acquaintance who may be a dybbuk," recounts Dana Stevens . "The import of this parable is cryptic to the point of inscrutability."

    It seems to me that the Coen Brothers’ dybbuk is the Jewish folkloric equivalent of Schrodinger’s Cat .

    When we first meet the main character, a physics professor named Larry Gopnik, he’s writing equations on the board: "So if that’s that, then we can do this, right? Is that right? Isn’t that right? And that’s Schrodinger’s paradox, right? Is the cat dead or is the cat not dead?" Likewise, we can’t know whether Fyvush Finkel [the aforementioned old acquaintance] is alive or a dybbuk. We can only evaluate probabilities. When a Korean student named Clive Park complains to Larry that he shouldn’t have failed the Physics midterm because "I understand the physics. I understand the dead cat," Larry says:

    You can’t really understand the physics without understanding the math. The math tells how it really works. That’s the real thing; the stories I give you in class are just illustrative; they’re like, fables, say, to help give you a picture. An imperfect model. I mean— even I don’t understand the dead cat. The math is how it really works.

    But the fable actually tells us that the math doesn’t capture reality.

    The story in images below summarizes a meditation suggested by this parable and by

    1. Tuesday's post "Fish Story"
       
    2. Today's AP thought:
      "Open-mindedness is not the same as empty-mindedness." –John Dewey
       
    3. "Zen mind, empty mind."
       
    4. Today's NY Times obituary for Selma G. Hirsh,
      author of The Fears Men Live By (Harper, 1955).
      Hirsh died on St. Bridget's Day.
       
    5. A search for the Hirsh book that led to a web page
      with a 1955 review of J. Robert Oppenheimer's book The Open Mind
       
    6. A search for the Oppenheimer book that led to
      LIFE magazine's issue of Oct. 10, 1949
       
    7. "Satori means 'awakening.'" — TIME magazine, Nov. 21, 1960

     

    Blackboard in "A Serious Man"–

    Physicist accelerated against his blackboard in 'A Serious Man'

     

    Blackboard at the Institute for Advanced Study–


    J. Robert Oppenheimer at his blackboard

    "Daddy's home! Daddy's home!"

    (Click to enlarge.)

    Oppenheimer homecoming, with ad for 'Pussy-Footer' alarm clock

     

    Related material–

    A Zen meditation from Robert Pirsig
    is suggested by the time on the above
    alarm clock– 8:20– interpreted,
    surrealistically, as a date — 8/20.

    Monday, February 1, 2010

    For St. Bridget’s Day

    Filed under: General,Geometry — m759 @ 12:25 pm

    "But wait, there's more!"
    Stanley Fish, NY Times Jan. 28

    From the editors at The New York Times who, left to their own devices, would produce yet another generation of leftist morons who don't know the difference between education and entertainment–

    A new Times column starts today–

    http://www.log24.com/log/pix10/100201-Strogatz.jpg

    The quality of the column's logo speaks for itself. It pictures a cone with dashed lines indicating height and base radius, but unlabeled except for a large italic x to the right of the cone. This enigmatic variable may indicate the cone's height or slant height– or, possibly, its surface area or volume.

    Instead of the column's opening load of crap about numbers and Sesame Street, a discussion of its logo might be helpful.

    The cone plays a major role in the historical development of mathematics.

    Some background from an online edition of Euclid

    "Euclid proved in proposition XII.10 that the cone with the same base and height as a cylinder was one third of the cylinder, but he could not find the ratio of a sphere to the circumscribed cylinder. In the century after Euclid, Archimedes solved this problem as well as the much more difficult problem of the surface area of a sphere."

    For Archimedes and the surface area of a sphere, see (for instance) a discussion by Kevin Brown. For more material on Archimedes, see "Archimedes: Volume of a Sphere," by Doug Faires (2001)– Archimedes' heuristic argument from mechanics that involves the volume of a cone– and Archimedes' more rigorous approach in The Works of Archimedes, edited by T. L. Heath (1897).

    The work of Euclid and Archimedes on volumes was, of course, long before the discovery of calculus.  For a helpful discussion of cone volumes involving high-school-level calculus, see, for instance,  the following–

    http://www.log24.com/log/pix10/100201-VolCalc.gif

    The Times editors apparently feel that
    few of their readers are capable of
    such high-school-level sophistication.

    For some other geometric illustrations
    perhaps more appealing than the Times's

    http://www.log24.com/log/pix10/100201-StrogatzLogo.png

    dunce cap, see the symbol of
      today's saint– a Bridget Cross
    and a web page on
    visualized quaternions.

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