Part I — Unity and Multiplicity
(Continued from The Talented and Galois Cube)
Part II — "A feeling, an angel, the moon, and Italy"—
Part I — Unity and Multiplicity
(Continued from The Talented and Galois Cube)
Part II — "A feeling, an angel, the moon, and Italy"—
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Related material: Exhibit B Julie Taymor |
A film by Julie Taymor, Across the Universe — ![]() Detail of the Strawberry Fields Forever Sacred Heart — Julie Taymor "Shinin' like a diamond, — Album "The Dark," |
"For Mr. Lumet, location mattered deeply."
— April 9th online New York Times
"That old Jew gave me this here."
Larger image (1.5 MB)
Catherine Elizabeth "Kate" Middleton, born 9 January 1982,
will marry Prince William of Wales on April 29th, 2011.
This suggests, by a very illogical and roundabout process
of verbal association, a search in this journal.
A quote from that search—
“‘Memory is non-narrative and non-linear.’
— Maya Lin in The Harvard Crimson , Friday, Dec. 2, 2005
A non-narrative image from the same
general time span as the bride's birthday—

For some context, see Stevens + "The Rock" + "point A".
A post in that search, April 4th's Rock Notes, links to an essay
on physics and philosophy, "The Discrete and the Continuous," by David Deutsch.
See also the article on Deutsch, "Dream Machine," in the current New Yorker
(May 2, 2011), and the article's author, "Rivka Galchen," in this journal.
Galchen writes very well. For example —
| Galchen on quantum theory—
"Our intuition, going back forever, is that to move, say, a rock, one has to touch that rock, or touch a stick that touches the rock, or give an order that travels via vibrations through the air to the ear of a man with a stick that can then push the rock—or some such sequence. This intuition, more generally, is that things can only directly affect other things that are right next to them. If A affects B without being right next to it, then the effect in question must be in direct—the effect in question must be something that gets transmitted by means of a chain of events in which each event brings about the next one directly, in a manner that smoothly spans the distance from A to B. Every time we think we can come up with an exception to this intuition—say, flipping a switch that turns on city street lights (but then we realize that this happens through wires) or listening to a BBC radio broadcast (but then we realize that radio waves propagate through the air)—it turns out that we have not, in fact, thought of an exception. Not, that is, in our everyday experience of the world. We term this intuition 'locality.' Quantum mechanics has upended many an intuition, but none deeper than this one." |
A sequel to Wednesday afternoon's post on The Harvard Crimson ,
Atlas Shrugged (illustrated below) —
Related material found today in Wikipedia—
|
See also Savage Logic (Oct. 19, 2010), as well as
Stellan Skarsgård in Lie Groups for Holy Week (March 30, 2010)
and in Exorcist: The Beginning (2004).
Continued from Good Friday —
The New Yorker , in the above excerpt, says of David Deutsch that
"his books have titles of colossal confidence
('The Fabric of Reality,' 'The Beginning of Infinity')."
The Fabric of Reality — A post from Good Friday —
| Friday, April 22, 2011
In memory of Hazel Dickens, two links — Weepin' like a willow, mournin' like a dove |
The Beginning of Infinity — Another Good Friday death—
Sidney Michaels, adapter of the 1962 play "Tchin-Tchin."
"At play's end they are Chaplinesque waifs living in the charmed circle
of innocents that includes saints, children, drunkards and madmen.
Subliminally, Tchin-Tchin is a Christian existential fable." — TIME
The title refers to an article in The Harvard Crimson , "Atlas to the Text," on March 8, 2011.
"Atlas to the Text," by Nicholas T. Rinehart —
"… a small set of undergraduates culminate their academic careers with a translation thesis. Ford is one such student, currently completing her edition of Euripides’ 'The Bacchae,' a Greek tragedy centered on the god Dionysus’ revenge against his mortal family."
"The guards return with Dionysus himself, disguised as his priest and the leader of the Asian maenads. Pentheus questions him, still not believing that Dionysus is a god. However, his questions reveal that he is deeply interested in the Dionysiac rites, which the stranger refuses to reveal fully to him. This greatly angers Pentheus, who has Dionysus locked up. However, being a god, he is quickly able to break free and creates more havoc, razing the palace of Pentheus to the ground in a giant earthquake and fire."
The illustration for the Crimson article formed part of a post in this journal, Paradigms Lost, on March 10—
From Nabokov's The Gift —
Click for more about the Pushkin verse.
See also Trevanian + meadow and Congregated Light.
The above points and hyperplanes underlie the symmetries discussed
in the diamond theorem. See The Oslo Version and related remarks
for a different use in art.
Today's earlier post mentions one approach to the concepts of unity and multiplicity. Here is another.

Unity:
The 3×3×3 Galois Cube
Multiplicity:
One of a group, GL(3,3), of 11,232
natural transformations of the 3×3×3 Cube
See also the earlier 1985 3×3 version by Cullinane.
"It's going to be accomplished in steps, this establishment of the Talented in the scheme of things."
— Anne McCaffrey, Radcliffe ’47, To Ride Pegasus
"Character, as we have stated, is revealed through action.
We are not yet telepathic; we must embody even the most intellectual traits
and express them physically."
— The Craftsmen of Dionysus: An Approach to Acting by Jerome Rockwood
Dionysus Meets Apollo
in "Thirty Two Short Films About Glenn Gould"—
Step I — Tiny Dancer in My Hand (0.48.46)

Step II — The Bridge (0.52.46)

Step III — Liftoff (1.27.37)

From the author of The Abacus Conundrum—
Harlan Kane's sequel to The Apollo Meme—
THE KRISTEN EFFECT
"Thus the universal mutual attraction between the sexes is represented."
— Hexagram 31
In the May Smithsonian magazine— "What Defines a Meme?"
Related — Seven is Heaven…

* For the connection to Apollo, see Oct. 9, 2006.
One approach to the storied philosophers' stone, that of Jim Dodge in Stone Junction , was sketched in yesterday's Easter post. Dodge described a mystical "spherical diamond." The symmetries of the sphere form what is called in mathematics a Lie group . The "spherical" of Dodge therefore suggests a review of the Lie group E8 in Garrett Lisi's poetic theory of everything.
A check of the Wikipedia article on Lisi's theory yields…

Diamond and E8 at Wikipedia
Related material — E8 as "a diamond with thousands of facets"—

Also from the New Yorker article—
“There’s a dream that underlying the physical universe is some beautiful mathematical structure, and that the job of physics is to discover that,” Smolin told me later. “The dream is in bad shape,” he added. “And it’s a dream that most of us are like recovering alcoholics from.” Lisi’s talk, he said, “was like being offered a drink.”
A simpler theory of everything was offered by Plato. See, in the Timaeus , the Platonic solids—

Figure from this journal on August 19th, 2008.
See also July 19th, 2008.
“It’s all in Plato, all in Plato:
bless me, what do they
teach them at these schools!”
— C. S. Lewis
Background —
From a 1990 novel —

"The Easter Vigil is the most important liturgy on the church's calendar, when the faithful mark the passage from Christ's death to his resurrection on Easter Sunday. It is rich with symbols: fire and light signifying Jesus' resurrection, and the water used to baptize people into the faith….
This year, students of the Legion of Christ, the conservative order undergoing a major Vatican-mandated overhaul, provided the liturgical service at the vigil. The Vatican took over the Legion last May 1 after confirming its founder was a pedophile."
— AP story
See also Naples in this journal.
Background— Why Me? and the Fritz Leiber story "Damnation Morning."
The story, about the afterlife of a dead drunk, contains an intriguing dark lady.
Related material — Search for the Spider Woman.
See also Julie Taymor in an interview published last Dec. 12 —
“I’ve got two Broadway shows, a feature film, and Mozart,’’ she said.
“It’s a very interesting place to be and to be able to move back and forth,
but at a certain point you have to be able to step outside and see,’’
and here she dropped her voice to a tranquil whisper, “it’s just theater.
It’s all theater. It’s all theater. The whole thing is theater.’’
— and search for Taymor + Spider in this journal.
Happy Shakespeare's Birthday.
"Oh Death oh Death please let me see
If Christ has turned his back on me
When you were called and asked to bow
You wouldn’t take heed
And it’s too late now
Oh Death oh Death please give me time
To fix my heart and change my mind
Your mind is fixed
Your heart is bound
And I have the shackles to drag you down
Farewell, farewell
To all farewell
My doom is fixed
I’m summoned to hell
As long as God
In heaven shall dwell
My soul my soul shall scream in hell"
— Sung by Hazel Dickens in "Songcatcher"
The rest of the lyrics, and a video, may be found
at PaganSpace.net — "The Meeting Place for the Occult Community."
See also Harrowing in this journal.
In memory of Hazel Dickens, two links — Unique Figure and Hello Stranger .
Weepin' like a willow, mournin' like a dove
Weepin' like a willow, mournin' like a dove
There's a girl of the country
That I really love
For the title, see Palm Sunday.
"There is a pleasantly discursive treatment of
Pontius Pilate's unanswered question 'What is truth?'" — H. S. M. Coxeter, 1987
From this date (April 22) last year—
![]() Richard J. Trudeau in The Non-Euclidean Revolution , chapter on "Geometry and the Diamond Theory of Truth"– "… Plato and Kant, and most of the philosophers and scientists in the 2200-year interval between them, did share the following general presumptions: (1) Diamonds– informative, certain truths about the world– exist. Presumption (1) is what I referred to earlier as the 'Diamond Theory' of truth. It is far, far older than deductive geometry." Trudeau's book was published in 1987. The non-Euclidean* figures above illustrate concepts from a 1976 monograph, also called "Diamond Theory." Although non-Euclidean,* the theorems of the 1976 "Diamond Theory" are also, in Trudeau's terminology, diamonds. * "Non-Euclidean" here means merely "other than Euclidean." No violation of Euclid's parallel postulate is implied. |
Trudeau comes to reject what he calls the "Diamond Theory" of truth. The trouble with his argument is the phrase "about the world."
Geometry, a part of pure mathematics, is not about the world. See G. H. Hardy, A Mathematician's Apology .
From a story about mathematician Emmy Noether and 1882, the year she was born—
"People were then slowly becoming 'modern'— fortunately they had finally discovered not just that there are no Easter bunnies and Santa Claus, but also that there probably never were women who were led to evil ways by their curiosity and ended up, depending on their level of education, as common witches, as 'wiccans,' or as those particularly mysterious 'benandanti.'"
"… in the Balkans people believe that the souls of the dead rise to heaven in the guise of butterflies."
— "The Fairytale of the Totally Symmetrical Butterfly," by Dietmar Dath, in Intoxicating Heights (Eichborn AG, Frankfurt 2003)
An insect perhaps more appropriate for the afternoon of Good Friday— the fly in the logo of Dath's publisher—
Related material— Holy Saturday of 2004 and Wittgenstein and the Fly Bottle.
(After clicking, scroll down to get past current post.)
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Literary remarks for Maundy Thursday—

— C. P. Snow, foreword to G. H. Hardy's A Mathematician's Apology
Related material—
Emory University press release of January 20th, 2011:
"In 1937, Hans Rademacher found an exact formula for calculating partition values. While the method was a big improvement over Euler's exact formula, it required adding together infinitely many numbers that have infinitely many decimal places. 'These numbers are gruesome,' Ono says….
… The final eureka moment occurred near another Georgia landmark: Spaghetti Junction. Ono and Jan Bruinier were stuck in traffic near the notorious Atlanta interchange. While chatting in the car, they hit upon a way to overcome the infinite complexity of Rademacher's method. They went on to prove a formula that requires only finitely many simple numbers.
'We found a function, that we call P, that is like a magical oracle,' Ono says. 'I can take any number, plug it into P, and instantly calculate the partitions of that number….'"
See also this journal on April 15 and a Google Groups [sage-devel] thread, Ono-Bruinier partition formula. That thread started on April 15 and was last updated this morning.
Part I— A Naples, Florida obituary for artist Robert Vickrey, who died Sunday.
(See also this evening's earlier post Soul Art.)
Part II— "Stairway to Heaven," by Vickrey
Part III— Definition of "cornette"
Part IV— Recent photo of artist Josefine Lyche

Picture by Robert Vickrey.
Vickrey died Sunday.
See Sunday School.
This journal at 5:48 PM EST on Thursday, March 10, 2011—
(Continued from February 19)
The cover of the April 1, 1970 second edition of
The Structure of Scientific Revolutions , by Thomas S. Kuhn—

Note the quote on the cover—
"A landmark in intellectual history."— Science
This afternoon's online New York Times—
Google today, asked to "define:landmark," yields—
It was a dark and stormy night…

— Page 180, Logicomix
“… the class of reflections is larger in some sense over an arbitrary field than over a characteristic zero field.”
– Julia Hartmann and Anne V. Shepler, “Jacobians of Reflection Groups”
For some context, see the small cube in “A Simple Reflection Group of Order 168.”
See also the larger cube in “Many Dimensions” + Whitehead in this journal (scroll down to get past the current post).
That search refers to a work by Whitehead published in 1906, the year at the top of the Logicomix page above—

A related remark on axiomatics that has metaphysical overtones suitable for a dark and stormy night—
“An adequate understanding of mathematical identity requires a missing theory that will account for the relationships between formal systems that describe the same items. At present, such relationships can at best be heuristically described in terms that invoke some notion of an ‘intelligent user standing outside the system.'”
— Gian-Carlo Rota, “Syntax, Semantics, and…” in Indiscrete Thoughts . See also the original 1988 article.
Today's news from Oslo suggests a review—
The circular sculpture in the foreground
is called by the artist "The Omega Point."
This has been described as
"a portal that leads in or out of time and space."
Some related philosophical remarks—
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