Log24

Sunday, April 10, 2022

Turning Nine continues.

Filed under: General — Tags: — m759 @ 1:31 pm

That was then, this is now —

Be careful what you wish for.

Wednesday, November 24, 2021

Turning Nine  Continues*

Filed under: General — Tags: , — m759 @ 10:20 pm

From Log24 on Epiphany 2012 —

IMAGE- Cathy Hull, detail from cover of Hillman's 'The Dream and the Underworld'

A version of the Zemeckis Cube —

* See Turning Nine (Log24, Nov. 8, 2021).

Monday, November 8, 2021

Turning Nine

Filed under: General — Tags: , — m759 @ 12:20 pm

From my hometown newspaper on the day I turned nine —

Hometown library's Thomas Mann

Monday, October 24, 2022

Turning Eight: Double Twist

Filed under: General — Tags: , — m759 @ 11:46 am

This post is a sequel to my earlier memoir, "Turning Nine."

Related material … "Double Twist" in …

Saturday, May 28, 2022

Nine Stories

Filed under: General — Tags: — m759 @ 9:50 pm

Art based on a cover of Salinger's 'Nine Stories'

Related material — Turning Nine and A Mad Day's Work.

Wednesday, February 22, 2023

Plan 9 from Warren Public Library*

Filed under: General — Tags: — m759 @ 6:45 am

Art based on a cover of Salinger's 'Nine Stories'

The above image is from "Nine Stories" in this journal.

* See "Turning Nine."

Wednesday, July 13, 2022

A New Yorker Child’s Progress

Filed under: General — Tags: , , — m759 @ 6:27 pm

A New Yorker  writer on why he wanted to
learn mathematics at an advanced age —

"The challenge, of course, especially in light of the collapsing horizon, since I was sixty-five when I started. Also, I wanted especially to study calculus because I never had. I didn’t even know what it was—I quit math after feeling that with Algebra II I had pressed my luck as far as I dared. Moreover, I wanted to study calculus because Amie told me that when she was a girl William Maxwell had asked her what she was studying, and when she said calculus he said, 'I loved calculus.' Maxwell would have been about the age I am now. He would have recently retired after forty years as an editor of fiction at The New Yorker , where he had handled such writers as Vladimir Nabokov, Eudora Welty, John Cheever, John Updike, Shirley Hazzard, and J. D. Salinger. When Salinger finished Catcher in the Rye , he drove to the Maxwells’ country house and read it to them on their porch. I grew up in a house on the same country road that Maxwell and his wife, Emily, lived on, and Maxwell was my father’s closest friend."

— Wilkinson, Alec. A Divine Language  (p. 5). Published
July 12, 2022, by Farrar, Straus and Giroux. Kindle Edition. 

See as well two versions of
a very short story, "Turning Nine."

Wilkinson's title is of course deplorable.
Related material: "Night Hunt" in a
Log24 search for the phrase "Good Question."

Sunday, November 28, 2021

The Fermi Question

Filed under: General — Tags: , — m759 @ 11:59 am

A fictional  version of Turning Nine

A bewildering phrase —"That famous lunch." 
What  famous lunch? This is the book's first
mention of Fermi.

Google solves the mystery —

Thursday, October 31, 2024

“Some events may require registration.”

Filed under: General — Tags: — m759 @ 11:53 am

Related reading —

http://m759.net/wordpress/?s=Turning+Nine .

Monday, October 9, 2017

Still Point for a Dance

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

"At the still point of the turning world. Neither flesh nor fleshless;
Neither from nor towards; at the still point, there the dance is,
But neither arrest nor movement. And do not call it fixity,
Where past and future are gathered. Neither movement from nor towards,
Neither ascent nor decline. Except for the point, the still point,
There would be no dance, and there is only the dance."

— T. S. Eliot, Four Quartets

See also a recurrent image
from this journal —

IMAGE- The ninefold square .

Center stage in a ninefold square

Sunday, July 26, 2015

Lit

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

"Passion simmers,
 Then it boils.
 To the victor
 Go the spoils."

—  The Spoils of Babylon
      (theme song, adapted)

Compare and contrast:

                                 " my song sounded
In the four-towered Caer, forever turning,
And of its Cauldron was my first song sung:
Nine maidens kindle the Cauldron by their breathing.
Of what nature is the Lord of Annwn’s Cauldron?
Enameled iridescence and pearly white its rim.
It will not boil the coward’s portion – not so its destiny."

The Spoils of Hell
     (title adapted)

Monday, July 1, 2013

Declamation

Filed under: General — Tags: , — m759 @ 2:07 pm

Continued from Sunday's post Book Award and last
midnight's post Holding the Frame

The nineteenth-century German writer Rudolf Haym on
German romantic Hellenism—

"In the enjoyment of this fair picture-world, our nation must 
needs delude itself a moment with the dream of Greek felicity 
and Greek repose to awaken directly poorer and more restless 
than before. To Poetry such a delusion was indeed natural, and 
who would dispute it with her after she had offered to our 
enjoyment what was sweetest and most perfect! But we see 
now all at once Metaphysic seized with the same illusion. 
Turning aside from the strait path of sober inquiry and from the 
labour of deliverance through the most conscientious criticism, 
Hegel begins to expand over our spiritual world his ideal that 
was found in Hellas, that was strengthened by exhaustive 
penetration into the ultimate grounds of all religion. A dreamed-of 
and yearned-for future is treated as present. A system tricked 
out with the entire dignity of the science of truth raises itself 
beside our poetry, and with diamond net spins us into an idea 
with which the want, the incompleteness, and the unbeauty of 
our political and historical actuality is at every point in contradiction."

Rudolf Haym, Hegel und seine Zeit  (1857), 91-92, translated 
and quoted in  The Secret of Hegel , by James Hutchison Stirling
(1898 edition, p. 626)

Saturday, June 19, 2010

Imago Creationis

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

Image-- The Four-Diamond Tesseract

In the above view, four of the tesseract's 16
vertices are overlaid by other vertices.
For views that are more complete and
moveable, see Smith's tesseract page.

Four-Part Tesseract Divisions

http://www.log24.com/log/pix10A/100619-TesseractAnd4x4.gif

The above figure shows how four-part partitions
of the 16 vertices  of a tesseract in an infinite
Euclidean  space are related to four-part partitions
of the 16 points  in a finite Galois  space

Euclidean spaces versus Galois spaces
in a larger context—


Infinite versus Finite

The central aim of Western religion —

"Each of us has something to offer the Creator...
the bridging of
                 masculine and feminine,
                      life and death.
It's redemption.... nothing else matters."
-- Martha Cooley in The Archivist  (1998)

The central aim of Western philosophy —

              Dualities of Pythagoras
              as reconstructed by Aristotle:
                 Limited     Unlimited
                     Odd     Even
                    Male     Female
                   Light      Dark
                Straight    Curved
                  ... and so on ....

"Of these dualities, the first is the most important; all the others may be seen as different aspects of this fundamental dichotomy. To establish a rational and consistent relationship between the limited [man, etc.] and the unlimited [the cosmos, etc.] is… the central aim of all Western philosophy."
— Jamie James in The Music of the Spheres  (1993)

Another picture related to philosophy and religion—

Jung's Four-Diamond Figure from Aion

http://www.log24.com/log/pix10A/100615-JungImago.gif

This figure was devised by Jung
to represent the Self. Compare the
remarks of Paul Valéry on the Self—

Flight from Eden: The Origins of Modern Literary Criticism and Theory, by Steven Cassedy, U. of California Press, 1990, pages 156-157—

Valéry saw the mind as essentially a relational system whose operation he attempted to describe in the language of group mathematics. "Every act of understanding is based on a group," he says (C, 1:331). "My specialty— reducing everything to the study of a system closed on itself and finite" (C, 19: 645). The transformation model came into play, too. At each moment of mental life the mind is like a group, or relational system, but since mental life is continuous over time, one "group" undergoes a "transformation" and becomes a different group in the next moment. If the mind is constantly being transformed, how do we account for the continuity of the self? Simple; by invoking the notion of the invariant. And so we find passages like this one: "The S[elf] is invariant, origin, locus or field, it's a functional property of consciousness" (C, 15:170 [2:315]). Just as in transformational geometry, something remains fixed in all the projective transformations of the mind's momentary systems, and that something is the Self (le Moi, or just M, as Valéry notates it so that it will look like an algebraic variable). Transformation theory is all over the place. "Mathematical science…  reduced to algebra, that is, to the analysis of the transformations of a purely differential being made up of homogeneous elements, is the most faithful document of the properties of grouping, disjunction, and variation in the mind" (O, 1:36). "Psychology is a theory of transformations, we just need to isolate the invariants and the groups" (C, 1:915). "Man is a system that transforms itself" (C, 2:896).

Notes:

  Paul Valéry, Oeuvres  (Paris: Pléiade, 1957-60)

C   Valéry, Cahiers, 29 vols. (Paris: Centre National de le Recherche Scientifique, 1957-61)

Note also the remarks of George David Birkhoff at Rice University
in 1940 (pdf) on Galois's theory of groups and the related
"theory of ambiguity" in Galois's testamentary letter—

… metaphysical reasoning always relies on the Principle of Sufficient Reason, and… the true meaning of this Principle is to be found in the “Theory of Ambiguity” and in the associated mathematical “Theory of Groups.”

If I were a Leibnizian mystic, believing in his “preestablished harmony,” and the “best possible world” so satirized by Voltaire in “Candide,” I would say that the metaphysical importance of the Principle of Sufficient Reason and the cognate Theory of Groups arises from the fact that God thinks multi-dimensionally* whereas men can only think in linear syllogistic series, and the Theory of Groups is the appropriate instrument of thought to remedy our deficiency in this respect.

* That is, uses multi-dimensional symbols beyond our grasp.

Related material:

Imago Creationis

A medal designed by Leibniz to show how
binary arithmetic mirrors the creation by God
of something (1) from nothing (0).

http://www.log24.com/log/pix10A/100618-LeibnizMedaille.jpg

Another array of 16 strings of 0's and 1's, this time
regarded as coordinates rather than binary numbers—

Frame of Reference

http://www.log24.com/log/pix10A/100619-ReferenceFrame.gif

The Diamond Theorem

http://www.log24.com/log/pix10A/100619-Dtheorem.gif

Some context by a British mathematician —

http://www.log24.com/log/pix10A/100619-Cameron.gif

Imago

by Wallace Stevens

Who can pick up the weight of Britain, 
Who can move the German load 
Or say to the French here is France again? 
Imago. Imago. Imago. 

It is nothing, no great thing, nor man 
Of ten brilliancies of battered gold 
And fortunate stone. It moves its parade 
Of motions in the mind and heart, 

A gorgeous fortitude. Medium man 
In February hears the imagination's hymns 
And sees its images, its motions 
And multitudes of motions 

And feels the imagination's mercies, 
In a season more than sun and south wind, 
Something returning from a deeper quarter, 
A glacier running through delirium, 

Making this heavy rock a place, 
Which is not of our lives composed . . . 
Lightly and lightly, O my land, 
Move lightly through the air again.

Thursday, January 29, 2009

Thursday January 29, 2009

Filed under: General — m759 @ 10:23 am
Dagger Definitions

From 'Ulysses,' 1922 first edition, page 178-- 'dagger definitions'
 
Midrash by a post-bac:

Wednesday, August 27, 2008

“Horseness is
the whatness of allhorse”:
Thingism vs. Thisness

By Amy Peterson

Jacques Derrida once asked the surly and self-revealing question, “Why is it the philosopher who is expected to be easier and not some scientist who is even more inaccessible?” As with philosophers generally, literary critics come with their own inaccessible argot, some terms of which are useful, but most of which are not and only add more loops to literary criticism’s spiraling abstraction. Take for example, James Wood’s neologism thisness (h/t: 3 Quarks Daily):

The project of modernity in Wood’s eyes is largely in revealing the contour and shape, the specific ‘feel’ of that essential mystery. He even borrows a concept from the medieval philosopher Duns Scotus, haecceitas or ‘thisness,’ to explain what he means: ‘By thisness, I mean any detail that draws abstraction toward itself and seems to kill that abstraction with a puff of palpability, any detail that centers our attention with its concretion.’ (my emphasis)

Wood is clearly taking his cue here from the new trend in literary criticism of referring to realism by its etymological meaning, thingism. Where thingism is meant to capture the materialism of late nineteenth and early 20th century Realist literature, thisness, it seems, is meant to capture the basic immaterialism of Modern realist literature. In this, it succeeds. Realism is no longer grounded in the thingism, or material aspect, of reality as it was during the Victorian era. In contemporary literature, it is a “puff of palpability” that hints at reality’s contours but does not disturb our essential understanding of existence as an impalpable mystery. So now we have this term that seems to encompass the Modern approach to reality, but is it useful as an accurate conception of reality (i.e. truth, human existence, and the like), and how are we to judge its accuracy?

I think that, as far as literature is concerned, the test of the term’s accuracy lies in the interpretation of the Modernist texts that Wood champions as truthful but largely abstract depictions of human experience:

‘Kafka’s ‘”Metamorphosis” and Hamsun’s “Hunger” and Beckett’s “Endgame” are not representations of likely or typical human activity but are nevertheless harrowingly truthful texts.’

For brevity’s sake, I’ll pick a passage from a different Modernist text that I think exemplifies the issues involved in the question of thingism and thisness’ reality. In James Joyce’s Ulysses, a pub discussionhttp://www.log24.com/images/asterisk8.gif of art’s purpose arises in which the writer Geoffrey Russell asserts that “Art has to reveal to us ideas, formless spiritual essences”; in his thoughts, Stephen Dedalus prepares to counter this:

Unsheathe your dagger definitions. Horseness is the whatness of allhorse. Streams of tendency and eons they worship. God: noise in the street: very peripatetic. Space: what you damn well have to see. Through spaces smaller than red globules of man’s blood they creepy crawl after [William] Blake’s buttocks into eternity of which this vegetable world is but a shadow. Hold to the now, the here, through which all future plunges to the past.

To give my best translation of Stephen-think: The physical being of the horse (“horseness”) grounds the over-arching, abstract idea of the horse (“allhorse”) in reality (“whatness”). God—the ultimate abstraction—is elusive and rarely manifests himself as a material reality (when listening to children playing earlier in the book, Stephen asserts that God is a “shout in the street”). Space—the material world—must be observed to make sense of abstract ideas (like God). Stephen’s opponents who believe that art must depict the abstract and the essential make claims about existence that have very little basis in material reality so that they can grasp at the divine through the work of such famously fantastic artists as William Blake, whose unrealistic poetry and paintings Stephen evidently holds in little esteem here, though he’s kinder to Blake elsewhere. Finally, the present makes concrete the abstract possibilities of the future by turning them into the realities of the past.

Ulysses elucidates the distinction between abstractly based and materially based realism because, while abstract to be sure, Joyce’s writing is deeply rooted in material existence, and it is this material existence which has given it its lasting meaning and influence. The larger point that I’m trying to make here is that material reality gives meaning to the abstract. (As a corollary, the abstract helps us to make sense of material reality.) There can be no truth without meaning, and there can be no meaning without a material form of existence against which to judge abstract ideas. To argue, as Wood does, that the abstract can produce concrete truths with little reference to material reality is to ignore the mutual nature of the relationship between material reality and truth. The more carefully we observe material reality, the more truth we gain from our abstractions of its phenomena, or, to state it in the vocabulary—though not the style—of literary criticism: thisness is a diluted form of thingism, which means that thisness is productive of fewer (and lesser) truths.

http://www.log24.com/images/asterisk8.gif “Space: what you
  damn well
     have to see.”

Amy Peterson
has failed to see
that the unsheathing
of dagger definitions
takes place not in
a pub, but in
The National Library
of Ireland
.

The Russell here is not
Geoffrey but rather
George William Russell,
also known as AE.

Related material:

Yesterday’s Log24 entry
for the Feast of
St. Thomas Aquinas,
Actual Being,”
and the four entries
that preceded it.

Friday, January 2, 2009

Friday January 2, 2009

Filed under: General — Tags: — m759 @ 5:48 am
Signs and Symbols

continued…
from the five entries
ending on June 3, 2008
and from yesterday,
New Year's Day

The end of a story by Vladimir Nabokov in The New Yorker of May 15, 1948:

Rotary telephone dial

"You have the incorrect number. I will tell you what you are doing: you are turning the letter O instead of the zero."

They sat down to their unexpected festive midnight tea. The birthday present stood on the table. He sipped noisily; his face was flushed; every now and then he imparted a circular motion to his raised glass so as to make the sugar dissolve more thoroughly. The vein on the side of his bald head where there was a large birthmark stood out conspicuously and, although he had shaved that morning, a silvery bristle showed on his chin. While she poured him another glass of tea, he put on his spectacles and re-examined with pleasure the luminous yellow, green, red little jars. His clumsy moist lips spelled out their eloquent labels: apricot, grape, beech plum, quince. He had got to crab apple, when the telephone rang again.

Art based on a cover of Salinger's 'Nine Stories'

Click for details.

Monday, October 31, 2005

Monday October 31, 2005

Filed under: General — Tags: , , , , , — m759 @ 2:00 am

Balance

The image “http://log24.com/log/pix03/030109-gridsmall.gif” cannot be displayed, because it contains errors.

"An asymmetrical balance is sought since it possesses more movement. This is achieved by the imaginary plotting of the character upon a nine-fold square, invented by some ingenious writer of the Tang dynasty. If the square were divided in half or in four, the result would be symmetrical, but the nine-fold square permits balanced asymmetry."

— Chiang Yee, Chinese Calligraphy, quoted in Aspen no. 10, item 8

"'Burnt Norton' opens as a meditation on time. Many comparable and contrasting views are introduced. The lines are drenched with reminiscences of Heraclitus' fragments on flux and movement….  the chief contrast around which Eliot constructs this poem is that between the view of time as a mere continuum, and the difficult paradoxical Christian view of how man lives both 'in and out of time,' how he is immersed in the flux and yet can penetrate to the eternal by apprehending timeless existence within time and above it. But even for the Christian the moments of release from the pressures of the flux are rare, though they alone redeem the sad wastage of otherwise unillumined existence. Eliot recalls one such moment of peculiar poignance, a childhood moment in the rose-garden– a symbol he has previously used, in many variants, for the birth of desire. Its implications are intricate and even ambiguous, since they raise the whole problem of how to discriminate between supernatural vision and mere illusion. Other variations here on the theme of how time is conquered are more directly apprehensible. In dwelling on the extension of time into movement, Eliot takes up an image he had used in 'Triumphal March': 'at the still point of the turning world.' This notion of 'a mathematically pure point' (as Philip Wheelwright has called it) seems to be Eliot's poetic equivalent in our cosmology for Dante's 'unmoved Mover,' another way of symbolising a timeless release from the 'outer compulsions' of the world. Still another variation is the passage on the Chinese jar in the final section. Here Eliot, in a conception comparable to Wallace Stevens' 'Anecdote of the Jar,' has suggested how art conquers time:

       Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness."

— F. O. Matthiessen, The Achievement of T.S. Eliot,
Oxford University Press, 1958, as quoted in On "Burnt Norton"

 

Sunday, November 30, 2003

Sunday November 30, 2003

Filed under: General — m759 @ 3:27 pm

The Proof and the Lie

A mathematical lie has been circulating on the Internet.

It concerns the background of Wiles’s recent work on mathematics related to Fermat’s last theorem, which involves the earlier work of a mathematician named Taniyama.

This lie states that at the time of a conjecture by Taniyama in 1955, there was no known relationship between the two areas of mathematics known as “elliptic curves” and “modular forms.”

The lie, due to Harvard mathematician Barry Mazur, was broadcast in a TV program, “The Proof,” in October 1997 and repeated in a book based on the program and in a Scientific American article, “Fermat’s Last Stand,” by Simon Singh and Kenneth Ribet, in November 1997.

“… elliptic curves and modular forms… are from opposite ends of the mathematical spectrum, and had previously been studied in isolation.”

Site on Simon Singh’s 1997 book Fermat’s Last Theorem

“JOHN CONWAY: What the Taniyama-Shimura conjecture says, it says that every rational elliptic curve is modular, and that’s so hard to explain.

BARRY MAZUR: So, let me explain.  Over here, you have the elliptic world, the elliptic curves, these doughnuts.  And over here, you have the modular world, modular forms with their many, many symmetries.  The Shimura-Taniyama conjecture makes a bridge between these two worlds.  These worlds live on different planets.  It’s a bridge.  It’s more than a bridge; it’s really a dictionary, a dictionary where questions, intuitions, insights, theorems in the one world get translated to questions, intuitions in the other world.

KEN RIBET: I think that when Shimura and Taniyama first started talking about the relationship between elliptic curves and modular forms, people were very incredulous….”

Transcript of NOVA program, “The Proof,” October 1997

The lie spread to other popular accounts, such as the column of Ivars Peterson published by the Mathematical Association of America:

“Elliptic curves and modular forms are mathematically so different that mathematicians initially couldn’t believe that the two are related.”

Ivars Peterson, “Curving Beyond Fermat,” November 1999 

The lie has now contaminated university mathematics courses, as well as popular accounts:

“Elliptic curves and modular forms are completely separate topics in mathematics, and they had never before been studied together.”

Site on Fermat’s last theorem by undergraduate K. V. Binns

Authors like Singh who wrote about Wiles’s work despite their ignorance of higher mathematics should have consulted the excellent website of Charles Daney on Fermat’s last theorem.

A 1996 page in Daney’s site shows that Mazur, Ribet, Singh, and Peterson were wrong about the history of the known relationships between elliptic curves and modular forms.  Singh and Peterson knew no better, but there is no excuse for Mazur and Ribet.

Here is what Daney says:

“Returning to the j-invariant, it is the 1:1 map betweem isomorphism classes of elliptic curves and C*. But by the above it can also be viewed as a 1:1 map j:H/r -> C.  j is therefore an example of what is called a modular function. We’ll see a lot more of modular functions and the modular group. These facts, which have been known for a long time, are the first hints of the deep relationship between elliptic curves and modular functions.”

“Copyright © 1996 by Charles Daney,
All Rights Reserved.
Last updated: March 28, 1996″

Update of Dec. 2, 2003

For the relationship between modular functions and modular forms, see (for instance) Modular Form in Wikipedia.

Some other relevant quotations:

From J. S. Milne, Modular Functions and Modular Forms:

“The definition of modular form may seem strange, but we have seen that such functions arise naturally in the [nineteenth-century] theory of elliptic functions.”

The next quote, also in a nineteenth-century context, relates elliptic functions to elliptic curves.

From Elliptic Functions, a course syllabus:

“Elliptic functions parametrize elliptic curves.”

Putting the quotes together, we have yet another description of the close relationship, well known in the nineteenth century (long before Taniyama’s 1955 conjecture), between elliptic curves and modular forms.

Another quote from Milne, to summarize:

“From this [a discussion of nineteenth-century mathematics], one sees that arithmetic facts about elliptic curves correspond to arithmetic facts about special values of modular functions and modular forms.”

Serge Lang apparently agrees:

Elliptic functions parametrize elliptic curves, and the intermingling of the analytic and algebraic-arithmetic theory has been at the center of mathematics since the early part of the nineteenth century.”

Editorial description of Lang’s Elliptic Functions (second edition, 1987)

Update of Dec. 3, 2003

The theory of modular functions and modular forms, defined on the upper half-plane H and subject to appropriate tranformation laws with respect to the group Gamma = SL(2, Z) of fractional linear transformations, is closely related to the theory of elliptic curves, because the family of all isomorphism classes of elliptic curves over C can be parametrized by the quotient Gamma\H. This is an important, although formal, relation that assures that this and related quotients have a natural structure as algebraic curves X over Q. The relation between these curves and elliptic curves predicted by the Taniyama-Weil conjecture is, on the other hand, far from formal.”

Robert P. Langlands, review of Elliptic Curves, by Anthony W. Knapp.  (The review  appeared in Bulletin of the American Mathematical Society, January 1994.)

Tuesday, September 24, 2002

Tuesday September 24, 2002

Filed under: General — m759 @ 11:33 pm

The Shining of Lucero

From my journal note, “Shining Forth“:

The Spanish for “Bright Star” is “Lucero.”

The Eye of the Beholder:

When you stand in the dark and look at a star a hundred light years away, not only have the retarded light waves from the star been travelling for a hundred years toward your eyes, but also advanced waves from your eyes have reached a hundred years into the past to encourage the star to shine in your direction.

— John Cramer, “The Quantum Handshake

From Broken Symmetries, by Paul Preuss, 1983:

He’d toyed with “psi” himself…. 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….   

Peter [Slater] 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.

………………

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. (Ch. 16)

From Secret Passages, by Paul Preuss, 1997:

Minakis caught up and walked beside him in silence, moving with easy strides over the bare ground, listening as Peter [Slater] spoke. “Delos One was ten years ago — quantum theory seemed as natural as water to me then; I could play in it without a care. If I’d had any sense of history, I would have recognized that I’d swallowed the Copenhagen interpretation whole.”

“Back then, you insisted that the quantum world is not a world at all,” Minakis prompted him. “No microworld, only mathematical descriptions.”

“Yes, I was adamant. Those who protested were naive — one has to be willing to tolerate ambiguity, even to be crazy.”

“Bohr’s words?”

“The party line. Of course Bohr did say, ‘It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.’ Meaning that when we start to talk what sounds like philosophy, our colleagues should rip us to pieces.” Peter smiled. “They smell my blood already.”

………………
 
Peter glanced at Minakis. “Let’s say there are indications — I have personal indications — not convincing, perhaps, but suggestive, that the quantum world penetrates the classical world deeply.” He was silent for a moment, then waved his hand at the ruins. “The world of classical physics, I mean. I suppose I’ve come to realize that the world is more than a laboratory.”

“We are standing where Apollo was born,” Minakis said. “Leto squatted just there, holding fast to a palm tree, and after nine days of labor gave birth to the god of light and music….”

From my journal note, “A Mass for Lucero“:

To Lucero, in memory of
1962 in Cuernavaca

From On Beauty, by Elaine Scarry,
Princeton University Press, 1999 —

“Homer sings of the beauty of particular things. Odysseus, washed up on shore, covered with brine, having nearly drowned, comes upon a human community and one person in particular, Nausicaa, whose beauty simply astonishes him. He has never anywhere seen a face so lovely; he has never anywhere seen any thing so lovely….

I have never laid eyes on anyone like you,
neither man nor woman…
I look at you and a sense of wonder takes me.

Wait, once I saw the like —
in Delos, beside Apollo’s altar —
the young slip of a palm-tree
springing into the light.”

From Secret Passages, by Paul Preuss, 1997:

“When we try to look inside atoms,” Peter said, “not only can we not see what’s going on, we cannot even construct a coherent picture of what’s going on.”

“If you will forgive me, Peter,” Minakis said, turning to the others. “He means that we can construct several pictures — that light and matter are waves, for example, or that light and matter are particles — but that all these pictures are inadequate. What’s left to us is the bare mathematics of quantum theory.”

…. “Whatever the really real world is like, my friend, it is not what you might imagine.”

………………

 
Talking physics, Peter tended to bluntness. “Tell me more about this real world you imagine but can’t describe.”

Minakis turned away from the view of the sunset. “Are you familiar with John Cramer’s transactional interpretation of quantum mechanics?”

“No I’m not.”

………………

“Read Cramer. I’ll give you his papers. Then we can talk.” 

 From John Cramer, “The Quantum Handshake“:

Advanced waves could perhaps, under the right circumstances, lead to “ansible-type” FTL communication favored by Le Guin and Card…. 

For more on Le Guin and Card, see my journal notes below.

For more on the meaning of “lucero,” see the Wallace Stevens poem “Martial Cadenza.”

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