A Startling Breakdown
Filed under: General — Tags: Lefebvre — m759 @ 10:45 AM
"… who shared the Nobel Prize …
for discovering a startling breakdown …."
— From "CP is for Consolation Prize" (Sept. 3, 2016)
See also Broken Symmetries in this journal.
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Filed under: General,Geometry — Tags: Apollo Psi, Swimmer — m759 @ 12:41 PM
A roundup of posts now tagged "Apollo Psi" led to the name
Evan Harris Walker in the post Dirac and Geometry of
Dec. 14, 2015. That post mentions …
"… 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."
— From the 1983 novel Broken Symmetries
by Paul Preuss
It turns out that Walker died "on the evening of August 17, 2006."
From this journal on that date —
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The Forking
Filed under: General,Geometry — m759 @ 12:00 PM
From the previous post:
"Neat, Dr. Walker, thought Peter Slater—
neat, and totally without content."
— Paul Preuss's 1983 novel Broken Symmetries
A background check yields …
"Dr. Evan Harris Walker died on the evening of
August 17, 2006…."
A synchronicity check of that date in this journal yields a diagram
that, taken by itself, is "neat, and totally without content." —
The diagram may be viewed as a tribute
to the late Yogi Berra, to the literary
"Garden of Forking Paths," or, more
seriously, to the modular group Γ.
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Dirac and Geometry
Filed under: General,Geometry — Tags: Apollo Psi, Dirac and Geometry — m759 @ 10:30 AM
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 —
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More Glass
Part I:
"…although a work of art 'is formed around something missing,' this 'void is its vanishing point, not its essence.' She shows deftly and delicately that the void inside Keats's urn, Heidegger's jug, or Wallace Stevens's jar forms the center around which we tend to organize our worlds."
— Harvard University Press on Persons and Things (April 30, 2008), by Barbara Johnson
Part II:
"Did you see more glass?"
Part III:
From the date of Barbara Johnson's death:
"Mathematical relationships were
enough to satisfy him, mere formal
relationships which existed at
all times, everywhere, at once."
– Broken Symmetries, 1983
The X's refer to the pattern on the
cover of a paperback edition
of Nine Stories, by J. D. Salinger.
Salinger died on Wednesday.
"You remember that book he sent me
from Germany? You know–
those German poems."
In Germany, Wednesday was
Holocaust Memorial Day, 2010.
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Filed under: General — m759 @ 3:09 PM
of Lucero
For John Cramer's
daughter Kathryn
(continued from
September 24, 2002)
"Mathematical relationships were
all times, everywhere, at once."
See also Art Wars at
(Jan. 19, 2007) and the
four entries preceding it.
Comments Off on Thursday August 27, 2009
Filed under: General — m759 @ 10:18 AM
Also Rises
The sun rises over the earth:
The image of PROGRESS.
— Classic of Change,
Hexagram 35
10:18:35 AM ET
Keillor Meets Thompson:
The Height of Folly
obituaries (previous entry)
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Filed under: General — m759 @ 9:00 AM
Hamilton's Whirligig
For details, see Visualizing GL(2,p).
"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…."
— Paul Preuss, Broken Symmetries
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Wednesday January 4, 2006
Filed under: General,Geometry — m759 @ 4:04 AM
In memory of Humphrey Carpenter, author of The Inklings, who attended The Dragon School. Carpenter died a year ago today.
From Log24 on Nov. 16, 2005:
Adam Gopnik on C. S. Lewis in the New Yorker:
"Lewis began with a number of haunted images…."
"The best of the books are the ones… where the allegory is at a minimum and the images just flow."
"'Everything began with images,' Lewis wrote…."
From Paul Preuss,
Broken Symmetries
(see previous entry):
Verbum Sat Sapienti?
Escher's Verbum
Solomon's Cube
Geometry of the I Ching
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The Shining according to
the Catholic Church:
"The Transfiguration of Christ is the culminating point of His public life…. Jesus took with him Peter and James and John and led them to a high mountain apart, where He was transfigured before their ravished eyes. St. Matthew and St. Mark express this phenomenon by the word metemorphothe, which the Vulgate renders transfiguratus est. The Synoptics explain the true meaning of the word by adding 'his face did shine as the sun: and his garments became white as snow,' according to the Vulgate, or 'as light,' according to the Greek text. This dazzling brightness which emanated from His whole Body was produced by an interior shining of His Divinity."
— The Catholic Encyclopedia of 1912
Paul Preuss:
From Broken Symmetries, 1983, Chapter 16:
"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."
Sunday February 20, 2005
Filed under: General,Geometry — Tags: Modal Diamond Box, on050220 — m759 @ 2:20 PM
Relativity Blues
Today, February 20, is the 19th anniversary of my note The Relativity Problem in Finite Geometry. Here is some related material.
In 1931, the Christian writer Charles Williams grappled with the theology of time, space, free will, and the many-worlds interpretation of quantum mechanics (anticipating by many years the discussion of this topic by physicists beginning in the 1950's).
(Some pure mathematics — untainted by physics or theology — that is nevertheless related, if only by poetic analogy, to Williams's 1931 novel, Many Dimensions, is discussed in the above-mentioned note and in a generalization, Solomon's Cube.)
On the back cover of Williams's 1931 novel, the current publisher, William B. Eerdmans Publishing Company of Grand Rapids, Michigan, makes the following statement:
"Replete with rich religious imagery, Many Dimensions explores the relation between predestination and free will as it depicts different human responses to redemptive transcendence."
One possible response to such statements was recently provided in some detail by a Princeton philosophy professor. See On Bullshit, by Harry G. Frankfurt, Princeton University Press, 2005.
A more thoughtful response would take into account the following:
1. The arguments presented in favor of philosopher John Calvin, who discussed predestination, in The Death of Adam: Essays on Modern Thought, by Marilynne Robinson
2. The physics underlying Einstein's remarks on free will, God, and dice
3. The physics underlying Rebecca Goldstein's novel Properties of Light and Paul Preuss's novels Secret Passages and Broken Symmetries
4. The physics underlying the recent so-called "free will theorem" of John Conway and Simon Kochen of Princeton University
5. The recent novel Gilead, by Marilynne Robinson, which deals not with philosophy, but with lives influenced by philosophy — indirectly, by the philosophy of the aforementioned John Calvin.
From a review of Gilead by Jane Vandenburgh:
"In The Death of Adam, Robinson shows Jean Cauvin to be the foremost prophet of humanism whose Protestant teachings against the hierarchies of the Roman church set in motion the intellectual movements that promoted widespread literacy among the middle and lower classes, led to both the American and French revolutions, and not only freed African slaves in the United States but brought about suffrage for women. It's odd then that through our culture's reverse historicism, the term 'Calvinism' has come to mean 'moralistic repression.'"
For more on what the Calvinist publishing firm Eerdmans calls "redemptive transcendence," see various July 2003 Log24.net entries. If these entries include a fair amount of what Princeton philosophers call bullshit, let the Princeton philosophers meditate on the summary of Harvard philosophy quoted here on November 5 of last year, as well as the remarks of November 5, 2003, and those of November 5, 2002.
From Many Dimensions (Eerdmans paperback, 1963, page 53):
"Lord Arglay had a suspicion that the Stone would be purely logical. Yes, he thought, but what, in that sense, were the rules of its pure logic?"
A recent answer:
Modal Theology
"We symbolize logical necessity
with the box ( )
and logical possibility
with the diamond ( )."
— Keith Allen Korcz,
(Log24.net, 1/25/05)
And what do we
symbolize by ?
"The possibilia that exist,
and out of which
the Universe arose,
are located in
a necessary being…."
— Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)
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Magic Hawaii
Today, the birthday of singer Jerry Lee Lewis, is also the feast of St. Michael and All Angels.
In honor of Lewis:
Killer Radio, an entry of July 31, 2003, that contains the following…
"When the light came she was sitting on the bed beside an open suitcase, toying with her diamond rings. She saw the light first in the depths of the largest stone."
— Paul Preuss, Broken Symmetries,
scene at Diamond Head, Oahu,
In honor of the angels:
Mathematics as an Adequate Language,
by Israel Gelfand, Sept. 2, 2003, which contains the following…
"Many people consider mathematics to be a boring and formal science. However, any really good work in mathematics always has in it: beauty, simplicity, exactness, and crazy ideas. This is a strange combination. I understood earlier that this combination is essential on the example of classical music and poetry. But it is also typical in mathematics. It is not by chance that many mathematicians enjoy serious music.
This combination of beauty, simplicity, exactness, and crazy ideas is, I think, common to both mathematics and music."
These qualities seem also to be sought by practitioners of religion and physics… for example, by the spiritually-minded physicist in Preuss's Broken Symmetries. Skeptics might prefer, to the word "religion," the word (pronounced with a sneer) "magic."
What do we find if, following in the footsteps of Gelfand and Preuss, we do a Google search on the following words…
"beauty simplicity exactness
crazy magic Hawaii"?
The search yields two results:
The Pupil: Poems by W. S. Merwin.
The above link is to a poem, "Prophecy," that seems suitable for these, the High Holy Days at the end of one year and the beginning of another.
For a follow-up to the poem, see
The Shining of Lucero.
"Striking Through the Mask, or
The Allegorical Meanings
in Moby Dick."
These two selections, both on the theme of light and darkness, offer a language that is perhaps more adequate than mathematics for dealing with the nature of the High Holy Days. For a more lighthearted approach to these concerns, also with a Hawaiian theme, see
The Aloha Mass.
Comments Off on Monday September 29, 2003
Filed under: General — Tags: Pascal's Diamond — m759 @ 6:41 PM
Killer Radio
"See the girl with the diamond ring?
She knows how to shake that thing."
— Jerry Lee "Killer" Lewis on
KHYI 95.3 FM, Plano, Texas,
at about 5:12 PM EDT 7/31/03,
introduced by DJ Allen Peck Sr.
"And on this point I pass the same judgment as those who say that geometricians give them nothing new by these rules, because they possessed them in reality, but confounded with a multitude of others, either useless or false, from which they could not discriminate them, as those who, seeking a diamond of great price amidst a number of false ones, but from which they know not how to distinguish it, should boast, in holding them all together, of possessing the true one equally with him who without pausing at this mass of rubbish lays his hand upon the costly stone which they are seeking and for which they do not throw away the rest."
— Blaise Pascal, De l'Esprit Géométrique
"When the light came she was sitting on the bed beside an open suitcase, toying with her diamond rings. She saw the light first in the depths of the largest stone."
scene at Diamond Head, Oahu, Hawaii
Now playing (6:41 PM EDT) on Killer Radio:
"Jack of Diamonds, that's
a hard card to find."
"This Jack, joke, poor potsherd, patch, matchwood, immortal diamond…."
— Gerard Manley Hopkins, Society of Jesus
Perhaps Sam Phillips was twanged by a Hawaiian guitar. (See previous two entries.)
The Big Time
"The place outside the cosmos where I and my pals do our nursing job I simply call the Place. A lot of my nursing consists of amusing and humanizing Soldiers fresh back from raids into time. In fact, my formal title is Entertainer…."
— The Big Time,
by Fritz Leiber
A Story That Works
"There is the dark, eternally silent, unknown universe;
there are the friend-enemy minds shouting and whispering their tales and always seeking the three miracles —
that minds should really touch, or
that the silent universe should speak, tell minds a story, or (perhaps the same thing)
that there should be a story that works, that is all hard facts, all reality, with no illusions and no fantasy;
and lastly, there is lonely, story-telling, wonder-questing, mortal me."
— Fritz Leiber in "The Button Molder"
See also "Top Ten Most Overheard Comments by new KHYI listeners" at Miss Lana's Anything Page, entry for
Pearl Harbor Day, December 7, 2002.
Comments Off on Thursday July 31, 2003
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."
"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."
Comments Off on Tuesday September 24, 2002