In memory of . . .
“Helene Lovie Aldwinckle,
codebreaker, broadcaster and gallerist,
born 26 October 1920; died 24 April 2020″ —
Other posts now also tagged The Cologne Sextet.
In memory of . . .
“Helene Lovie Aldwinckle,
codebreaker, broadcaster and gallerist,
born 26 October 1920; died 24 April 2020″ —
Other posts now also tagged The Cologne Sextet.
For those who prefer fiction —
“Twenty-four glyphs, each one representing not a letter, not a word,
but a concept, arranged into four groups, written in Boris’s own hand,
an artifact that seemed to have resurrected him from the dead. It was
as if he were sitting across from Bourne now, in the dim antiquity of
the museum library.
This was what Bourne was staring at now, written on the unfolded
bit of onionskin.”
— “Robert Ludlum’s” The Bourne Enigma , published on June 21, 2016
Passing, on June 21, 2016, into a higher dimension —
The previous post reported, perhaps inaccurately, a publication
date of February 13, 2020, for the novel The Enigma Cube .
A variant publication date, Jan. 21, 2020, is reported below.
This journal on that date —
Promotional material —
“Did you buckle up?” — Harlan Kane
The publication date of The Enigma Cube reported above was February 13, 2020.
Related material — Log24 posts around that date now tagged The Reality Bond.
Grothendieck reportedly died on Thursday, November 13, 2014.
From this journal a year earlier:
After clicking on the link “a grave intellectual whole” from the Nov. 13, 2013, post
see also Benedict Cumberbatch’s less serious approach to Bletchley Park:
“I want to see this film; this film’s been up my ass for the last five years.”
For Yom Kippur
4. Image— Argument for the Existence of Rebecca
Some literary and cinematic background—
"Are you the butterfly… ?"
Yesterday evening's Telegraph—
Didi Nearne was inspired by her strong Catholic faith
to believe that she would be well received, and the priest,
appalled at the state of the women, hid them in the bell tower.
In 1944 Nearne, an agent of the Special Operations Executive (SOE) who had
parachuted into France, was captured, interrogated and tortured by the Gestapo,
sent to a concentration camp, and later escaped.
She died at 89 on September 2, 2010. See this journal on that date.
See also Geheimnis des Glockenturms.
"… JoAnna Novak becomes obsessed with the enigmatic
abstract expressionist painter Agnes Martin. She is drawn to
the contradictions in Martin’s life as well as her art—the soft
and exacting brushstrokes she employs for grid-like compositions
that are both rigid and dreamy."
See as well Agnes Martin in this journal.
Data:
"The rockers said via their record label:
'It is with the deepest sadness that we must
announce the passing of the lyricist Keith Reid,
who died suddenly on 23 March 2023,
in hospital in London. He had been receiving
cancer treatment for the past couple of years.
Keith was the co-founder and lyricist for the band
Procol Harum, notably penning their biggest hit
A Whiter Shade of Pale, which contains some of
the most enigmatic lyrics of all time.' "
— https://www.mirror.co.uk/3am/celebrity-news/
breaking-procol-harums-keith-reid-29586101
A note from Log24 on the above March 23 date —
The above Del Shannon upload date
was November 1, 2021 — All Saints' Day.
Synchronicity check —
“Twenty-four glyphs, each one representing not a letter, not a word,
but a concept, arranged into four groups, written in Boris’s own hand,
an artifact that seemed to have resurrected him from the dead. It was
as if he were sitting across from Bourne now, in the dim antiquity of
the museum library.
This was what Bourne was staring at now, written on the unfolded
bit of onionskin.”
— The Bourne Enigma , published on June 21, 2016
Passing, on June 21, 2016, into a higher dimension —
For those who prefer Borges to Bourne —
For the Sith Pyramid, see posts tagged Pyramid Game.
For the Jedi Cube, see posts tagged Enigma Cube
and cube-related remarks by Aitchison at Hiroshima.
This post was suggested by two events of May 16, 2019 —
A weblog post by Frans Marcelis on the Miracle Octad
Generator of R. T. Curtis (illustrated with a pyramid),
and the death of I. M. Pei, architect of the Louvre pyramid.
That these events occurred on the same date is, of course,
completely coincidental.
Perhaps Dan Brown can write a tune to commemorate
the coincidence.
From Log24 posts tagged Structure and Mutability —
“… an artifact that seemed to have resurrected him from the dead.”
— “Robert Ludlum’s” The Bourne Enigma , published on June 21, 2016
See as well the 2020 film Archive , and the related 2018 film Replicas
in Oslo Variations.
“He recounted the story of Adam and Eve, who were banished
from paradise because of their curiosity. Their inability to resist
the temptation of the forbidden fruit. Which itself was a metaphorical
stand-in for knowledge and power. He urged us to find the restraint
needed to resist the temptation of the cube—the biblical apple
in modern garb. He urged us to remain in Eden until we were able
to work out the knowledge the apple offered, all by ourselves.”
— Richards, Douglas E.. The Enigma Cube (Alien Artifact Book 1)
(pp. 160-161). Paragon Press, 2020. Kindle Edition.
The biblical apple also appears in the game, and film, Assassin's Creed .
Related material —
See the cartoon version of Alfred North Whitehead in the previous post,
and some Whitehead-related projective geometry —
Related reading —
"I closed my eyes and saw the number 137—
so very close to the reciprocal of alpha—
on the chest of the runner in Van Cortlandt Park.
Should I start the story there? "
— Alpert, Mark. Saint Joan of New York
(Science and Fiction) (p. 103).
Springer International Publishing. Kindle edition.
Cover detail:
See as well St. Joan in this journal.
Finkelstein reportedly died on Sunday, January 24, 2016.
“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 , or malevolent spirit (and who’s played by the Yiddish theater actor Fyvush Finkel). The import of this parable is cryptic to the point of inscrutability, making it a perfect introduction to the rest of the movie.”
— Dana Stevens at Slate.com on Oct. 1, 2009 |
See also Finkelstein in this journal.
See as well posts now tagged Oct. 4, 2018,
in the context of today’s previous post.
In the recent science fiction film "Arrival," Amy Adams portrays
a linguist, Louise Banks, who must learn to translate the language of
aliens ("Heptapods") who have just arrived in their spaceships.
The point of this tale seems to have something to do with Banks
learning, along with the aliens' language, their skill of seeing into
the future.
Louise Banks wannabes might enjoy the works of one
Metod Saniga, who thinks that finite geometry might have
something to do with perceptions of time.
See Metod Saniga, “Algebraic Geometry: A Tool for Resolving
the Enigma of Time?”, in R. Buccheri, V. Di Gesù and M. Saniga (eds.),
Studies on the Structure of Time: From Physics to Psycho(patho)logy,
Kluwer Academic / Plenum Publishers, New York, 2000, pp. 137–166.
Available online at www.ta3.sk/~msaniga/pub/ftp/mathpsych.pdf .
Although I share an interest in finite geometry with Saniga —
see, for instance, his remarks on Conwell heptads in the previous post
and my own remarks in yesterday's post "Schoolgirls and Heptads" —
I do not endorse his temporal speculations.
Publisher's description of a book about everything —
"When the whole is greater than the sum of the parts—
indeed, so great that the sum far transcends the parts
and represents something utterly new and different—
we call that phenomenon emergence."
— Oxford University Press
Titles for Harlan Kane, from the date that
the above book's author reportedly died —
The above title is intended to contrast with the title
of this evening's previous post,
Focus and Clarity in the New Year.
For the Blur and Murk, click on the screenshot below.
Alternate title: Enigma Variations …
Symbol —
Monday, November 7, 2011
|
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 "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 —
Review:
Monday, November 7, 2011
|
See also the phrase "a dance results" in the original
source and in yesterday's Valentine Dance.
Corrections to the NY Times obituary of Alexander Grothendieck
are shown below. For the original Sunday, Nov. 16, NY Times
print obituary (with its online date, Nov. 14), see a copy taken
from a weblog.
For another poetic remark in memory of Grothendieck,
see a Log24 post from November 13, the day of his death.
Related material:
Lead obituary in today’s online New York Times and Los Angeles Times —
Maazel reportedly died on Sunday, July 13, 2014.
From a search in this journal for Iconic Notation,
a related image from August 14, 2010—
See also…
Epiphany
From the obituary of a Bletchley Park
codebreaker who reportedly died on
Armistice Day (Monday, Nov. 11)—
"The main flaw of the Enigma machine,
seen by the inventors as a security-enhancing
measure, was that it would never encipher
a letter as itself…."
Update of 9 PM ET Nov. 13—
"The rogue’s yarn that will run through much of
the material is the algebraic symmetry to which
the name of Galois is attached…."
— Robert P. Langlands,
Institute for Advanced Study, Princeton
"All the turmoil, all the emotions of the scenes
have been digested by the mind into
a grave intellectual whole. It is as though
Bach had written the 1812 Overture."
— Aldous Huxley, "The Best Picture," 1925
Maya Alexandri on September 7, 2009—
… Blixen herself may have cut closer to the truth In it, a character explains,
What exactly [the imposter to the Prince] has told
Later, the imposter utters the following enigma: "Life and Death Stylist or fraud, that's the question. |
The books pictured above are From Discrete to Continuous ,
by Katherine Neal, and Geometrical Landscapes , by Amir Alexander.
Commentary—
“Harriot has given no indication of how to resolve
such problems, but he has pasted in in English,
at the bottom of his page, these three enigmatic
lines:
‘Much ado about nothing.
Great warres and no blowes.
Who is the foole now?’
Harriot’s sardonic vein of humour, and the subtlety of
his logical reasoning still have to receive their full due.”
— “Minimum and Maximum, Finite and Infinite:
Bruno and the Northumberland Circle,” by Hilary Gatti,
Journal of the Warburg and Courtauld Institutes ,
Vol. 48 (1985), pp. 144-163
Click images for further details.
See also Crimson Tide, Rubik, and Cuber.
For another monochromatic enigma without
guaranteed equality of results, see
Finite Geometry of the Square and Cube.
From a review of Truth and Other Enigmas , a book by the late Michael Dummett—
"… two issues stand out as central, recurring as they do in many of the
essays. One issue is the set of debates about realism, that is, those debates that ask
whether or not one or another aspect of the world is independent of the way we
represent that aspect to ourselves. For example, is there a realm of mathematical
entities that exists fully formed independently of our mathematical activity? Are
there facts about the past that our use of the past tense aims to capture? The other
issue is the view— which Dummett learns primarily from the later Wittgenstein—
that the meaning of an expression is fully determined by its use, by the way it
is employed by speakers. Much of his work consists in attempts to argue for this
thesis, to clarify its content and to work out its consequences. For Dummett one
of the most important consequences of the thesis concerns the realism debate and
for many other philosophers the prime importance of his work precisely consists
in this perception of a link between these two issues."
— Bernhard Weiss, pp. 104-125 in Central Works of Philosophy , Vol. 5,
ed. by John Shand, McGill-Queen's University Press, June 12, 2006
The above publication date (June 12, 2006) suggests a review of other
philosophical remarks related to that date. See …
"Every partitioning of the set of sixteen ontic states
into four disjoint pure epistemic states
yields a maximally informative measurement."—
For some more-personal remarks on Dummett, see yesterday afternoon's
"The Stone" weblog in The New York Times.
I caught the sudden look of some dead master….
Religion for stoners,♦ in memory of Horselover Fat
Amazon.com gives the publication date of a condensed
version* of Philip K. Dick's Exegesis as Nov. 7, 2011.
The publisher gives the publication date as Nov. 8, 2011.
Here, in memory of the author, Philip K. Dick (who sometimes
called himself, in a two-part pun, "Horselover Fat"), is related
material from the above two dates in this journal—
Tuesday, November 8, 2011 m759 @ 12:00 PM …. Update of 9:15 PM Nov. 8, 2011— From a search for the word "Stoned" in this journal—
See also Monday's post "The X Box" with its illustration . Monday, November 7, 2011
"Design is how it works." — Steve Jobs, quoted in .
For some background on this enigmatic equation,
|
Merry Xmas.
♦ See also last night's post and the last words of Steve Jobs.
* Houghton Mifflin Harcourt, the publisher, has, deliberately or not, sown confusion
about whether this is only the first of two volumes.
"Design is how it works." — Steve Jobs, quoted in
The New York Times Magazine on St. Andrew's Day, 2003
.
For some background on this enigmatic equation,
see Geometry of the I Ching.
The following was suggested by the Sermon
of October 30 (the day preceding Devil's Night)
and by yesterday's Beauty, Truth, Halloween.
"The German language has itself been influenced by Goethe's Faust , particularly by the first part. One example of this is the phrase 'des Pudels
See also the following readings (click to enlarge)—
Note particularly…
"The main enigma of any description of a patternless
unus mundus is to find appropriate partitions which
create relevant patterns." —Hans Primas, above
"In general, the partition of G into right cosets
can differ from its partition into left cosets. Galois
was the first to recognize the importance of when
these partitions agree. This happens when the
subgroup H is normal." — David A. Cox,
Galois Theory , Wiley, 2004, p. 510
The April Scientific American on the partition function p (n )—
"… in January, Ono and another collaborator [Bruinier] described the first formula that directly calculates p (n ) for any n, a feat that had eluded number theorists for centuries."
Exercise: Is this remarkable claim true or false?
For commentary here, see Jan. 27, "Indiana Jones and the Magical Oracle."
For further comments (the most recent from March 11), see mathoverflow.net, "Exact formulas for the partition function?"
Saturday Night Live on December 4, 2010 —
If you liked Harlan Kane's THE ABACUS CONUNDRUM, you'll love…
THE LOTTERY ENIGMA —
New York Lottery on Sunday, December 5, 2010
Related links— For 076, yesterday's entry on "Independence Day."
For 915, see 9/15, "Holy Cross Day Revisited," and its prequel,
linked to on 9/15 as "Ready When You Are, C.B."
See also "Citizen Harlan" and "The Beaver."
Ode magazine, June 2007, on Ivan Illich—
When Ivan was 12, Hitler invaded Austria, prompting his decision never to bring children into this world. At the age of 16, before fleeing Vienna, he bribed the secretary of Nazi leader Hermann Goering – who had claimed Illich's family home – to free his grandfather. Ultimately, Illich did do well in school, studying philosophy and theology at the elite Pontifical Gregorian University in the Vatican, later earning a Ph.D. at the University of Salzburg. He travelled to India and soaked up Eastern philosophy during long discussions with the Indian Hindu and Catholic priest Ramon Panikkar in Varanasi (Benares), along the Ganges river. He was later ordained as a Roman Catholic priest in New York City. He became a professor at the Catholic University of Puerto Rico and moved to Mexico, where he founded an educational centre that challenged the Church’s embrace of modern development. He resigned from priesthood in the late 1960s because he no longer felt at home with the dogmas of the Catholic Church – "I have enough Jewish blood to be able to get angry with God" – and began his life as a philosopher and author.
Illich greeted us at his home in Bremen….
Panikkar died on August 26, 2010. See this journal on that date ("Home from Home continued"), with its link to math16.com and the reference there to Stevens's "The Owl in the Sarcophagus."
Related material—
A Mystery Wrapped in an Enigma (letters to The Guardian on Stephen Hawking's new book)
and Panikkar's book (published in Paris in 2002 and in Minneapolis, by a Lutheran press, in 2006)
The Experience of God: Icons of the Mystery.
Enigma Variations
The intercept control room in Hut 6 at Bletchley Park, 1943—
Photo: GETTY
The above photo is from today's London Telegraph obituary of Keith Batey, a Bletchley Park codebreaker who died at 91 on St. Augustine's Day, 2010. Also from that obituary—
Batey himself was responsible for some important breakthroughs in decrypting the Abwehr Enigma system, helping MI5 to control the entire German espionage network in Britain. The intelligence was crucial to the Double Cross system – under which MI5 turned German agents sent to Britain and used them to feed the Abwehr false information – as it showed that the information was being accepted as genuine; it further revealed what the Germans did and did not know about the D-Day invasion plans.
William Lubtchansky, a cinematographer, was born on October 26, 1937, and died on May 4, 2010.
Yesterday's post included an illustration from this journal on the date of his death.
Here is a Log24 entry from last year on the date of his birth—
Monday, October 26, 2009 The Keys Enigma Related material: |
Clicking on the Shift Lock key leads to the following page—
—The Philosopher's Gaze,
by David Michael Levin,
University of California Press, 1999
Related images—
Detail from May 4 image:
Holocaust Museum, Washington, DC:
(http://www.scrapbookpages.com/USHMM/Exterior.html)
See also Lubtchansky's Duelle and
Art Wars for Trotsky's Birthday, 2003.
Or: "Gopnik Meets Oppenheimer in Heaven"
(Or, for those less philosophically minded, "Raiders of the Lost Pussy")
Midrash on "A Serious Man" "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
Blackboard in "A Serious Man"–
Blackboard at the Institute for Advanced Study–
"Daddy's home! Daddy's home!"
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.
"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–
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–
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
dunce cap, see the symbol of
today's saint– a Bridget Cross—
and a web page on
visualized quaternions.
More Than Matter
Wheel in Webster’s Revised Unabridged Dictionary, 1913
(f) Poetry The burden or refrain of a song. ⇒ “This meaning has a low degree of authority, but is supposed from the context in the few cases where the word is found.” Nares. You must sing a-down a-down, An you call him a-down-a. O, how the wheel becomes it! Shak. |
“In one or other of G. F. H. Shadbold’s two published notebooks, Beyond Narcissus and Reticences of Thersites, a short entry appears as to the likelihood of Ophelia’s enigmatic cry: ‘Oh, how the wheel becomes it!’ referring to the chorus or burden ‘a-down, a-down’ in the ballad quoted by her a moment before, the aptness she sees in the refrain.”
— First words of Anthony Powell’s novel “O, How the Wheel Becomes It!” (See Library Thing.)
Related material:
Photo uploaded on January 14, 2009
with caption “This nothing’s more than matter”
and the following nothings from this journal
on the same date– Jan. 14, 2009—
"Have your people
call my people."
— George Carlin
Diamond life, lover boy;
we move in space
with minimum waste
and maximum joy.
— Sade, quoted here on
Lincoln's Birthday, 2003
This is perhaps suitable
for the soundtrack of
the film "Blockheads"
(currently in development)–
Related material from Wikipedia:
"Uta Frith, in her book Autism: Explaining the Enigma,[5] addresses the superior performance of autistic individuals on the block design [link not in Wikipedia] test. This was also addressed in [an] earlier paper.[6] A particularly interesting article demonstrates the differences in construction time in the performance of the block design task by Asperger syndrome individuals and non-Asperger's individuals. An essential point here is that in an unsegmented version of the task, Asperger's individuals performed dramatically faster than non-Asperger's individuals: [7]."
5. Frith, Uta (2003). Autism: explaining the enigma (2nd ed. ). Cambridge, MA: Blackwell Pub. ISBN 0-631-22901-9.
6. Shah A, Frith U (Nov 1993). "Why do autistic individuals show superior performance on the block design task?". J Child Psychol Psychiatry 34 (8): 1351–64. PMID 8294523.
7. Caron MJ, Mottron L, Berthiaume C, Dawson M (Jul 2006). "Cognitive mechanisms, specificity and neural underpinnings of visuospatial peaks in autism". Brain 129 (Pt 7): 1789–802. doi: . PMID 16597652. "Fig 3".
Related material from a film (see Calvinist Epiphany, June 17):
For the relevance of this maxim to autism, see Markoff Process (March 4, 2009).
Getting All
the Meaning In
Webpage heading for the
2009 meeting of the
American Comparative
Literature Association:
The mysterious symbols on
the above map suggest the
following reflections:
From A Cure of the Mind: The Poetics of Wallace Stevens, by Theodore Sampson, published by Black Rose Books Ltd., 2000–
Page x:
"… if what he calls 'the spirit's alchemicana' (CP [Collected Poems] 471) addresses itself to the irrational element in poetry, to what extent is such an element dominant in his theory and practice of poetry, and therefore in what way is Stevens' intricate verbal music dependent on his irrational use of language– a 'pure rhetoric of a language without words?' (CP 374)?"
From "'When Novelists Become Cubists:' The Prose Ideograms of Guy Davenport," by Andre Furlani:
Laurence Zachar argues that Davenport's writing is situated "aux frontieres intergeneriques" where manifold modes are brought into concord: "L'etonnant chez Davenport est la facon don't ce materiau qui parait l'incarnation meme du chaos– hermetique, enigmatique, obscur, avec son tropplein de references– se revele en fait etre construit, ordonne, structure. Plus l'on s'y plonge, et plus l'on distingue de cohesion dans le texte." 'What astonishes in Davenport is the way in which material that seems the very incarnation of chaos– hermetic, enigmatic, obscure, with its proliferation of allusions– in fact reveals itself to be constructed, organized, structured. The more one immerses oneself in them the more one discerns the texts' cohesion.' (62). Davenport also works along the intergeneric border between text and graphic, for he illustrates many of his texts. (1) "The prime use of words is for imagery: my writing is drawing," he states in an interview (Hoeppfner 123). Visual imagery is not subordinated to writing in Davenport, who draws on the assemblage practice of superimposing image and writing. "I trust the image; my business is to get it onto the page," he writes in the essay "Ernst Machs Max Ernst." "A page, which I think of as a picture, is essentially a texture of images. […] The text of a story is therefore a continuous graph, kin to the imagist poem, to a collage (Ernst, Willi Baumeister, El Lissitzky), a page of Pound, a Brakhage film" (Geography 374-75). Note: (1.) Davenport is an illustrator of books (such as Hugh Kenner's The Stoic Comedians and The Counterfeiters) and journals (such as The Kenyon Review, Parnassus, and Paideuma). His art is the subject of Erik Anderson Reece's monograph, A Balance of Quinces, which reveals the inseparable relationship between Davenport's literary and pictorial work. References: Davenport, Guy. The Geography of the Imagination. San Francisco: North Point Press, 1981. Rpt. New York: Pantheon, 1992. Hoepffner, Bernard. "Pleasant Hill: An Interview with Guy Davenport." Conjunctions 24 (1995): 118-24. Reece, Erik Anderson. A Balance of Quinces: The Paintings and Drawings of Guy Davenport. New York: New Directions, 1996. Zachar, Laurence. "Guy Davenport: Une Mosaique du genres." Recherches Anglaises et Nord-Americaines 21 (1994): 51-63. |
"… when novelists become Cubists; that is, when they see the possibilities of making a hieroglyph, a coherent symbol, an ideogram of the total work. A symbol comes into being when an artist sees that it is the only way to get all the meaning in."
— Guy Davenport, The Geography of the Imagination
Quantum of Solace
Lottery Numbers
for November 11, 2008:
PA midday 007, evening 628
NY midday 153, evening 069
Experienced readers of this journal will have little difficulty interpreting these results, except for 153. For that enigmatic number, see Object Lesson.
The Last Theorem, a novel by
Arthur C. Clarke and Frederik Pohl
"The Last Theorem is a story of one man’s mathematical obsession, and a celebration of the human spirit and the scientific method. It is also a gripping intellectual thriller….
In 1637, the French mathematician Pierre de Fermat scrawled a note in the margin of a book about an enigmatic theorem: 'I have discovered a truly marvelous proof of this proposition which this margin is too narrow to contain.' He also neglected to record his proof elsewhere. Thus began a search for the Holy Grail of mathematics– a search that didn’t end until 1994, when Andrew Wiles published a 150-page proof. But the proof was burdensome, overlong, and utilized mathematical techniques undreamed of in Fermat’s time, and so it left many critics unsatisfied– including young Ranjit Subramanian, a Sri Lankan with a special gift for mathematics and a passion for the famous 'Last Theorem.'
When Ranjit writes a three-page proof of the theorem that relies exclusively on knowledge available to Fermat, his achievement is hailed as a work of genius, bringing him fame and fortune…."
For a similar third-world fantasy about another famous theorem, see the oeuvre of Ashay Dharwadker.
Note the amazing conclusion of Dharwadker's saga (thus far)–
Dharwadker devises a proof of the four-color theorem that leads to…
For another connection with Sri Lanka, see
The conclusion of yesterday’s commentary on the May 30-31 Pennsylvania Lottery numbers:
Thomas Pynchon, Gravity’s Rainbow:
“The fear balloons again inside his brain. It will not be kept down with a simple Fuck You…. A smell, a forbidden room, at the bottom edge of his memory. He can’t see it, can’t make it out. Doesn’t want to. It is allied with the Worst Thing.
He knows what the smell has to be: though according to these papers it would have been too early for it, though he has never come across any of the stuff among the daytime coordinates of his life, still, down here, back here in the warm dark, among early shapes where the clocks and calendars don’t mean too much, he knows that’s what haunting him now will prove to be the smell of Imipolex G.
Then there’s this recent dream he is afraid of having again. He was in his old room, back home. A summer afternoon of lilacs and bees and
286”
What are we to make of this enigmatic 286? (No fair peeking at page 287.)
One possible meaning, given The Archivist‘s claim that “existence is infinitely cross-referenced”–
Page 286 of Ernest G. Schachtel, Metamorphosis: On the Conflict of Human Development and the Psychology of Creativity (first published in 1959), Hillsdale NJ and London, The Analytic Press, 2001 (chapter– “On Memory and Childhood Amnesia”):
“Both Freud and Proust speak of the autobiographical [my italics] memory, and it is only with regard to this memory that the striking phenomenon of childhood amnesia and the less obvious difficulty of recovering any past experience may be observed.”
The concluding “summer afternoon of lilacs and bees” suggests that 286 may also be a chance allusion to the golden afternoon of Disney’s Alice in Wonderland. (Cf. St. Sarah’s Day, 2008)
Some may find the Disney afternoon charming; others may see it as yet another of Paul Simon’s dreaded cartoon graveyards.
More tastefully, there is poem 286 in the 1919 Oxford Book of English Verse– “Love.”
For a midrash on this poem, see Simone Weil, who became acquainted with the poem by chance:
“I always prefer saying chance rather than Providence.”
— Simone Weil, letter of about May 15, 1942
Weil’s brother André might prefer Providence (source of the Bulletin of the American Mathematical Society.)
For more on the mathematical significance of this figure, see (for instance) Happy Birthday, Hassler Whitney, and Combinatorics of Coxeter Groups, by Anders Björner and Francesco Brenti, Graduate Texts in Mathematics, vol. 231, Springer, New York, 2005.
This book is reviewed in the current issue (July 2008) of the above-mentioned Providence Bulletin.
The review in the Bulletin discusses reflection groups in continuous spaces.
“It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy.”
— Simon Blackburn, Think (Oxford, 1999)
Michael Harris, mathematician at the University of Paris:
“… three ‘parts’ of tragedy identified by Aristotle that transpose to fiction of all types– plot (mythos), character (ethos), and ‘thought’ (dianoia)….”
— paper (pdf) to appear in Mathematics and Narrative, A. Doxiadis and B. Mazur, eds.
Mythos —
A visitor from France this morning viewed the entry of Jan. 23, 2006: “In Defense of Hilbert (On His Birthday).” That entry concerns a remark of Michael Harris.
A check of Harris’s website reveals a new article:
“Do Androids Prove Theorems in Their Sleep?” (slighly longer version of article to appear in Mathematics and Narrative, A. Doxiadis and B. Mazur, eds.) (pdf).
From that article:
“The word ‘key’ functions here to structure the reading of the article, to draw the reader’s attention initially to the element of the proof the author considers most important. Compare E.M. Forster in Aspects of the Novel:
[plot is] something which is measured not be minutes or hours, but by intensity, so that when we look at our past it does not stretch back evenly but piles up into a few notable pinnacles.”
Ethos —
“Forster took pains to widen and deepen the enigmatic character of his novel, to make it a puzzle insoluble within its own terms, or without. Early drafts of A Passage to India reveal a number of false starts. Forster repeatedly revised drafts of chapters thirteen through sixteen, which comprise the crux of the novel, the visit to the Marabar Caves. When he began writing the novel, his intention was to make the cave scene central and significant, but he did not yet know how:
When I began a A Passage to India, I knew something important happened in the Malabar (sic) Caves, and that it would have a central place in the novel– but I didn’t know what it would be… The Malabar Caves represented an area in which concentration can take place. They were to engender an event like an egg.”
— E. M. Forster: A Passage to India, by Betty Jay
Dianoia —
“Despite the flagrant triviality of the proof… this result is the key point in the paper.”
— Michael Harris, op. cit., quoting a mathematical paper
Online Etymology Dictionary:
flagrant c.1500, “resplendent,” from L. flagrantem (nom. flagrans) “burning,” prp. of flagrare “to burn,” from L. root *flag-, corresponding to PIE *bhleg– (cf. Gk. phlegein “to burn, scorch,” O.E. blæc “black”). Sense of “glaringly offensive” first recorded 1706, probably from common legalese phrase in flagrante delicto “red-handed,” lit. “with the crime still blazing.”
A related use of “resplendent”– applied to a Trinity, not a triviality– appears in the Liturgy of Malabar:
— The Liturgies of SS. Mark, James, Clement, Chrysostom, and Basil, and the Church of Malabar, by the Rev. J.M. Neale and the Rev. R.F. Littledale, reprinted by Gorgias Press, 2002
Judy Davis in the Marabar Caves
In mathematics
(as opposed to narrative),
somewhere between
a flagrant triviality and
a resplendent Trinity we
have what might be called
“a resplendent triviality.”
For further details, see
“A Four-Color Theorem.”
Let No Man
Write My Epigraph
"His graceful accounts of the Bach Suites for Unaccompanied Cello illuminated the works’ structural logic as well as their inner spirituality."
—Allan Kozinn on Mstislav Rostropovich in The New York Times, quoted in Log24 on April 29, 2007
"At that instant he saw, in one blaze of light, an image of unutterable conviction…. the core of life, the essential pattern whence all other things proceed, the kernel of eternity."
— Thomas Wolfe, Of Time and the River, quoted in Log24 on June 9, 2005
"… the stabiliser of an octad preserves the affine space structure on its complement, and (from the construction) induces AGL(4,2) on it. (It induces A8 on the octad, the kernel of this action being the translation group of the affine space.)"
— Peter J. Cameron, "The Geometry of the Mathieu Groups" (pdf)
"… donc Dieu existe, réponse!"
(Faust, Part Two, as
quoted by Jung in
Memories, Dreams, Reflections)
"Pauli as Mephistopheles
in a 1932 parody of
Goethe's Faust at Niels Bohr's
institute in Copenhagen.
The drawing is one of
many by George Gamow
illustrating the script."
— Physics Today
'To meet someone' was his enigmatic answer. 'To search for the stone that the Great Architect rejected, the philosopher's stone, the basis of the philosophical work. The stone of power. The devil likes metamorphoses, Corso.'"
— The Club Dumas, basis for the Roman Polanski film "The Ninth Gate" (See 12/24/05.)
— The Innermost Kernel
(previous entry)
And from
"Symmetry in Mathematics
and Mathematics of Symmetry"
(pdf), by Peter J. Cameron,
a paper presented at the
International Symmetry Conference,
Edinburgh, Jan. 14-17, 2007,
we have
The Epigraph–
(Here "whatever" should
of course be "whenever.")
Also from the
Cameron paper:
Local or global?
Among other (mostly more vague) definitions of symmetry, the dictionary will typically list two, something like this:
• exact correspondence of parts; Mathematicians typically consider the second, global, notion, but what about the first, local, notion, and what is the relationship between them? A structure M is homogeneous if every isomorphism between finite substructures of M can be extended to an automorphism of M; in other words, "any local symmetry is global." |
Some Log24 entries
related to the above politically
(women in mathematics)–
Global and Local:
One Small Step
and mathematically–
Structural Logic continued:
Structure and Logic (4/30/07):
This entry cites
Alice Devillers of Brussels–
"The aim of this thesis
is to classify certain structures
which are, from a certain
point of view, as homogeneous
as possible, that is which have
as many symmetries as possible."
"There is such a thing
as a tesseract."
"Mistakes are inevitable and may be either in missing a true signal or in thinking there is a signal when there is not. I am suggesting that believers in the paranormal (called 'sheep' in psychological parlance) are more likely to make the latter kind of error than are disbelievers (called 'goats')."
— "Psychic Experiences:
Psychic Illusions,"
by Susan Blackmore,
Skeptical Inquirer, 1992
— Freeman Dyson, quoted in Log24
on the day Mosteller died
From Log24 on
Mosteller's last birthday,
December 24, 2005:
The Club Dumas
|
"Only gradually did I discover
what the mandala really is:
'Formation, Transformation,
Eternal Mind's eternal recreation'"
(Faust, Part Two)
— Carl Gustav Jung,
born on this date
“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
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.”
— Foucault’s Pendulum
by Umberto Eco,
Professor of Semiotics
The Club Dumasby Arturo Perez-Reverte
|
“Only gradually did I discover
what the mandala really is:
‘Formation, Transformation,
Eternal Mind’s eternal recreation'”
(Faust, Part Two)
Mathematics and Metaphor
The current (June/July) issue of the Notices of the American Mathematical Society has two feature articles. The first, on the vulgarizer Martin Gardner, was dealt with here in a June 19 entry, Darkness Visible. The second is related to a letter of André Weil (pdf) that is in turn related to mathematician Barry Mazur’s attempt to rewrite mathematical history and to vulgarize other people’s research by using metaphors drawn, it would seem, from the Weil letter.
A Mathematical Lie conjectures that Mazur’s revising of history was motivated by a desire to dramatize some arcane mathematics, the Taniyama conjecture, that deals with elliptic curves and modular forms, two areas of mathematics that have been known since the nineteenth century to be closely related.
Mazur led author Simon Singh to believe that these two areas of mathematics were, before Taniyama’s conjecture of 1955, completely unrelated —
“Modular forms and elliptic equations live in completely different regions of the mathematical cosmos, and nobody would ever have believed that there was the remotest link between the two subjects.” — Simon Singh, Fermat’s Enigma, 1998 paperback, p. 182
This is false. See Robert P. Langlands, review of Elliptic Curves, by Anthony W. Knapp, Bulletin of the American Mathematical Society, January 1994.
It now appears that Mazur’s claim was in part motivated by a desire to emulate the great mathematician André Weil’s manner of speaking; Mazur parrots Weil’s “bridge” and “Rosetta stone” metaphors —
From Peter Woit’s weblog, Feb. 10, 2005:
“The focus of Weil’s letter is the analogy between number fields and the field of algebraic functions of a complex variable. He describes his ideas about studying this analogy using a third, intermediate subject, that of function fields over a finite field, which he thinks of as a ‘bridge‘ or ‘Rosetta stone.'”
In “A 1940 Letter of André Weil on Analogy in Mathematics,” (pdf), translated by Martin H. Krieger, Notices of the A.M.S., March 2005, Weil writes that
“The purely algebraic theory of algebraic functions in any arbitrary field of constants is not rich enough so that one might draw useful lessons from it. The ‘classical’ theory (that is, Riemannian) of algebraic functions over the field of constants of the complex numbers is infinitely richer; but on the one hand it is too much so, and in the mass of facts some real analogies become lost; and above all, it is too far from the theory of numbers. One would be totally obstructed if there were not a bridge between the two. And just as God defeats the devil: this bridge exists; it is the theory of the field of algebraic functions over a finite field of constants….
On the other hand, between the function fields and the ‘Riemannian’ fields, the distance is not so large that a patient study would not teach us the art of passing from one to the other, and to profit in the study of the first from knowledge acquired about the second, and of the extremely powerful means offered to us, in the study of the latter, from the integral calculus and the theory of analytic functions. That is not to say that at best all will be easy; but one ends up by learning to see something there, although it is still somewhat confused. Intuition makes much of it; I mean by this the faculty of seeing a connection between things that in appearance are completely different; it does not fail to lead us astray quite often. Be that as it may, my work consists in deciphering a trilingual text {[cf. the Rosetta Stone]}; of each of the three columns I have only disparate fragments; I have some ideas about each of the three languages: but I know as well there are great differences in meaning from one column to another, for which nothing has prepared me in advance. In the several years I have worked at it, I have found little pieces of the dictionary. Sometimes I worked on one column, sometimes under another.”
Here is another statement of the Rosetta-stone metaphor, from Weil’s translator, Martin H. Krieger, in the A.M.S. Notices of November 2004, “Some of What Mathematicians Do” (pdf):
“Weil refers to three columns, in analogy with the Rosetta Stone’s three languages and their arrangement, and the task is to ‘learn to read Riemannian.’ Given an ability to read one column, can you find its translation in the other columns? In the first column are Riemann’s transcendental results and, more generally, work in analysis and geometry. In the second column is algebra, say polynomials with coefficients in the complex numbers or in a finite field. And in the third column is arithmetic or number theory and combinatorial properties.”
For greater clarity, see Armand Borel (pdf) on Weil’s Rosetta stone, where the three columns are referred to as Riemannian (transcendental), Italian (“algebraico-geometric,” over finite fields), and arithmetic (i.e., number-theoretic).
From Fermat’s Enigma, by Simon Singh, Anchor paperback, Sept. 1998, pp. 190-191:
Barry Mazur: “On the one hand you have the elliptic world, and on the other you have the modular world. Both these branches of mathematics had been studied intensively but separately…. Than along comes the Taniyama-Shimura conjecture, which is the grand surmise that there’s a bridge between these two completely different worlds. Mathematicians love to build bridges.”
Simon Singh: “The value of mathematical bridges is enormous. They enable communities of mathematicians who have been living on separate islands to exchange ideas and explore each other’s creations…. The great potential of the Taniyama-Shimura conjecture was that it would connect two islands and allow them to speak to each other for the first time. Barry Mazur thinks of the Taniyama-Shimura conjecture as a translating device similar to the Rosetta stone…. ‘It’s as if you know one language and this Rosetta stone is going to give you an intense understanding of the other language,’ says Mazur. ‘But the Taniyama-Shimura conjecture is a Rosetta stone with a certain magical power.'”
If Mazur, who is scheduled to speak at a conference on Mathematics and Narrative this July, wants more material on stones with magical powers, he might consult The Blue Matrix and The Diamond Archetype.
— Foucault’s Pendulum
by Umberto Eco,
Professor of Semiotics at
Europe’s oldest university,
the University of Bologna.
The Club Dumasby Arturo Perez-Reverte
|
“In 1603, at Monte Paderno, outside Bologna, an alchemist (by day a cobbler) named Vicenzo Cascariolo discovered the Philosopher’s Stone, catalyst in the transformation of base metals into gold, focus of the imagination, talisman for abstruse thought. Silver in some lights, white in others, it glowed blue in darkness, awesome to behold.”
“For the University of Bologna hosting an International Conference on Bioluminescence and Chemiluminescence has a very special significance. Indeed, it is in our fair City that modern scientific research on these phenomena has its earliest roots….
‘After submitting the stone
to much preparation, it was not
the Pluto of Aristophanes
that resulted; instead, it was
the Luciferous Stone’ ”
From one of the best books
of the 20th century: The Hawkline Monsterby Richard Brautigan
|
Shape Note
A variation on the theme of the previous entry, Quartet.
The first |
Derek Taunt |
As in the previous entry, the illustration on the left is from a Log24 entry on the date of death of the person on the right.
Relevant quotations:
“It was rather like solving a crossword puzzle.”
— Derek Taunt, on breaking the Enigma Code
“… history is a pattern
Of timeless moments.”
“He [Dr. Taunt] and Angela [his wife] founded the Friends of Kettle’s Yard when the Arts Council cut its grant in 1984 and together organised countless fundraising activities for the museum and gallery.”
“How do we relate to the past? How are our memories affected by the cultural context that shapes our present? How many, and what kind of narratives compete in the representation of a historical moment? Rear View Mirror sets out to explore these questions and examine the devices we use to reconstruct events and people through different lenses….”
— On a future Kettle’s Yard exhibition
Time past and time future
What might have been
and what has been
Point to one end,
which is always present.
“The diamonds will be shining,
no longer in the rough.”
See the Log24 remarks on Jesus College— Taunt’s college– in a web page for June Carter Cash, The Circle is Unbroken.
Perichoresis, or Coinherence
Edward Gibbon, Decline and Fall of the Roman Empire, Chapter XXI —
Gibbon, discussing the theology of the Trinity, defines perichoresis as
“… the internal connection and spiritual penetration which indissolubly unites the divine persons59 ….
59 … The or ‘circumincessio,’ is perhaps the deepest and darkest corner of the whole theological abyss.”
“Whoever fights monsters should see to it that in the process he does not become a monster. And when you look long into an abyss, the abyss also looks into you.”
Perichoresis does NOT mean “dancing around” ….
From a mailing list message:
If [a correspondent] will but open a lexicon, she will see that perichoresis (with a long o, omega) has nothing to do with “the Greek word for dance,” which is spelt with a short o (omicron). As a technical term in trinitarian theology, perichoresis means “interpenetration.”
Interpenetration in Arthur Machen
Interpenetration in T. S. Eliot:
“Between two worlds
become much like each other….”
On the Novels of Charles Williams
Coinherence in Charles Williams
The Per Speculum link is to a discussion of coinherence and the four last films of Kieslowski —
La Double Vie de Veronique (1991),
Trois Couleurs: Bleu (1993),
Trois Couleurs: Blanc (1993), and
Trois Couleurs: Rouge (1994).
See, too, previous log24 entries related to Kieslowski’s work and to coinherence:
Moulin Bleu (12/16/03),
Quarter to Three (12/20/03), and
White, Geometric, and Eternal (12/20/03).
O'Hara's Fingerpost
In The New York Times Book Review of next Sunday (August 24, 2003), Book Review editor Charles McGrath writes that author John O'Hara
"… discovered a kind of story… in which a line of dialogue or even a single observed detail indicates that something crucial has changed."
From the Online Etymology Dictionary:
crucial – 1706, from Fr. crucial… from L. crux (gen. crucis) "cross." The meaning "decisive, critical" is extended from a logical term, Instantias Crucis, adopted by Francis Bacon (1620); the notion is of cross fingerboard signposts at forking roads, thus a requirement to choose.
The remainder of this note deals with the "single observed detail" 162.
|
Instantias Crucis
Francis Bacon says
"Among Prerogative Instances I will put in the fourteenth place Instances of the Fingerpost, borrowing the term from the fingerposts which are set up where roads part, to indicate the several directions. These I also call Decisive and Judicial, and in some cases, Oracular and Commanding Instances. I explain them thus. When in the investigation of any nature the understanding is so balanced as to be uncertain to which of two or more natures the cause of the nature in question should be assigned on account of the frequent and ordinary concurrence of many natures, instances of the fingerpost show the union of one of the natures with the nature in question to be sure and indissoluble, of the other to be varied and separable; and thus the question is decided, and the former nature is admitted as the cause, while the latter is dismissed and rejected. Such instances afford very great light and are of high authority, the course of interpretation sometimes ending in them and being completed. Sometimes these instances of the fingerpost meet us accidentally among those already noticed, but for the most part they are new, and are expressly and designedly sought for and applied, and discovered only by earnest and active diligence."
Inter praerogativas instantiarum, ponemus loco decimo quarto Instantias Crucis; translato vocabulo a Crucibus, quae erectae in biviis indicant et signant viarum separationes. Has etiam Instantias Decisorias et Judiciales, et in casibus nonnullis Instantias Oraculi et Mandati, appellare consuevimus. Earum ratio talis est. Cum in inquisitione naturae alicujus intellectus ponitur tanquam in aequilibrio, ut incertus sit utri naturarum e duabus, vel quandoque pluribus, causa naturae inquisitae attribui aut assignari debeat, propter complurium naturarum concursum frequentem et ordinarium, instantiae crucis ostendunt consortium unius ex naturis (quoad naturam inquisitam) fidum et indissolubile, alterius autem varium et separabile ; unde terminatur quaestio, et recipitur natura illa prior pro causa, missa altera et repudiata. Itaque hujusmodi instantiae sunt maximae lucis, et quasi magnae authoritatis; ita ut curriculum interpretationis quandoque in illas desinat, et per illas perficiatur. Interdum autem Instantiae Crucis illae occurrunt et inveniuntur inter jampridem notatas; at ut plurimum novae sunt, et de industria atque ex composito quaesitae et applicatae, et diligentia sedula et acri tandem erutae.
— Francis Bacon, Novum Organum, Book Two, "Aphorisms," Section XXXVI
A Cubist Crucifixion
An alternate translation:
"When in a Search of any Nature the Understanding stands suspended, the Instances of the Fingerpost shew the true and inviolable Way in which the Question is to be decided. These Instances afford great Light…"
From a review by Adam White Scoville of Iain Pears's novel titled An Instance of the Fingerpost:
"The picture, viewed as a whole, is a cubist description, where each portrait looks strikingly different; the failings of each character's vision are obvious. However, in a cubist painting the viewer often can envision the subject in reality. Here, even after turning the last page, we still have a fuzzy view of what actually transpired. Perhaps we are meant to see the story as a cubist retelling of the crucifixion, as Pilate, Barabbas, Caiaphas, and Mary Magdalene might have told it. If so, it is sublimely done so that the realization gradually and unexpectedly dawns upon the reader. The title, taken from Sir Francis Bacon, suggests that at certain times, 'understanding stands suspended' and in that moment of clarity (somewhat like Wordsworth's 'spots of time,' I think), the answer will become apparent as if a fingerpost were pointing at the way. The final narrative is also titled An Instance of the Fingerpost, perhaps implying that we are to see truth and clarity in this version. But the biggest mystery of this book is that we have actually have no reason to credit the final narrative more than the previous three and so the story remains an enigma, its truth still uncertain."
For the "162" enigma, see
The Matthias Defense, and
The Still Point and the Wheel.
See also the December 2001 Esquire and
the conclusion of my previous entry.
Mental Health Month, Day 23:
The Prime Cut Gospel
On Christmas Day, 1949,
Mary Elizabeth Spacek was born in Texas.
Lee Marvin, Sissy Spacek in “Prime Cut”
Exercises for Mental Health Month:
Read this discussion of the phrase, suggested by Spacek’s date of birth, “God’s gift to men.”
Read this discussion of the phrase “the same yesterday, today, and forever,” suggested by the previous reading.
Read the more interesting of these discussions of the phrase “the eternal in the temporal.”
Read this discussion of eternal, or “necessary,” truths versus other sorts of alleged “truths.”
Read this discussion of unimportant mathematical properties of the prime number 23.
Read these discussions of important properties of 23:
Introduction to the Theory of Groups of Finite Order, Ginn, Boston, 1937 (reprinted by Dover in 1956), final chapter, “Tactical Configurations,” and
J. H. Conway, “Three Lectures on Exceptional Groups,” pp. 215-247 in Finite Simple Groups (Oxford, 1969), edited by M. B. Powell and G. Higman, Academic Press, London, 1971….. Reprinted as Ch. 10 in Sphere Packings, Lattices, and Groups
Read this discussion of what might be called “contingent,” or “literary,” properties of the number 23.
Read also the more interesting of these discussions of the phrase “the 23 enigma.”
Having thus acquired some familiarity with both contingent and necessary properties of 23…
Read this discussion of Aquinas’s third proof of the existence of God.
Note that the classic Spacek film “Prime Cut” was released in 1972, the year that Spacek turned 23:
1949
+ 23 1972 |
Whirligig
Thus the whirligig of time brings in his revenges.
Twelfth Night. Act v. Sc. 1.
Twelfth night is the night of January 5-6.
Tonight is twelfth night in Australia; 4 AM Jan. 5
in New York City is 8 PM Jan. 5 in Sydney.
An October 6 entry:
Twenty-first Century Fox
On Sunday, October 6, 1889, the Moulin Rouge music hall opened in Paris, an event that to some extent foreshadowed the opening of Fox Studios Australia in Sydney on November 7, 1999. The Fox ceremonies included, notably, Kylie Minogue singing "Diamonds are a Girl's Best Friend."
Red Windmill |
Kylie Minogue |
For the mathematical properties of the red windmill (moulin rouge) figure at left, see Diamond Theory.
An October 5 entry:
The Message from Vega
"Mercilessly tasteful"
— Andrew Mueller,
review of Suzanne Vega's
"Songs in Red and Gray"
In accordance with the twelfth-night
"whirligig of time" theme,
here are two enigmatic quilt blocks:
Devil's Claws, or |
Yankee Puzzle, or |
The Artist’s Signature
This title is taken from the final chapter of Carl Sagan’s novel Contact.
“There might be a game in which paper figures were put together to form a story, or at any rate were somehow assembled. The materials might be collected and stored in a scrap-book, full of pictures and anecdotes. The child might then take various bits from the scrap-book to put into the construction; and he might take a considerable picture because it had something in it which he wanted and he might just include the rest because it was there.”
— Ludwig Wittgenstein, Lectures and Conversations on Aesthetics, Psychology and Religious Belief
“Not games. Puzzles. Big difference. That’s a whole other matter. All art — symphonies, architecture, novels — it’s all puzzles. The fitting together of notes, the fitting together of words have by their very nature a puzzle aspect. It’s the creation of form out of chaos. And I believe in form.”
— Stephen Sondheim, in Stephen Schiff, Deconstructing Sondheim,” The New Yorker, March 8, 1993, p. 76
“All goods in this world, all beauties, all truths, are diverse and partial aspects of one unique good. Therefore they are goods which need to be ranged in order. Puzzle games are an image of this operation. Taken all together, viewed from the right point and rightly related, they make an architecture. Through this architecture the unique good, which cannot be grasped, becomes apprehensible. All architecture is a symbol of this, an image of this. The entire universe is nothing but a great metaphor.” — Simone Weil, sister of Princeton mathematician André Weil, First and Last Notebooks, p. 98 |
This passage from Weil is quoted in
Gateway to God,
p. 42, paperback, fourth impression,
printed in Glasgow in 1982 by
Fontana Books
“He would leave enigmatic messages on blackboards,
signed Ya Ya Fontana.”
— Brian Hayes on John Nash,
The Sciences magazine, Sept.-Oct., 1998
“I have a friend who is a Chief of the Aniunkwia (Cherokee) people and I asked him the name of the Creator in which
he replied… Ya Ho Wah. This is also how it is spoken in Hebrew. In my native language it is spoken
Ya Ya*,
which is also what Moses was told
at the ‘Burning Bush’ incident.”
— “Tank” (of Taino ancestry), Bronx, NY, Wednesday, April 17, 2002
From a website reviewing books published by
Fontana:
1/17/02: NEW YORK (Variety) – Russell Crowe is negotiating to star in 20th Century Fox’s “Master and Commander,” the Peter Weir-directed adaptation of the Patrick O’Brian book series.
Hmmm.
*For another religious interpretation of this phrase, see my note of October 4, 2002, “The Agony and the Ya-Ya.”
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….”
To Lucero, in memory of
1962 in CuernavacaFrom 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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