"Core" (in the original, Kern ) is perhaps
not the best translation of hypokeimenon :
See also Heidegger's original German:
Related material: In this journal, "underlie" and "underlying."
Thursday, April 4, 2013
A Philosopher’s Stone
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Monday, November 29, 2010
Philosopher’s Stone
Happy Ending
Part I —
Plato's
Tombstone
Part II —
Star and Diamond
United
(See previous post and
a note on design.)
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Sunday, July 11, 2010
Philosophers’ Keystone
(Background— Yesterday's Quarter to Three,
A Manifold Showing, Class of 64, and Child's Play.)
Hermeneutics
Fans of Gregory Chaitin and Harry Potter
may consult Writings for Yom Kippur
for the meaning of yesterday's evening 673.
(See also Lowry and Cabbala.)
Fans of Elizabeth Taylor, Ava Gardner,
and the Dark Lady may consult Prime Suspect
for the meaning of yesterday's midday 17.
For some more serious background, see Dante—
"….mirando il punto 
a cui tutti li tempi son presenti "
– Dante, Paradiso, XVII, 17-18
“The symbol 
is used throughout the entire book
in place of such phrases as ‘Q.E.D.’ or
‘This completes the proof of the theorem’
to signal the end of a proof.”
— Measure Theory, by Paul R. Halmos, Van Nostrand, 1950
Halmos died on the date of Yom Kippur —
October 2, 2006.
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Friday, March 18, 2016
The Stone…
of Woody Allen's philosopher …
"Deadline reports that Stone is finalizing a deal
to star in Maniac , a 30-minute television series with
her former Superbad castmate Jonah Hill.
The project, a dark comedy, will be directed by
True Detective alum Cary Fukunaga and is based
on a 2014 Norwegian series about a mental-institution
patient living out a fantasy life in his dreams."
See as well the previous post and Jews Telling Stories.
Update of 11:07 PM ET —
From Variety today — "Hill and Stone would also make their
TV producing debut as the two stars are attached to exec produce
with … Anonymous Content’s Michael Sugar and Doug Wald …."
"The problem is having a solid business plan and knowing what
you're doing, whether it's a movie, a TV series or a company."
— Steve Golin in The Hollywood Reporter , Sept. 4, 2013
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Tuesday, September 3, 2013
“The Stone” Today Suggests…
|
The Philosopher's Gaze , by David Michael Levin, The post-metaphysical question—question for a post-metaphysical phenomenology—is therefore: Can the perceptual field, the ground of perception, be released from our historical compulsion to represent it in a way that accommodates our will to power and its need to totalize and reify the presencing of being? In other words: Can the ground be experienced as ground? Can its hermeneutical way of presencing, i.e., as a dynamic interplay of concealment and unconcealment, be given appropriate respect in the receptivity of a perception that lets itself be appropriated by the ground and accordingly lets the phenomenon of the ground be what and how it is? Can the coming-to-pass of the ontological difference that is constitutive of all the local figure-ground differences taking place in our perceptual field be made visible hermeneutically, and thus without violence to its withdrawal into concealment? But the question concerning the constellation of figure and ground cannot be separated from the question concerning the structure of subject and object. Hence the possibility of a movement beyond metaphysics must also think the historical possibility of breaking out of this structure into the spacing of the ontological difference: différance , the primordial, sensuous, ekstatic écart . As Heidegger states it in his Parmenides lectures, it is a question of "the way historical man belongs within the bestowal of being (Zufügung des Seins ), i.e., the way this order entitles him to acknowledge being and to be the only being among all beings to see the open" (PE* 150, PG** 223. Italics added). We might also say that it is a question of our response-ability, our capacity as beings gifted with vision, to measure up to the responsibility for perceptual responsiveness laid down for us in the "primordial de-cision" (Entscheid ) of the ontological difference (ibid.). To recognize the operation of the ontological difference taking place in the figure-ground difference of the perceptual Gestalt is to recognize the ontological difference as the primordial Riß , the primordial Ur-teil underlying all our perceptual syntheses and judgments—and recognize, moreover, that this rift, this division, decision, and scission, an ekstatic écart underlying and gathering all our so-called acts of perception, is also the only "norm" (ἀρχή ) by which our condition, our essential deciding and becoming as the ones who are gifted with sight, can ultimately be judged. * PE: Parmenides of Heidegger in English— Bloomington: Indiana University Press, 1992 ** PG: Parmenides of Heidegger in German— Gesamtausgabe , vol. 54— Frankfurt am Main: Vittorio Klostermann, 1992 |
Examples of "the primordial Riß " as ἀρχή —
For an explanation in terms of mathematics rather than philosophy,
see the diamond theorem. For more on the Riß as ἀρχή , see
Function Decomposition Over a Finite Field.
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Tuesday, May 18, 2010
Stone Junction*
The Philosophers' Stone
according to
The New York Times—
Related material
from French cinema—
"a 'non-existent myth' of a battle between
goddesses of the sun and the moon
for a mysterious blue diamond
that has the power to make
mortals immortal and vice versa."
See also
* The title is a reference to Jim Dodge's 1989 novel Stone Junction: An Alchemical Potboiler.
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Monday, May 17, 2010
Rolling the Stone
A new NY Times column:
Today's New York Times
re-edited for philosophers:
See also
John Baez's paper
Duality in Logic and Physics
(for a May 29 meeting at Oxford),
Lubtchansky's Key, with its links
to Duelle (French, f. adj., dual)
and Art Wars for Trotsky's Birthday.
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Wednesday, June 21, 2023
Annals of Magical Thinking: The Rushmore Embedding
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Monday, June 7, 2021
Scholastic Observation . . .
In memory of the U.S. publisher of Harry Potter and the Sorcerer's Stone ,*
who, The New York Times reports this evening, died Saturday (June 5, 2021) —
* Original British title: Harry Potter and the Philosopher's Stone .
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Wednesday, January 27, 2021
Game of Royalties
For Holocaust Remembrance Day —
Little reportedly died at 79 on Jan. 7.
“Mr. Little submitted the manuscript for ‘Harry Potter and the Philosopher’s Stone’
to 12 publishers. He received 12 rejections in response, before selling it for £2,500,
or about $3,400 (the equivalent of about $5,800 today). It was a meager amount,
but his genius was in the details: He sold only the rights to publish it in Britain and
the Commonwealth, and he asked for high royalties.” — Clay Risen, New York Times
Leachman reportedly died at 94 today.
Dr. Frederick Frankenstein : And it was you… who left my grandfather’s
book out for me to find.
Frau Blücher : Yes.
Dr. Frederick Frankenstein : So that I would…
Frau Blücher : Yes.
Dr. Frederick Frankenstein : Then you and Victor were…
Frau Blücher : YES. YES. Say it. He vas my… BOYFRIEND!
In the spirit of Kinbote…
The real Frau Blücher was of course Hannah Arendt,
whose boyfriend was Martin Heidegger.
Cf. a Log24 post of April 10, 2017 —
| From “Heidegger for Passover”
“Propriation1 gathers the rift-design2 of the saying — p. 415 of Heidegger‘s Basic Writings , “Das Ereignis versammelt den Aufriß der Sage — Heidegger, Weg zur Sprache 1. “Mirror-Play of the Fourfold” |
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Tuesday, December 15, 2020
Connection
Hurt’s dies natalis (date of death, in the saints’ sense) was,
it now seems, 25 January 2017, not 27.
A connection, for fantasy fans, between the Philosopher’s Stone
(represented by the eightfold cube) and the Deathly Hallows
(represented by the usual Fano-plane figure) —
Images from a Log24 search for “Holocron.”
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Thursday, April 18, 2019
Expanding the Unfolding*
From a New York Times book review of a new novel about
Timothy Leary that was in the Times online on April 10 —
"Most of the novel resides in the perspective
of Fitzhugh Loney, one of Leary’s graduate students."
"A version of this article appears in print on ,
on Page 10 of the Sunday Book Review with the headline:
Strange Days."
For material about one of Leary's non -fictional grad students,
Ralph Metzner, see posts now tagged Metzner's Pi Day.
Related material —
The reported publication date of Searching for the Philosophers' Stone
was January 1, 2019.
A related search published here on that date:
* Title suggested by two of Ralph Metzner's titles,
The Expansion of Consciousness and The Unfolding Self .
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Sunday, April 7, 2019
Block Talk
David Brooks in The New York Times Sunday Review today —
" 'In the deeps are the violence and terror of which psychology
has warned us,' Annie Dillard writes in 'Teaching a Stone to Talk.'
'But if you ride these monsters deeper down, if you drop with them
farther over the world’s rim, you find what our sciences cannot locate
or name, the substrate, the ocean or matrix or ether which buoys
the rest, which gives goodness its power for good, and evil its power
for evil, the unified field: our complex and inexplicable caring for
each other.' "
Annie Dillard on the legendary philosopher's stone —
“… if Holy the Firm is matter at its dullest, Aristotle’s materia prima ,
absolute zero, and since Holy the Firm is in touch with the Absolute
at base, then the circle is unbroken. And it is…. Holy the Firm is
in short the philosopher’s stone.”
See also "The Thing and I."
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Friday, January 25, 2019
Crucible Raiders Continues.
Fans of the New York Times philosophy series "The Stone"
(named for the legendary philosophers' stone) may consult
posts tagged "Crucible Raiders" in this journal.
Some context — the previous post, "Night at the Social Media."
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Thursday, October 11, 2018
Spelling
Related adcraft — "Harry Potter and the Philosopher's Stone"
became, for the U.S. market, "… and the Sorcerer's Stone."
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Friday, August 31, 2018
Perception of Number
Review of yesterday's post Perception of Space —
From Harry Potter and the Philosopher's Stone (1997),
republished as "… and the Sorcerer's Stone ," Kindle edition:
In a print edition from Bloomsbury (2004), and perhaps in the
earliest editions, the above word "movements" is the first word
on page 168:
Click the above ellipse for some Log24 posts on the eightfold cube,
the source of the 168 automorphisms ("movements") of the Fano plane.
"Refined interpretation requires that you know that
someone once said the offspring of reality and illusion
is only a staggering confusion."
— Poem, "The Game of Roles," by Mary Jo Bang
Related material on reality and illusion —
an ad on the back cover of the current New Yorker —
"Hey, the stars might lie, but the numbers never do." — Song lyric
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Thursday, August 30, 2018
Twenty Years
This post was suggested by the final inside page, 23,
of next Sunday's New York Times Book Review ,
"Memorabilia/ Happy 20th Anniversary, Harry Potter."
From VOA Learning English, June 26, 2017 —
|
J.K. Rowling's Harry Potter Books . . . . " J.K. Rowling’s first book about Harry and his friends at Hogwarts School of Witchcraft and Wizardry was released on June 26, 1997. The publisher, Bloomsbury, only released 500 copies to stores in Britain and sent 500 to British libraries. Now, thanks to 450 million more copies of the first book and six others, Harry Potter and his friends are known around the world. Adults and children loved the books. But 12 publishers rejected the first one, known in many countries as 'Harry Potter and the Philosopher’s Stone.' " . . . . |
See as well this journal on June 26, 2017 in
posts now tagged Ron Shaw In Memoriam.
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Perception* of Space
* A footnote in memory of a dancer who reportedly died
yesterday, August 29 — See posts tagged Paradigm Shift.
"Birthday, death-day — what day is not both?" — John Updike
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Monday, May 7, 2018
Glitter Ball for Cannes
In memory of a French film publicist who worked with Clint Eastwood
in 1971 on the release of "The Beguiled" —
From a New York Times graphic review dated Sept. 16, 2016 —
It's Chapter 1 of George Eliot's "Middlemarch."
Dorothea Brooke, young and brilliant, filled with passion
no one needs, is beguiled by some gemstones . . . .
The characters, moving through the book,
glitter as they turn their different facets toward us . . . .
Cf. a glitter-ball-like image in today's New York Times philosophy column
"The Stone" — a column named for the legendary philosophers' stone.
The publicist, Pierre Rissient, reportedly died early Sunday.
See as well Duelle in this journal.
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Saturday, April 7, 2018
Word and Image: Backstory for James Spader
Actor James Spader in a 2014 interview —
". . . my father taught English. My mother taught art . . . ."
Detail of part of a text by Magritte (1929) that appeared
without attribution in the online New York Times today —
See also, from a search for the phrase "Word and Image"
in this journal —
The Philosophers' Stone as originally
illustrated in The New York Times —
.
Related images —
See as well a Log24 search for "Philosophers' Stone"
and remarks related to the Magritte pictures above
in the post Story of March 13, 2014.
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Thursday, July 20, 2017
Undeniable
From "Silicon Valley’s Bonfire of the Vainglorious"
By W. Patrick McCray in the Los Angeles Review of Books
on Monday, July 17, 2017 —
"Whether people are information, chemistry, or indeed
'spirit' or 'soul' has kept stoned undergraduates talking
into the wee hours and philosophers employed, but
there’s now an undeniable commercial aspect to all of
this."
"You have my (divided) attention." — The Singularity.
(See the link on "At" in this journal on Monday.)
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Saturday, February 4, 2017
♫ Are You Going to Vanity Fair?
"In those days, the occult sciences were cultivated with ardor well calculated to surprise the incredulous minds of our own sovereignly analytical age; perhaps they may detect in this historical sketch the germ of the positive sciences, widely studied in the nineteenth century, but without the poetic grandeur which was ascribed to them by the audacious investigators of the sixteenth century; who, instead of devoting their energy to industry, magnified art and made thought fruitful. The patronage universally accorded to art by the sov- ereigns of that time was justified, too, by the mar- vellous creations of inventors who started in quest of the philosopher's stone and reached amazing re- sults." — Balzac, Catherine de' Medici
Honoré de Balzac, Sur Catherine de Médicis :
— Hé! bien, sire, en ôtant Dieu de ce monde, que reste-t-il?
L’homme! Examinons alors notre domaine?
Le monde matériel est composé d’éléments, ces éléments
ont eux-mêmes des principes. Ces principes se résolvent
en un seul qui est doué de mouvement. Le nombre TROIS est
la formule de la création: la Matière, le Mouvement, le Produit!
— La preuve? Halte-là, s’écria le roi.
Illustration by Frederick Alfred Rhead of Vanity Fair,
page 96 in the John Bunyan classic Pilgrim's Progress
(New York, The Century Co., 1912)
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Friday, July 1, 2016
Party Phone
Revisiting August 31, 2006 —
"It's not the twilight zone no,
it's not the twilight zone
Yes it's just a party phone,
pure
honeycomb,
honeycomb,
honeycomb"
— Van Morrison, "Twilight Zone,"
in The Philosopher's Stone
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Sunday, April 17, 2016
The Thing and I
The New York Times philosophy column yesterday —
The Times's philosophy column "The Stone" is named after the legendary
"philosophers' stone." The column's name, and the title of its essay yesterday
"Is that even a thing?" suggest a review of the eightfold cube as "The object
most closely resembling a 'philosophers' stone' that I know of" (Page 51 of
the current issue of a Norwegian art quarterly, KUNSTforum.as).
The eightfold cube —
|
Definition of Epiphany
From James Joyce’s Stephen Hero , first published posthumously in 1944. The excerpt below is from a version edited by John J. Slocum and Herbert Cahoon (New York: New Directions Press, 1959). Three Times: … By an epiphany he meant a sudden spiritual manifestation, whether in the vulgarity of speech or of gesture or in a memorable phase of the mind itself. He believed that it was for the man of letters to record these epiphanies with extreme care, seeing that they themselves are the most delicate and evanescent of moments. He told Cranly that the clock of the Ballast Office was capable of an epiphany. Cranly questioned the inscrutable dial of the Ballast Office with his no less inscrutable countenance: — Yes, said Stephen. I will pass it time after time, allude to it, refer to it, catch a glimpse of it. It is only an item in the catalogue of Dublin’s street furniture. Then all at once I see it and I know at once what it is: epiphany. — What? — Imagine my glimpses at that clock as the gropings of a spiritual eye which seeks to adjust its vision to an exact focus. The moment the focus is reached the object is epiphanised. It is just in this epiphany that I find the third, the supreme quality of beauty. — Yes? said Cranly absently. — No esthetic theory, pursued Stephen relentlessly, is of any value which investigates with the aid of the lantern of tradition. What we symbolise in black the Chinaman may symbolise in yellow: each has his own tradition. Greek beauty laughs at Coptic beauty and the American Indian derides them both. It is almost impossible to reconcile all tradition whereas it is by no means impossible to find the justification of every form of beauty which has ever been adored on the earth by an examination into the mechanism of esthetic apprehension whether it be dressed in red, white, yellow or black. We have no reason for thinking that the Chinaman has a different system of digestion from that which we have though our diets are quite dissimilar. The apprehensive faculty must be scrutinised in action. — Yes … — You know what Aquinas says: The three things requisite for beauty are, integrity, a wholeness, symmetry and radiance. Some day I will expand that sentence into a treatise. Consider the performance of your own mind when confronted with any object, hypothetically beautiful. Your mind to apprehend that object divides the entire universe into two parts, the object, and the void which is not the object. To apprehend it you must lift it away from everything else: and then you perceive that it is one integral thing, that is a thing. You recognise its integrity. Isn’t that so? — And then? — That is the first quality of beauty: it is declared in a simple sudden synthesis of the faculty which apprehends. What then? Analysis then. The mind considers the object in whole and in part, in relation to itself and to other objects, examines the balance of its parts, contemplates the form of the object, traverses every cranny of the structure. So the mind receives the impression of the symmetry of the object. The mind recognises that the object is in the strict sense of the word, a thing , a definitely constituted entity. You see? — Let us turn back, said Cranly. They had reached the corner of Grafton St and as the footpath was overcrowded they turned back northwards. Cranly had an inclination to watch the antics of a drunkard who had been ejected from a bar in Suffolk St but Stephen took his arm summarily and led him away. — Now for the third quality. For a long time I couldn’t make out what Aquinas meant. He uses a figurative word (a very unusual thing for him) but I have solved it. Claritas is quidditas . After the analysis which discovers the second quality the mind makes the only logically possible synthesis and discovers the third quality. This is the moment which I call epiphany. First we recognise that the object is one integral thing, then we recognise that it is an organised composite structure, a thing in fact: finally, when the relation of the parts is exquisite, when the parts are adjusted to the special point, we recognise that it is that thing which it is. Its soul, its whatness, leaps to us from the vestment of its appearance. The soul of the commonest object, the structure of which is so adjusted, seems to us radiant. The object achieves its epiphany. Having finished his argument Stephen walked on in silence. He felt Cranly’s hostility and he accused himself of having cheapened the eternal images of beauty. For the first time, too, he felt slightly awkward in his friend’s company and to restore a mood of flippant familiarity he glanced up at the clock of the Ballast Office and smiled: — It has not epiphanised yet, he said. |
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Monday, March 28, 2016
Easter, 2016
"Minute by minute they live:
The stone's in the midst of all."
— "Easter, 1916"
A Philosophers' Stone
— St. Patrick's Day, 2016
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Wednesday, January 6, 2016
Epiphany for Jews
A quarter to three …
… and a philosopher's Stone —
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Saturday, November 7, 2015
Clarifying Dyson
The previous post quoted a passage from Turing's Cathedral ,
a 2012 book by George Dyson —
It should be noted that Dyson's remarks on "two species of
bits," space, time, "structure and sequence" and logic gates
are from his own idiosyncratic attempt to create a philosophy
based on the workings of computers. These concepts are not,
so far as I can tell, part of anyone else's approach to the subject.
For a more standard introduction to how computers work, see
(for instance) a book by an author Dyson admires:
The Pattern on the Stone , by W. Daniel Hillis (Basic Books, 1998).
PREFACE: MAGIC IN THE STONE
I etch a pattern of geometric shapes onto a stone.
To the uninitiated, the shapes look mysterious and
complex, but I know that when arranged correctly
they will give the stone a special power, enabling it
to respond to incantations in a language no human
being has ever spoken. I will ask the stone questions
in this language, and it will answer by showing me a
vision: a world created by my spell, a world imagined
within the pattern on the stone.
A few hundred years ago in my native New England,
an accurate description of my occupation would have
gotten me burned at the stake. Yet my work involves
no witchcraft; I design and program computers. The
stone is a wafer of silicon, and the incantations are
software. The patterns etched on the chip and the
programs that instruct the computer may look
complicated and mysterious, but they are generated
according to a few basic principles that are easily
explained. . . . .
Hillis's title suggests some remarks unrelated to computers —
See Philosopher + Stone in this journal.
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Sunday, November 1, 2015
Double Consciousness
A check of the New York Times 's version of the
philosophers' stone yields…
"And as Du Bois, a student of Hegel’s, reminds us,
the one who is in the dominated position is aware
of the perspective of the master: She is conscious
of herself as being seen by the other. It is this
double-consciousness that we must learn to understand."
— Seyla Benhabib, quoted by the Times
on Oct. 29, 2015, 3:30 AM ET
A check of Benhabib's words yields…
"It is a peculiar sensation, this double-consciousness,
this sense of always looking at one's self through
the eyes of others, of measuring one's soul by the tape
of a world that looks on in amused contempt and pity."
That, for example, looks on Harvard in amused contempt and pity…
See Con Vocation.
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Saturday, October 31, 2015
Raiders of the Lost Crucible
Stanford Encyclopedia of Philosophy
on the date Friday, April 5, 2013 —
“First published Tue Sep 24, 1996;
substantive revision Fri Apr 5, 2013”
This journal on the date Friday, April 5, 2013 —
The object most closely resembling a “philosophers’ stone”
that I know of is the eightfold cube .
For some related philosophical remarks that may appeal
to a general Internet audience, see (for instance) a website
by I Ching enthusiast Andreas Schöter that displays a labeled
eightfold cube in the form of a lattice diagram —
Related material by Schöter —
A 20-page PDF, “Boolean Algebra and the Yi Jing.”
(First published in The Oracle: The Journal of Yijing Studies ,
Vol 2, No 7, Summer 1998, pp. 19–34.)
I differ with Schöter’s emphasis on Boolean algebra.
The appropriate mathematics for I Ching studies is,
I maintain, not Boolean algebra but rather Galois geometry.
See last Saturday’s post Two Views of Finite Space.
Unfortunately, that post is, unlike Schöter’s work, not
suitable for a general Internet audience.
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Saturday, September 26, 2015
Posthumous Man
The above book, a tribute by admirers of the late Michael Weinstein
(not, as a campus obituary states, by Weinstein himself),
was reportedly published by Routledge on December 19, 2014.
This journal on that date had a post on an early Greek philosopher who
supposedly was killed because he discovered irrational numbers.
A later approach to academic life —
Emma Stone being directed by Woody Allen in the recent "Irrational Man":
Fans of Allen and Stone may also enjoy Magic in the Moonlight.
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Saturday, July 26, 2014
OOPs
Or: Two Rivets Short of a Paradigm
Detail from an author photo:
|
From rivet-rivet.net:
The philosopher Graham Harman is invested in re-thinking the autonomy of objects and is part of a movement called Object-Oriented-Philosophy (OOP). Harman wants to question the authority of the human being at the center of philosophy to allow the insertion of the inanimate into the equation. With the aim of proposing a philosophy of objects themselves, Harman puts the philosophies of Bruno Latour and Martin Heidegger in dialogue. Along these lines, Harman proposes an unconventional reading of the tool-being analysis made by Heidegger. For Harman, the term tool does not refer only to human-invented tools such as hammers or screwdrivers, but to any kind of being or thing such as a stone, dog or even a human. Further, he uses the terms objects, beings, tools and things, interchangeably, placing all on the same ontological footing. In short, there is no “outside world.” Harman distinguishes two characteristics of the tool-being: invisibility and totality. Invisibility means that an object is not simply used but is: “[an object] form(s) a cosmic infrastructure of artificial and natural and perhaps supernatural forces, power by which our last action is besieged.” For instance, nails, wooden boards and plumbing tubes do their work to keep a house “running” silently (invisibly) without being viewed or noticed. Totality means that objects do not operate alone but always in relation to other objects–the smallest nail can, for example, not be disconnected from wooden boards, the plumbing tubes or from the cement. Depending on the point of view of each entity (nail, tube, etc.) a different reality will emerge within the house. For Harman, “to refer to an object as a tool-being is not to say that it is brutally exploited as a means to an end, but only that it is torn apart by the universal duel between the silent execution of an object’s reality and the glistening aura of its tangible surface.” — From "The Action of Things," an M.A. thesis at the Center for Curatorial Studies, Bard College, by Manuela Moscoso, May 2011, edited by Sarah Demeuse |
From Wikipedia, a programming paradigm:
See also posts tagged Turing's Cathedral, and Alley Oop (Feb. 11, 2003).
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Wednesday, July 9, 2014
Fashion Statements
From Monday in this journal —
Related news this morning —
Anne Hollander, Scholar of Style, Dies at 83
By William Yardley in The New York Times ,
10:26 PM ET July 8, 2014
Anne Hollander, a historian who helped elevate
the study of art and dress by revealing the often striking
relationships between the two, died on Sunday at her home
in Manhattan. She was 83.
The cause was cancer, said her husband, the philosopher
Thomas Nagel.
. . . .
She received a degree in art history from Barnard College
in 1952. The next year she married the poet John Hollander.
Their marriage ended in divorce.
Related material from this journal last year —
"Be serious, because
The stone may have contempt
For too-familiar hands"
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Saturday, June 22, 2013
Stevens and the Rock
Passage quoted in A Philosopher's Stone (April 4, 2013)—
This passage from Heidegger suggested the lexicon excerpt on
to hypokeimenon (the underlying) in yesterday's post Lexicon.
A related passage:
The Eliade passage was quoted in a 1971 Ph.D. thesis
on Wallace Stevens.
Some context— Stevens's Rock in this journal.
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Friday, April 5, 2013
Reflections (continued)
From a search for Mirror-Play in this journal:
That search was suggested by a much lengthier
search, for Core, that itself was suggested
by yesterday's post (on Katherine Neville's birthday)
titled A Philosopher's Stone.
See, too, Tom Hanks (shown above as symbologist
Robert Langdon) in "Lucky Guy" (reviewed by TIME
yesterday), and a related poem:
Yes, you! You’re the Lucky One…
Prospective purchasers of the poet's work
may consult a press release from LSU Press
dated 4/4/2013. The poet died, apparently*
unlamented by his publisher, on 3/30.
* But only apparently.
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The Crucible
"Though we had many pieces, we did not have the whole.
It was thirty years before we deciphered the formula.
But we did it at last.
There at night in the darkness of Fourier’s laboratory,
the four of us stood and watched the philosophers’ stone
forming in the crucible."
— The Eight , by Katherine Neville
(2008 Ballantine Books mass market edition, p. 640)
A journal post from August 25, 2009:
Image from a different journal earlier that same day, August 25, 2009:
Thirty-year medallion from Alcoholics Anonymous —
See also, in this journal, "The Eight" + Damnation.
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Wednesday, May 23, 2012
Now What?
(Rhetorical question on the NY Times online front page,
10:01 PM May 23, 2012, in teaser for "The Stone" column
about Philip K. Dick, "Sci-Fi Philosopher")
Perhaps The Last Airbender ?
The NY Times philosophy column "The Stone" is currently about gnosticism
and science fiction.
The Last Airbender is about an avatar who is master of the four elements
air, water, earth, and fire. For a more sophisticated approach to gnosticism
and the four elements, see Irenaeus: Against Heresies.
See, too, Elements Diamond in this journal.
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Monday, May 21, 2012
Child’s Play (continued*)
we are just like a couple of tots…
— Sinatra
Born 1973 in Bergen. Lives and works in Oslo.
Education
2000 – 2004 National Academy of Fine Arts, Oslo
1998 – 2000 Strykejernet Art School, Oslo, NO
1995 – 1998 Philosophy, University of Bergen
University of Bergen—
|
It might therefore seem that the idea of digital and analogical systems as rival fundaments to human experience is a new suggestion and, like digital technology, very modern. In fact, however, the idea is as old as philosophy itself (and may be much older). In his Sophist, Plato sets out the following ‘battle’ over the question of ‘true reality’: What we shall see is something like a battle of gods and giants going on between them over their quarrel about reality [γιγαντομαχία περì της ουσίας] ….One party is trying to drag everything down to earth out of heaven and the unseen, literally grasping rocks and trees in their hands, for they lay hold upon every stock and stone and strenuously affirm that real existence belongs only to that which can be handled and offers resistance to the touch. They define reality as the same thing as body, and as soon as one of the opposite party asserts that anything without a body is real, they are utterly contemptuous and will not listen to another word. (…) Their adversaries are very wary in defending their position somewhere in the heights of the unseen, maintaining with all their force that true reality [την αληθινήν ουσίαν] consists in certain intelligible and bodiless forms. In the clash of argument they shatter and pulverize those bodies which their opponents wield, and what those others allege to be true reality they call, not real being, but a sort of moving process of becoming. On this issue an interminable battle is always going on between the two camps [εν μέσω δε περι ταυτα απλετος αμφοτέρων μάχη τις (…) αει συνέστηκεν]. (…) It seems that only one course is open to the philosopher who values knowledge and truth above all else. He must refuse to accept from the champions of the forms the doctrine that all reality is changeless [and exclusively immaterial], and he must turn a deaf ear to the other party who represent reality as everywhere changing [and as only material]. Like a child begging for 'both', he must declare that reality or the sum of things is both at once [το όν τε και το παν συναμφότερα] (Sophist 246a-249d). The gods and the giants in Plato’s battle present two varieties of the analog position. Each believes that ‘true reality’ is singular, that "real existence belongs only to" one side or other of competing possibilities. For them, difference and complexity are secondary and, as secondary, deficient in respect to truth, reality and being (την αληθινήν ουσίαν, το όν τε και το παν). Difference and complexity are therefore matters of "interminable battle" whose intended end for each is, and must be (given their shared analogical logic), only to eradicate the other. The philosophical child, by contrast, holds to ‘both’ and therefore represents the digital position where the differentiated two yet belong originally together. Here difference, complexity and systematicity are primary and exemplary. It is an unfailing mark of the greatest thinkers of the tradition, like Plato, that they recognize the digital possibility and therefore recognize the principal difference of it from analog possibilities.
— Cameron McEwen, "The Digital Wittgenstein," |
* See that phrase in this journal.
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Sunday, April 15, 2012
Fun and Games
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Thursday, March 8, 2012
Light
For Women's Day—
- Reviews of GCB from Dallas and Toronto
- Sweater, a post of 2:02 PM EST Monday
(1:02 PM Monday, Dallas time) - Schedule for a Monday afternoon event in Dallas
- NY Times front page Monday evening, featuring
remarks by "The Stone" philosopher Colin McGinn - A 10 PM Monday link to a Harvard Crimson review
of a book by McGinn
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Thursday, January 5, 2012
Precisely
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 …
- a June 12, 2006 link (in a 2007 post) to Geometry of the 4×4 Square,
- some related remarks on Dummett and Universals in this journal, and
- the following excerpt from Spekkens's toy model—
"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….
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Saturday, November 12, 2011
Professor Dodge
From today's previous post, a fragmentary thought—
"Professor Dodge and the underground artists
whose work he helped save are the subjects of a book…"
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Jim Dodge, Stone Junction (a novel first published in 1989) From pages 206-208, Kindle Edition— `Have you seen it?' Volta hesitated. `Well, I've dreamed it.' Daniel shook his head. `I'm getting lost. You want me to vanish into your dreams?' `Good Lord, no,' Volta blanched. `That's exactly what I don't want you to do.' `So, what is it exactly you do want me to do?' `Steal the diamond.' `So, it's a diamond?' `Yes, though it's a bit like saying the ocean is water. The diamond is perfectly spherical,* perfectly clear— though it seems to glow— and it's about two-thirds the size of a bowling ball. I think of it as the Diamond. Capital D.' `Who owns it?' `No one. The United States government has it at the moment. We want it. And to be honest with you, Daniel, I particularly want it, want it dearly. I want to look at it, into it, hold it in my hands. I had a vision involving a spherical diamond, a vision that changed my life, and I want to confirm that it was a vision of something real, the spirit embodied, the circuit complete.' Daniel was smiling. `You're going to love this. That dream I wanted to talk to you about, my first since the explosion? It just happened to feature a raven with a spherical diamond in its beak. Obviously, it wasn't as big as a bowling ball, and there was a thin spiral flame running edge to edge through its center, which made it seem more coldly brilliant than warmly glowing, but it sounds like the same basic diamond to me.' `And what do you think it is?' `I think it's beautiful.' Volta gave him a thin smile. `If I were more perverse than I already lamentably am, I would say it is the Eye of the Beholder. In fact, I don't know what it is.' `It might be a dream,' Daniel said. `Very possibly,' Volta agreed, `but I don't think so. I think— feel , to be exact— that the Diamond is an interior force given exterior density, the transfigured metaphor of the prima materia , the primordial mass, the Spiritus Mundi . I'm assuming you're familiar with the widely held supposition that the entire universe was created from a tiny ball of dense matter which exploded, sending pieces hurtling into space, expanding from the center. The spherical diamond is the memory, the echo, the ghost of that generative cataclysm; the emblematic point of origin. Or if, as some astrophysicists believe, the universe will reach some entropic point in its expansion and begin to collapse back into itself, in that case the Diamond may be a homing point, the seed crystal, to which it will all come hurtling back together— and perhaps through itself, into another dimension entirely. Or it might be the literal Philosopher's Stone we alchemists speak of so fondly. Or I might be completely wrong. That's why I want to see it. If I could actually stand in its presence, I'm convinced I'd know what it is. I would even venture to say, at the risk of rabid projection, that it wants to be seen and known.' `But you're not even sure it exists,' Daniel said. `Right? And hey, it's tough to steal something that doesn't exist, even if you can be invisible. The more I think about this the less sense it makes.' * Here Dodge's mystical vision seems akin to that of Anthony Judge in "Embodying the Sphere of Change" (St. Stephen's Day, 2001). Actually, the cube, not the sphere, is the best embodiment of Judge's vision. |
See also Tuesday's "Stoned" and the 47 references
to the term "bowling" in the Kindle Stone Junction .
Furthermore… Live from New York, it's Saturday Night!
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Monday, July 18, 2011
Voldemort
Continuing yesterday's lottery meditation…
The NY evening numbers yesterday were 244 and 2962.
The latter suggests Post 2962—
There is no Post 244 here, but a search within this journal for 244 yields…
See also Halmos Tombstone and Death Proof.
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Monday, July 11, 2011
The Witch of And/Or
AND: Logical conjunction, symbolized as… ∧
OR: Logical disjunction, symbolized as… ∨
AND/OR: Logical confusion, symbolized as… 
according to a woman Lacanian analyst in this journal.
See also another female disciple of Lacan
writing as co-author with a philosophy professor
in Saturday's online New York Times 's "The Stone"—
Let Be: An Answer to Hamlet’s Question."
Perhaps they thought the question was…
|
|
Wikipedia portrait of New School "To be and/or not to be?" |
For a more philosophically respectable approach to
the same shape, see Sunday morning's Wittgenstein's Diamond.
"We're gonna need more holy water." —Hollywood saying
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Monday, April 25, 2011
Poetry and Physics
One approach to the storied philosophers' stone, that of Jim Dodge in Stone Junction , was sketched in yesterday's Easter post. Dodge described a mystical "spherical diamond." The symmetries of the sphere form what is called in mathematics a Lie group . The "spherical" of Dodge therefore suggests a review of the Lie group E8 in Garrett Lisi's poetic theory of everything.
A check of the Wikipedia article on Lisi's theory yields…
Diamond and E8 at Wikipedia
Related material — E8 as "a diamond with thousands of facets"—
Also from the New Yorker article—
“There’s a dream that underlying the physical universe is some beautiful mathematical structure, and that the job of physics is to discover that,” Smolin told me later. “The dream is in bad shape,” he added. “And it’s a dream that most of us are like recovering alcoholics from.” Lisi’s talk, he said, “was like being offered a drink.”
A simpler theory of everything was offered by Plato. See, in the Timaeus , the Platonic solids—
Figure from this journal on August 19th, 2008.
See also July 19th, 2008.
“It’s all in Plato, all in Plato:
bless me, what do they
teach them at these schools!”
— C. S. Lewis
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Monday, December 27, 2010
Church Diamond
Also known, roughly speaking, as confluence or the Church-Rosser property.
From “NYU Lambda Seminar, Week 2” —
[See also the parent page Seminar in Semantics / Philosophy of Language or:
What Philosophers and Linguists Can Learn From Theoretical Computer Science But Didn’t Know To Ask)]
A computational system is said to be confluent, or to have the Church-Rosser or diamond property, if, whenever there are multiple possible evaluation paths, those that terminate always terminate in the same value. In such a system, the choice of which sub-expressions to evaluate first will only matter if some of them but not others might lead down a non-terminating path.
The untyped lambda calculus is confluent. So long as a computation terminates, it always terminates in the same way. It doesn’t matter which order the sub-expressions are evaluated in.
A computational system is said to be strongly normalizing if every permitted evaluation path is guaranteed to terminate. The untyped lambda calculus is not strongly normalizing: ω ω doesn’t terminate by any evaluation path; and (\x. y) (ω ω) terminates only by some evaluation paths but not by others.
But the untyped lambda calculus enjoys some compensation for this weakness. It’s Turing complete! It can represent any computation we know how to describe. (That’s the cash value of being Turing complete, not the rigorous definition. There is a rigorous definition. However, we don’t know how to rigorously define “any computation we know how to describe.”) And in fact, it’s been proven that you can’t have both. If a computational system is Turing complete, it cannot be strongly normalizing.
There is no connection, apart from the common reference to an elementary geometric shape, between the use of “diamond” in the above Church-Rosser sense and the use of “diamond” in the mathematics of (Cullinane’s) Diamond Theory.
Any attempt to establish such a connection would, it seems, lead quickly into logically dubious territory.
Nevertheless, in the synchronistic spirit of Carl Jung and Arthur Koestler, here are some links to such a territory —
Link One — “Insane Symmetry” (Click image for further details)—
See also the quilt symmetry in this journal on Christmas Day.
Link Two — Divine Symmetry
(George Steiner on the Name in this journal on Dec. 31 last year (“All about Eve“)) —
“The links are direct between the tautology out of the Burning Bush, that ‘I am’ which accords to language the privilege of phrasing the identity of God, on the one hand, and the presumptions of concordance, of equivalence, of translatability, which, though imperfect, empower our dictionaries, our syntax, our rhetoric, on the other. That ‘I am’ has, as it were, at an overwhelming distance, informed all predication. It has spanned the arc between noun and verb, a leap primary to creation and the exercise of creative consciousness in metaphor. Where that fire in the branches has gone out or has been exposed as an optical illusion, the textuality of the world, the agency of the Logos in logic—be it Mosaic, Heraclitean, or Johannine—becomes ‘a dead letter.'”
– George Steiner, Grammars of Creation
(See also, from Hanukkah this year, A Geometric Merkabah and The Dreidel is Cast.)
Link Three – Spanning the Arc —
Part A — Architect Louis Sullivan on “span” (see also Kindergarten at Stonehenge)
Part B — “Span” in category theory at nLab —
Also from nLab — Completing Spans to Diamonds
“It is often interesting whether a given span in some partial ordered set can be completed into a diamond. The property of a collection of spans to consist of spans which are expandable into diamonds is very useful in the theory of rewriting systems and producing normal forms in algebra. There are classical results e.g. Newman’s diamond lemma, Širšov-Bergman’s diamond lemma (Širšov is also sometimes spelled as Shirshov), and Church-Rosser theorem (and the corresponding Church-Rosser confluence property).”
The concepts in this last paragraph may or may not have influenced the diamond theory of Rudolf Kaehr (apparently dating from 2007).
They certainly have nothing to do with the Diamond Theory of Steven H. Cullinane (dating from 1976).
For more on what the above San Francisco art curator is pleased to call “insane symmetry,” see this journal on Christmas Day.
For related philosophical lucubrations (more in the spirit of Kaehr than of Steiner), see the New York Times “The Stone” essay “Span: A Remembrance,” from December 22—
“To understand ourselves well,” [architect Louis] Sullivan writes, “we must arrive first at a simple basis: then build up from it.”
Around 300 BC, Euclid arrived at this: “A point is that which has no part. A line is breadthless length.”
See also the link from Christmas Day to remarks on Euclid and “architectonic” in Mere Geometry.
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Saturday, November 27, 2010
Simplex Sigillum Veri
An Adamantine View of "The [Philosophers'] Stone"
The New York Times column "The Stone" on Sunday, Nov. 21 had this—
"Wittgenstein was formally presenting his Tractatus Logico-Philosophicus , an already well-known work he had written in 1921, as his doctoral thesis. Russell and Moore were respectfully suggesting that they didn’t quite understand proposition 5.4541 when they were abruptly cut off by the irritable Wittgenstein. 'I don’t expect you to understand!' (I am relying on local legend here….)"
Proposition 5.4541*—
Related material, found during a further search—
A commentary on "simplex sigillum veri" leads to the phrase "adamantine crystalline structure of logic"—
For related metaphors, see The Diamond Cube, Design Cube 2x2x2, and A Simple Reflection Group of Order 168.
Here Łukasiewicz's phrase "the hardest of materials" apparently suggested the commentators' adjective "adamantine." The word "diamond" in the links above refers of course not to a material, but to a geometric form, the equiangular rhombus. For a connection of this sort of geometry with logic, see The Diamond Theorem and The Geometry of Logic.
For more about God, a Stone, logic, and cubes, see Tale (Nov. 23).
* 5.4541 in the German original—
Die Lösungen der logischen Probleme müssen einfach sein,
denn sie setzen den Standard der Einfachheit.
Die Menschen haben immer geahnt, dass es
ein Gebiet von Fragen geben müsse, deren Antworten—
a priori—symmetrisch, und zu einem abgeschlossenen,
regelmäßigen Gebilde vereint liegen.
Ein Gebiet, in dem der Satz gilt: simplex sigillum veri.
Here "einfach" means "simple," not "neat," and "Gebiet" means
"area, region, field, realm," not (except metaphorically) "sphere."
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Monday, August 2, 2010
Specific and Robust
The New York Times version of the philosophers' stone:
In the Times 's latest sermon from THE STONE, Gary Gutting, a professor of philosophy at Notre Dame, discusses
"…the specific and robust claims of Judaism, Christianity and Islam about how God is concretely and continually involved in our existence."
A search shows that Gutting's phrase "specific and robust" has many echoes in biotechnology, and a few in software development. The latter is of more interest to me than the former. (The poetically inclined might say that Professor Gutting's line of work is a sort of software development.)
"As a developer, you need a specific and robust set of development tools in the smallest and simplest package possible."
— EasyEclipse web page
Here are two notes on related material:
Specific— The Pit:
See a search for "harrowing of Hell" in this journal.
("…right through hell there is a path…." –Malcolm Lowry)
Robust— The Pendulum:
See a search for "Foucault's Pendulum" in this journal.
(“Others say it is a stone that posseses mysterious powers…. often depicted as a dazzling light. It’s a symbol representing power, a source of immense energy. It nourishes, heals, wounds, blinds, strikes down…. Some have thought of it as the philosopher’s stone of the alchemists….”
Those puzzled by why the NY Times would seek the opinions of a professor at a Catholic university may consult Gutting's home page.
He is an expert on the gay Communist Michel Foucault, a student of Althusser.
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Thursday, July 1, 2010
Plato’s Code
John Allen Paulos yesterday at Twitter—
"Plato's code cracked? http://bit.ly/ad6k1S
Fascinating if not a hoax or hype."
The story that Paulos linked to is about a British
academic who claims to have found some
symbolism hidden in Plato's writings by
splitting each into 12 parts and correlating
the 12 parts with semitones of a musical scale.
I prefer a different approach to Plato that is
related to the following hoax and hype—
HOAX:
From Dan Brown's novel Angels & Demons (2000)—
HYPE:
This four-elements diamond summarizes the classical
four elements and four qualities neatly, but some scholars
might call the figure "hype" since it deals with an academically
disreputable subject, alchemy, and since its origin is unclear.
For the four elements' role in some literature more respectable
than Dan Brown's, see Poetry's Bones.
Although an author like Brown might spin the remarks
below into a narrative— The Plato Code — they are
neither hoax nor hype.
NOT HOAX:
NOT HYPE:
For related non-hoax, non-hype remarks, see
The Rational Enterprise: Logos in Plato's Theaetetus,
by Rosemary Desjardins.
Those who prefer hoax and hype in their philosophy may consult
the writings of, say, Barbara Johnson, Rosalind Krauss, and—
in yesterday's NY Times's "The Stone" column— Nancy Bauer.
— The New York Times
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Thursday, February 12, 2009
Thursday February 12, 2009
Headliners
Today, many observe
the 200th anniversary
of the birth of two
noted philosophers
of death:
Charles Darwin and
Abraham Lincoln.
A fitting headline:
FAUST VIVIFIES DEATH
(Harvard Crimson ,
February 7, 2008)
Happy birthday,
Cotton Mather.
Robert Stone,
A Flag for Sunrise :
"Our secret culture is as frivolous as a willow on a tombstone. It's a wonderful thing– or it was. It was strong and dreadful, it was majestic and ruthless. It was a stranger to pity. And it's not for sale, ladies and gentlemen."
Comments Off on Thursday February 12, 2009
Monday, September 8, 2008
Monday September 8, 2008
Related material:
Tuesday, July 31, 2007Aesthetics for JesuitsJoke The Guardian, July 26, “… inspired satire, laced with Jewish and Christian polemics, sparkling wit and dazzlingly simple effects. For Golgotha a stagehand brings on three crosses. ‘Just two,’ says Jay. ‘The boy is bringing his own.’ Tabori often claimed that the joke was the most perfect literary form.” |
Update at noon,
Sept. 9, 2008:
Tabori, a Jew from Hungary
and former screenwriter
(“No Exit“), died at 93
on July 23, 2007.
For related material on
another Jew from Hungary
click on the black monolith
(also known as
the Halmos tombstone).
Comments Off on Monday September 8, 2008
Sunday, July 6, 2008
Sunday July 6, 2008
"Hancock" Powers to the Top
of July Fourth Box Office
— This evening's online
New York Times
|
New York Lottery
Sunday, July 6, 2008:
Mid-day 307
Evening 921 |
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Symbols:
|
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"The consolations of form,
the clean crystalline work"
— Iris Murdoch,
"Against Dryness" |
Will Smith
on Chess
Will Smith
"A devoted father, Smith passes on his philosophy of life to his children through chess, among other things.
'My father taught me how to play chess at seven and introduced beautiful concepts that I try to pass on to my kids. The elements and concepts of life are so perfectly illustrated on a chess board. The ability to accurately assess your position is the key to chess, which I also think is the key to life.'
He pauses, searching for an example. 'Everything you do in your life is a move. You wake up in the morning, you strap on a gun, and you walk out on the street– that's a move. You've made a move and the universe is going to respond with its move.
'Whatever move you're going to make in your life to be successful, you have to accurately access the next couple of moves– like what's going to happen if you do this? Because once you've made your move, you can't take it back. The universe is going to respond.'
Smith has just finished reading The Alchemist, by the Brazilian writer Paulo Coelho: 'It says the entire world is contained in one grain of sand, and you can learn everything you need to learn about the entire universe from that one grain of sand. That is the kind of concept I'm teaching my kids.'"
Related material:
Comments Off on Sunday July 6, 2008
Friday, June 6, 2008
Friday June 6, 2008
The Dance of Chance
"Harvard seniors have
every right to demand a
Harvard-calibre speaker."
— Adam Goldenberg in
The Harvard Crimson
"Look down now, Cotton Mather"
— Wallace Stevens,
Harvard College
Class of 1901
For Thursday, June 5, 2008,
commencement day for Harvard's
Class of 2008, here are the
Pennsylvania Lottery numbers:
Mid-day 025
Evening 761
Thanks to the late
Harvard professor
Willard Van Orman Quine,
the mid-day number 025
suggests the name
"Isaac Newton."
(For the logic of this suggestion,
see On Linguistic Creation
and Raiders of the Lost Matrix.)
Thanks to Google search, the
name of Newton, combined with
Thursday's evening number 761,
suggests the following essay:
PHILOSOPHY OF SCIENCE:
|
What can a non-scientist add?
Perhaps the Log24 entries for
the date of Koshland's death:
The Philosopher's Stone
and The Rock.
Or perhaps the following
observations:
On the figure of 25 parts
discussed in
"On Linguistic Creation"–
"The Moslems thought of the
central 1 as being symbolic
of the unity of Allah. "
— Clifford Pickover
"At the still point,
there the dance is."
— T. S. Eliot,
Harvard College
Class of 1910
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Wednesday, July 25, 2007
Wednesday July 25, 2007
The Comedy of
George Tabori
George Tabori
From AP “Obituaries in the News”–
Filed with The New York Times
at 11:16 p.m. ET July 24, 2007–
Filed with The New York Times
at 11:16 p.m. ET July 24, 2007–
George Tabori
“BERLIN (AP) — Hungarian-born playwright and director George Tabori, a legend in Germany’s postwar theater world whose avant-garde works confronted anti-Semitism, died Monday [July 23, 2007]. He was 93.
Tabori, who as recently as three years ago dreamed of returning to stage to play the title role in Shakespeare’s ‘King Lear,’ died in his apartment near the theater, the Berliner Ensemble said Tuesday, noting that friends and family had accompanied him through his final days. No cause of death was given.
Born into a Jewish family in Budapest on May 24, 1914, Tabori fled in 1936 to London, where he started working for the British Broadcasting Corp., and became a British citizen. His father, and other members of his family, were killed at Auschwitz.
Tabori moved to Hollywood in the 1950s, where he worked as a scriptwriter, most notably co-writing the script for Alfred Hitchcock’s 1953 film, ‘I Confess.’
He moved to Germany in the 1970s and launched a theater career that spanned from acting to directing to writing. He used sharp wit and humor in his plays to examine the relationship between Germany and the Jews, as well as attack anti-Semitism.
Among his best-known works are ‘Mein Kampf,’ set in the Viennese hostel where Adolf Hitler lived from 1910-1913, and the ‘Goldberg Variations,’ both dark farces that poke fun at the Nazis.”
From Year of Jewish Culture:
“The year 2006 marks the 100th anniversary of the establishment of the Jewish Museum in Prague.”
From the related page Programme (October-December):
“Divadlo v Dlouhé
George Tabori: GOLDBERGOVSKÉ VARIACE / THE GOLDBERG VARIATIONS, 19 October, 7 p.m. A comedy on creation and martyrdom.”
|
From Log24 on the date of 
The above is from Variable Resolution 4–k Meshes: Concepts and Applications (pdf), by Luiz Velho and Jonas Gomes. See also Symmetry Framed |
|
Theme (Plato, Meno)
Click on “variations” above |
Comments Off on Wednesday July 25, 2007
Monday, July 23, 2007
Monday July 23, 2007
Today’s Birthday:
Daniel Radcliffe
(“Harry Potter”)
Daniel Radcliffe
(“Harry Potter”)
Theme
(Plato, Meno)
Click on picture for details.
“A diamond jubilance
beyond the fire,
That gives its power
to the wild-ringed eye”
— Wallace Stevens,
“The Owl in the Sarcophagus”
Comments Off on Monday July 23, 2007
Thursday, July 19, 2007
Thursday July 19, 2007
Death Flight
Lord Voldemort (in French vol de mort meaning “flight of death” or “steals of/in death,” in Portuguese volta da morte meaning “return from death”) made his debut in Harry Potter and the Philosopher’s Stone.
— Wikipedia folk etymology; corrected, but may still contain errors.
Related material: Yesterday’s entries and the remarks from Porto Alegre, Brazil, quoted here on January 25, 2005.
Comments Off on Thursday July 19, 2007
Thursday July 19, 2007
Death Flight
Lord Voldemort (vol de mort meaning “flying in death,” or “steals of/in death”, or, more likely, ‘death flight’ in French. volta de morte in portuguese means return from the dead) made his debut in Harry Potter and the Philosopher’s Stone.
— Wikipedia
Comments Off on Thursday July 19, 2007
Thursday, June 21, 2007
Thursday June 21, 2007
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!"
"Only gradually did I discover
what the mandala really is:
'Formation, Transformation,
Eternal Mind's eternal recreation'"
what the mandala really is:
'Formation, Transformation,
Eternal Mind's eternal recreation'"
(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
"Borja dropped the mutilated book on the floor with the others. He was looking at the nine engravings and at the circle, checking strange correspondences between them.
"Pauli linked this symbolism
with the concept of automorphism."
'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.)
"Pauli linked this symbolism
with the concept of automorphism."
— 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."
Comments Off on Thursday June 21, 2007
Friday, November 10, 2006
Friday November 10, 2006
Today's
numbers:
numbers:
Today is the day that
Stanley found Livingstone.
Click on picture for details.
"Stone 588,
I presume?"
Related material:
This afternoon's entry
on color symmetry
and
Click on picture for details.
See, too, the following from
a Log24 entry of last Monday–
"To von Eschenbach, the Grail
was never really a material cup,
but a jewel like the
jewel in the lotus,
a symbol of enlightenment,
of something intangible
and always beyond reach."
— Arcadian Functor
was never really a material cup,
but a jewel like the
jewel in the lotus,
a symbol of enlightenment,
of something intangible
and always beyond reach."
— Arcadian Functor
— in this context:
"Philosophers ponder the idea
of identity: what it is to give
something a name
on Monday
and have it respond
to that name
on Friday…."
— Bernard Holland in
The New York Times
Monday, May 20, 1996
something a name
on Monday
and have it respond
to that name
on Friday…."
— Bernard Holland in
The New York Times
Monday, May 20, 1996
Comments Off on Friday November 10, 2006
Tuesday, October 24, 2006
Tuesday October 24, 2006
Another illustration
of the previous entry's concept of
a "critical mass" of weblog entries,
a concept reflected in
the saying
"You can't win the lottery
if you don't buy a ticket."
of the previous entry's concept of
a "critical mass" of weblog entries,
a concept reflected in
the saying
"You can't win the lottery
if you don't buy a ticket."
Mathematics and Narrative:
A Two-Part Invention
Here are today's
numbers from the
Keystone State:
Here is an interpretation
of those numbers:
of those numbers:
8/21 — Mathematics:
"The geometrization conjecture, also known as Thurston's geometrization conjecture, concerns the geometric structure of compact 3-manifolds. The geometrization conjecture can be considered an analogue for 3-manifolds of the uniformization theorem for surfaces. It was proposed by William Thurston in the late 1970s. It 'includes' other conjectures, such as the Poincaré conjecture and the Thurston elliptization conjecture."
The second sentence, in bold type, was added on 8/21 by yours truly. No deep learning or original thought was required to make this important improvement in the article; the sentence was simply copied from the then-current version of the article on Grigori Perelman (who has, it seems, proved the geometrization conjecture).
This may serve as an example of the "mathematics" part of the above phrase "Mathematics and Narrative" — a phrase which served, with associated links, as the Log24 entry for 8/21.
7/23 — Narrative:
"Each step in the story is a work of art, and the story as a whole is a sequence of episodes of rare beauty, a drama built out of nothing but numbers and imagination." –Freeman Dyson
This quotation appeared in the Log24 entry for 7/23, "Dance of the Numbers." What Dyson calls a "story" or "drama" is in fact mathematics. (Dyson calls the "steps" in the story "works of art," so it is clear that Dyson (a former student of G. H. Hardy) is discussing mathematical steps, not paragraphs in someone's account– perhaps a work of art, perhaps not– of mathematical history.) I personally regard the rhetorical trick of calling the steps leading to a mathematical result a "story" as contemptible vulgarization, but Dyson, as someone whose work (pdf) led to the particular result he is discussing, is entitled to dramatize it as he pleases.
For related material on mathematics, narrative, and vulgarization, click here.
The art of interpretation (applied above to a lottery) is relevant to narrative and perhaps also, in some sense, to the arts of mathematical research and exposition (if not to mathematics itself). This art is called hermeneutics.
For more on the subject, see the Stanford Encyclopedia of Philosophy article on Hans-Georg Gadamer, "the decisive figure in the development of twentieth-century hermeneutics."
See also the work of Msgr. Robert Sokolowski of the Catholic University of America, which includes
"Foreword" in Gian-Carlo Rota,
Indiscrete Thoughts,
Boston: Birkhäuser Verlag,
1996, xiii-xvii, and
"Gadamer's Theory of Hermeneutics" in
The Philosophy of Hans-Georg Gadamer,
edited by Lewis E. Hahn,
The Library of Living Philosophers, Vol. 24,
Chicago: Open Court Publishers,
1997, 223-34.
Comments Off on Tuesday October 24, 2006
Thursday, October 5, 2006
Thursday October 5, 2006
In Touch with God
(Title of an interview with
the late Paul Halmos, mathematician)
Since Halmos died on Yom Kippur, his thoughts on God may be of interest to some.
And, more simply,
April 28, 2004:
From a 1990 interview:
“What’s the best part of being a mathematician? I’m not a religious man, but it’s almost like being in touch with God when you’re thinking about mathematics. God is keeping secrets from us, and it’s fun to try to learn some of the secrets.”
I personally prefer Annie Dillard on God:
“… if Holy the Firm is matter at its dullest, Aristotle’s materia prima, absolute zero, and since Holy the Firm is in touch with the Absolute at base, then the circle is unbroken. And it is…. Holy the Firm is in short the philosopher’s stone.”
Some other versions of
the philosopher’s stone:
April 28, 2004:
This last has the virtue of
being connected with Halmos
via his remarks during the
“In Touch with God” interview:
“…at the root of all deep mathematics there is a combinatorial insight… the really original, really deep insights are always combinatorial….”
“Combinatorics, the finite case, is where the genuine, deep insight is.”
“Combinatorics, the finite case, is where the genuine, deep insight is.”
See also the remark of Halmos that serves as an epigraph to Theme and Variations.
Finally, it should be noted that
the 4×9 black rectangle
the 4×9 black rectangle
has also served
at least one interpreter
as a philosopher’s stone,
and is also the original
“Halmos tombstone.”
Comments Off on Thursday October 5, 2006
Thursday, August 31, 2006
Thursday August 31, 2006
Party Phone
for Van Morrison
on his birthday
A few words for M.C.C.:
 |
Honey Blonde She's as sweet as |
From March 24, 2006:
|
Life of the Party From Alfred Bester's Related material: "… it's going to be — Anne McCaffrey,
|
"It's not the twilight zone no,
it's not the twilight zone
Yes it's just a party phone,
pure
honeycomb,
honeycomb,
honeycomb"
— Van Morrison, "Twilight Zone,"
in The Philosopher's Stone
Comments Off on Thursday August 31, 2006
Saturday, August 26, 2006
Saturday August 26, 2006
"Alcatraz, Spanish for pelican, was named Isla de los Alcatraces after the birds that were the island's only inhabitants." —Bay City Guide
Related material
Thomas Kuhn's "Pelican Brief":
"… the Philosopher’s Stone was a psychic rather than a physical product. It symbolized one’s Self…."
"The formula presents a symbol of the self…."
"… Jung presents a diagram to illustrate the dynamic movements of the self…."
…the movement of
a self in the rock…
— Wallace Stevens:
The Poems of Our Climate,
by Harold Bloom,
Cornell U. Press, 1977
Comments Off on Saturday August 26, 2006
Wednesday, July 26, 2006
Wednesday July 26, 2006
Partitions,
continued
continued
"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
"… a drama built out of nothing
but numbers and imagination"
but numbers and imagination"
— 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
Today's other birthday:
Mick Jagger
Mick Jagger
Comments Off on Wednesday July 26, 2006
Saturday, March 11, 2006
Saturday March 11, 2006
|
Holy the Firm
by Annie Dillard Esoteric Christianity, I read, posits a substance. It is a created substance, lower than metals and minerals on a “spiritual scale” and lower than salts and earths, occurring beneath salts and earths in the waxy deepness of planets, but never on the surface of planets where men could discern it; and it is in touch with the Absolute, at base. In touch with the Absolute! At base. The name of this substance is Holy the Firm. These are only ideas, by the single handful. Lines, lines, and their infinite points! Hold hands and crack the whip, and yank the Absolute out of there and into the light, God pale and astounded, spraying a spiral of salts and earths, God footloose and flung. And cry down the line to his passing white ear, “Old Sir! Do you hold space from buckling by a finger in its hole? O Old! Where is your other hand?” His right hand is clenching, calm, round the exploding left hand of Holy the Firm. — Annie Dillard, Holy the Firm, Harper & Row 1977, reissued by Harper Perennial Library in 1988 as a paperback, pp. 68-71. |
Comments Off on Saturday March 11, 2006
Saturday, December 24, 2005
Saturday December 24, 2005
The Stone of Power
“Others say it is a stone that posseses mysterious powers…. often depicted as a dazzling light. It’s a symbol representing power, a source of immense energy. It nourishes, heals, wounds, blinds, strikes down…. Some have thought of it as the philosopher’s stone of the alchemists….”
— 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)
Comments Off on Saturday December 24, 2005
Sunday, February 20, 2005
Sunday February 20, 2005
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)
Comments Off on Sunday February 20, 2005
Thursday, February 17, 2005
Thursday February 17, 2005
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 ?
On the Lapis Philosophorum,
the Philosophers' Stone –
"'What is this Stone?' Chloe asked….
'…It is told that, when the Merciful One
made the worlds, first of all He created
that Stone and gave it to the Divine One
whom the Jews call Shekinah,
and as she gazed upon it
the universes arose and had being.'"
– Many Dimensions,
by Charles Williams, 1931
(Eerdmans paperback,
April 1979, pp. 43-44)
"The lapis was thought of as a unity
and therefore often stands for
the prima materia in general."
– Aion, by C. G. Jung, 1951
(Princeton paperback,
1979, p. 236)
"Its discoverer was of the opinion that
he had produced the equivalent of
the primordial protomatter
which exploded into the Universe."
– The Stars My Destination,
by Alfred Bester, 1956
(Vintage hardcover,
July 1996, p. 216)
"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)
See also
The Diamond Archetype.
For more on modal theology, see
Kurt Gödel's Ontological Argument
and
The Ontological Argument
from Anselm to Gödel.
Sunday, January 9, 2005
Sunday January 9, 2005
Light at Bologna
“Others say it is a stone that posseses mysterious powers…. often depicted as a dazzling light. It’s a symbol representing power, a source of immense energy. It nourishes, heals, wounds, blinds, strikes down…. Some have thought of it as the philosopher’s stone of the alchemists….”
— Foucault’s Pendulum
by Umberto Eco,
Professor of Semiotics at
Europe’s oldest university,
the University of Bologna.
The Club Dumasby Arturo Perez-Reverte
|
Eclogues: Eight Stories
by Guy Davenport
Johns Hopkins paperback, 1993, page 127 —
Lo Splendore della Luce a Bologna, VI:
“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.”
The Discovery of Luminescence:
The Bolognian Stone
Bologna, 16th Century
“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
|
Comments Off on Sunday January 9, 2005
Thursday, September 4, 2003
Thursday September 4, 2003
Epitaphs
The late philosopher Donald Davidson (see previous entry) had a gift for titles. For example:
“The Folly of Trying to Define Truth”
(Journal of Philosophy June 1996, pp. 263-278) and
“A Nice Derangement of Epitaphs”
(In R. Grandy and R. Warner (eds.), Philosophical Grounds of Rationality, Oxford: Oxford University Press, 1986).
For my thoughts on the former, see
Pilate, Truth, and Friday the Thirteenth,
The Diamond Theory of Truth, and
Sept. 2, 2002 (Laurindo Almeida’s Birthday).
For my thoughts on the latter, see
Happy Birthday, Mary Shelley (2003),
For Mary Shelley’s Birthday (2002),
and, in honor of J. R. R. Tolkien, who died on the date September 2,
at Wikipedia Encyclopedia, which contains the following:
“J. R. R. Tolkien is buried next to his wife, and on their tombstone the names ‘Beren’ and ‘Luthien’ are engraved, a fact that sheds light on the love story of Beren and Luthien which is recorded in several versions in his works.”
A nice derangement, indeed.
Comments Off on Thursday September 4, 2003
Thursday September 4, 2003
Monolith
“Music can name the unnameable
and communicate the unknowable.”
— Quotation attributed to Leonard Bernstein
“Finally we get to Kubrick’s ultimate trick…. His secret is in plain sight…. The film is the monolith. In a secret that seems to never have been seen by anyone: the monolith in the film has the same exact dimensions as the movie screen on which 2001 was projected.”
— Alchemical Kubrick 2001, by Jay Weidner
My entry of Saturday, August 30,
included the following illustration:
My entry of Monday, September 1,
concluded with the black monolith.
“There is little doubt that the black monolith
in 2001 is the Philosopher’s Stone.”
— Alchemical Kubrick 2001, by Jay Weidner
The philosopher Donald Davidson
died on Saturday, August 30.
The New York Times says that as an undergraduate, Davidson “persuaded Harvard to let him put on ‘The Birds’ by Aristophanes and played the lead, Peisthetairos, which meant memorizing 700 lines of Greek. His friend and classmate Leonard Bernstein, with whom he played four-handed piano, wrote an original score for the production.”
Perhaps they are still making music together.
Comments Off on Thursday September 4, 2003
Saturday, June 14, 2003
Saturday June 14, 2003
 |
Indiana Jones |
In memory of Bernard Williams,
Oxford philosopher, who died Tuesday, June 10, 2003.
“…in… Truth and Truthfulness [September, 2002], he sought to speak plainly, and took on the post-modern, politically correct notion that truth is merely relative…”
“People have always longed for truths about the world — not logical truths, for all their utility; or even probable truths, without which daily life would be impossible; but informative, certain truths, the only ‘truths’ strictly worthy of the name. Such truths I will call ‘diamonds’; they are highly desirable but hard to find….
A new epistemology is emerging to replace the Diamond Theory of truth. I will call it the ‘Story Theory’ of truth: There are no diamonds. People make up stories about what they experience. Stories that catch on are called ‘true.’ The Story Theory of truth is itself a story that is catching on. It is being told and retold, with increasing frequency, by thinkers of many stripes…. My own viewpoint is the Story Theory….”
— Richard J. Trudeau, The Non-Euclidean Revolution, Birkhauser Boston, 1987
Today is the feast day of Saint Jorge Luis Borges (b. Buenos Aires, August 24, 1899 – d. Geneva, June 14, 1986).
From Borges’s “The Aleph“:
“The Faithful who gather at the mosque of Amr, in Cairo, are acquainted with the fact that the entire universe lies inside one of the stone pillars that ring its central court…. The mosque dates from the seventh century; the pillars come from other temples of pre-Islamic religions…. Does this Aleph exist in the heart of a stone?”
(“Los fieles que concurren a la mezquita de Amr, en el Cairo, saben muy bien que el universo está en el interior de una de las columnas de piedra que rodean el patio central…. la mezquita data del siglo VII; las columnas proceden de otros templos de religiones anteislámicas…. ¿Existe ese Aleph en lo íntimo de una piedra?”)
From The Hunchback of Notre Dame:
Un cofre de gran riqueza
Hallaron dentro un pilar,
Dentro del, nuevas banderas
Con figuras de espantar.*
* A coffer of great richness
In a pillar’s heart they found,
Within it lay new banners,
With figures to astound.
See also the figures obtained by coloring and permuting parts of the above religious symbol.
Lena Olin and Harrison Ford
in “Hollywood Homicide“
Sunday, September 15, 2002
Sunday September 15, 2002
Evariste Galois and
The Rock That Changed Things
An article in the current New York Review of Books (dated Sept. 26) on Ursula K. Le Guin prompted me to search the Web this evening for information on a short story of hers I remembered liking. I found the following in the journal of mathematician Peter Berman:
- A Fisherman of the Inland Sea, Ursula K. Le Guin, 1994:
A book of short stories. Good, entertaining. I especially liked “The Rock That Changed Things.” This story is set in a highly stratified society, one split between elite and enslaved populations. In this community, the most important art form is a type of mosaic made from rocks, whose patterns are read and interpreted by scholars from the elite group. The main character is a slave woman who discovers new patterns in the mosaics. The story is slightly over-the-top but elegant all the same.
I agree that the story is elegant (from a mathematician, a high compliment), so searched Berman’s pages further, finding this:
between The French Mathematician (a novel about Galois) and Harry Potter and the Sorcerer’s Stone.
My own version of the Philosopher’s Stone (the phrase used instead of “Sorcerer’s Stone” in the British editions of Harry Potter) appears in my profile picture at top left; see also the picture of Plato’s diamond figure in my main math website. The mathematics of finite (or “Galois”) fields plays a role in the underlying theory of this figure’s hidden symmetries. Since the perception of color plays a large role in the Le Guin story and since my version of Plato’s diamond is obtained by coloring Plato’s version, this particular “rock that changes things” might, I hope, inspire Berman to extend his table to include Le Guin’s tale as well.
Even the mosaic theme is appropriate, this being the holiest of the Mosaic holy days.
Dr. Berman, G’mar Chatimah Tova.