Thursday, December 9, 2021
Wednesday, July 8, 2015
Threshold
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Tuesday, October 1, 2024
Blue Review
From this journal on September 24, 2012—
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"A single self-transcendence" — Aldous Huxley
From an anonymous author at the website
"This little story… has that climactic moment of Kill Devil Hills also appears in a 1983 film—
"Suppose it were possible to transfer
— Trailer for "Brainstorm" (1983), |
"… that 'good' threshold . . . ." — See Threshold in this journal.
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Thursday, December 16, 2021
Overarching Story
Six uses of "overarching" in an Aeon essay today —
- "an overarching story of life"
- "the overarching themes of thresholds and energy flows"
- "the overarching stages of human history"
- "an overarching evolutionary perspective"
- "overarching directional development"
- "the overarching laws of science"
See also "overarching" in this journal.
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Thursday, August 12, 2021
A Square Crystal Paperweight
Friday March 31, 2006
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Tuesday, May 26, 2020
Introduction to Cyberspace
Or approaching.
On the Threshold:
Click the search result above for the July 1982 Omni
story that introduced into fiction the term "cyberspace."
Part of a page from the original Omni version —
For some other kinds of space, see my notes from the 1980's.
Some related remarks on space (and illustrated clams) —
— George Steiner, "A Death of Kings," The New Yorker ,
September 7, 1968, pp. 130 ff. The above is from p. 133.
See also Steiner on space, algebra, and Galois.
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Wednesday, October 21, 2015
Liminal Figures
"On the threshold of heaven, the figures in the street…."
On an artist who reportedly died last Thursday, October 15 —
See yesterday's post Liminal for a different sort of figure.
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Monday, October 13, 2014
Raiders of the Lost Theorem
(Continued from Nov. 16, 2013.)
The 48 actions of GL(2,3) on a 3×3 array include the 8-element
quaternion group as a subgroup. This was illustrated in a Log24 post,
Hamilton’s Whirligig, of Jan. 5, 2006, and in a webpage whose
earliest version in the Internet Archive is from June 14, 2006.
One of these quaternion actions is pictured, without any reference
to quaternions, in a 2013 book by a Netherlands author whose
background in pure mathematics is apparently minimal:
In context (click to enlarge):
Update of later the same day —
Lee Sallows, Sept. 2011 foreword to Geometric Magic Squares —
“I first hit on the idea of a geometric magic square* in October 2001,**
and I sensed at once that I had penetrated some previously hidden portal
and was now standing on the threshold of a great adventure. It was going
to be like exploring Aladdin’s Cave. That there were treasures in the cave,
I was convinced, but how they were to be found was far from clear. The
concept of a geometric magic square is so simple that a child will grasp it
in a single glance. Ask a mathematician to create an actual specimen and
you may have a long wait before getting a response; such are the formidable
difficulties confronting the would-be constructor.”
* Defined by Sallows later in the book:
“Geometric or, less formally, geomagic is the term I use for
a magic square in which higher dimensional geometrical shapes
(or tiles or pieces ) may appear in the cells instead of numbers.”
** See some geometric matrices by Cullinane in a March 2001 webpage.
Earlier actual specimens — see Diamond Theory excerpts published in
February 1977 and a brief description of the original 1976 monograph:
“51 pp. on the symmetries & algebra of
matrices with geometric-figure entries.”
— Steven H. Cullinane, 1977 ad in
Notices of the American Mathematical Society
The recreational topic of “magic” squares is of little relevance
to my own interests— group actions on such matrices and the
matrices’ role as models of finite geometries.
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Saturday, April 7, 2012
The Void
(Continued from March 10, 2012)
An inaccuracy in a passage linked to yesterday—
“The created universe, the whole of things, is,
in words from Joyce’s Ulysses , ‘predicated on the void.'”
The “predicated” phrase seems to be absent from Ulysses .
Joyce does, however, have the following (from ricorso.net)—
| “William Blake” (March 1912) – cont.: ‘Armed with this two-edged sword, the art of Michaelangelo and the revelations of Swedenborg, Blake killed the dragon of experience and natural wisdom, and, by minimising space and time and denying the existence of memory and the senses, he tried to paint his works on the void of the divine bosom. [See note, infra.]To him, each moment shorter than a pulse-beat was equivalent in its duration to six thousand years, because in such an infinitely short instant the work of the poet is conceived and born. To him, all space larger than a red globule of human blood was visionary, created by the hammer of Los, while in a space smaller than a globule of blood we approach eternity, of which our vegetable world is but a shadow. Not with the eye, then, but beyond the eye, the soul and the supreme move must look, because the eye, which was born in the night while the soul was sleeping in rays of light, will also die in the night. […] The mental process by which Blake arrives at the threshold of the infinite is a similar process. Flying from the infinitely small to the infinitely large, from a drop of blood to the universe of stars, his soul is consumed by the rapidity of flight, and finds itself renewed and winged and immortal on the edge of th dark ocean of God. And althought he based his art on such idealist premises, convinced that eternity was in love with the products of time, this sons of God with the sons of [MS ends here].’ (Critical Writings, 1959, 1966 Edn., pp.221-22; quoted [in part] in Richard Ellmann, James Joyce, 1965 Edn., p.330.) [For full text, see RICORSO Library, “Major Authors”, via index, or direct.] Note – for “void” [supra] , cf. Stephen in “Scylla & Charybdis”: ‘Fatherhood […] is a mystical estate, an apostolic succession, from only begetter to only begotten. On that mystery and not on the madonna which the cunning Italian intellect flung to the mob of Europe the church is founded and founded irremovably because founded, like the world, macro- and microcosm, upon the void.’ (Ulysses, Penguin Edn. 1967, p.207; [my itals.].) |
Some academics may prefer a more leftist version of
“predicated on the void”—
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Sunday, June 5, 2011
Edifice Complex
"Total grandeur of a total edifice,
Chosen by an inquisitor of structures
For himself. He stops upon this threshold,
As if the design of all his words takes form
And frame from thinking and is realized."
— Wallace Stevens, "To an Old Philosopher in Rome"
The following edifice may be lacking in grandeur,
and its properties as a configuration were known long
before I stumbled across a description of it… still…
"What we do may be small, but it has
a certain character of permanence…."
— G.H. Hardy, A Mathematician's Apology
The Kummer 166 Configuration
as seen by Kantor in 1969— (pdf, 2.5 MB)
For some background, see Configurations and Squares.
For some quite different geometry of the 4×4 square that is
original with me, see a page with that title. (The geometry's
importance depends in part on its connection with the
Miracle Octad Generator (MOG) of R.T. Curtis. I of course
had nothing to do with the MOG's discovery, but I do claim credit
for discovering some geometric properties of the 4×4 square
that constitutes two-thirds of the MOG as originally defined .)
Related material— The Schwartz Notes of June 1.
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Friday, July 13, 2007
Friday July 13, 2007
Today’s birthday:
Harrison Ford is 65.
Harrison Ford is 65.
| “Three times the concentred self takes hold, three times The thrice concentred self, having possessed The object, grips it in savage scrutiny, Once to make captive, once to subjugate Or yield to subjugation, once to proclaim The meaning of the capture, this hard prize, Fully made, fully apparent, fully found.” — “Credences of Summer,” VII, |
“It was Plato who best expressed– who veritably embodied– the tension between the narrative arts and mathematics….
Plato clearly loved them both, both mathematics and poetry. But he approved of mathematics, and heartily, if conflictedly, disapproved of poetry. Engraved above the entrance to his Academy, the first European university, was the admonition: Oudeis ageometretos eiseto. Let none ignorant of geometry enter. This is an expression of high approval indeed, and the symbolism could not have been more perfect, since mathematics was, for Plato, the very gateway for all future knowledge. Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason. Mathematics is the threshold we cross to pass into the ideal, the truly real.”
— Rebecca Goldstein, Mathematics and the Character of Tragedy
Related material:
Previous entry,
entries of July 1, 2007,
and A Little Story
(9/30/06)
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Saturday, August 19, 2006
Saturday August 19, 2006
Metaphysical
Wonderlands
Wonderlands
"With no means to verify its truth, superstring theory, in the words of Burton Richter, director emeritus of the Stanford Linear Accelerator Center, may turn out to be 'a kind of metaphysical wonderland.' Yet it is being pursued as vigorously as ever, its critics complain, treated as the only game in town."
— "The Inelegant Universe," by George Johnson, in the Sept. 2006 Scientific American
Some may prefer metaphysics of a different sort:
"To enter Cervantes’s world, we cross a threshold that is Shakespearean and quixotic into a metaphysical wonderland where time expands to become space and vast vaulted distances bend back on themselves, where the threads of fiction and the strands of history shuttle back and forth in the great loom of the artist’s imagination."
As wonderlands go, I personally prefer Clive Barker's Weaveworld.
Wednesday, May 3, 2006
Wednesday May 3, 2006
Ontology Alignment
continued
continued
“Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason. Mathematics is the threshold we cross to pass into the ideal, the truly real.”
— Rebecca Goldstein,
Mathematics and
the Character of Tragedy
Pennsylvania Lottery:
The winning numbers
for Tuesday, May 2–
the feast of
St. Athanasius:
Mid-day 703
Evening 462
“You gotta be true to your code”
— Sinatra (see previous entry)
| Dewey Decimal Code:
703 The Arts: Related material: For the arts, see |
The numbers 703 and 462 are, in Goldstein’s phrase, “truly real.” However, their link to St. Athanasius and to the Spanish language is, as purveyors of fiction* say, “purely coincidental”– as is much of what makes life interesting.
“All persons living and dead are purely coincidental….”– Kurt Vonnegut, epigraph to Bagombo Snuff Box
* For instance,
David Auburn in Proof,
which also involves
Dewey decimal numbers
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Friday, March 31, 2006
Friday March 31, 2006
Women's History Month continues…
Ontology Alignment
"He had with him a small red book of Mao's poems, and as he talked he squared it on the table, aligned it with the table edge first vertically and then horizontally. To understand who Michael Laski is you must have a feeling for that kind of compulsion."
— Joan Didion in the
Saturday Evening Post,
Nov. 18, 1967 (reprinted in
Slouching Towards Bethlehem)
"Or were you," I said.
He said nothing.
"Raised a Catholic," I said.
He aligned a square crystal paperweight with the edge of his desk blotter.
— Joan Didion in
The Last Thing He Wanted,
Knopf, 1996
"It was Plato who best expressed– who veritably embodied– the tension between the narrative arts and mathematics….
Plato clearly loved them both, both mathematics and poetry. But he approved of mathematics, and heartily, if conflictedly, disapproved of poetry. Engraved above the entrance to his Academy, the first European university, was the admonition: Oudeis ageometretos eiseto. Let none ignorant of geometry enter. This is an expression of high approval indeed, and the symbolism could not have been more perfect, since mathematics was, for Plato, the very gateway for all future knowledge. Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason. Mathematics is the threshold we cross to pass into the ideal, the truly real."
— Rebecca Goldstein,
Mathematics and
the Character of Tragedy
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Tuesday, April 27, 2004
Tuesday April 27, 2004
Last Exit:
A Meditation for Poetry Month
Click on the picture below for details.
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Notes on the compiling of Only the Dead:
Today’s obituary of the author of Last Exit to Brooklyn suggested I look up Wolfe’s short story, “Only the Dead Know Brooklyn.” That story contained, near its end, a reference to drowning. Thoughts of drowning and of Brooklyn suggested (this being poetry month) Hart Crane’s classic The Bridge. When I looked for material on Crane on the Web, I found, to my considerable surprise, that today is the anniversary of Crane’s death.
As Wolfe says, apropos of Selby and Brooklyn,
“Red Hook! Jesus!”
As Crane says, apropos of Wolfe and the Brooklyn Bridge,
“Terrific threshold of the prophet’s pledge,
Prayer of pariah, and the lover’s cry….”
Unfortunately, the bridge is not for sale. However….
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Sunday, September 28, 2003
Sunday September 28, 2003
Spirit of East St. Louis
On Miles Davis and Philly Joe Jones:
Miles said to Jones, "I think this is it." Jones agreed having said of the group, "The first time we played together…we just looked around at each other and said, ‘hum here it is right here. We’ve got musical telepathy here. We have five people who always know what’s going to happen next.’" And those five people became legendary as the classic Miles Davis Quintet was baptized for its first time.
From The American Art Form:
While singing work songs, a leader would call out a phrase, and the rest of the people would answer. This is known as call and response. In Cindy Blackman's "Telepathy" , the lead saxophone who is playing the melody calls out a phrase, and another horn responds. In some jazz music, there is what is known as "trading 4's". This is when one instrument plays 4 measures, and then another plays 4 measures off what the first person played, and so on. This is a modern rendition of call and response.
See also
Desmond and Mulligan, Two of a Mind,
Google search, "musical telepathy,"
and a novel dealing with East St. Louis (where Miles Davis grew up) and telepathy,
The Hollow Man, by Dan Simmons.
From the jacket of The Hollow Man:
Jeremy Bremen has a secret. All his life he has been cursed with the unwanted ability to read minds. He can hear the secret thoughts behind the placid expressions of strangers, colleagues, and friends. Their dreams, their fears, their most secret desires are as intimate to him as his own. For years his wife, Gail, has served as a shield between Jeremy and the intrusive thoughts of those around him. Her presence has protected him from the outside world and allowed him to continue his work as one of the world's leading mathematicians. But now Gail is dying, her mind slipping slowly away, and Jeremy comes face-to-face with the horror of his own omniscience. Vulnerable and alone, he is suddenly exposed to a chaotic flood of others' thoughts, threatening to fill him with the world's pain and longing, to sweep away his very sanity. His mathematical studies have taken him to the threshold of knowledge and enabled him to map uncharted regions of the mind, to recognize the mind itself as a mirror of the universe…and to see in that mirror the fleeting reflection of the creator himself. But his studies taught him nothing at all about the death of the mind, about the loss of love and trust, and about the terrible loneliness of mortality. Now Jeremy is on the run – from his mind, from his past, from himself – hoping to find peace in isolation. Instead he witnesses an act of brutality that sends him on a treacherous odyssey across America, from a fantasy theme park to the mean streets of an uncaring city, from the lair of a killer to the gaudy casinos of Las Vegas, and at last to a sterile hospital room in St. Louis in search of the voice that is calling him to the secret of existence itself.