… A Mantra with Benefits
Monday, October 14, 2024
Sunday, January 21, 2024
Intake Manifold . . .
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See More Glass
A story today about a new Rose Glass film at Sundance
suggests a review —
See also today's previous post and other posts tagged Verwandlungslehre.
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Sunday, December 31, 2023
Cuaderno for a Pale King
"The King turned pale, and shut his notebook hastily."
— Alice in Wonderland , quoted here on December 22.
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Thursday, December 21, 2023
“The Center Cannot Hold” — Yeats
"… Drei Ecken hat mein Hut " — Song lyric
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Mutternacht
"Ich bin ein Teil des Teils, der anfangs alles war
Ein Teil der Finsternis, die sich das Licht gebar
Das stolze Licht, das nun der Mutter Nacht
Den alten Rang, den Raum ihr streitig macht,
Und doch gelingt’s ihm nicht, da es, so viel es strebt,
Verhaftet an den Körpern klebt.
Von Körpern strömt’s, die Körper macht es schön,
Ein Körper hemmt’s auf seinem Gange;
So, hoff ich, dauert es nicht lange,
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"The title of the book … is taken from a speech by Mephistopheles in Goethe’s Faust. As translated by Carlyle F. MacIntyre (New Directions, 1941), the speech is this: I am a part of the part that at first was all, part of the darkness that gave birth to light, that supercilious light which now disputes with Mother Night her ancient rank and space, and yet can not succeed; no matter how it struggles, it sticks to matter and can’t get free. Light flows from substance, makes it beautiful; solids can check its path, so I hope it won’t be long till light and the world’s stuff are destroyed together."
— Vonnegut, Kurt. Mother Night: A Novel |
Mutternacht , as opposed to Mutter Nacht , is tonight,
the night of December 20-21, Winter Solstice Eve.
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Wednesday, December 20, 2023
For the Circle Girl
" I think I just like saying 'intake manifold.' " — Emma Watson in "The Circle."
"The manifold that Heraclitus wishes to communicate is a dense, multi-
dimensional complex of ideas and experiences, but speech and writing are
linear. It would be very inefficient to try to communicate with precision the
multidimensional complexity of such a manifold by a simple, literal linear
description."
— Word and Flux, by Bruce J. MacLennan,
p. 357 of the January 2, 2021, version.
See also MacLennan in a Log24 post of Christmas Eve, 2012.
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Sunday, December 17, 2023
Thursday, December 14, 2023
For a Small Language Model: “771, My Dear Watson.”
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Friday, May 5, 2023
The Singularity Speaks
"Extremely elementary," my dear Watson.
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Sunday, December 18, 2022
“Square Round” — Ulysses, end of Ch. 17
Circle and Square at the Court of King Minos —
Harmonic analysis based on the circle involves the
circular functions. Dyadic harmonic analysis involves …
For some related history, see (for instance) . . .
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Saturday, December 10, 2022
Sunday, April 10, 2022
“Program or be programmed” — Douglas Rushkoff
For the Unicorn School —
<time class="_1o9PC"
datetime="2022-04-10T06:41:25.000Z"
title="Apr 10, 2022">4 hours ago
</time>
From posts tagged Unicorn Language —
Some will prefer the Dragon School . . .
of Tom Hiddleston, Emma Watson, and Humphrey Carpenter.
"National Unicorn Day" was yesterday . Today's mythical creature —
the villainous spymaster of The Eiger Sanction , Yurasis Dragon.
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Friday, August 20, 2021
Diamond Brackets*
For more on the phrase "diamond brackets," see the post
Artistic Style of July 24, 2018.
This was the dies natalis (in the Catholic sense) of philosophy
professor Garth L. Kemerling.
From Kemerling's internet "Philosophy Pages" —
"First, it must be possible in principle to arrange and organize
the chaos of our many individual sensory images by tracing
the connections that hold among them. This Kant called
the synthetic unity of the sensory manifold.
Second, it must be possible in principle for a single subject
to perform this organization by discovering the connections
among perceived images. This is satisfied by what Kant called
the transcendental unity of apperception."
Related Log24 phrases —
"Intake Manifold" and "Bulk Apperception."
* See also Bracketing (phenomenology) in Wikipedia.
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Monday, September 9, 2019
A Word of Warning
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Monday, July 30, 2018
Accio Watson, Continued*
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Friday, July 14, 2017
Squares
Box-style I Ching, January 6, 1989 —
(Click on images for background.)
Detail:
See also yesterday's illustration of
the 1965 paperback edition
of Whittaker and Watson …
Detail:
.
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Thursday, July 13, 2017
Knowing
"Knowing is good … but knowing everything is better."
— Tom Hanks in "The Circle"
"OK …" — The Singularity
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Monday, December 24, 2012
Eternal Recreation
Memories, Dreams, Reflections
by C. G. Jung
Recorded and edited By Aniela Jaffé, translated from the German
by Richard and Clara Winston, Vintage Books edition of April 1989
From pages 195-196:
"Only gradually did I discover what the mandala really is:
'Formation, Transformation, Eternal Mind's eternal recreation.'*
And that is the self, the wholeness of the personality, which if all
goes well is harmonious, but which cannot tolerate self-deceptions."
* Faust , Part Two, trans. by Philip Wayne (Harmondsworth,
England, Penguin Books Ltd., 1959), p. 79. The original:
… Gestaltung, Umgestaltung,
Des ewigen Sinnes ewige Unterhaltung….
Jung's "Formation, Transformation" quote is from the realm of
the Mothers (Faust , Part Two, Act 1, Scene 5: A Dark Gallery).
The speaker is Mephistopheles.
See also Prof. Bruce J. MacLennan on this realm
in a Web page from his Spring 2005 seminar on Faust:
"In alchemical terms, F is descending into the dark, formless
primary matter from which all things are born. Psychologically
he is descending into the deepest regions of the
collective unconscious, to the source of life and all creation.
Mater (mother), matrix (womb, generative substance), and matter
all come from the same root. This is Faust's next encounter with
the feminine, but it's obviously of a very different kind than his
relationship with Gretchen."
The phrase "Gestaltung, Umgestaltung " suggests a more mathematical
approach to the Unterhaltung . Hence…
Part I: Mothers
"The ultimate, deep symbol of motherhood raised to
the universal and the cosmic, of the birth, sending forth,
death, and return of all things in an eternal cycle,
is expressed in the Mothers, the matrices of all forms,
at the timeless, placeless originating womb or hearth
where chaos is transmuted into cosmos and whence
the forms of creation issue forth into the world of
place and time."
— Harold Stein Jantz, The Mothers in Faust:
The Myth of Time and Creativity ,
Johns Hopkins Press, 1969, page 37
Part II: Matrices
Part III: Spaces and Hypercubes
Click image for some background.
Part IV: Forms
Forms from the I Ching :
Click image for some background.
Forms from Diamond Theory :
Click image for some background.
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Friday, March 23, 2012
Embedding the Stone
"Imbedding the God character in a holy book's very detailed narrative
and building an entire culture around this narrative
seems by itself to confer a kind of existence on Him."
— John Allen Paulos in the philosophy column "The Stone,"
New York Times online, Oct. 24, 2010
A related post from Log24 later that year—
Sunday, November 28, 2010
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"Next come the crown of thorns and Jesus' agonized crawl across the stage,
bearing the weight of his own crucifix. And at last, after making
yet another entrance, Mr. Nolan strikes the pose immortalized
in centuries of art, clad in a demure loincloth, arms held out to his sides,
one leg artfully bent in front of the other, head hanging down
in tortured exhaustion. Gently spotlighted, he rises from the stage
as if by magic, while a giant cross, pulsing with hot gold lights,
descends from above to meet him. Mr. Lloyd Webber's churning guitar rock
hits a climactic note, and the audience erupts in excited applause."
— Charles Isherwood, review of "Jesus Christ Superstar" in today's New York Times
Other remarks on embedding —
Part I
Review of a new book on linguistics, embedding, and a South American tribe—
"Imagine a linguist from Mars lands on Earth to survey the planet's languages…."
— Chronicle of Higher Education , March 20, 2012
Part II
The Embedding , by Ian Watson (Review of a 1973 novel from Shakespeare's birthday, 2006)
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Friday, March 16, 2012
For the Clueless
"And she provided him besides with a ball of thread,
bidding him to fasten the end of it to the entrance
of the Labyrinth, and unwind it as he went in, that
it might serve him as a clue to find his way out again."
— "Theseus and Ariadne," by Charles Morris
From "Ariadne's Clue," a post of March 1 last year—
The Watson here is not Emma, but Victor—
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Monday, October 25, 2010
The Embedding*
A New York Times "The Stone" post from yesterday (5:15 PM, by John Allen Paulos) was titled—
Stories vs. Statistics
Related Google searches—
"How to lie with statistics"— about 148,000 results
"How to lie with stories"— 2 results
What does this tell us?
Consider also Paulos's phrase "imbedding the God character." A less controversial topic might be (with the spelling I prefer) "embedding the miraculous." For an example, see this journal's "Mathematics and Narrative" entry on 5/15 (a date suggested, coincidentally, by the time of Paulos's post)—
* Not directly related to the novel The Embedding discussed at Tenser, said the Tensor on April 23, 2006 ("Quasimodo Sunday"). An academic discussion of that novel furnishes an example of narrative as more than mere entertainment. See Timothy J. Reiss, "How can 'New' Meaning Be Thought? Fictions of Science, Science Fictions," Canadian Review of Comparative Literature , Vol. 12, No. 1, March 1985, pp. 88-126. Consider also on this, Picasso's birthday, his saying that "Art is a lie that makes us realize truth…."
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Thursday, October 24, 2002
Thursday October 24, 2002
A (Very Brief) Course of
Modern Analysis
In honor of today's anniversary of the 1873 birth of Edmund Taylor Whittaker, here are some references to a topic that still interests some mathematicians of today.
From A Course of Modern Analysis, by E. T. Whittaker and G. N. Watson, Fourth Edition, Cambridge University Press, 1927, reprinted 1969:
Section 20.7 "…the fact, that x and y can be expressed as one-valued functions of the variable z, makes this variable z of considerable importance… z is called the uniformizing variable of the equation…. When the genus of the algebraic curve f(x,y) = 0 is greater than unity, the uniformisation can be effected by means of what are known as automorphic functions. Two classes of such functions of genus greater than unity have been constructed, the first by Weber…(1886), the second by Whittaker…(1898)…."
The topic of uniformisation of algebraic curves has appeared frequently lately in connection with Wiles's attack on Fermat's Last Theorem. See, for instance, Lang's 1995 AMS Notices article
"Shimura's… insight was that the ordinary modular functions for a congruence subgroup of SL2(Z) suffice to uniformize elliptic curves defined over the rationals."
"The property of an elliptic curve [over Q] of being parameterized by modular functions is one way of defining a modular elliptic curve, and the Taniyama-Shimura conjecture asserts that every elliptic curve is modular."
For a deeper discussion of uniformisation in the context of Wiles's efforts, see "Elliptic curves and p-adic uniformisation," by H. Darmon, 1999.
For a more traditional approach to uniformisation, see "On the uniformisation of algebraic curves," by Yu. V. Brezhnev (24 May, 2002), which cites two of Whittaker's papers on automorphic functions (from 1898 and 1929) and a 1930 paper, "The uniformisation of algebraic curves," by J. M. Whittaker, apparently E. T. Whittaker's son.
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