See the title in this journal. This review was suggested by
a phrase of Catherine Flynn:
Sunday, April 11, 2021
Space Itself
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Wednesday, December 21, 2016
Space Itself
Consider Stevens’s verse from “The Rock” (1954):
“That in which space itself is contained.”
Consider also Whitehead in 1906 —
"This is proved by the consideration
of a three dimensional geometry in which
there are only fifteen points."
— and Stevens on the sublime (1935):
"And the sublime comes down
To the spirit itself,
The spirit and space,
The empty spirit
In vacant space."
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Tuesday, July 16, 2013
Space Itself
"How do you get young people excited
about space? How do you get them interested
not just in watching movies about space,
or in playing video games set in space …
but in space itself?"
— Megan Garber in The Atlantic , Aug. 16, 2012
One approach:
"There is such a thing as a tesseract" and
Diamond Theory in 1937.
See, too, Baez in this journal.
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Sunday, April 14, 2013
Space Itself
From The Cambridge Companion to Wallace Stevens ,
John N. Serio, ed., "Stevens's Late Poetry," by B.J. Leggett,
pp. 62-75, an excerpt from page 70:
Click the above image for further details.
See also Nothingness and "The Rock" in this journal.
Further readings along these lines:
For pure mathematics, rather than theories of the physical world,
see the properties of the cube illustrated on the second (altered)
book cover above.
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Sunday, August 11, 2024
Double Duals
"That in which space itself is contained"
— Wallace Stevens
In the ninefold square,
projective-perspectivity duality
corresponds to
projective-correlation duality.
Illustrations —
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Thursday, May 23, 2024
Friday, April 12, 2024
Carmel Review
"Clint Eastwood, 93, appears frail but spirited
as he is seen in rare public appearance at
primatologist Dr. Jane Goodall event in Carmel"
— By Karen Ruiz For Dailymail.com
Published: 10:39 am EDT, 12 April 2024
The event, on Sunday, March 24, 2024, suggests a review —
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Monday, October 3, 2022
The Abstract and the Concrete
The above art by Steven H. Cullinane is not unrelated to
art by Josefine Lyche. Her work includes sculpted replicas
of the above abstract Platonic solids, as well as replicas of
my own work related to properties of the 4×6 rectangle above.
Symmetries of both the solids and the rectangle may be
viewed as permutations of parts — In the Platonic solids,
the parts are permuted by continuous rotations of space itself.
In the rectangle, the parts are permuted by non-continuous
transformations, as in the I Ching . . . i.e., by concrete illustrations
of change.
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Sunday, July 21, 2019
Space Speaks, Time Listens
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Sunday, September 9, 2018
Plan 9 Continues.
"The role of Desargues's theorem was not understood until
the Desargues configuration was discovered. For example,
the fundamental role of Desargues's theorem in the coordinatization
of synthetic projective geometry can only be understood in the light
of the Desargues configuration.
Thus, even as simple a formal statement as Desargues's theorem
is not quite what it purports to be. The statement of Desargues's theorem
pretends to be definitive, but in reality it is only the tip of an iceberg
of connections with other facts of mathematics."
— From p. 192 of "The Phenomenology of Mathematical Proof,"
by Gian-Carlo Rota, in Synthese , Vol. 111, No. 2, Proof and Progress
in Mathematics (May, 1997), pp. 183-196. Published by: Springer.
Stable URL: https://www.jstor.org/stable/20117627.
Related figures —
Note the 3×3 subsquare containing the triangles ABC, etc.
"That in which space itself is contained" — Wallace Stevens
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Saturday, March 3, 2018
Space
For the Marvel Comics surgeon Dr. Stephen Strange —
For a real-life surgeon who reportedly died on Feb. 24,
a quotation from this journal on that date —
"What of the night
That lights and dims the stars?
Do you know, Hans Christian,
Now that you see the night?"
— The concluding lines of "Sonatina to Hans Christian,"
by Wallace Stevens (in Harmonium (second edition, 1931))
Related material —
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Friday, February 16, 2018
Nicht Spielerei
"What of the night
That lights and dims the stars?
Do you know, Hans Christian,
Now that you see the night?"
— The concluding lines of
"Sonatina to Hans Christian,"
by Wallace Stevens
(in Harmonium (second edition, 1931))
". . . in the end the space itself is the star. . . ."
Related material — The death Tuesday night
of Prince Consort Henrik of Denmark, and the
New Year's Eve speech on Dec. 31, 2015, of
Queen Margrethe II of Denmark.
Distantly related material — Yesterday morning's
post The Search for Child's Play.
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Monday, February 12, 2018
Sunday, February 11, 2018
Visions of Hell
In memory of a Manhattan art figure
who reportedly died on
Wednesday, February Seventh, 2018 —
ABOUT 'ASCENSION VARIATIONS'
“Ascension Variations is a magical adventure
woven from grand and pedestrian touches, and
in the end the space itself is the star —
or Ms. Monk's transformation of it.
For an hour, we've lived in a spiral,
where up is down and down is up.
It's a sacred place.”
— Gia Kourlas, The New York Times , March 6, 2009
See also the previous post — yesterday's Into the Upside Down —
and two posts of February Seventh:
Conceptual Art and Conceptual Minimalism.
For some related artistic remarks, see this journal on March 6-7, 2009.
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Wednesday, August 24, 2016
Core Statements
"That in which space itself is contained" — Wallace Stevens
An image by Steven H. Cullinane from April 1, 2013:
The large Desargues configuration of Euclidean 3-space can be
mapped canonically to the 4×4 square of Galois geometry —
On an Auckland University of Technology thesis by Kate Cullinane —
The thesis reportedly won an Art Directors Club award on April 5, 2013.
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Sunday, January 17, 2016
Sunday School
Some narrative for a ghost writer —
I prefer the following narrative —
Part I: Stevens’s verse from “The Rock” (1954) —
“That in which space itself is contained”
Part II: Mystery Box III: Inside, Outside (2014)
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Friday, February 21, 2014
Night’s Hymn of the Rock
One way of interpreting the symbol 
at the end of yesterday's post is via
the phrase "necessary possibility."
See that phrase in (for instance) a post
of July 24, 2013, The Broken Tablet .
The Tablet post may be viewed in light
of a Tom Wolfe passage quoted here on
the preceding day, July 23, 2013—
On that day (July 23) another weblog had
a post titled
Wallace Stevens: Night's Hymn of the Rock.
Some related narrative —
I prefer the following narrative —
Part I: Stevens's verse from "The Rock" (1954) —
"That in which space itself is contained"
Part II: Mystery Box III: Inside, Outside (2014)
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Tuesday, April 17, 2012
Monday, April 16, 2012
Carroll Thanks the Academy
Gary Gutting, "Arguing About Language," in "The Stone,"
The New York Times philosophy column, yesterday—
There's a sense in which we speak language
and a sense in which, in Mallarmé's famous phrase,
“language itself speaks.”
Famous? A Google Book Search for
"language itself speaks" Mallarmé
yields 2 results, neither helpful.
But a Google Book Search for
"language itself speaks" Heidegger
yields "about 312 results."
A related search yields the following—
Paul Valéry, encountering Un Coup de Dés in Mallarmé’s worksheets in 1897, described the text as tracing the pattern of thought itself:
It seemed to me that I was looking at the form and pattern of a thought, placed for the first time in finite space. Here space itself truly spoke, dreamed, and gave birth to temporal forms….
… there in the same void with them, like some new form of matter arranged in systems or masses or trailing lines, coexisted the Word! (Leonardo 309*)
* The page number is apparently a reference to The Collected Works of Paul Valéry: Leonardo, Poe, Mallarmé , translated by Malcolm Cowley and James R. Lawler, Princeton University Press, 1972. (As a temporal form, "309" might be interpreted as a reference to 3/09, March 9, the date of a webpage on the Void.)
For example—
Background:
Deconstructing Alice
and Symbology.
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Wednesday, August 10, 2011
Objectivity
From math16.com—
Quotations on Realism
|
The story of the diamond mine continues
(see Coordinated Steps and Organizing the Mine Workers)—
From The Search for Invariants (June 20, 2011):
The conclusion of Maja Lovrenov's
"The Role of Invariance in Cassirer’s Interpretation of the Theory of Relativity"—
"… physical theories prove to be theories of invariants
with regard to certain groups of transformations and
it is exactly the invariance that secures the objectivity
of a physical theory."
— SYNTHESIS PHILOSOPHICA 42 (2/2006), pp. 233–241
Related material from Sunday's New York Times travel section—
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Monday, July 25, 2011
The Game
Virginia Heffernan in Sunday's online New York Times—
"… In the past, information on paper was something to read. Bricks and mortar were a place to be. But, since the first appearance of the Web in 1990, we have come to accept that information in pixels is something to read— and also a place to be . That familiar and yet still jaw-dropping metaphor takes energy to maintain. The odd shared sense that there’s three-dimensionality and immersion and real-world consequences on the Web as in no book or board game— that’s the Web’s sine qua non. Hence, cyberspace . And 'being on' the Internet….
… The dominant social networks are fantasy games built around rigged avatars, outright fictions and a silent— and often unconscious— agreement among players that the game and its somewhat creaky conceits influence the real world…."
— "The Confidence Game at Google+"
"It's just another manic Monday
I wish it was Sunday
'Cause that's my funday"
— The Bangles
"Accentuate the Positive"
— Clint Eastwood, soundtrack album
for "Midnight in the Garden of Good and Evil"
This journal on All Saints' Day, Sunday, November 1, 2009—
|
Suggested by the New York State lottery numbers on All Hallows’ Eve [2009]— 430 (mid-day) and 168 (evening)… From 430 as a date, 4/30— Beyond Grief and Nothing: A Reading of Don DeLillo , by Joseph Dewey, University of South Carolina Press, 2006, page 123: “It is as if DeLillo himself had moved to an endgame….” For such an endgame, see yesterday’s link to a Mira Sorvino drama. The number 168 suggested by the Halloween lottery deals with the properties of space itself and requires a more detailed exegesis… For the full picture, consider the Log24 entries of Feb. 16-28 this year, esp. the entries of Feb. 27 and the phrase they suggest— Flores, flores para los muertos. |
See also Pearly Gates of Cyberspace in this journal.
For flores para los muertos , see today's Times .
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Sunday, November 1, 2009
October Endgame
Suggested by the New York State lottery numbers on All Hallows' Eve–
430 (mid-day) and 168 (evening)…
From 430 as a date, 4/30— Beyond Grief and Nothing: A Reading of Don DeLillo, by Joseph Dewey, University of South Carolina Press, 2006, page 123:
"It is as if DeLillo himself had moved to an endgame…."
For such an endgame, see yesterday's link to a Mira Sorvino drama. The number 168 suggested by the Halloween lottery deals with the properties of space itself and requires a more detailed exegesis… For the full picture, consider the Log24 entries of Feb. 16-28 this year, esp. the entries of Feb. 27 and the phrase they suggest–
Flores, Flores para los muertos.
Consider also Xinhua today, with its discussion of rocket science and seal-cutting:
Click image for context.
For space technology, see the above link to Feb. 16-28 this year as well as the following (click on image for details)–
As for seal-cutting, see the following seal from a Korean Christian site:
See Mizian Translation Service for some background on the seal's designer.
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Tuesday, February 24, 2009
Tuesday February 24, 2009
Hollywood Nihilism
Meets
Pantheistic Solipsism
Meets
Pantheistic Solipsism
Tina Fey to Steve Martin
at the Oscars:
"Oh, Steve, no one wants
to hear about our religion
… that we made up."
|
From Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 117:
… in 'The Pediment of Appearance,' a slight narrative poem in Transport to Summer… A group of young men enter some woods 'Hunting for the great ornament, The pediment of appearance.' Though moving through the natural world, the young men seek the artificial, or pure form, believing that in discovering this pediment, this distillation of the real, they will also discover the 'savage transparence,' the rude source of human life. In Stevens's world, such a search is futile, since it is only through observing nature that one reaches beyond it to pure form. As if to demonstrate the degree to which the young men's search is misaligned, Stevens says of them that 'they go crying/The world is myself, life is myself,' believing that what surrounds them is immaterial. Such a proclamation is a cardinal violation of Stevens's principles of the imagination. |
Superficially the young men's philosophy seems to resemble what Wikipedia calls "pantheistic solipsism"– noting, however, that "This article has multiple issues."
As, indeed, does pantheistic solipsism– a philosophy (properly called "eschatological pantheistic multiple-ego solipsism") devised, with tongue in cheek, by science-fiction writer Robert A. Heinlein.
Despite their preoccupation with solipsism, Heinlein and Stevens point, each in his own poetic way, to a highly non-solipsistic topic from pure mathematics that is, unlike the religion of Martin and Fey, not made up– namely, the properties of space.
"Sharpie, we have condensed six dimensions into four, then we either work by analogy into six, or we have to use math that apparently nobody but Jake and my cousin Ed understands. Unless you can think of some way to project six dimensions into three– you seem to be smart at such projections."
I closed my eyes and thought hard. "Zebbie, I don't think it can be done. Maybe Escher could have done it."
|
A discussion of Stevens's late poem "The Rock" (1954) in Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 120:
For Stevens, the poem "makes meanings of the rock." In the mind, "its barrenness becomes a thousand things/And so exists no more." In fact, in a peculiar irony that only a poet with Stevens's particular notion of the imagination's function could develop, the rock becomes the mind itself, shattered into such diamond-faceted brilliance that it encompasses all possibilities for human thought:
The rock is the gray particular of man's life,
The stone from which he rises, up—and—ho,
The step to the bleaker depths of his descents ...
The rock is the stern particular of the air,
The mirror of the planets, one by one,
But through man's eye, their silent rhapsodist,
Turquoise the rock, at odious evening bright
With redness that sticks fast to evil dreams;
The difficult rightness of half-risen day.
The rock is the habitation of the whole,
Its strength and measure, that which is near,
point A
In a perspective that begins again
At B: the origin of the mango's rind.
(Collected Poems, 528)
|
Stevens's rock is associated with empty space, a concept that suggests "nothingness" to one literary critic:
B. J. Leggett, "Stevens's Late Poetry" in The Cambridge Companion to Wallace Stevens— On the poem "The Rock":
"… the barren rock of the title is Stevens's symbol for the nothingness that underlies all existence, 'That in which space itself is contained'…. Its subject is its speaker's sense of nothingness and his need to be cured of it."
This interpretation might appeal to Joan Didion, who, as author of the classic novel Play It As It Lays, is perhaps the world's leading expert on Hollywood nihilism.
More positively…
Space is, of course, also a topic
in pure mathematics…
For instance, the 6-dimensional
affine space (or the corresponding
5-dimensional projective space)
over the two-element Galois field
can be viewed as an illustration of
Stevens's metaphor in "The Rock."
Heinlein should perhaps have had in mind the Klein correspondence when he discussed "some way to project six dimensions into three." While such a projection is of course trivial for anyone who has taken an undergraduate course in linear algebra, the following remarks by Philippe Cara present a much more meaningful mapping, using the Klein correspondence, of structures in six (affine) dimensions to structures in three.
Cara:
Here the 6-dimensional affine
space contains the 63 points
of PG(5, 2), plus the origin, and
the 3-dimensional affine
space contains as its 8 points
Conwell's eight "heptads," as in
Generating the Octad Generator.
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Tuesday, February 6, 2007
Tuesday February 6, 2007
The Poetics of Space
The title is from Bachelard.
I prefer Stevens:
The rock is the habitation of the whole, Its strength and measure, that which is near, point A In a perspective that begins again At B: the origin of the mango's rind. It is the rock where tranquil must adduce Its tranquil self, the main of things, the mind, The starting point of the human and the end, That in which space itself is contained, the gate To the enclosure, day, the things illumined By day, night and that which night illumines, Night and its midnight-minting fragrances, Night's hymn of the rock, as in a vivid sleep.
— Wallace Stevens,
"The Rock," 1954
Joan Ockman in Harvard Design Magazine (Fall 1998):
"'We are far removed from any reference to simple geometrical forms,' Bachelard wrote…."
No, we are not. See Log24, Christmas 2005:
Compare and contrast:
(Click on pictures for details.)
More on Bachelard from Harvard Design Magazine:
"The project of discerning a loi des quatre éléments would preoccupy him until his death…."
For such a loi, see Theme and Variations and…
(Click on design for details.)
Thought for Today:
"If you can talk brilliantly
about a problem, it can create
the consoling illusion that
it has been mastered."
— Stanley Kubrick, American
movie director (1928-1999).
(AP, "Today in History,"
February 6, 2007)
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Wednesday, January 11, 2006
Wednesday January 11, 2006
Time in the Rock
"a world of selves trying to remember the self
before the idea of self is lost–
Walk with me world, upon my right hand walk,
speak to me Babel, that I may strive to assemble
of all these syllables a single word
before the purpose of speech is gone."
— Conrad Aiken, "Prelude" (1932),
later part of "Time in the Rock,
or Preludes to Definition, XIX" (1936),
in Selected Poems, Oxford U. Press
paperback, 2003, page 156
"The rock is the habitation of the whole,
Its strength and measure, that which is near, point A
In a perspective that begins again
At B: the origin of the mango's rind.
It is the rock where tranquil must adduce
Its tranquil self, the main of things, the mind,
The starting point of the human and the end,
That in which space itself is contained, the gate
To the enclosure, day, the things illumined
By day, night and that which night illumines,
Night and its midnight-minting fragrances,
Night's hymn of the rock, as in a vivid sleep."
— Wallace Stevens in The Rock (1954)
"Poetry is an illumination of a surface,
the movement of a self in the rock."
— Wallace Stevens, introduction to
The Necessary Angel, 1951
Related material:
Jung's Imago and Solomon's Cube.
Jung's Imago and Solomon's Cube.
The following may help illuminate the previous entry:
"I want, as a man of the imagination, to write poetry with all the power of a monster equal in strength to that of the monster about whom I write. I want man's imagination to be completely adequate in the face of reality."
— Wallace Stevens, 1953 (Letters 790)
The "monster" of the previous entry is of course not Reese Witherspoon, but rather Vox Populi itself.
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