Tuesday, August 30, 2022
Quartets.space
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Friday, June 10, 2022
Songlines.space
To me, the new URL "Songlines.space" suggests both the Outback
and the University of Western Australia. For the former, see
"'Max Barry' + Lexicon" in this journal. For the latter, see SymOmega.
The new URL forwards to a combination of these posts.
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Thursday, May 19, 2022
Wednesday, February 12, 2020
Fano.space
The above new URL fano.space redirects to finitegeometry.org/sc.
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Sunday, February 18, 2024
Vocabulary Note
The URLs powerset.space and powerset.group are now operative.
Related vocabulary: See Boolean Functions Review (Log24, May 15, 2023).
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Tuesday, October 24, 2023
A Bond with Reality: The Geometry of Cuts
Illustrations of object and gestures
from finitegeometry.org/sc/ —
Object
Gestures
An earlier presentation of the above
seven partitions of the eightfold cube:
|
|
Related mathematics:
|
The use of binary coordinate systems
Natural physical transformations of square or cubical arrays See "The Thing and I." |
and . . .
Related entertainment:
Or Matt Helm by way of a Jedi cube.
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Saturday, May 13, 2023
The Identity of an Entity
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Sunday, April 30, 2023
For Harlan Kane: The Walpurgisnacht Hallucination
Note that if the "compact Riemann surface" is a torus formed by
joining opposite edges of a 4×4 square array, and the phrase
"vector bundle" is replaced by "projective line," and so forth,
the above ChatGPT hallucination is not completely unrelated to
the following illustration from the webpage "galois.space" —
See as well the Cullinane diamond theorem.
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Saturday, January 14, 2023
Châtelet on Weil — A “Space of Gestures”
|
From Gilles Châtelet, Introduction to Figuring Space Metaphysics does have a catalytic effect, which has been described in a very beautiful text by the mathematician André Weil: Nothing is more fertile, all mathematicians know, than these obscure analogies, these murky reflections of one theory in another, these furtive caresses, these inexplicable tiffs; also nothing gives as much pleasure to the researcher. A day comes when the illusion vanishes: presentiment turns into certainty … Luckily for researchers, as the fogs clear at one point, they form again at another.4 André Weil cuts to the quick here: he conjures these 'murky reflections', these 'furtive caresses', the 'theory of Galois that Lagrange touches … with his finger through a screen that he does not manage to pierce.' He is a connoisseur of these metaphysical 'fogs' whose dissipation at one point heralds their reforming at another. It would be better to talk here of a horizon that tilts thereby revealing a new space of gestures which has not as yet been elucidated and cut out as structure. 4 A. Weil, 'De la métaphysique aux mathématiques', (Oeuvres, vol. II, p. 408.) |
For gestures as fogs, see the oeuvre of Guerino Mazzola.
For some clearer remarks, see . . .
Illustrations of object and gestures
from finitegeometry.org/sc/ —
Object
Gestures
An earlier presentation
of the above seven partitions
of the eightfold cube:
|
|
Related material: Galois.space .
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Tuesday, August 30, 2022
Space Notes
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Sunday, June 12, 2022
Vocabulary: Trisquare Theorem
See also trisquare.space.
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Friday, June 10, 2022
Space Wars
An image from posts tagged The Fano Hallows —
Related material —
The new URL Combinatorics.space forwards to . . .
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Tuesday, May 31, 2022
Tuesday, May 10, 2022
At the Center
From the Centre de recherches mathématiques (CRM) —
Related remarks —
"The form, the pattern" — T. S. Eliot — and . . .
See as well the new URLs ternary.space and ternary.group.
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Thursday, April 7, 2022
Wednesday, April 6, 2022
Programmes: Warburgian vs. Hessian
For the former, see Warburg in this journal.
For the latter, see beadgame.space on the Web.
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Saturday, March 26, 2022
Box Geometry: Space, Group, Art (Work in Progress)
| Name Tag | .Space | .Group | .Art |
|---|---|---|---|
| Box4 |
2×2 square representing the four-point finite affine geometry AG(2,2). (Box4.space) |
S4 = AGL(2,2) (Box4.group) |
(Box4.art) |
| Box6 |
3×2 (3-row, 2-column) rectangular array representing the elements of an arbitrary 6-set. |
S6 | |
| Box8 | 2x2x2 cube or 4×2 (4-row, 2-column) array. | S8 or A8 or AGL(3,2) of order 1344, or GL(3,2) of order 168 | |
| Box9 | The 3×3 square. | AGL(2,3) or GL(2,3) | |
| Box12 | The 12 edges of a cube, or a 4×3 array for picturing the actions of the Mathieu group M12. | Symmetries of the cube or elements of the group M12 | |
| Box13 | The 13 symmetry axes of the cube. | Symmetries of the cube. | |
| Box15 |
The 15 points of PG(3,2), the projective geometry of 3 dimensions over the 2-element Galois field. |
Collineations of PG(3,2) | |
| Box16 |
The 16 points of AG(4,2), the affine geometry of 4 dimensions over the 2-element Galois field. |
AGL(4,2), the affine group of |
|
| Box20 | The configuration representing Desargues's theorem. | ||
| Box21 | The 21 points and 21 lines of PG(2,4). | ||
| Box24 | The 24 points of the Steiner system S(5, 8, 24). | ||
| Box25 | A 5×5 array representing PG(2,5). | ||
| Box27 |
The 3-dimensional Galois affine space over the 3-element Galois field GF(3). |
||
| Box28 | The 28 bitangents of a plane quartic curve. | ||
| Box32 |
Pair of 4×4 arrays representing orthogonal Latin squares. |
Used to represent elements of AGL(4,2) |
|
| Box35 |
A 5-row-by-7-column array representing the 35 lines in the finite projective space PG(3,2) |
PGL(3,2), order 20,160 | |
| Box36 | Eurler's 36-officer problem. | ||
| Box45 | The 45 Pascal points of the Pascal configuration. | ||
| Box48 | The 48 elements of the group AGL(2,3). | AGL(2,3). | |
| Box56 |
The 56 three-sets within an 8-set or |
||
| Box60 | The Klein configuration. | ||
| Box64 | Solomon's cube. |
— Steven H. Cullinane, March 26-27, 2022
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Friday, March 18, 2022
Found† in Space*
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Thursday, March 10, 2022
Space Group Art
Supercube.space, supercube.group, supercube.art.
See also the Supercube channel at are.na.
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Wednesday, March 9, 2022
Supercube Space
The new URL supercube.space forwards to http://box759.wordpress.com/.
The term supercube is from a 1982 article by Solomon W. Golomb.
The related new URL supercube.group forwards to a page that
describes how the 2x2x2 (or eightfold, or "super") cube's natural
underlying automorphism group is Klein's simple group of order 168.
For further context, see the new URL supercube.art.
For some background, see the phrase Cube Space in this journal.
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Sunday, February 20, 2022
Thursday, February 17, 2022
Four Dots, Six Lines
"There is such a thing as a tesseract."
— Mrs. Whatsit in A Wrinkle in Time (1962)
"Simplify, simplify." — Henry David Thoreau in Walden (1854)
|
A Jungian on this six-line figure:
“They are the same six lines that exist in the I Ching…. Now observe the square more closely: four of the lines are of equal length, the other two are longer…. For this reason symmetry cannot be statically produced and a dance results.” |
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Thursday, December 9, 2021
Lo Shu Space . . .
. . . is now at loshu.space. (Update on 10 Dec. — See also loshu.group.)
See as well GL(2,3) in this journal.
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Wednesday, April 28, 2021
Tuesday, November 24, 2020
Monday, November 16, 2020
Physics Jeopardy: “What Is a Particle?”
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Monday, November 2, 2020
Q Bits
The new domain name q-bits.space does not refer to
the q in “quantum ,” but rather to the q that symbolizes
the order of a Galois field .
See the Wikipedia article “Finite field.”
The “space” suffix refers to a web page on geometry.
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Friday, April 3, 2020
Thursday, October 3, 2019
Apocalypse* Note
For a first look at octad.space, see that domain.
For a second look, see octad.design.
For some other versions, see Aitchison in this journal.
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Sunday, November 4, 2018
“Look Up” — The Breakthrough Prize* Theme This Evening
Looking up images for "The Space Theory of Truth" this evening —
Detail (from the post "Logos" of Oct. 14) —
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Friday, June 22, 2018
Monday, February 12, 2018
The Void
In memory of Professor Donald Lynden-Bell,
Emeritus Professor of Astrophysics at the University of Cambridge
Lynden-Bell with colleagues at Meteor Crater, Arizona, reportedly in 1960 —
Lynden-Bell was one of the subjects of the 2015 film "Star Men."
Related material —
"After peering into the void from a perch
outside the visitor center, young Henry, 9,
said he liked the rugged landscape.
'It’s a good place to film a space movie,' he said.
Funny he should mention that —
the crater was the setting for the climactic scenes
of the 1984 sci-fi film 'Starman,' with Jeff Bridges
and Karen Allen arriving for a rendezvous with
an alien mother ship."
— Henry Fountain in The New York Times , Jan. 22, 2009
Lynden-Bell reportedly died at 82 on Feb. 5, 2018 (British time).
See as well this journal on that date.
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Sunday, June 28, 2015
New Meaning
1985 — Church window in "Broken Wings" music video —
For Kristen Wiig, whose performances
-
in "MacGruber" (2010) to the accompaniment of
the above 1985 Mr. Mister song "Broken Wings," and -
as NASA spokesperson Annie Montrose in the upcoming
film "The Martian"
give a new meaning to the phrase "flying fuck."
2015 — NASA video of June 28 Falcon 9 launch —
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Thursday, October 10, 2013
Continued
|
"… the walkway between here and there would be colder than a witch’s belt buckle. Or a well-digger’s tit. Or whatever the saying was. Vera had been hanging by a thread for a week now, comatose, in and out of Cheyne-Stokes respiration, and this was exactly the sort of night the frail ones picked to go out on. Usually at 4 a.m. He checked his watch. Only 3:20, but that was close enough for government work."
— King, Stephen (2013-09-24). |
From Space.com, the death of an astronaut this morning —
"Carpenter passed at 5:30 a.m. MDT (7:30 a.m. EDT; 1130 GMT)."
A link, "Continued," in this journal at 3:26 a.m. EDT today led to…
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Friday, February 20, 2009
Friday February 20, 2009
A Kind of Cross
"For every kind of vampire,
there is a kind of cross."
— Thomas Pynchon in
Gravity's Rainbow
Related material:
A memorial service
held at 2 PM today at the
U.S. Space & Rocket Center
in Huntsville, Alabama, and
today's previous entry.
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Wednesday, September 3, 2003
Wednesday September 3, 2003
Reciprocity
From my entry of Sept. 1, 2003:
"…the principle of taking and giving, of learning and teaching, of listening and storytelling, in a word: of reciprocity….
… E. M. Forster famously advised his readers, 'Only connect.' 'Reciprocity' would be Michael Kruger's succinct philosophy, with all that the word implies."
— William Boyd, review of Himmelfarb, New York Times Book Review, October 30, 1994
Last year's entry on this date:
|
Today's birthday:
"Mathematics is the music of reason."
Sylvester, a nineteenth-century mathematician, coined the phrase "synthematic totals" to describe some structures based on 6-element sets that R. T. Curtis has called "rather unwieldy objects." See Curtis's abstract, Symmetric Generation of Finite Groups, John Baez's essay, Some Thoughts on the Number 6, and my website, Diamond Theory. |
The picture above is of the complete graph
Diamond theory describes how the 15 two-element subsets of a six-element set (represented by edges in the picture above) may be arranged as 15 of the 16 parts of a 4×4 array, and how such an array relates to group-theoretic concepts, including Sylvester's synthematic totals as they relate to constructions of the Mathieu group M24.
If diamond theory illustrates any general philosophical principle, it is probably the interplay of opposites…. "Reciprocity" in the sense of Lao Tzu. See
Reciprocity and Reversal in Lao Tzu.
For a sense of "reciprocity" more closely related to Michael Kruger's alleged philosophy, see the Confucian concept of Shu (Analects 15:23 or 24) described in
Kruger's novel is in part about a Jew: the quintessential Jewish symbol, the star of David, embedded in the
Click on the design for details.
Those who prefer a Jewish approach to physics can find the star of David, in the form of
A Graphical Representation
of the Dirac Algebra.
The star of David also appears, if only as a heuristic arrangement, in a note that shows generating partitions of the affine group on 64 points arranged in two opposing triplets.
Having thus, as the New York Times advises, paid tribute to a Jewish symbol, we may note, in closing, a much more sophisticated and subtle concept of reciprocity due to Euler, Legendre, and Gauss. See