Thursday, November 20, 2025
Country Music Award: Whirlwind Dreamcatcher
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Friday, July 4, 2025
1984-1985
Meanwhile . . .
|
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Saturday, April 5, 2025
Diamond Theorem Unit Cube
View rotatable cube at https://3dthis.com/player.htm?h=LTk5ODY3NzQ .
I discovered the 3dthis site only yesterday. If I use it again, the results will
be at https://3dthis.com/profile.htm?owner=Cullinane.
For other such "photo cube" results at the site, see
https://3dthis.com/overview.htm?app=photocube&cat=all&order=date&start=0 .
To create such a cube at 3dthis, see https://3dthis.com/photocube.htm .
There is a "Resources for developers" page at
https://3dthis.com/developers.htm .
For some background on the Diamond Theorem Unit Cube, see
http://m759.net/wordpress/?s="Diamonds+and+Whirls".
Update of 2:30 PM EDT April 5 —
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Monday, February 6, 2023
Interality Studies
|
You, Xi-lin; Zhang, Peter. "Interality in Heidegger."
The term "interology" is meant as an interventional alternative to traditional Western ontology. The idea is to help shift people's attention and preoccupation from subjects, objects, and entities to the interzones, intervals, voids, constitutive grounds, relational fields, interpellative assemblages, rhizomes, and nothingness that lie between, outside, or beyond the so-called subjects, objects, and entities; from being to nothing, interbeing, and becoming; from self-identicalness to relationality, chance encounters, and new possibilities of life; from "to be" to "and … and … and …" (to borrow Deleuze's language); from the actual to the virtual; and so on. As such, the term wills nothing short of a paradigm shift. Unlike other "logoi," which have their "objects of study," interology studies interality, which is a non-object, a no-thing that in-forms and constitutes the objects and things studied by other logoi. |
Some remarks from this journal on April 1, 2015 —
Manifest O
|
| 83-06-21 | An invariance of symmetry The diamond theorem on a 4x4x4 cube, and a sketch of the proof. |
| 83-10-01 | Portrait of O A table of the octahedral group O using the 24 patterns from the 2×2 case of the diamond theorem. |
| 83-10-16 | Study of O A different way of looking at the octahedral group, using cubes that illustrate the 2x2x2 case of the diamond theorem. |
| 84-09-15 | Diamonds and whirls Block designs of a different sort — graphic figures on cubes. See also the University of Exeter page on the octahedral group O. |
The above site, finitegeometry.org/sc, illustrates how the symmetry
of various visual patterns is explained by what Zhang calls "interality."
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Saturday, May 23, 2020
Structure for Linguists
"MIT professor of linguistics Wayne O’Neil died on March 22
at his home in Somerville, Massachusetts."
— MIT Linguistics, May 1, 2020
The "deep structure" above is the plane cutting the cube in a hexagon
(as in my note Diamonds and Whirls of September 1984).
See also . . .
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Saturday, July 6, 2019
Mythos and Logos
Mythos
Logos
The six square patterns which, applied as above to the faces of a cube,
form "diamond" and "whirl" patterns, appear also in the logo of a coal-
mining company —
.
Related material —
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Monday, December 3, 2018
The Relativity Problem at Hiroshima
“This is the relativity problem: to fix objectively a class of
equivalent coordinatizations and to ascertain the group of
transformations S mediating between them.”
— Hermann Weyl, The Classical Groups ,
Princeton University Press, 1946, p. 16
See also Relativity Problem and Diamonds and Whirls.
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Friday, March 23, 2018
From the Personal to the Platonic
On the Oslo artist Josefine Lyche —
"Josefine has taken me through beautiful stories,
ranging from the personal to the platonic
explaining the extensive use of geometry in her art.
I now know that she bursts into laughter when reading
Dostoyevsky, and that she has a weird connection
with a retired mathematician."
— Ann Cathrin Andersen,
http://bryggmagasin.no/2017/behind-the-glitter/
Personal —
The Rushkoff Logo
— From a 2016 graphic novel by Douglas Rushkoff.
See also Rushkoff and Talisman in this journal.
Platonic —
Compare and contrast the shifting hexagon logo in the Rushkoff novel above
with the hexagon-inside-a-cube in my "Diamonds and Whirls" note (1984).
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Thursday, March 22, 2018
The Diamond Cube
The Java applets at the webpage "Diamonds and Whirls"
that illustrate Cullinane cubes may be difficult to display.
Here instead is an animated GIF that shows the basic unit
for the "design cube" pages at finitegeometry.org.
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Saturday, August 6, 2016
Mystic Correspondence:
The Cube and the Hexagram
The above illustration, by the late Harvey D. Heinz,
shows a magic cube* and a corresponding magic
hexagram, or Star of David, with the six cube faces
mapped to the six hexagram lines and the twelve
cube edges mapped to the twelve hexagram points.
The eight cube vertices correspond to eight triangles
in the hexagram (six small and two large).
Exercise: Is this noteworthy mapping** of faces to lines,
edges to points, and vertices to triangles an isolated
phenomenon, or can it be viewed in a larger context?
* See the discussion at magic-squares.net of
"perimeter-magic cubes"
** Apparently derived from the Cube + Hexagon figure
discussed here in various earlier posts. See also
"Diamonds and Whirls," a note from 1984.
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Wednesday, April 1, 2015
Manifest O
The title was suggested by
http://benmarcus.com/smallwork/manifesto/.
The "O" of the title stands for the octahedral group.
See the following, from http://finitegeometry.org/sc/map.html —
|
|
An invariance of symmetry The diamond theorem on a 4x4x4 cube, and a sketch of the proof. |
| 83-10-01 | Portrait of O A table of the octahedral group O using the 24 patterns from the 2×2 case of the diamond theorem. |
| 83-10-16 | Study of O A different way of looking at the octahedral group, using cubes that illustrate the 2x2x2 case of the diamond theorem. |
| 84-09-15 | Diamonds and whirls Block designs of a different sort — graphic figures on cubes. See also the University of Exeter page on the octahedral group O. |
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Friday, October 24, 2008
Friday October 24, 2008
“The Cube Space” is a name given to the eightfold cube in a vulgarized mathematics text, Discrete Mathematics: Elementary and Beyond, by Laszlo Lovasz et al., published by Springer in 2003. The identification in a natural way of the eight points of the linear 3-space over the 2-element field GF(2) with the eight vertices of a cube is an elementary and rather obvious construction, doubtless found in a number of discussions of discrete mathematics. But the less-obvious generation of the affine group AGL(3,2) of order 1344 by permutations of parallel edges in such a cube may (or may not) have originated with me. For descriptions of this process I wrote in 1984, see Diamonds and Whirls and Binary Coordinate Systems. For a vulgarized description of this process by Lovasz, without any acknowledgement of his sources, see an excerpt from his book.
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Sunday, April 22, 2007
Sunday April 22, 2007
Built
continued from
March 25, 2006
continued from
March 25, 2006
In honor of Scarlett Johansson's recent London films "Match Point" and "Scoop," here is a link to an entry of Women's History Month, 2006, with a discussion of an exhibition of the works of artist Liza Lou at London's White Cube Gallery. That entry includes the following illustrations:
This work might aptly be
retitled "Brick Shithouse."
Related material:
See also this morning's entry —
"She's a brick… house…
The lady's stacked
and that's a fact,
Ain't holdin' nothin' back."
— and last year's entry
on this date:
"Her wall is filled with pictures,
She gets 'em one by one."
The bricks and "white cube"
above and in this morning's entry
may be contrasted with the
bricks of Diamonds and Whirls
and the cube of On Beauty.
Poetic allusions such as these
may help provide
entertainment in the afterlife
for Beavis, Butt-Head, and
other inmates of Plato's Cave:
"The Garden of Eden is behind us
and there is no road back to innocence;
we can only go forward."
— Anne Morrow Lindbergh,
Earth Shine, p. xii
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Thursday, March 9, 2006
Thursday March 9, 2006
Finitegeometry.org Update
(Revised May 21, 2006)
Finitegeometry.org now has permutable JavaScript views of the 2x2x2 and 4x4x4 design cubes. Solomon’s Cube presented a claim that the 4x4x4 design cube retains symmetry under a group of about 1.3 trillion transformations. The JavaScript version at finitegeometry.org/sc/64/view/ lets the reader visually verify this claim. The reader should first try the Diamond 16 Puzzle. The simpler 2x2x2 design cube, with its 1,344 transformations, was described in Diamonds and Whirls; the permutable JavaScript version is at finitegeometry.org/sc/8/view/.
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Wednesday, February 18, 2004
Wednesday February 18, 2004
Diamonds and Whirls
New applets have rotating 3D versions of the diamond and whirl cubes in Block Designs.
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