Wednesday, November 5, 2025
The Gospel According to Commonweal . . .
Via CHE, The Chronicle of Higher Education*
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Via CHE, The Chronicle of Higher Education*
Via CHE, The Chronicle of Higher Education*
Baggage Claim
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“Remember, Remember, the Fifth of November”
And perhaps also . . .
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Wednesday, May 15, 2024
Annals of Philosophy: Savoir “La Différance”
August 26, 2022, was the opening date of
the Nathalie Emmanuel film "The Invitation."
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Saturday, May 4, 2024
What Lies Between
"I perceived . . . cinema is that which is between things,
not things [themselves] but between one and another."
— Jean-Luc Godard, "Introduction à une véritable histoire
du cinéma," Albatros , Paris, 1980, p. 145
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Log24 on 10 Dec. 2008 —
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Log24 on 12 Dec. 2008 —
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Between the two image-dates above . . .
" 'The jury is still out on how long – and whether – people are actually
going to understand this.' It took the world 150 years to realize
the true power of the printing press . . . ." — Cade Metz
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Saturday, February 24, 2024
Li
The Chinese concept of li in yesterday's post "Logos" is related,
if only by metaphor, to the underlying form (sets of "line diagrams")
of patterns in the Cullinane diamond theorem:
"But very possibly the earliest use of li is the one instance that
it appears in the Classic of Poetry (Ode 210) where it refers to
the borders or boundary lines marking off areas in a field.
Here it appears in conjunction with chiang and is explained
as 'to divide into lots (or parcels of land)' (fen-ti )."
— P. 33 of "Li Revisited and Other Explorations"
by Allen Wittenborn, Bulletin of Sung and Yüan Studies
No. 17 (1981), pp. 32-48 (17 pages),
https://www.jstor.org/stable/23497457.
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Friday, January 12, 2024
From Sources of the Self , by Charles Taylor
Interspaces
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Wednesday, January 3, 2024
Negative Space
A recently coined phrase — "Negative Mathematics" — is related to the
better-known phrase "Negative Space."
The latter is closely related to the proof of the Cullinane diamond theorem.
For the former, see . . .
Related material: The proof symbol, i.e. the Halmos Tombstone.
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Monday, February 6, 2023
Clown
For Bill Irwin —
<meta property="article:published_time"
content="2023-02-06T11:00:00.000Z"/>
The Source —
view-source:https://www.newyorker.com/magazine/2023/02/13/
finding-laughs-amid-the-gray-in-becketts-endgame
See as well the previous post and . . .
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Interality Studies
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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
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| 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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Sunday, February 5, 2023
Negative Space: Examples
Patterns in the space
between subsquares —
Figures in the space
between fingers —
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Monday, November 28, 2022
L’écart, l’entre and so forth
See as well . . .
"But let us return to the concepts of the divide [écart ]
and interspace [l'entre ], which figure prominently in my work…."
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Friday, August 19, 2022
Mathematical Evolution
From the Stillwell remembrance, a Shenitzer quote —
"An English major may or may not be a novelist or a poet,
but would undoubtedly be expected to be able to evaluate
a novel or a poem. The term 'English major' implies some
historical, philosophical, and evaluative training and
competence. It is sad but true that the term 'mathematician'
does not imply corresponding training and competence."
Related material — The previous post, and posts tagged Super-8.
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Cut Geometry
"… the new geometries … provide the best example of
the power of the human mind, for the mind had to defy
and overcome habit, intuition, and sense perceptions
to produce these geometries."
— Morris Kline, Mathematics in Western Culture ,
Oxford University Press, 1953, page 430.
Points as Cuts —
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Thursday, August 18, 2022
The Razr’s Edge
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Monday, August 1, 2022
Interality Again: The Art of the Gefüge
"Schufreider shows that a network of linguistic relations
is set up between Gestalt, Ge-stell, and Gefüge, on the
one hand, and Streit, Riß, and Fuge, on the other . . . ."
— From p. 14 of French Interpretations of Heidegger ,
edited by David Pettigrew and François Raffoul.
State U. of New York Press, Albany, 2008. (Links added.)
One such "network of linguistic relations" might arise from
a non-mathematician's attempt to describe the diamond theorem.
(The phrase "network of linguistic relations" appears also in
Derrida's remarks on Husserl's Origin of Geometry .)
For more about "a system of slots," see interality in this journal.
The source of the above prefatory remarks by editors Pettigrew and Raffoul —
"If there is a specific network that is set up in 'The Origin of the Work of Art,'
a set of structural relations framed in linguistic terms, it is between
Gestalt, Ge-stell and Gefüge, on the one hand, and Streit, Riß and Fuge,
on the other; between (as we might try to translate it)
configuration, frame-work and structure (system), on the one hand, and
strife, split (slit) and slot, on the other. On our view, these two sets go
hand in hand; which means, to connect them to one another, we will
have to think of the configuration of the rift (Gestalt/Riß) as taking place
in a frame-work of strife (Ge-stell/Streit) that is composed through a system
of slots (Gefüge/Fuge) or structured openings."
— Quotation from page 197 of Schufreider, Gregory (2008):
"Sticking Heidegger with a Stela: Lacoue-Labarthe, art and politics."
Pp. 187-214 in David Pettigrew & François Raffoul (eds.),
French Interpretations of Heidegger: An Exceptional Reception.
State University of New York Press, 2008.
Update at 5:14 AM ET Wednesday, August 3, 2022 —
See also "six-set" in this journal.
"There is such a thing as a six-set."
— Saying adapted from a 1962 young-adult novel.
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Saturday, May 7, 2022
Interality Meets the Seven Seals
Related material — Posts tagged Interality and Seven Seals.
From Hermann Weyl's 1952 classic Symmetry —
"Galois' ideas, which for several decades remained
a book with seven seals but later exerted a more
and more profound influence upon the whole
development of mathematics, are contained in
a farewell letter written to a friend on the eve of
his death, which he met in a silly duel at the age of
twenty-one. This letter, if judged by the novelty and
profundity of ideas it contains, is perhaps the most
substantial piece of writing in the whole literature
of mankind."
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Friday, May 6, 2022
Interality and the Bead Game
WIkipedia on the URL suffix ".io" —
"In computer science, "IO" or "I/O" is commonly used
as an abbreviation for input/output, which makes the
.io domain desirable for services that want to be
associated with technology. .io domains are often used
for open source projects, application programming
interfaces ("APIs"), startup companies, browser games,
and other online services."
An association with the Bead Game from a post of April 7, 2018 —
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Glasperlenspiel passage quoted here in Summa Mythologica —
“"I suddenly realized that in the language, or at any rate A less poetic meditation on the above 4x4x4 design cube —
"I saw that in the alternation between front and back, See also a related remark by Lévi-Strauss in 1955:
"…three different readings become possible: |
The recent use by a startup company of the URL "interality.io" suggests
a fourth reading for the 1955 list of Lévi-Strauss — in and out —
i.e., inner and outer group automorphisms — from a 2011 post
on the birthday of T. S. Eliot :
A transformation:
Click on the picture for details.
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Interality and the I Ching
See "Flusser and the I Ching," by Peter Zhang.
Zhang has written extensively on the concept of "interality,"
a term coined by his colleague Geling Shang.
For interality as the mathematics underlying the natural
automorphism group of the I Ching, see my own work.
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Thursday, May 5, 2022
“Interality” as a Metaverse Term
See also "Interality" in this journal.
Update of 8:56 AM ET
Friday, May 6, 2022:
“You have to all have a shared language of all this stuff,
otherwise it can get pretty confusing,” Waldron said.
The Waldron quote is from . . .
Later, at 9:29 AM ET . . .
See as well other posts now tagged Strange Change.
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Sunday, April 24, 2022
Structuralism: Three Betweens
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Tuesday, November 3, 2009 Filed under: General,Geometry — Tags: Glasperlenspiel, Solomon Marcus — m759 @ 10:10 PM Book review by Jadran Mimica in Oceania, Vol. 74, 2003: "In his classic essay of 1955 'The Structural Study of Myth' Levi-Strauss came up with a universal formula of mythopoeic dynamics [fx(a) : fy(b) :: fx(b) : fa-1(y)] that he called canonical 'for it can represent any mythic transformation'. This formulation received its consummation in the four massive Mythologiques volumes, the last of which crystallises the fundamental dialectics of mythopoeic thought: that there is 'one myth only' and the primal ground of this 'one' is 'nothing'. The elucidation of the generative matrix of the myth-work is thus completed as is the self-totalisation of both the thinker and his object." So there. At least one mathematician has claimed that the Levi-Strauss formula makes sense. (Jack Morava, arXiv pdf, 2003.) I prefer the earlier (1943) remarks of Hermann Hesse on transformations of myth: "…in the spirit of the Glass Bead Game, everything actually was all-meaningful, that every symbol and combination of symbols led not hither and yon, not to single examples, experiments, and proofs, but into the center, the mystery and innermost heart of the world, into primal knowledge. Every transition from major to minor in a sonata, every transformation of a myth or a religious cult, every classical or artistic formulation was, I realized in that flashing moment, if seen with a truly meditative mind, nothing but a direct route into the interior of the cosmic mystery, where in the alternation between inhaling and exhaling, between heaven and earth, between Yin and Yang, holiness is forever being created." |
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Wednesday, March 30, 2022
“Design is how it works.” — Steve Jobs
See box-space.design.
Related cinematic remarks —
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From Third Text , 2013, Vol. 27, No. 6, pp. 774–785 — "Genealogy of the Image in Histoire(s) du Cinéma : Godard, Warburg and the Iconology of the Interstice" * * * * P. 777 — Godard conceives of the image only in the plural, in the intermediate space between two images, be it a prolonged one (in Histoire(s) there are frequent instances of black screens) or a non-existent one (superimposition, co-presence of two images on screen). He comments: ‘[For me] it’s always two, begin by showing two images rather than one, that’s what I call image, the one made up of two’ [18] and elsewhere, ‘I perceived . . . cinema is that which is between things, not things [themselves] but between one and another.’ [19] 18. Jean-Luc Godard and Youssef Ishaghpour, "Archéologie du cinéma et mémoire du siècle," Farrago ,Tours, 2000, p. 27. The title of this work is reflective of the Godardian agenda that permeates Histoire(s) . 19. Jean-Luc Godard, "Introduction à une véritable histoire du cinéma," Albatros , Paris,1980, p. 145 |
See as well Warburg in this journal.
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Tuesday, December 21, 2021
Square to Block
Related geometry . . .
Many, of course, have not yet mastered the square.
Related art . . .
See Object of Beauty.
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Monday, November 29, 2021
Abstraction and Structure
For the mathematical properties of the vertical and horizontal
white grid lines above, see the Cullinane theorem.
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Wednesday, September 15, 2021
The Shining Darkness
"what shines, the shining darkness, yes, is the invisible in the visible"
— From Jon Fosse — The Other Name: Septology I-II .
Translated from the Norwegian by Damion Searls.
Fitzcarraldo Editions (October 10, 2019).
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Monday, August 9, 2021
The Tune (Suggested by “Hum: Seek the Void”)
"Two years ago . . . ." — Synopsis of the August 3 film "Hum"
Two years ago on August 3 . . .
What is going on in this picture?
The above is an image from
the August 3, 2019,
post "Butterfield's Eight."
"Within the week . . . ."
— The above synopsis of "Hum"
This suggests a review of a post
from August 5, 2019, that might
be retitled . . .
"The void she knows,
the tune she hums."
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Sunday, March 21, 2021
Mind the Gaps…
Continues from March 17.
See as well some remarks on Chinese perspective
in the Log24 post “Gate” of June 13, 2013.
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Wednesday, March 17, 2021
Saturday, October 17, 2020
Modernist Cuts
"The bond with reality is cut."
— Hans Freudenthal, 1962
Related screenshot of a book review
from the November AMS Notices —
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