Monday, September 8, 2025
Monday, February 6, 2023
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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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 —
|
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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Thursday, January 2, 2020
Thursday, September 13, 2018
Godard and Interality
The previous post, "One Plus One," suggests some further
art-historical remarks on interality —
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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. 775 — My discussion will focus on the significance of the concept of the ‘space in-between,’ its importance for Godard’s work and its role in a relational historiography of images more broadly. I hope to corroborate how Godard functions as a twenty-first century archaeologist of the moving image, constructing a meta-cinematic collage that, while consisting of an indexing of (almost exclusively) pre-existing filmic samples, ends up becoming a hybrid work of art in its own right. Godard, in the final analysis, expands the Warburgian programme of iconology into that of a cinematographic 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 * * * * P. 783 — If it is in ‘the in-between’ that thought is born, then for Godard cinematography as ‘a form that thinks . . . was born with the advent of modern painting.’ [62] 62. Godard and Ishaghpour, op. cit., pp 45–46. * * * * P. 785 — Warburg commented on the signification of the black spaces that he placed between images in his analysis of the network of intervals in Mnemosyne , by quoting Johann Wolfgang Goethe’s dictum ‘the truth inhabits the middle space.’ [68] This citation induces a feeling of déjà-vu for the viewer of Histoire(s). The link was not missed by Warburg himself, as one of his diary entries testifies: ‘We can compare this phenomenon [the iconology of the interval] to that of the cinematic montage, the domain of the interpretation is an intervallic one.’ [69] 68. Warburg, Mnemosyne , pp 135–146. 69. Warburg is quoted in Didi-Huberman, L’image survivante, p. 503. (Georges Didi-Huberman, L’image survivante. Histoire de l’art et temps des fantômes selon Aby Warburg , Minuit, Paris, 2002) |
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Friday, January 5, 2018
Seven Types of Interality*
* See the term interality in this journal.
For many synonyms, see
“The Human Seriousness of Interality,”
by Peter Zhang, Grand Valley State University,
China Media Research 11(2), 2015, 93-103.
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Monday, January 16, 2017
Interality Illustrated
For the "interality" of the title, click on the tag.
Click the above image for posts tagged "The Positive."
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Sunday, January 15, 2017
April First Interality
Data for an essay titled "Interality in Heidegger" —
See also Log24 posts
on that same date —
April 1, 2015.
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Sunday, September 7, 2025
Numberland: Watson Gets Her Groove Back
Daily Mail headline yesterday . . .
Emma Watson dazzles in TWO
jaw-dropping designer looks
on the final day of Venice Film Festival
as she swaps a green Emilia Wickstead
mini dress for a Gucci number
The swap reportedly took place at
"the luxurious Hotel Excelsior."
Annals of interality —
Excelsior!
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Thursday, March 2, 2023
Bullshit Studies
The above phrase "interpellative assemblages" suggests . . .
See also this journal on the above Won Choi date —
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Saturday, December 3, 2022
The Primes of LCM:
2 and 3.
(See The Rimshot Muse
and Interality Again.)
This post was suggested in part by
a thoughtful obituary yesterday for
the author of The Number Devil .
I prefer Numberland .
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Wednesday, March 30, 2022
“Design is how it works.” — Steve Jobs
See box-space.design.
Related cinematic remarks —
|
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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Monday, March 28, 2022
The Omega Oracle
"Design is how it works ." — Steve Jobs. See interality.org.
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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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Thursday, January 7, 2021
The Purloined* Void
From a post of Tuesday, May 7, 2019 —
“Honored in the Breach:
Graham Bader on Absence as Memorial”
Artforum International , April 2012
| . . . .
“In the wake of a century marked by inconceivable atrocity, the use of emptiness as a commemorative trope has arguably become a standard tactic, a default style of public memory. The power of the voids at and around Ground Zero is generated by their origin in real historical circumstance rather than such purely commemorative intent: They are indices as well as icons of the losses they mark. Nowhere is the negotiation between these two possibilities–on the one hand, the co-optation of absence as tasteful mnemonic trope; on the other, absence’s disruptive potential as brute historical scar–more evident than in Berlin, a city whose history, as Andreas Huyssen has argued, can be seen as a ‘narrative of voids.’ Writing in 1997, Huyssen saw this tale culminating in Berlin’s post-wall development, defined equally by an obsessive covering-over of the city’s lacunae–above all in the elaborate commercial projects then proliferating in the miles-long stretch occupied until 1989 by the Berlin Wall–and a carefully orchestrated deployment of absence as memorial device, particularly in the ‘voids’ integrated by architect Daniel Libeskind into his addition to the Berlin Museum, now known as the Jewish Museum Berlin.” |
See also Breach in this journal, as well as Void.
* Literary background — The word “Purloined” in this journal.
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Sunday, November 1, 2020
Art Theory
“If you have built castles in the air, your work need not be lost;
that is where they should be. Now put the foundations under them.”
— Henry David Thoreau
Between, or: Interality Illustrated (according to Sherald)
“We live in between the lines;
in between the cracks . . . .
That’s where the bonds are formed. ”
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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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Thursday, August 20, 2020
“One More Reality Show”
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Wednesday, February 12, 2020
The Reality Bond
The plane at left is modeled naturally by
seven types of “cuts” in the cube at right.
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Sunday, September 22, 2019
Colorful Tale
“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”
— Hermann Weyl, Philosophy of Mathematics and
Natural Science , Princeton, 1949, p. 237
"The bond with reality is cut."
— Hans Freudenthal, 1962
From page 180, Logicomix — It was a dark and stormy night …
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Monday, May 20, 2019
The Bond with Reality
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Thursday, March 21, 2019
Geometry of Interstices
Finite Galois geometry with the underlying field the simplest one possible —
namely, the two-element field GF(2) — is a geometry of interstices :
For some less precise remarks, see the tags Interstice and Interality.
The rationalist motto "sincerity, order, logic and clarity" was quoted
by Charles Jencks in the previous post.
This post was suggested by some remarks from Queensland that
seem to exemplify these qualities —
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Thursday, November 29, 2018
The White Cube
Clicking on Zong in the above post leads to a 2005 article
in the Bulletin of the American Mathematical Society .
See also the eightfold cube and interality .
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Saturday, September 15, 2018
Eidetic Reduction in Geometry
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"Husserl is not the greatest philosopher of all times. — Kurt Gödel as quoted by Gian-Carlo Rota Some results from a Google search — Eidetic reduction | philosophy | Britannica.com Eidetic reduction, in phenomenology, a method by which the philosopher moves from the consciousness of individual and concrete objects to the transempirical realm of pure essences and thus achieves an intuition of the eidos (Greek: “shape”) of a thing—i.e., of what it is in its invariable and essential structure, apart … Phenomenology Online » Eidetic Reduction
The eidetic reduction: eidos. Method: Bracket all incidental meaning and ask: what are some of the possible invariate aspects of this experience? The research Eidetic reduction – New World Encyclopedia Sep 19, 2017 – Eidetic reduction is a technique in Husserlian phenomenology, used to identify the essential components of the given phenomenon or experience. |
For example —
The reduction of two-colorings and four-colorings of a square or cubic
array of subsquares or subcubes to lines, sets of lines, cuts, or sets of
cuts between* the subsquares or subcubes.
See the diamond theorem and the eightfold cube.
* Cf. posts tagged Interality and Interstice.
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