Log24

Monday, February 6, 2023

Interality Studies

Filed under: General — Tags: , — m759 @ 12:26 pm
 

You, Xi-lin; Zhang, Peter. "Interality in Heidegger." 
The Free Library , April 1, 2015.  
. . . .

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

Tags:  

— m759 @ 4:44 AM April 1, 2015

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 —

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."

Monday, August 1, 2022

Interality Again: The Art of the Gefüge

Filed under: General — Tags: , , — m759 @ 2:52 pm

"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.

Saturday, May 7, 2022

Interality Meets the Seven Seals

Filed under: General — Tags: , , , — m759 @ 8:41 pm

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."

Friday, May 6, 2022

Interality and the Bead Game

Filed under: General — Tags: , , — m759 @ 3:00 pm

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 companiesbrowser games,
and other online services."

An association with the Bead Game from a post of April 7, 2018

IMAGE- 'Solomon's Cube'

Glasperlenspiel  passage quoted here in Summa Mythologica 

“"I suddenly realized that in the language, or at any rate
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.”

A less poetic meditation on the above 4x4x4 design cube —

"I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created."

See also a related remark by Lévi-Strauss in 1955

"…three different readings become possible:
left to right, top to bottom, front to back."

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:

Inner and outer group automorphisms

Click on the picture for details.

Interality and the I Ching

Filed under: General — Tags: , , — m759 @ 12:57 am

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.

Thursday, May 5, 2022

“Interality” as a Metaverse Term

Filed under: General — Tags: , , — m759 @ 11:01 pm

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 . . .

"‘Doctor Strange 2’ Writer Michael Waldron Wishes
That He Didn’t Make So Many Multiverse Rules In ‘Loki’
 .

Later, at 9:29 AM ET . . .

See as well other posts now tagged Strange Change.

Thursday, January 2, 2020

Interality

Filed under: General — Tags: , — m759 @ 8:25 pm

Structure of the eightfold cube

Thursday, September 13, 2018

Godard and Interality

Filed under: General,Geometry — Tags: , — m759 @ 12:14 am

The previous post, "One Plus One," suggests some further
art-historical remarks on interality

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"

By Dimitrios S. Latsis

* * * * 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)

Friday, January 5, 2018

Seven Types of Interality*

Filed under: General,Geometry — Tags: , , — m759 @ 1:00 am

'Paradise of CHildhood'— on Froebel's Third Gift

* 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.

Monday, January 16, 2017

Interality Illustrated

Filed under: General,Geometry — Tags: , — m759 @ 11:18 am

For the "interality" of the title, click on the tag.

Click the above image for posts tagged "The Positive."

Sunday, January 15, 2017

Interality

Filed under: General — Tags: — m759 @ 11:48 pm

See also previous posts now tagged with this term.

April First Interality

Filed under: General — Tags: — m759 @ 12:00 pm

Data for an essay titled "Interality in Heidegger" —

See also Log24 posts
on that same date —
April 1, 2015.

Thursday, March 2, 2023

Bullshit Studies

Filed under: General — Tags: , — m759 @ 11:01 pm

The above phrase "interpellative assemblages" suggests . . .

See also this  journal on the above Won Choi date —

Saturday, December 3, 2022

The Primes of LCM:

Filed under: General — Tags: — m759 @ 12:00 am
 

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 .

Wednesday, March 30, 2022

“Design is how it works.” — Steve Jobs

Filed under: General — Tags: — m759 @ 5:57 am

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"

By Dimitrios S. Latsis

* * * * 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.

Monday, March 28, 2022

The Omega Oracle

Filed under: General — m759 @ 6:38 am

"Design is how it works ." — Steve Jobs.  See interality.org.

Monday, November 29, 2021

Abstraction and Structure

Filed under: General — Tags: , , , — m759 @ 6:46 pm

'The Nothing That Is' — The hidden structure of 'Vertical-Horizontal Composition,' 1916, by Sophie Taeuber-Arp

For the mathematical  properties of the vertical and horizontal
white grid lines above, see the Cullinane theorem.

Thursday, January 7, 2021

The Purloined* Void

Filed under: General — m759 @ 4:11 pm

From a post of Tuesday, May 7, 2019 —

Breach

Filed under: General —
Tags:  — m759 @ 12:00 PM

“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.

Sunday, November 1, 2020

Art Theory

Filed under: General — Tags: , — m759 @ 2:37 pm

“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. ”

Amy Sherald

Saturday, October 17, 2020

Modernist Cuts

Filed under: General — Tags: , , — m759 @ 10:05 pm

"The bond with reality is cut."

— Hans Freudenthal, 1962

Indeed it is.

Related screenshot of a book review
from the November AMS Notices

Thursday, August 20, 2020

“One More Reality Show”

Filed under: General — Tags: — m759 @ 9:27 am

“The bond with reality is cut.”

— Hans Freudenthal, 1962

Indeed it is.

Wednesday, February 12, 2020

The Reality Bond

Filed under: General — Tags: , , — m759 @ 3:33 pm

The plane at left is modeled naturally by
seven types of “cuts” in the cube at right.

Structure of the eightfold cube

 

Sunday, September 22, 2019

Colorful Tale

Filed under: General — Tags: , , — m759 @ 7:59 pm

“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

Indeed it is.

From page 180, Logicomix — It was a dark and stormy night

http://www.log24.com/log/pix11/110420-DarkAndStormy-Logicomix.jpg

Monday, May 20, 2019

The Bond with Reality

Filed under: General — Tags: , , , , — m759 @ 10:00 pm


"The bond with reality is cut."

— Hans Freudenthal, 1962

Indeed it is.

Thursday, March 21, 2019

Geometry of Interstices

Filed under: General — Tags: , , , — m759 @ 10:18 pm

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 —

Thursday, November 29, 2018

The White Cube

Filed under: G-Notes,General,Geometry — m759 @ 9:57 am

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 .

Saturday, September 15, 2018

Eidetic Reduction in Geometry

Filed under: G-Notes,General,Geometry — Tags: , , , , , — m759 @ 1:23 am
 

"Husserl is not the greatest philosopher of all times.
He is the greatest philosopher since Leibniz."

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.

Terminology: Eidos

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.

Saturday, September 8, 2018

Space

Filed under: General,Geometry — Tags: , — m759 @ 9:26 pm

'Space' in Chinese

For example —

'Projective space' in Chinese

See also Interality in this journal.

Monday, July 23, 2018

Space 101

Filed under: General,Geometry — Tags: — m759 @ 1:01 am

From the April 1st publication date of "Interality Shows Through,"
by Geling Shang —

See too yesterday's post  Space.

Sunday, July 22, 2018

Space

Filed under: General,Geometry — Tags: , , , — m759 @ 10:29 am

See also interality in the eightfold cube.

IMAGE- The Trinity Cube (three interpenetrating planes that split the eightfold cube into its eight subcubes)

Sunday, January 7, 2018

Clueless:

Filed under: General — Tags: — m759 @ 11:00 am

Peter Zhang and Eric McLuhan on Interality

Space Program

Filed under: General,Geometry — Tags: , — m759 @ 12:00 am

Or:  Interality Illustrated

See also Seven Seals.

Saturday, January 6, 2018

Report from Red Mountain

Filed under: General,Geometry — Tags: , , — m759 @ 4:00 pm

Tom Wolfe in The Painted Word  (1975):

“It is important to repeat that Greenberg and Rosenberg
did not create their theories in a vacuum or simply turn up
with them one day like tablets brought down from atop
Green Mountain or Red Mountain (as B. H. Friedman once
called the two men). As tout le monde  understood, they
were not only theories but … hot news,
straight from the studios, from the scene.”

Harold Rosenberg in The New Yorker  (click to enlarge)

See also Interality  and the Eightfold Cube .

Friday, January 5, 2018

Types of Ambiguity

Filed under: General,Geometry — Tags: , — m759 @ 2:56 am

From "The Principle of Sufficient Reason," by George David Birkhoff
in "Three Public Lectures on Scientific Subjects,"
delivered at the Rice Institute, March 6, 7, and 8, 1940 —

From the same lecture —

Up to the present point my aim has been to consider a variety of applications of the Principle of Sufficient Reason, without attempting any precise formulation of the Principle itself. With these applications in mind I will venture to formulate the Principle and a related Heuristic Conjecture in quasi-mathematical form as follows:

PRINCIPLE OF SUFFICIENT REASON. If there appears in any theory T a set of ambiguously  determined ( i e . symmetrically entering) variables, then these variables can themselves be determined only to the extent allowed by the corresponding group G. Consequently any problem concerning these variables which has a uniquely determined solution, must itself be formulated so as to be unchanged by the operations of the group G ( i e . must involve the variables symmetrically).

HEURISTIC CONJECTURE. The final form of any scientific theory T is: (1) based on a few simple postulates; and (2) contains an extensive ambiguity, associated symmetry, and underlying group G, in such wise that, if the language and laws of the theory of groups be taken for granted, the whole theory T appears as nearly self-evident in virtue of the above Principle.

The Principle of Sufficient Reason and the Heuristic Conjecture, as just formulated, have the advantage of not involving excessively subjective ideas, while at the same time retaining the essential kernel of the matter.

In my opinion it is essentially this principle and this conjecture which are destined always to operate as the basic criteria for the scientist in extending our knowledge and understanding of the world.

It is also my belief that, in so far as there is anything definite in the realm of Metaphysics, it will consist in further applications of the same general type. This general conclusion may be given the following suggestive symbolic form:

Image-- Birkhoff diagram relating Galois's theory of ambiguity to metaphysics

While the skillful metaphysical use of the Principle must always be regarded as of dubious logical status, nevertheless I believe it will remain the most important weapon of the philosopher.

Related remarks by a founding member of the Metaphysical Club:

See also the previous post, "Seven Types of Interality."

Thursday, January 4, 2018

Perspectives from a Chinese Jar

Filed under: General,Geometry — Tags: , — m759 @ 4:40 pm

" . . . Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness."

— T. S. Eliot, Four Quartets

"The Grand Valley spirit never dies."

— Adapted from the Tao Te Ching

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