Log24

Saturday, September 28, 2024

The Matrix Revisited:
The World Will Always Welcome . . . I-Beams?

Filed under: General — Tags: , , — m759 @ 4:38 am

Friday, March 22, 2024

Matrix for the Corinthians

Filed under: General — Tags: — m759 @ 8:56 pm

Sunday, January 21, 2024

Review: Matrix Meets Grid

Filed under: General — Tags: — m759 @ 12:08 pm

For Day 21 of 2024, some posts related to Witt's construction of M24.

Saturday, December 31, 2022

Matrix Rotator

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

This post was suggested by a "matrix rotator" photo dated 1953-03-02.

Some context — Kracauer's notion of "mass ornament."

Saturday, December 24, 2022

Window as Matrix

Filed under: General — Tags: , — m759 @ 9:57 am

Grids

Author: Rosalind Krauss
Source: October , Vol. 9 (Summer, 1979), pp. 50-64
Published by: The MIT Press
Stable URL: http://www.jstor.org/stable/778321

From page 59:

"Flowing and freezing; glace  in French means glass, mirror, and ice;
transparency, opacity, and water. In the associative system
of symbolist thought this liquidity points in two directions.
First, towards the flow of birth-the amniotic fluid, the 'source'-
but then, towards the freezing into stasis or death-
the unfecund immobility of the mirror. For Mallarmé, particularly,
the window functioned as this complex, polysemic sign by which
he could also project the 'crystallization  of reality into art.' 5
Mallarmé's Les Fenêtres  dates from 1863;
Redon's most evocative window, Le Jour , appeared in 1891
in the volume Songes . If the window is this matrix of
ambi- or multivalence, and the bars of the windows-the grid-
are what help us to see, to focus on, this matrix, they are
themselves the symbol of the symbolist work of art.
They function as the multilevel representation through which
the work of art can allude, and even reconstitute, the forms of Being."

5 Robert G. Cohn, "Mallarmé's Windows," Yale French Studies ,
no. 54 (1977), 23-31.

Another evocative example — See Galois Window in this  journal.

Wednesday, June 8, 2022

From the New URL “Matrix.Bingo” —

Filed under: General — m759 @ 5:21 pm

Image from Matrix.Bingo

Commentary added on June 8, 2022 —

"First we'll show and tell
'Till I reach your pony tail"

— Song lyric

Another image from Matrix.Bingo

http://www.log24.com/log/pix18/180903-Womens_Night_Bingo-at48.41-The_Net.jpg

From a more recent Sandra Bullock film —

The times are still a-changin'.

(Remark adapted from a webpage of Halloween 2020.)

Tuesday, December 21, 2021

Matrix 4 Meets Plan 9

Filed under: General — m759 @ 1:37 am

http://m759.net/wordpress/?s="Plan+9"+Resurrection

Related reading:

.

Thursday, December 9, 2021

Tune for a Matrix Dance

Filed under: General — Tags: — m759 @ 9:50 pm

"… inextricably intertwined in the fate of the Matrix …."

Screen Rant  today

See as well The Eddington Song in this  journal.

'The Eddington Song'

(The "intertwining" part is at Sex Textiles (March 26, 2021).)

Saturday, September 18, 2021

Color Matrix

Filed under: General — m759 @ 3:14 am

Tuesday, August 31, 2021

Matrix Reloaded

Filed under: General — Tags: , — m759 @ 6:01 pm

In today's online New York Times , Kathryn Harrison reviews a new novel:

MATRIX
By Lauren Groff

From the online New York Times Book Review  on May 24, 2018 —

From this  journal on May 24, 2018 —

Further remarks by Lauren Groff on May 24, 2018 —

"Something invisible and pernicious seems to be preventing
even good literary men from either reaching for books with
women’s names on the spines, or from summoning women’s
books to mind when asked to list their influences. I wonder
what such a thing could possibly be."

Quentin Tarantino?

   — 

"It seems no coincidence that all of these titles
are written by women, for a primary angle of 
Gunpowder Milkshake  is one that tries its best
to promote 'feminism' in a Quentin Tarantino
sort of way." 

Or Lévi-Strauss?

See Log24 posts on The Matrix of Lévi-Strauss

Wednesday, April 1, 2020

Adventures in the Matrix

Filed under: General — m759 @ 11:01 pm

Thursday, June 21, 2018

Cavell’s Matrix

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

From an obituary for Stanley Cavell, Harvard philosopher
who reportedly died at 91 on Tuesday,  June 19:

The London Review of Books  weblog yesterday —

"Michael Wood reviewed [Cavell’s] 
Philosophy the Day after Tomorrow  in 2005:

'The ordinary slips away from us. If we ignore it, we lose it.
If we look at it closely, it becomes extraordinary, the way
words or names become strange if we keep staring at them.
The very notion turns into a baffling riddle.' "

See also, in this  journal, Tuesday morning's Ici vient M. Jordan  and
this  morning's previous post.

Update of 3:24 AM from my RSS feed —

Sunday, April 22, 2018

The Omega Matrix

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

(Continued)

Angels and Demons cross within a diamond (page 306), and Finite Geometry logo

Friday, April 20, 2018

Once Upon a Matrix

Filed under: General — Tags: — m759 @ 2:01 pm

(Continued)

Friday, December 1, 2017

The Architect and the Matrix

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

In memory of Yale art historian Vincent Scully, who reportedly
died at 97 last night at his home in Lynchburg, Va., some remarks
from the firm of architect John Outram and from Scully —

Update from the morning of December 2 —

The above 3×3 figure is of course not unrelated to
the 4×4 figure in The Matrix for Quantum Mystics:

 .

See as well Tsimtsum in this journal.

Harold Bloom on tsimtsum as sublimation

Thursday, November 30, 2017

The Matrix for Quantum Mystics

Filed under: G-Notes,General,Geometry — Tags: , , , — m759 @ 10:29 pm

Scholia on the title — See Quantum + Mystic in this journal.

The Matrix of Lévi-Strauss

"In Vol. I of Structural Anthropology , p. 209, I have shown that
this analysis alone can account for the double aspect of time
representation in all mythical systems: the narrative is both
'in time' (it consists of a succession of events) and 'beyond'
(its value is permanent)." — Claude Lévi-Strauss, 1976

I prefer the earlier, better-known, remarks on time by T. S. Eliot
in Four Quartets , and the following four quartets (from
The Matrix Meets the Grid) —

.

From a Log24 post of June 26-27, 2017:

A work of Eddington cited in 1974 by von Franz

See also Dirac and Geometry and Kummer in this journal.

Ron Shaw on Eddington's triads "associated in conjugate pairs" —

For more about hyperbolic  and isotropic  lines in PG(3,2),
see posts tagged Diamond Theorem Correlation.

For Shaw, in memoriam — See Contrapuntal Interweaving and The Fugue.

Friday, November 24, 2017

The Matrix Meets the Grid

Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 2:00 pm

The Matrix —

  The Grid —

  Picturing the Witt Construction

     "Read something that means something." — New Yorker  ad

Thursday, November 23, 2017

The Matrix

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

David Brooks in The New York Times  today

"We once had a unifying national story, celebrated each Thanksgiving.
It was an Exodus story. Americans are the people who escaped oppression,
crossed a wilderness and are building a promised land. The Puritans brought
this story with them. Each wave of immigrants saw themselves in this story.
The civil rights movement embraced this story.

But we have to admit that many today do not resonate with this story. . . .

Today, we have no common national narrative, no shared way
of interpreting the flow of events. Without a common story,
we don’t know what our national purpose is. We have no
common set of goals or ideals.

We need a new national narrative."

From a post of August 15, 2010

http://www.log24.com/log/pix10B/100815-NeoAndOracle.jpg

For some background, see Java Jive and Today's Theology.

Related readings —

From 1928:

From the previous post:

"Thus, instead of Propp's chronological scheme,
in which the order of succession of events
is a feature of the structure . . .
another scheme should be adopted, which would present
a structural model defined as the group of transformations
of a small number of elements. This scheme would appear
as a matrix . . . ."

Claude Lévi-Strauss, 1960 

Wednesday, March 8, 2017

The Matrix Hypothesis

Filed under: General — Tags: , — m759 @ 9:20 am

"And so both of these bizarre events put one in mind of
a simple but arresting thesis: that we are  living in the Matrix,
and something has gone wrong with the controllers. . . .
The people or machines or aliens who are supposed to be
running our lives are having some kind of breakdown.
There’s a glitch, and we are in it.

Once this insight is offered, it must be said, everything  else
begins to fall in order."

Adam Gopnik in The New Yorker , Feb. 27, 2017 

More recently

Sunday, March 5, 2017

The Omega Matrix

Filed under: General,Geometry — Tags: — m759 @ 5:00 pm

Richard Evan Schwartz on
the mathematics of the 4×4 square

See also Priority in this journal.

Saturday, October 1, 2016

“A Matrix of Four”

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

The title is from a book quoted in the previous post.

A related illustration from 7:31 AM Tuesday, September 27 —

"The matrix at left below represents the feminine yin  principle
and the diamond at right represents the masculine yang ."

Friday, November 27, 2015

Once Upon a Matrix

Filed under: General,Geometry — Tags: , — m759 @ 10:20 pm

Or:  The Strife of Luminosity and Obscurity

(Continued from "Once Upon a Time," November 25, 2015)

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison


Monday, June 15, 2015

Omega Matrix

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

See that phrase in this journal.

See also last night's post.

The Greek letter Ω is customarily used to
denote a set that is acted upon by a group.
If the group is the affine group of 322,560
transformations of the four-dimensional
affine space over the two-element Galois
field, the appropriate Ω is the 4×4 grid above.

See the Cullinane diamond theorem.

Saturday, April 25, 2015

A Matrix for Corliss

Filed under: General — m759 @ 3:00 am

See Richard Corliss's 1999 review of "The Matrix," "Popular Metaphysics." 

See as well the previous Log 24 post and the following publisher's
book description —

Harvard Heart of Gold   by Dustin Aguilar

You may be a storybook character after all!!!  

This philosophic, fantastical journey is a new-fangled fairy-tale
where fun and unusual happenings are all too common, and
you—the reader—become a character just like Harvard or Kansas
and are subject to the all-knowing, all-powerful, author of the story.
This daring piece tests the bounds of reality and subtly suggests
that you should question everything you know —

While most people in this story believe they are real-life, walking
talking humans, a small, somewhat violent sect of society has
realized they are actually part of a book. They lash out and
demand that the story have a happy ending, and they'll whomever
they have to. [Sic] An enormous battle erupts catching Harvard
and Kansas trapped in the middle forced to rely on their cunning
and a little help from an extra-large talking tarantula to save the day.

Thursday, November 13, 2014

Progressive Matrix

Filed under: General,Geometry — Tags: , — m759 @ 6:00 am

Yesterday's post and recent Hollywood news suggest
a meditation on a Progressive Matrix —

Oct. 12-14, 2005:

'A Poem for Pinter,' conclusion: 'Tick Tick Hash.'

'The Interpreter'-- Sean Penn to Nicole Kidman-- 'My Card.'

Click to enlarge.

"My card."

Structurally related images —

A sample Raven's Progressive Matrices  test item
(such items share the 3×3 structure of the hash symbol above):

IMAGE- Raven's Progressive Matrices item with symbols from Cullinane's box-style I Ching

Structural background —

Tuesday, September 23, 2014

Matrix

Filed under: General — m759 @ 11:00 am

From AP’s Today in History:

Happy birthday.

“It all adds up.” — Saul Bellow

The Matrix:

Monday, September 22, 2014

The Matrix continues…

Filed under: General — m759 @ 8:15 pm

From the opening credits of the 2013 film “Paranoia,”
a hint that you may have taken the red pill:

(Note the reflection.)

Friday, August 15, 2014

The Omega Matrix

Filed under: General,Geometry — Tags: — m759 @ 11:00 pm

(Continued)

The webpage Rosenhain and Göpel Tetrads in PG(3,2)
has been updated to include more material on symplectic structure.

Sunday, August 3, 2014

The Omega Matrix

Filed under: General,Geometry — Tags: , , — m759 @ 10:31 pm

Shown below is the matrix Omega from notes of Richard Evan Schwartz.
See also earlier versions (1976-1979) by Steven H. Cullinane.

IMAGE- The matrix Omega from notes of Richard Evan Schwartz. See also earlier versions (1977-1979) by Steven H. Cullinane.

Backstory:  The Schwartz Notes (June 1, 2011), and Schwartz on
the American Mathematical Society's current home page:

(Click to enlarge.)

Friday, May 30, 2014

Combinatorial Matrix Classes

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

A book by this title, Richard A. Brualdi’s  Combinatorial Matrix Classes ,
was published by Cambridge University Press in 2006:

For some related remarks, see The Counter (March 13, 2011).

My own work deals with combinatorial properties of matrices
of 0’s and 1’s, but in the context of Galois  (i.e., finite) fields,
not the real or complex fields. Despite the generality of
their titles, Combinatorial Matrix Theory  and Combinatorial
Matrix Classes  do not deal with Galois  matrices.

Saturday, June 2, 2012

Matrix Problem Revolutions

Filed under: General — m759 @ 1:28 am

(The sequel to yesterday's Matrix Problem Reloaded)

Wikipedia on the sci-fi weblog  io9.com

Newitz explained the significance of the name "io9":

"Well, io9s are input-output devices that let you see into the future.
They're brain implants that were outlawed because they drove
anyone who used one insane. We totally made that (device) up
to name the blog."

Jenna Wortham at wired.com, Jan. 2, 2008

From io9.com itself—

"Science fiction writer Ken MacLeod has another term for io9ers.
He calls them rapture fuckers.*"

— io9.com/explanations/

For the relevance of the term "revolutions" in this post's title, see
Wikipedia on Ken MacLeod.

I prefer to associate the number 9 with The Holy Field.

 

 

* MacLeod used this phrase in one of his novels, Newton's Wake.

Friday, June 1, 2012

Matrix Problem Reloaded

Filed under: General — Tags: , — m759 @ 5:24 pm

For Frigg's Day—

"The newest badass fantasy flick to hit theaters is Snow White and the Huntsman , out today, and I believe it proves my theory that Kristen Stewart is the Keanu Reeves of her generation…. With few lines but a lot of convincingly heroic facial expressions, Kristen Stewart does a great job channeling Keanu Reeves in The Matrix  (one of the dwarfs even calls her 'the one'!)."

— Annalee Newitz this morning, "The Awesome Terribleness of Snow White and the Huntsman "

See also yesterday's Matrix Problem.

Thursday, May 31, 2012

Matrix Problem

Filed under: General,Geometry — Tags: — m759 @ 7:20 pm

IMAGE- Charlize Theron as Ravenna with raven in poster for 'Snow White and the Huntsman'

Poster from Walpurgisnacht 2012

Raven’s Progressive Matrices problem:

IMAGE- Raven's Progressive Matrices problem based on triangular quarter- and half-diamonds

Click the problem for a related story.

For some related geometry, see Elements Diamond.
See also a post (Dream Time, May 3, 2010)
about geometry and an earlier Walpurgisnacht.

Sunday, May 8, 2011

Matrix

Filed under: General,Geometry — m759 @ 7:59 am

For Mother's Day

http://www.log24.com/log/pix10/100121-Trigrams.jpg

http://www.log24.com/log/pix11A/110508-Trigrams.jpg

From Thomas Mann, "Schopenhauer," 1938, in Essays of Three Decades , translated by H. T. Lowe-Porter, Alfred A. Knopf, 1947, pp. 372-410—

Page 372: THE PLEASURE we take in a metaphysical system, the gratification purveyed by the intellectual organization of the world into a closely reasoned, complete, and balanced structure of thought, is always of a pre-eminently aesthetic kind. It flows from the same source as the joy, the high and ever happy satisfaction we get from art, with its power to shape and order its material, to sort out life's manifold confusions so as to give us a clear and general view.

Truth and beauty must always be referred the one to the other. Each by itself, without the support given by the other, remains a very fluctuating value. Beauty that has not truth on its side and cannot have reference to it, does not live in it and through it, would be an empty chimera— and "What is truth?"

Saturday, August 7, 2010

The Matrix Reloaded

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

   For aficionados of mathematics and narrative

Illustration from
"The Galois Quaternion— A Story"

The Galois Quaternion

This resembles an attempt by Coxeter in 1950 to represent
a Galois geometry in the Euclidean plane—
Coxeter's 1950 representation in the Euclidean plane of the 9-point affine plane over GF(3)

The quaternion illustration above shows a more natural way to picture this geometry—
not with dots representing points in the Euclidean  plane, but rather with unit squares
representing points in a finite Galois  affine plane. The use of unit squares to
represent points in Galois space allows, in at least some cases, the actions
of finite groups to be represented more naturally than in Euclidean space.

See Galois Geometry, Geometry Simplified, and
Finite Geometry of the Square and Cube.

Thursday, August 5, 2010

The Matrix

Filed under: General — m759 @ 9:26 pm

The Presence of God in the Group: A Neglected Dimension
Ronald Sandison, Ledbury, Herefordshire, HR8 2EY, UK

Group Analysis  March 1993, vol. 26 no. 1, 55-65

Abstract

When people gather in small groups they are often aware of an indefinable supra-personal dimension. Anyone who has taken part in a camp-fire sing-song will have experienced this. The group setting at sundown was the time and place when folk-tales and fairy stories were woven. It was the time when the elders met to discuss the events of the day, when evensong or compline was sung or said in churches. There is something "special" about this conjunction of the group and the "going down of the sun." In this article I develop the idea that to take part in a small group can be, and often is, a spiritual experience. In giving a name to this experience I consider the proposition that God, or Spirit, is ever present in the group. I view the matrix as not only nurturing and holding but also as a dynamic container, and perhaps even generator, of spiritual force.

Related material

Dr. Sandison's obituary in this evening's Telegraph  and this journal on the date of his death.

Wednesday, October 23, 2024

The Delta Transform

Filed under: General — Tags: , , , — m759 @ 7:04 am

Rothko — "… the elimination of all obstacles between the painter and
the idea, and between the idea and the observer."

Walker Percy has similarly discussed elimination of obstacles between
the speaker and the word, and between the word and the hearer.

Walker Percy's chapter on 'The Delta Factor' from 'Message in the Bottle'

Click images to enlarge.

Related mathematics —

The source: http://finitegeometry.org/sc/gen/typednotes.html.

A document from the above image —

AN INVARIANCE OF SYMMETRY

BY STEVEN H. CULLINANE

We present a simple, surprising, and beautiful combinatorial
invariance of geometric symmetry, in an algebraic setting.

DEFINITION. A delta transform of a square array over a 4-set is
any pattern obtained from the array by a 1-to-1 substitution of the
four diagonally-divided two-color unit squares for the 4-set elements.

THEOREM. Every delta transform of the Klein group table has
ordinary or color-interchange symmetry, and remains symmetric under
the group G of 322,560 transformations generated by combining
permutations of rows and colums with permutations of quadrants.

PROOF (Sketch). The Klein group is the additive group of GF (4);
this suggests we regard the group's table  T as a matrix over that
field. So regarded, T is a linear combination of three (0,1)-matrices
that indicate the locations, in  T, of the 2-subsets of field elements.
The structural symmetry of these matrices accounts for the symmetry
of the delta transforms of  T, and is invariant under G.

All delta transforms of the 45 matrices in the algebra generated by
the images of  T under G are symmetric; there are many such algebras. 

THEOREM. If 1 m ≤ n2+2, there is an algebra of 4m
2n x 2n matrices over GF(4) with all delta transforms symmetric.

An induction proof constructs sets of basis matrices that yield
the desired symmetry and ensure closure under multiplication.

REFERENCE

S. H. Cullinane, Diamond theory (preprint).

Update of 1:12 AM ET on Friday, Oct. 25, 2024 —

The above "invariance of symmetry" document was written in 1978
for submission to the "Research Announcements" section of the
Bulletin of the American Mathematical Society .  This pro forma 
submission was, of course, rejected.  Though written before
I learned of similar underlying structures in the 1974 work of
R. T. Curtis on his "Miracle Octad Generator," it is not without
relevance to his work.

Thursday, September 26, 2024

Words and Images

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

From a post on "Matrix Bingo"

http://www.log24.com/log/pix18/180903-Womens_Night_Bingo-at48.41-The_Net.jpg

From a Log24 search for "Women's Night" —

The Mackey material, from St. Patrick's Day 2006, suggests a look
at the angels of Noah Jacobs' 1958 classic  Naming Day in Eden

Jacobs on angels —

"Their sensuous functions have been extinguished so that they
have no idea of sensible images, metaphor, tones or gestures.
They have no need in their noumenal sphere of these seductive
and puzzling artifices. Their penchant for unashamed abstraction
is the deepest strain in their make-up."

Compare and contrast —

Quilts  (for instance) as "seductive and puzzling artifices"
that embody symmetry.

Quilt geometry  as the exploitation  of symmetry.

Puzzle Art

Filed under: General — Tags: , — m759 @ 12:41 am

From the post Belgian Puzzle Art  —

'The Resort' S1E5 - Shapes Puzzle

Related reading . . .

— "The Devil, unlike the angels, was at home in the world of phenomena.
He knew how to combine pure concepts with empirical intuitions
which is the basic principle of linguistic creation."
(Noah Jonathan Jacobs, Naming-Day in Eden, Macmillan, 1958
In Macmillan 1969 revised edition, page 21.)

The figure of 25 parts discussed in
"On Linguistic Creation"–

5x5 ultra super magic square

— "Such is the square dance of Numbers."
(Jacques Derrida, Dissemination, 1972)

— "It all adds up."
(Saul Bellow, book title, 1994)

Saturday, September 14, 2024

Notes on a Friday the 13th Death

Filed under: General — Tags: , , , — m759 @ 8:40 pm

A passage accessed via the new URL Starbrick.art*

Thursday, February 25, 2021

Compare and Contrast

Filed under: General — Tags: , ,
,
— m759 @ 12:31 pm

“… What is your dream—your ideal? 
What is your News from Nowhere, or, rather,
What is the result of the little shake your hand has given
to the old pasteboard toy with a dozen bits of colored glass
for contents? And, most important of all, can you present it
in a narrative or romance which will enable me to pass an
idle hour not disagreeably? How, for instance, does it compare
in this respect with other prophetic books on the shelf?”

— Hudson, W. H.. A Crystal Age , 1887.
Open Road Media, Kindle Edition, page 2.

A related cultural note suggested by the New York Times  obituary today
of fashion designer Mary McFadden, who reportedly died yesterday
(a Friday the Thirteenth) and is described by the Times  as a late-life
partner of "eightfold-way" physicist Murray Gell-Mann —

* A reference to the 2-column 4-row matrix (a "brick") that underlies
the patterns in the Miracle Octad Generator  of R. T. Curtis. The only
connection of this eight-part matrix to Gell-Mann's "Eightfold Way"
that I know of is simply the number 8 itself.

Tuesday, August 13, 2024

For Sutton Foster

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

Once Upon a Matrix

Thursday, May 2, 2024

AI on Diamond Theory

Filed under: General — Tags: — m759 @ 1:55 am

The website PopAi.pro uses GPT-4 to summarize documents from the Web.

Input at PopAi on May 2, 2024:

The URL "http://www.log24.com/log/Diamond_Theory-1976-pp-1-12.pdf"

Output at PopAi, after a quick reading and analysis by GPT-4:

Diamond_Theory-1976-pp-1-12.pdf

12 Pages

The document appears to be an excerpt from a preprint titled "Diamond Theory" by Steven H. Cullinane, dated 1976. The text discusses theoretical aspects of matrices composed of geometric figures, focusing on properties related to symmetry, permutations, and abstract structure.

Main Concepts and Definitions:

The author introduces the concept of a "geometric matrix," a matrix whose elements are geometric figures, specifically triangular subsets of a square. He defines a "diamond" as a foursquare matrix with triangular elements. The text details the remarkable properties of a diamond-like matrix D, including its symmetrical behavior under various permutations of elements, rows, columns, and sub-squares. Additionally, the text addresses the algebraic properties of matrices by relating their elements to those of a finite field.

Theoretical Properties and Theorems:

Several key theorems are proposed, demonstrating the structural properties of matrices. One fundamental theorem states that any matrix from a set F can be expressed as a linear combination of block matrices. Other theorems delve into the regularity of matrices, defining a matrix as "regular" if it remains unchanged or converts to its complement under certain flips and rotations. The text also describes the process of forming a "normal" matrix and the conditions under which matrices can be considered plaid or normal based on the behavior of their block maps and regularities.

Applications and Miscellaneous Problems:

The author reflects on the discovery of these properties during the process of creating an abstract painting and extends the exploration to include various types of matrices such as cyclic, quadratic, and skew foursquares. The document concludes with miscellaneous problems and an addendum on generalized matrix multiplication, suggesting further research directions and applications of the theory presented.

In summary, "Diamond Theory" presents an intricate analysis of the structural and algebraic properties of matrices composed of geometric shapes, with implications for other mathematical domains. The work is a blend of geometry and abstract algebra, providing a foundation for understanding the symmetry and transformations of matrices with an artistic origin.

Some questions you may ask:

What properties of the diamond-like matrix D did the author discover in 1975?

What is the relationship between the properties of D and the four group according to the document?

How does the document define a 'good set' of four black and white geometric figures?

What theorem is used to explain the behavior of superimposing two members of Mn(F) according to the document?

Thursday, March 14, 2024

For Aestheticians:  Seeds, Good and Not So Good

Filed under: General — Tags: , , , — m759 @ 7:08 pm

In memory of . . .

Good Seed:  Sydell.

Not So Good:  Pearl.

This post was suggested by Sam Levinson's work in Whanganui NZ
and Alan D. Perlis's work in Birmingham AL

From South Dakota, related material for Bible fans —

Sunday, January 21, 2024

See More Glass

Filed under: General — Tags: , — m759 @ 1:00 pm

A story today about a new Rose Glass film at Sundance
suggests a review —

See also today's previous post and other posts tagged Verwandlungslehre.

Monday, January 15, 2024

Tuesday, September 26, 2023

If It’s Tuesday, This Must Be Belgium

Filed under: General — Tags: , , — m759 @ 9:19 am

Art Space: The Missing Links

Tuesday, Sept. 12, 2023. Tags:  — m759 @ 4:07 PM

Related material:  "Ducky" died,  Circle Zen,  Palmervision

Wednesday, June 21, 2023

Annals of Magical Thinking: The Rushmore Embedding

Filed under: General — Tags: , — m759 @ 11:53 am

http://www.log24.com/log/pix18/180830-Harry_Potter-Phil_Stone-Bloomsbury-2004-p168.jpg

Less magical: "What are vector embeddings?"

Thursday, June 15, 2023

Michaelmas 2019

Filed under: General — Tags: — m759 @ 1:06 pm

Transcribed from a PDF:

Received September 29, 2019, accepted October 15, 2019,
date of publication October 24, 2019, date of current version
November 7, 2019.

Digital Object Identifier 10.1109/ACCESS.2019.2949310

A Method for Determining
the Affine Equivalence of Boolean Functions

ZIYU WANG1 , XIAO ZENG1 , JINZHAO WU2,3, AND
GUOWU YANG1

1Big Data Research Center, School of Computer Science
and Engineering, University of Electronic Science and Technology
of China, Chengdu 611731, China

2Guangxi Key Laboratory of Hybrid Computation and
IC Design Analysis, Guangxi University for Nationalities,
Nanning 530006, China

3School of Computer and Electronic Information,
Guangxi University, Nanning 530004, China

Corresponding authors:
Jinzhao Wu (gxmdwjzh@aliyun.com) and
Guowu Yang (ygwuestc@163.com)

This work was supported in part by the National Natural Science Foundation
of China under Grant 61772006 and Grant 61572109, in part by the
State Key Laboratory of Information Security, Institute of Information Engineering, 
Chinese Academy of Sciences, Beijing, in part by the Science and Technology
Program of Guangxi  under Grant AB17129012, in part by the Science and
Technology Major Project of Guangxi under Grant AA17204096, in part by 
the Special Fund for Scientific and Technological Bases and Talents
of Guangxi under Grant 2016AD05050, and in part by the Special Fund for
Bagui Scholars of Guangxi, in part by the Open fund of State Key Laboratory 
of Information Security.

ABSTRACT 
Determining the affine equivalence of Boolean functions
has significant applications in circuit and cryptography.
Previous methods for determining this require a large
amount of computation when Boolean functions are bent
functions or when the truth table is sparse. This paper
presents a new method to determine the affine equivalence
based on matrix algebra. By transforming Boolean function
to the corresponding matrix representation, we first propose
and prove the congruent standard form of Boolean function.
It lays the foundation for the determination of equivalence
because affine Boolean functions must have the same
standard form. Then we find the generators of orthogonal
matrix group and symplectic matrix group, which greatly
reduce the search space. The computation complexity of
our method is o (2r2/2+n∗(nr) ), where is the number of
bit operations, and r  is the rank of the matrix, which is
the product of Boolean-1 matrix of the test Boolean function
and its transposition. The experimental results show that our
method is useful when the test Boolean function is no more
than 7 bits and r  is greater than 2.

INDEX TERMS  Logic synthesis, Boolean functions,
affine equivalence, matrix group, algorithm.

Meanwhile . . .

Saturday, April 15, 2023

Arrival

Filed under: General — Tags: , — m759 @ 12:58 pm

See as well this  journal on June 1, 2012 — Matrix Problem Reloaded.

Wednesday, February 15, 2023

Categorization Theory

Filed under: General — Tags: — m759 @ 5:55 pm

"And then there’s the ultimate unknown known:
the 'enlightenment' (satori, kensho) of Zen practice.
If my sense of it from accounts I have read is accurate,
it involves seeing the world and realizing that you always
knew its true nature, but you just didn’t know you knew
because you were too busy putting it into boxes and
matrices and categories and words. Which reminds us
again that while logical deductions and categorizations
can lead us to discoveries, they can also lead us away
from them."

James Harbeck on Groundhog Day, 2023

This post was suggested by a Log24 image from All Saints' Day, 2018

Related verbiage: Unthought Known.

Friday, January 13, 2023

The “Diamond Space” of Mazzola

Filed under: General — Tags: , , — m759 @ 11:30 am

The Source —

Some similar notions from my own work . . .

The "Digraph" of Mazzola might correspond to a directed graph
indicating the structure of a permutation, as at right below —

Mazzola's "Formula" might correpond to a matrix and translation that
transform the above "Space" of eight coordinates, and his "Gesture"
to a different way of generating affine transformations of that space . . . 
as in my webpage "Cube Space, 1984-2003."

Tuesday, December 27, 2022

The Forms of Being

Filed under: General — Tags: , — m759 @ 1:25 pm

"If the window is this matrix of ambi- or multivalence,
and the bars of the windows-the grid-are what help us
to see, to focus on, this matrix, they are themselves 
the symbol of the symbolist work of art. They function as
the multilevel representation through which the work of art
can allude, and even reconstitute, the forms of Being."

Page 59, Rosalind Krauss, "Grids," MIT Press,
October , Vol. 9 (Summer, 1979), pp. 50-64

Related material —

Click the above image for a related Log24 post of 15 years ago today.

A related literary remark —

"Imagine Raiders of the Lost Ark  set in 20th-century London, and then
imagine it written by a man steeped not in Hollywood movies but in Dante
and the things of the spirit, and you might begin to get a picture…."

— Doug Thorpe in an Amazon.com book review, not  of Dark Materials.

Monday, November 14, 2022

Plot Structure

Filed under: General — Tags: , — m759 @ 2:21 pm

From Peter J. Cameron's weblog today

"It happens sometimes that researchers working in different fields
study the same thing, give it different names, and don’t realise that
there is further work on the subject somewhere else…."

Cameron's example of a theorem connecting work on 
the same thing in different fields —

"Theorem  A partition Δ is equitable for a graph Γ if and only if
the projection matrix onto the subspace of functions constant
on parts of Δ commutes with the adjacency matrix of Γ."

A phrase from Cameron's remarks today —

"Thus we have to consider 'plot structure'…."

For more remarks on different fields and plot structure , see
"Quantum Tesseract Theorem" in this  weblog.

Wednesday, November 2, 2022

Groups and Spaces, 1979-2022

Filed under: General — Tags: , — m759 @ 1:15 pm

1979 —

2022 —

Tuesday, October 25, 2022

Orison Metadata

Filed under: General — Tags: — m759 @ 10:47 am

See also "Marxism" in Varadharajan's CV and . . .

Thursday, October 20, 2022

Déjà Vu All Over Again

Filed under: General — m759 @ 12:33 pm

"Ignore the red dot, for it is an illusion."

   "Red and Yellow, Blue and Green"

 

Saturday, October 8, 2022

Chandler Davis, 1926-2022

Filed under: General — m759 @ 10:04 am

Log24 art (colored Unicode symbols) from the above date of death:

"Click the red symbol, and"

— Adapted from "The Matrix."

Thursday, September 15, 2022

A Grid for Agent Smith*

Filed under: General — Tags: — m759 @ 3:23 pm

* See Hugo Weaving in "The Matrix" and "V for Vendetta."

Friday, August 19, 2022

The Guy Embedding

Filed under: General — Tags: , , — m759 @ 3:43 pm

M. J. T. Guy discovered that the lexicographic  version
of the Golay code contains, embedded within it, the
Miracle Octad Generator  (MOG)  of R. T. Curtis.

For 12 basis vectors of the lexicographic version, see below.

Basis vectors for the lexicographic version of the binary Golay code

For some context, click the embedded guy.

For a closely related, but simpler, mathematical
structure, see posts tagged The Omega Matrix.

Sunday, August 7, 2022

For the Church of the Wicked Stepmother:

Filed under: General — Tags: — m759 @ 9:00 am

Progressive Matrices

A sample Raven's Progressive Matrices  test item —

IMAGE- Raven's Progressive Matrices item with symbols from Cullinane's box-style I Ching

IMAGE- Charlize Theron as Ravenna with raven in poster for 'Snow White and the Huntsman'

Update of 10 AM ET Sunday, August 7, 2022 —

See as well Siobhan Roberts on geometry in The New York Times
on March 22, 2022, and a Log24 post on geometry on that date.

Tuesday, June 7, 2022

A Square for the Circle

Filed under: General — Tags: — m759 @ 10:36 am

The new URL matrix.bingo forwards to 

http://m759.net/wordpress/?s=5×5 .

IMAGE- Right 3-4-5 triangle with squares on sides and hypotenuse as base

“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

Saturday, May 21, 2022

Analysis, Real and Complex*

Filed under: General — m759 @ 1:48 pm
 

Jason Kehe at WIRED today —

"The Real Reason Matrix Resurrections  Bombed"

. . . .

"Lana Wachowski’s film practically burns with mirrors, with self-scrutiny. The very first shot is of an upside-down someone walking toward us. It’s a reflection, it turns out, in a puddle. We’re in for inversions and reversals, Wachowski is signaling, and not just cinematographically. The first third of the movie or so recapitulates the events of the first Matrix, but badly, unconvincingly. 'Why use old code,' one character asks, 'to mirror something new?' The movie critiques, even hates on, itself. It looks in the mirror and doesn’t like what it sees."

. . . .


Dr. Robert Ford — "Analysis."

* Title suggested by a textbook.

Thursday, May 12, 2022

Compare and Contrast

Filed under: General — Tags: , — m759 @ 1:04 am

Related reading:
 Shibumi: A N
ovel 
and
"The Diamond Theorem
  in Basque Country."

Sunday, April 24, 2022

Structuralism: Three Betweens

Filed under: General — Tags: , , , — m759 @ 10:44 am
 

Tuesday, November 3, 2009

Summa Mythologica

Filed under: General,Geometry — Tags:  — 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."

Wednesday, April 20, 2022

Physics for Poets

Filed under: General — Tags: , , — m759 @ 9:23 am

Excerpt from a long poem by Eliza Griswold


The square array above does not  contain Arfken's variant
labels
for ρ1, ρ2, and ρ3, although those variant labels were
included in Arfken's 1985 square array and in Arfken's 1985
list of six anticommuting sets, copied at MathWorld as above.
The omission of variant labels prevents a revised list of the
six anticommuting sets from containing more  distinct symbols
than there are matrices.

Revised list of anticommuting sets:

α1   α2   α3  ρ2  ρ3

γ1   γ2   γ3   ρ1   ρ

δ δ2   δ ρ1   ρ2 

α1    γ1   δσ2  σ3 

α  γ2   δσ1   σ3

α  γ3   δ3  σ1   σ2  .

Context for the poem: Quark Rock.
Context for the physics: Dirac Matrices.

Wednesday, February 23, 2022

Monday, December 27, 2021

Dated

Filed under: General — Tags: , — m759 @ 8:14 pm

Sunday, December 26, 2021

For Agent Smith

Filed under: General — Tags: — m759 @ 4:25 am

From Screen Rant — "datePublished": "2021-12-23T22:40:34Z" —

Related material —

James Hillman, "Egalitarian Typologies Versus 
The Perception of the Unique"  at . . .

http://www.compilerpress.ca/Competitiveness/
Anno/Anno%20Hillman%20Egal%201.htm
 .

Musical accompaniment for Storyville — Iko Iko
lyrics and background and performance

Saturday, December 25, 2021

Opposites Attract?

Filed under: General — Tags: — m759 @ 4:15 pm

The New Yorker  has illustrated Smith's remarks
with the following art print from 2001 —

An imposition of a public  space on a writer:

For the nature of the public  space, see Geometry of the I Ching .

Wednesday, December 22, 2021

Not a Hood Ornament

Filed under: General — Tags: — m759 @ 11:01 am

Tuesday, December 21, 2021

Raiders of the Inarticulate . . .

Filed under: General — Tags: , , — m759 @ 11:58 pm

. . . Continues.

". . . thematic preoccupations with binaries
(free will and destiny,
fact and fiction,
conscious and unconscious,
desire and fear)
and with the overarching notion
that stories become real
when they profoundly stir
one’s heart and mind.
These elements aren’t dramatized
as much as bluntly articulated . . . ."

— Nick Schager, thedailybeast.com, Dec. 21, 2021

Wednesday, December 15, 2021

In Memoriam:  Welcome to Westview

Filed under: General — Tags: , — m759 @ 7:48 am

Cicely Tyson  as  Matrix Oracle  continues…

Tuesday, December 14, 2021

Meta Verse

Filed under: General — Tags: , — m759 @ 11:35 pm

"Meta  isn't such a new thing 
 Meta  started long ago."

Log24 on All Souls' Day (Nov. 2), 2021

Anthony Garreffa at tweaktown.com

PUBLISHED SAT, DEC 11 2021 10:23 PM CST

When asked about the metaverse by The Verge in their interview [Dec. 9] with The Matrix Resurrections stars Keanu Reeves and Carrie-Anne Moss, Keanu said: "can we just not have metaverse be invented by Facebook".

He was asked by The Verge "you're not a fan?" to which Keanu replied: "No, but just the concept of metaverse is like way older than that. It's like a way older, and so for that moment to get to… I'm just like, 'Come on, man'".

Read more: https://www.tweaktown.com/news/83337/keanu-reeves-wants-you-to-know-facebook-didnt-invent-the-metaverse/index.html

See also Log24 posts tagged Date Time (Nov. 4, 2021).

 

Friday, December 10, 2021

Dance of the Lo Shu

Filed under: General — Tags: , , — m759 @ 4:46 am

The ancient Chinese matrix known as the Lo Shu
is one of 432 matrices equivalent under the action of . . .

The Lo Shu Group:

For related material, see (for instance) AGL(2,3) in . . .

"Let be be finale of seem.
The only emperor is the emperor of ice-cream."

— Wallace Stevens

Tuesday, December 7, 2021

“Maybe this isn’t the story we think it is.”

Filed under: General — Tags: — m759 @ 3:22 pm

Click for further details.

Thursday, December 2, 2021

Something Old, Something New

Filed under: General — Tags: , , — m759 @ 2:35 am

Night at the Museum:

Fictional Version —

Not So Fictional —

The Lo Shu as a Finite Space

Thursday, October 21, 2021

SIX — The Musical!

Filed under: General — m759 @ 10:11 am

From an Instagram post today:

As for SIX — the non-musical —

For further details, see Lost in the Matrix.

Monday, September 13, 2021

Duck Sup

Filed under: General — Tags: , — m759 @ 3:27 pm

Thursday, September 9, 2021

Enlarging the Spielraum… Continues.

Filed under: General — m759 @ 12:30 pm

Click the chessboard for some Chinese hermeneutics.

Wednesday, September 8, 2021

Adventures in Mix-and-Match Reality

Filed under: General — Tags: , — m759 @ 8:31 pm

See as well Gender Issues: Sleeping Beauty  (April 9, 2021).

Exalted Perception

Filed under: General — Tags: , — m759 @ 2:23 pm

The title is from an August 31 book review —

More recent cultural news —

"Simplify, simplify." — Thoreau.
 

The 4-Point Dream

::

Friday, September 3, 2021

IT (Plan 9 Continues.)

Filed under: General — m759 @ 2:46 am

From the Field of Manifestation link above —

"The number 9, that is to say, relates traditionally
to the Great Goddess of Many Names (Devi, 
Inanna, Ishtar, Astarte, Artemis, Venus, etc.)
as matrix of the cosmic process, whether in the
macrocosm or in a microcosmic field of manifestation."

— Joseph Campbell,
     The Inner Reaches of Outer Space

For Stephen King:

"I held my nose, I closed my eyes, I took a drink."

— "Love Potion Number 9

Tuesday, July 27, 2021

Dancing in the Moonlight

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


Instagram screenshot with added note.

Easy E for an Accountant:

 

Not So Easy:  E-Operators

"A great many other properties of  E-operators
have been found, which I have not space
to examine in detail."

— Sir Arthur EddingtonNew Pathways in Science ,
Cambridge University Press, 1935, page 271.
(This book also presents Eddington's unfortunate
speculations on the fine-structure constant.)

Update of 4:04 AM  ET:
Here is the not-so-tiny-dancer in
the above Instagram screenshot.

Friday, January 29, 2021

The Oracle

Filed under: General — Tags: , — m759 @ 2:02 pm

http://www.log24.com/log/pix10B/100815-NeoAndOracle.jpg

Miss Jane Pittman reportedly said that . . .

"People are always looking for someone to lead them
through the trials and tribulations." She said, "Every time
a child is born, the old folks looked in its face and asked,

'Are you the one?' ”

Thursday, January 21, 2021

Cock Tale for Rikki

Filed under: General — Tags: , — m759 @ 4:50 pm

With apologies to those readers unable to follow knight moves .

The Queen's Gambit , by Walter Tevis,
published Feb. 1983

“Would you care for a cocktail?” he asked pleasantly.
She looked around her at 
the quiet restaurant,
at the people eating lunch, at the 
table with desserts
near the velvet rope at the entrance to 
the dining room.
“A Gibson,” she said. “On the rocks.”

Omni  July 1982

"A silver tide of phosphenes boiled across my field of vision
as the matrix began to unfold in my head, a 3-D chessboard,
infinite and perfectly transparent."

Steely Dan, 1974 —

"'Rikki Don't Lose That Number' is a single
released in 1974 by rock/jazz rock group Steely Dan
and the opening track of their third album Pretzel Logic .
It was the most successful single of the group's career,
peaking at number 4 on the Billboard  Hot 100 in
the summer of 1974." — Wikipedia

Brian Harley, Mate in Two Moves , 1931—

The key is the cocktail that begins the proceedings.”

See as well my post "Introduction to Cyberspace" (May 26, 2020).

 

Monday, January 18, 2021

Interestingly

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

"Take out the papers and the trash"

—The first line of the song Yakety-Yak (1958).

Related cultural observation —

The above passage is from "The Matrix," a post of Nov. 23, 2017 —

Thursday, December 3, 2020

Bunker Bingo

Filed under: General — Tags: — m759 @ 11:59 am

See as well 5×5The Matrix of Abraham,  and Deutsche Schule Montevideo .

IMAGE- Right 3-4-5 triangle with squares on sides and hypotenuse as base

“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

Wednesday, October 21, 2020

Riddle for a Code Girl*

Filed under: General — Tags: , — m759 @ 10:28 am

Space People Lightbulb Puzzle
by presentationgo.com

“How many space people does it take
  to screw in a lightbulb?”

I.e. , the code girl of  the previous post.

Monday, September 14, 2020

Socrates in the Marketplace

Filed under: General — Tags: — m759 @ 7:39 am

Plato's diamond in Jowett's version of the Meno dialogue

Diamond Matrix slide template at presentationgo.com

“The 2×2 matrix is commonly used in business strategy
as a representational tool to show conflicting concepts and
for decision making. This four-quadrant matrix diagram
is perfect to be used for business or marketing matrices
like BCG, SWOT, Ansoff, risk assessment…

Additionally, it will also be suitable to illustrate 4 ideas or
concepts.” [Link on “illustrate” added.]

See also a Log24 search for “Resplendent.”

Sunday, August 23, 2020

Jung on the Quaternity…

Filed under: General — Tags: , — m759 @ 3:12 pm

Or:  "1, 2, 3 , 4, who are we  for?"

Related material —

Friday, November 15, 2019

Operators

Filed under: General — Tags: , — m759 @ 2:40 pm

Easy E

 

Not So Easy:  E-Operators

"A great many other properties of  E-operators
have been found, which I have not space
to examine in detail."

Sir Arthur Eddington, New Pathways in Science ,
Cambridge University Press, 1935, page 271.
(This book also presents Eddington's unfortunate
speculations on the fine-structure constant.)

Saturday, September 21, 2019

Annals of Random Fandom

Filed under: General — Tags: , , , — m759 @ 5:46 pm

For Dan Brown fans …

… and, for fans of The Matrix, another tale
from the above death date: May 16, 2019 —

An illustration from the above
Miracle Octad Generator post:

Related mathematics — Tetrahedron vs. Square.

Tuesday, August 13, 2019

Putting the Structure  in Structuralism

Filed under: General — Tags: , , , — m759 @ 8:34 pm

The Matrix of Lévi-Strauss —

(From his “Structure and Form: Reflections on a Work by Vladimir Propp.”
Translated from a 1960 work in French. It appeared in English as
Chapter VIII of Structural Anthropology, Volume 2  (U. of Chicago Press, 1976).
Chapter VIII was originally published in Cahiers de l’Institut de Science
Économique Appliquée 
, No. 9 (Series M, No. 7) (Paris: ISEA, March 1960).)

The structure  of the matrix of Lévi-Strauss —

Illustration from Diamond Theory , by Steven H. Cullinane (1976).

The relevant field of mathematics is not Boolean algebra, but rather
Galois geometry.

The Central Myth

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

Wikipedia on film producer Lorenzo di Bonaventura
(Harvard AB (1980) in Intellectual History*) —

“His tenure at Warner Bros. included discovering and
shepherding The Matrix  into production, and the
purchase of the rights to the Harry Potter  books by
J. K. Rowling.”

From the previous post

“But he enters into the central myth of
this book at another, higher level as well;
for he is an artist, a potter . . . .

— Wendy Doniger O’Flaherty on
Claude Lévi-Strauss, author of
The Jealous Potter

* See as well “What is Intellectual History?” and
Magic for Liars .

Wednesday, July 24, 2019

The Batty Farewell

Filed under: General — Tags: , , — m759 @ 8:40 pm

Adam Rogers today on "Rutger Hauer in Blade Runner , playing
the artificial* person Roy Batty in his death scene." 

* See the word "Artifice" in this  journal,
   as well as Tears in Rain . . .

Game Over

The film "The Matrix," illustrated
Coordinates for generating the Miracle Octad Generator

and Adam Rogers in
    the previous post.

 

Friday, May 3, 2019

The Structure of Story Space

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

T. S. Eliot

Four Quartets

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

Lévi-Strauss

A Permanent Order of Wondertale Elements

In Vol. I of Structural Anthropology , p. 209, I have shown that this analysis alone can account for the double aspect of time representation in all mythical systems: the narrative is both “in time” (it consists of a succession of events) and “beyond” (its value is permanent). With regard to Propp’s theories my analysis offers another advantage: I can reconcile much better than Propp himself  his principle of a permanent order of wondertale elements with the fact that certain functions or groups of functions are shifted from one tale to the next (pp. 97-98. p. 108). If my view is accepted, the chronological succession will come to be absorbed into an atemporal matrix structure whose form is indeed constant. The shifting of functions is then no more than a mode of permutation (by vertical columns or fractions of columns).

Or by congruent quarter-sections.

Sunday, April 7, 2019

Block Talk

Filed under: General — Tags: — m759 @ 5:48 am

David Brooks in The New York Times  Sunday  Review   today

" 'In the deeps are the violence and terror of which psychology 
has warned us,' Annie Dillard writes in 'Teaching a Stone to Talk.' 
'But if you ride these monsters deeper down, if you drop with them
farther over the world’s rim, you find what our sciences cannot locate 
or name, the substrate, the ocean or matrix or ether which buoys
the rest, which gives goodness its power for good, and evil its power
for evil, the unified field: our complex and inexplicable caring for
each other.' "

Annie Dillard on the legendary philosopher's stone

“… if Holy the Firm is matter at its dullest, Aristotle’s materia prima ,
absolute zero, and since Holy the Firm is in touch with the Absolute
at base, then the circle is unbroken.  And it is…. Holy the Firm is
in short the philosopher’s stone.”

See also "The Thing and I."

Monday, March 25, 2019

Espacement

(Continued from the previous post.)

In-Between "Spacing" and the "Chôra "
in Derrida: A Pre-Originary Medium?

By Louise Burchill

(Ch. 2 in Henk Oosterling & Ewa Plonowska Ziarek (Eds.),  Intermedialities: Philosophy, Arts, Politics , Lexington Books, October 14, 2010)

"The term 'spacing' ('espacement ') is absolutely central to Derrida's entire corpus, where it is indissociable from those of différance  (characterized, in the text from 1968 bearing this name, as '[at once] spacing [and] temporizing' 1), writing  (of which 'spacing' is said to be 'the fundamental property' 2) and deconstruction (with one of Derrida's last major texts, Le Toucher: Jean-Luc Nancy , specifying 'spacing ' to be 'the first word of any deconstruction' 3)."

1  Jacques Derrida, “La Différance,” in Marges – de la philosophie  (Paris: Minuit, 1972), p. 14. Henceforth cited as  D  .

2  Jacques Derrida, “Freud and the Scene of Writing,” trans. A. Bass, in Writing and  Difference  (Chicago: University of Chicago Press, 1978), p. 217. Henceforth cited as FSW .

3  Jacques Derrida, Le Toucher, Jean-Luc Nancy  (Paris: Galilée, 2000), p. 207.

. . . .

"… a particularly interesting point is made in this respect by the French philosopher, Michel Haar. After remarking that the force Derrida attributes to différance  consists simply of the series of its effects, and is, for this reason, 'an indefinite process of substitutions or permutations,' Haar specifies that, for this process to be something other than a simple 'actualisation' lacking any real power of effectivity, it would need “a soubassement porteur ' – let’s say a 'conducting underlay' or 'conducting medium' which would not, however, be an absolute base, nor an 'origin' or 'cause.' If then, as Haar concludes, différance  and spacing show themselves to belong to 'a pure Apollonism' 'haunted by the groundless ground,' which they lack and deprive themselves of,16 we can better understand both the threat posed by the 'figures' of space and the mother in the Timaeus  and, as a result, Derrida’s insistent attempts to disqualify them. So great, it would seem, is the menace to différance  that Derrida must, in a 'properly' apotropaic  gesture, ward off these 'figures' of an archaic, chthonic, spatial matrix in any and all ways possible…."

16  Michel Haar, “Le jeu de Nietzsche dans Derrida,” Revue philosophique de la France et de l’Etranger  2 (1990): 207-227.

. . . .

… "The conclusion to be drawn from Democritus' conception of rhuthmos , as well as from Plato's conception of the chôra , is not, therefore, as Derrida would have it, that a differential field understood as an originary site of inscription would 'produce' the spatiality of space but, on the contrary, that 'differentiation in general' depends upon a certain 'spatial milieu' – what Haar would name a 'groundless ground' – revealed as such to be an 'in-between' more 'originary' than the play of differences it in-forms. As such, this conclusion obviously extends beyond Derrida's conception of 'spacing,' encompassing contemporary philosophy's continual privileging of temporization in its elaboration of a pre-ontological 'opening' – or, shall we say, 'in-between.'

For permutations and a possible "groundless ground," see
the eightfold cube and group actions both on a set of eight
building blocks arranged in a cube (a "conducting base") and
on the set of seven natural interstices (espacements )  between
the blocks. Such group actions provide an elementary picture of
the isomorphism between the groups PSL(2,7) (acting on the
eight blocks) and GL(3,2) (acting on the seven interstices).

Espacements
 

For the Church of Synchronology

See also, from the reported publication date of the above book
Intermedialities , the Log24 post Synchronicity.

Saturday, February 23, 2019

Code Rain

Filed under: General — Tags: — m759 @ 11:30 pm

See 031105-code in this journal, the Wachowskis
at Wikipedia, and The Omega Matrix in this journal.

Friday, February 15, 2019

A Simple Interlacing

Filed under: General — m759 @ 1:07 pm

Paul Valéry, "Introduction to the Method of Leonardo da Vinci,"
La Nouvelle Revue , Paris, Vol. 95 (1895)—

"Regarded thus, the ornamental conception is to the individual arts
what mathematics is to the other sciences. …the objects chosen
and arranged with a view to a particular effect seem as if disengaged
from most of their properties and only reassume them in the effect,
in, that is to say, the mind of the detached spectator. It is thus
by means of an abstraction that the work of art can be constructed,
and is more or less easy to define according as the elements borrowed
from reality for it are more or less complex. Inversely it is by a sort of
induction, by the production of mental images, that all works of art are
appreciated, and this production must equally be more or less active,
more or less tiring, according as it is set in motion by a simple interlacing
on a vase or a broken phrase by Pascal."

— Translated by Thomas McGreevy (Valéry's Selected Writings,
     New Directions, 1950)

Related art —

Sunday, January 13, 2019

The Clifford Narrative

Filed under: General — Tags: — m759 @ 3:17 am

See also Clifford in this  journal, in particular 
The Matrix for Quantum Mystics 
(Log24, St. Andrew's Day, 2017).

Monday, July 9, 2018

Beaty Confidential

Filed under: General — Tags: — m759 @ 2:24 pm

See also Lumet's "Child's Play."

Related entertainment —

Thursday, July 5, 2018

Paz:

Filed under: General,Geometry — Tags: , , — m759 @ 1:44 pm

Some context for what Heidegger called
das Spiegel-Spiel des Gevierts

From Helen Lane's translation of El Mono Gramático ,
a book by Nobel winner Octavio Paz first published
in Barcelona by Seix Barral in 1974 —

Simultaneous perspective does not look upon language as a path because it is not the search for meaning that orients it. Poetry does not attempt to discover what there is at the end of the road; it conceives of the text as a series of transparent strata within which the various parts—the different verbal and semantic currents—produce momentary configurations as they intertwine or break apart, as they reflect each other or efface each other. Poetry contemplates itself, fuses with itself, and obliterates itself in the crystallizations of language. Apparitions, metamorphoses, volatilizations, precipitations of presences. These configurations are crystallized time: although they are perpetually in motion, they always point to the same hour—the hour of change. Each one of them contains all the others, each one is inside the others: change is only the oft-repeated and ever-different metaphor of identity.

— Paz, Octavio. The Monkey Grammarian 
(Kindle Locations 1185-1191). 
Arcade Publishing. Kindle Edition. 

A related 1960 meditation from Claude Lévi-Strauss taken from a 
Log24 post of St. Andrew's Day 2017,  "The Matrix for Quantum Mystics":

The Matrix of Lévi-Strauss —

"In Vol. I of Structural Anthropology , p. 209, I have shown that
this analysis alone can account for the double aspect of time
representation in all mythical systems: the narrative is both
'in time' (it consists of a succession of events) and 'beyond'
(its value is permanent)." — Claude Lévi-Strauss

I prefer the earlier, better-known, remarks on time by T. S. Eliot
in Four Quartets , and the following four quartets
(from The Matrix Meets the Grid) —

.

Tuesday, July 3, 2018

Lost in Quantum Space

Filed under: General,Geometry — Tags: , — m759 @ 10:45 am

Combining concepts from earlier posts today, we have the above title.

A more concise alternative title

Lost in the Matrix

For some related non -fiction, see posts tagged Dirac and Geometry.

Monday, June 25, 2018

The Trials of Device

Filed under: General — Tags: , , — m759 @ 9:34 am

"A blank underlies the trials of device."

Wallace Stevens

"Designing with just a blank piece of paper is very quiet."

Kate Cullinane

Related material —

An image posted at 12 AM ET December 25, 2014:

The image stands for the
phrase "five by five,"
meaning "loud and clear."

Other posts featuring the above 5×5 square with some added structure:

Thursday, June 21, 2018

Kummerhenge

Filed under: General,Geometry — Tags: , , — m759 @ 2:19 am

See also the Omega Matrix in this  journal.

Tuesday, May 29, 2018

The Schwartz Meme

Filed under: General — Tags: — m759 @ 1:33 pm

IMAGE- The matrix Omega from notes of Richard Evan Schwartz. See also earlier versions (1977-1979) by Steven H. Cullinane.

Aficionados of the preposterous joke 
(see yesterday's post Epstein on Art
may consult a Google Image Search for
Schwartz Meme.

I prefer Schwartz même —

Saturday, April 14, 2018

Immanentizing the Transcendence

Filed under: General — Tags: , — m759 @ 10:15 am

The title refers to the previous two posts.

Related literature —

Plato's Ghost: The Modernist Transformation of Mathematics
(Princeton University Press, 2008)  and . . .

Plato's diamond-in-a-matrix:

Plato's diamond in Jowett's version of the Meno dialogue

Tuesday, February 27, 2018

Raiders of the Lost Images

Filed under: General,Geometry — Tags: , — m759 @ 11:28 am

On the recent film "Justice League" —

From DC Extended Universe Wiki, "Mother Box" —

"However, during World War I, the British rediscovered
mankind's lost Mother Box. They conducted numerous studies
but were unable to date it due to its age. The Box was then
shelved in an archive, up until the night Superman died,
where it was then sent to Doctor Silas Stone, who
recognized it as a perpetual energy matrix. . . ." [Link added.]

The cube shape of the lost Mother Box, also known as the
Change Engine, is shared by the Stone in a novel by Charles Williams,
Many Dimensions . See the Solomon's Cube webpage.

See too the matrix of Claude Lévi-Strauss in posts tagged
Verwandlungslehre .

Some literary background:

Who speaks in primordial images speaks to us
as with a thousand trumpets, he grips and overpowers,
and at the same time he elevates that which he treats
out of the individual and transitory into the sphere of
the eternal. 
— C. G. JUNG

"In the conscious use of primordial images—
the archetypes of thought—
one modern novelist stands out as adept and
grand master: Charles Williams.
In The Place of the Lion  he incarnates Plato’s
celestial archetypes with hair-raising plausibility.
In Many Dimensions  he brings a flock of ordinary
mortals face to face with the stone bearing
the Tetragrammaton, the Divine Name, the sign of Four.
Whether we understand every line of a Williams novel
or not, we feel something deep inside us quicken
as Williams tells the tale.

Here, in The Greater Trumps , he has turned to
one of the prime mysteries of earth . . . ."

— William Lindsay Gresham, Preface (1950) to
Charles Williams's The Greater Trumps  (1932)

For fans of what the recent series Westworld  called "bulk apperception" —

Monday, November 27, 2017

The Golay Code via Witt’s Construction

Filed under: General,Geometry — Tags: — m759 @ 2:08 pm

Reference

Hansen, Robert Peter, "Construction and Simplicity of
the Large Mathieu Groups" (2011). Master's Theses. 4053. 
http://scholarworks.sjsu.edu/etd_theses/4053.

See also The Matrix Meets the Grid (Log24, Nov. 24).
More generally, see SPLAG in this journal.

Saturday, November 25, 2017

Night at the Museum

Filed under: General — Tags: — m759 @ 9:45 pm

The previous post suggests a review of remarks by Adam Gopnik
in The New Yorker  on February 27, 2017 on "The Matrix" hypothesis—

"The thesis that we are in a simulation is, as people who
track such things know—my own college-age son has
explained it to me—far from a joke, or a mere conceit.
The argument, actually debated at length at the
American Museum of Natural History just last year, is that
the odds are overwhelming that ours is a simulated universe.
The argument is elegant."

No, it is not. 

See as well my own remarks on the date of the above museum debate
Tuesday, April 5, 2016.

From those remarks, a Halloween 2014 image that provides a
companion-piece to the "Easy E" of today's previous post

E-Elements

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

German mathematician Wolf Barth reportedly died
on December 30, 2016.

Flashback to this journal on that date *

From "The Man Who Tried to Redeem the World with Logic" —

"The following June, 1945, von Neumann penned
what would become a historic document entitled
'First Draft of a Report on the EDVAC,' the first published
description of a stored-program binary computing machine—
the modern computer."

Image from von Neumann's report —

Version converted to text —


* And, of course, to the later post  Easy E for Cullinan  (Feb. 28, 2017).
    Cullinan, second from left below, is the now-famous Oscars accountant.

Thursday, November 23, 2017

Lévi-Strauss vs. Propp

Filed under: General,Geometry — Tags: , , , — m759 @ 12:25 pm
​Claude Lévi-Strauss

From his Structure and Form:
Reflections on a Work by Vladimir Propp
” *

To maintain. as I have done. that the permutability of contents is not arbitrary amounts to saying that, if the analysis is carried to a sufficiently deep level, behind diversity we will discover constancy. And, of course. the avowed constancy of form must not hide from us that functions are also permutable.

The structure of the folktale as it is illustrated by Propp presents a chronological succession of qualitatively distinct functions. each constituting an independent genre. One can wonder whether—as with dramatis personae and their attributes— Propp does not stop too soon, seeking the form too close to the level of empirical observation. Among the thirty-one functions that he distinguishes, several are reducible to the same  function reappearing at different  moments of the narrative but after undergoing one or a number of transformations . I have already suggested that this could be true of the false hero (a transformation of the villain), of assigning a difficult task (a transformation of the test), etc. (see p. 181 above), and that in this case the two parties  constituting the fundamental tale would themselves be transformations of each other.

Nothing prevents pushing this reduction even further and analyzing each separate partie  into a small number of recurrent functions, so that several of Propp’s functions would constitute groups of transformations of one and the same function. We could treat the “violation” as the reverse of the “prohibition” and the latter as a negative transformation of the “injunction.” The “departure” of the hero and his “return” would appear as the negative and positive expressions of the same disjunctive function. The “quest” of the hero (hero pursues someone or something) would become the opposite of “pursuit” (hero is pursued by something or someone), etc.

In Vol. I of Structural Anthropology , p. 209, I have shown that this analysis alone can account for the double aspect of time representation in all mythical systems: the narrative is both “in time” (it consists of a succession of events) and “beyond” (its value is permanent). With regard to Propp’s theories my analysis offers another advantage: I can reconcile much better than Propp himself  his principle of a permanent order of wondertale elements with the fact that certain functions or groups of functions are shifted from one tale to the next (pp. 97-98. p. 108) If my view is accepted, the chronological succession will come to be absorbed into an atemporal matrix structure whose form is indeed constant. The shifting of functions is then no more than a mode of permutation (by vertical columns or fractions of columns).

These critical remarks are certainly valid for the method used by Propp and for his conclusions. However. it cannot be stressed enough that Propp envisioned them and in several places formulated with perfect clarity the solutions I have just suggested. Let us take up again from this viewpoint the two essential themes of our discussion: constancy of the content (in spite of its permutability) and permutability of functions (in spite of their constancy).

* Translated from a 1960 work in French.  It appeared in English as Chapter VIII
of Structural Anthropology, Volume 2  (U. of Chicago Press, 1976).  Chapter VIII
was originally published in Cahiers de l’Institut de Science 
Économique Appliquée , 
No. 9 (Series M, No. 7) (Paris: ISEA, March 1960).

See also “Lévi-Strauss” + Formula  in this journal.

Some background related to the previous post

Sunday, August 13, 2017

The Red Pill

Filed under: General — m759 @ 11:45 am

"We have passed through the looking glass
and down the rabbit hole."

Kurt Andersen in the Sept. 2017 Atlantic

See as well "the desert of the real" and, 
for comparison, College of the Desert in this  journal.

Tuesday, March 21, 2017

Requiescat in Pace

Filed under: General — Tags: — m759 @ 7:45 pm

The Chicago Tribune  today —

H. Wilbert Norton, college president
and Christian missionary, dies

Norton reportedly died at 102 on Feb. 20, 2017.

This evening's previous post linked the death dates of two
academics to two Log24 posts that both contained the
following image —

For some backstory, see the Log24 posts from the date
of Norton's reported death, February 20.

Wednesday, March 8, 2017

Inscapes

Filed under: General,Geometry — Tags: — m759 @ 6:42 pm

"The particulars of attention,
whether subjective or objective,
are unshackled through form,
and offered as a relational matrix …."

— Kent Johnson in a 1993 essay

Illustration

Commentary

The 16 Dirac matrices form six anticommuting sets of five matrices each (Arfken 1985, p. 214):

1. alpha_1alpha_2alpha_3alpha_4alpha_5,

2. y_1y_2y_3y_4y_5,

3. delta_1delta_2delta_3rho_1rho_2,

4. alpha_1y_1delta_1sigma_2sigma_3,

5. alpha_2y_2delta_2sigma_1sigma_3,

6. alpha_3y_3delta_3sigma_1sigma_2.

SEE ALSO:  Pauli Matrices

REFERENCES:

Arfken, G. Mathematical Methods for Physicists, 3rd ed.  Orlando, FL: Academic Press, pp. 211-217, 1985.

Berestetskii, V. B.; Lifshitz, E. M.; and Pitaevskii, L. P. "Algebra of Dirac Matrices." §22 in Quantum Electrodynamics, 2nd ed.  Oxford, England: Pergamon Press, pp. 80-84, 1982.

Bethe, H. A. and Salpeter, E. Quantum Mechanics of One- and Two-Electron Atoms.  New York: Plenum, pp. 47-48, 1977.

Bjorken, J. D. and Drell, S. D. Relativistic Quantum Mechanics.  New York: McGraw-Hill, 1964.

Dirac, P. A. M. Principles of Quantum Mechanics, 4th ed.  Oxford, England: Oxford University Press, 1982.

Goldstein, H. Classical Mechanics, 2nd ed.  Reading, MA: Addison-Wesley, p. 580, 1980.

Good, R. H. Jr. "Properties of Dirac Matrices." Rev. Mod. Phys. 27, 187-211, 1955.

Referenced on Wolfram|Alpha:  Dirac Matrices

CITE THIS AS:

Weisstein, Eric W.  "Dirac Matrices."

From MathWorld— A Wolfram Web Resource. 
http://mathworld.wolfram.com/DiracMatrices.html

Tuesday, March 7, 2017

Signature Backdrop

Filed under: General — Tags: , — m759 @ 9:00 pm

"The Bitter End’s signature stage backdrop —
a bare 150-year-old brick wall — helped distinguish it from
other popular bohemian hangouts like the Village Gate  
and the Village Vanguard. It appeared on the cover of
Peter, Paul and Mary’s first album."

The New York Times  this evening on a Sunday death

Commentary

“Looking carefully at Golay’s code is like staring into the sun.”

— Richard Evan Schwartz

See also Schwartz in "The Omega Matrix," a post of 5 PM ET Sunday:

Monday, February 20, 2017

Mathematics and Narrative

Filed under: General,Geometry — Tags: , , — m759 @ 2:40 pm

Mathematics —

Hudson's parametrization of the
4×4 square, published in 1905:

A later parametrization, from this date in 1986:

http://www.log24.com/log/pix11/110220-relativprob.jpg

A note from later in 1986 shows the equivalence of these
two parametrizations:

Narrative —

Posts tagged Memory-History-Geometry.

The mathematically challenged may prefer the narrative of the
Creation Matrix from the religion of the Transformers:

"According to religious legend, the core of the Matrix
was created from Solomus, the god of wisdom,
trapped in the form of a crystal by Mortilus, the god
of death. Following the defeat of Mortilus, Solomus
managed to transform his crystal prison into the Matrix—
a conduit for the energies of Primus, who had himself
transformed into the life-giving computer Vector Sigma."

Monday, December 12, 2016

Raiders of the Lost Chord

Filed under: General — Tags: — m759 @ 11:30 am

Readings for Sinatra's birthday

Tuesday, November 22, 2016

Jargon

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

See "sacerdotal jargon" in this journal.

For those who prefer scientific  jargon —

"… open its reading to
combinational possibilities
outside its larger narrative flow.
The particulars of attention,
whether subjective or objective,
are unshackled through form,
and offered as a relational matrix …."

— Kent Johnson in a 1993 essay

For some science that is not just jargon, see

and, also from posts tagged Dirac and Geometry

Anticommuting Dirac matrices as spreads of projective lines

The above line complex also illustrates an outer automorphism
of the symmetric group S6. See last Thursday's post "Rotman and
the Outer Automorphism
."

Older Posts »

Powered by WordPress