Log24

Monday, September 26, 2016

Myspace China

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

Revisited

Thursday, May 31, 2018

Eightfold Suffering:

Filed under: General,Geometry — Tags: — m759 @ 9:23 PM

A New, Improved Version of  Quantum Suffering !

Background for group actions on the eightfold cube

See also other posts now tagged Quantum Suffering 
as well as — related to the image above of the Great Wall

Myspace China.

Tuesday, September 26, 2017

Happy Birthday, T. S. Eliot

Filed under: General — m759 @ 2:56 AM

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

Four Quartets

See posts now tagged Myspace China.

Friday, June 14, 2013

Object of Beauty

Filed under: General,Geometry — Tags: , — m759 @ 2:01 AM

This journal on July 5, 2007 —

The Eightfold Cube and its Inner Structure

“It is not clear why MySpace China will be successful."

— The Chinese magazine Caijing  in 2007, quoted in
Asia Sentinel  on July 12, 2011

This  journal on that same date,  July 12, 2011 —

http://www.log24.com/log/pix11B/110712-ObjectOfBeauty.jpg

See also the eightfold cube and kindergarten blocks
at finitegeometry.org/sc.

Friedrich Froebel, Froebel's Chief Writings on Education ,
Part II, "The Kindergarten," Ch. III, "The Third Play":

"The little ones, who always long for novelty and change,
love this simple plaything in its unvarying form and in its
constant number, even as they love their fairy tales with
the ever-recurring dwarfs…."

This journal, Group Actions, Nov. 14, 2012:

"Those who insist on vulgarizing their mathematics
may regard linear and affine group actions on the eight
cubes as the dance of  Snow White (representing (0,0,0))
and the Seven Dwarfs—

  ."

Edwin M. Knowles Fine China Company, 1991

Monday, September 26, 2016

The Embedding

Filed under: General — Tags: — m759 @ 10:45 AM

From this morning's 3:33 AM ET post

Adapted from a post of Dec. 8, 2012, "Defining the Contest" —

      From a post of Sept. 22,
  "Binary Opposition Illustrated" —

From Sunday's news

Palmervision

Filed under: General — Tags: — m759 @ 3:33 AM

Eleanor Arroway and Palmer Joss in the "Occam's Razor"
scene from the 1997 film "Contact"

Sunday, September 25, 2016

Introduction to Pragmatism

Filed under: General — Tags: — m759 @ 7:29 AM

Stanford Encyclopedia of Philosophy
on the origins of Pragmatism:

"Pragmatism had been born in the discussions at
a ‘metaphysical club’ in Harvard around 1870
(see Menand…*). Peirce and James participated
in these discussions along with some other philosophers
and philosophically inclined lawyers. As we have
already noted, Peirce developed these ideas in his
publications from the 1870s."

From "How to Make Our Ideas Clear,"
by Charles Sanders Peirce in 1878 —

"The very first lesson that we have a right to demand that logic shall teach us is, how to make our ideas clear; and a most important one it is, depreciated only by minds who stand in need of it. To know what we think, to be masters of our own meaning, will make a solid foundation for great and weighty thought. It is most easily learned by those whose ideas are meagre and restricted; and far happier they than such as wallow helplessly in a rich mud of conceptions. A nation, it is true, may, in the course of generations, overcome the disadvantage of an excessive wealth of language and its natural concomitant, a vast, unfathomable deep of ideas. We may see it in history, slowly perfecting its literary forms, sloughing at length its metaphysics, and, by virtue of the untirable patience which is often a compensation, attaining great excellence in every branch of mental acquirement. The page of history is not yet unrolled which is to tell us whether such a people will or will not in the long-run prevail over one whose ideas (like the words of their language) are few, but which possesses a wonderful mastery over those which it has. For an individual, however, there can be no question that a few clear ideas are worth more than many confused ones. A young man would hardly be persuaded to sacrifice the greater part of his thoughts to save the rest; and the muddled head is the least apt to see the necessity of such a sacrifice. Him we can usually only commiserate, as a person with a congenital defect. Time will help him, but intellectual maturity with regard to clearness comes rather late, an unfortunate arrangement of Nature, inasmuch as clearness is of less use to a man settled in life, whose errors have in great measure had their effect, than it would be to one whose path lies before him. It is terrible to see how a single unclear idea, a single formula without meaning, lurking in a young man's head, will sometimes act like an obstruction of inert matter in an artery, hindering the nutrition of the brain, and condemning its victim to pine away in the fullness of his intellectual vigor and in the midst of intellectual plenty. Many a man has cherished for years as his hobby some vague shadow of an idea, too meaningless to be positively false; he has, nevertheless, passionately loved it, has made it his companion by day and by night, and has given to it his strength and his life, leaving all other occupations for its sake, and in short has lived with it and for it, until it has become, as it were, flesh of his flesh and bone of his bone; and then he has waked up some bright morning to find it gone, clean vanished away like the beautiful Melusina of the fable, and the essence of his life gone with it. I have myself known such a man; and who can tell how many histories of circle-squarers, metaphysicians, astrologers, and what not, may not be told in the old German story?"

Peirce himself may or may not have been entirely successful
in making his ideas clear.  See Where Credit Is Due  (Log24, 
June 11, 2016) and the Wikipedia article Categories (Peirce).

* Menand, L., 2001. The Metaphysical Club A Story of
Ideas in America
 
, New York:  Farrar, Straus and Giroux

Saturday, September 24, 2016

The Seven Seals

Filed under: General,Geometry — Tags: — m759 @ 7:23 AM

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."

Some Galois geometry —

See the previous post for more narrative.

Core Structure

Filed under: General,Geometry — Tags: — m759 @ 6:40 AM

For the director of "Interstellar" and "Inception"

At the core of the 4x4x4 cube is …

 


                                                      Cover modified.

The Eightfold Cube

Sunday, November 9, 2014

Sermon

Filed under: General — Tags: , , , — m759 @ 11:00 AM

The Ideas

“We tell ourselves stories in order to live….
We interpret what we see, select the most workable
of multiple choices. We live entirely, especially if we
are writers, by the imposition of a narrative line upon
disparate images, by the ‘ideas’  with which we have
learned to freeze the shifting phantasmagoria
which is our actual experience.”
— Joan Didion

See Didion and the I Ching  and posts tagged Plato in China .

Tuesday, August 30, 2011

Boundary

Filed under: General — Tags: — m759 @ 11:07 AM

A comment yesterday on the New York Times  philosophy column “The Stone” quoted Karl Barth—

Man is the creature of the boundary between heaven and earth.”

See also Plato’s theory of ideas (or “forms”) and the I Ching

The eight trigrams are images not so much of objects as of states of change. This view is associated with the concept expressed in the teachings of Lao-tse, as also in those of Confucius, that every event in the visible world is the effect of an “image,” that is, of an idea in the unseen world. Accordingly, everything that happens on earth is only a reproduction, as it were, of an event in a world beyond our sense perception; as regards its occurrence in time, it is later than the suprasensible event. The holy men and sages, who are in contact with those higher spheres, have access to these ideas through direct intuition and are therefore able to intervene decisively in events in the world. Thus man is linked with heaven, the suprasensible world of ideas, and with earth, the material world of visible things, to form with these a trinity of the primal powers.

— Richard Wilhelm, Introduction to the I Ching

Friday, March 31, 2006

Friday March 31, 2006

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

Women's History Month continues…
 
Ontology Alignment

"He had with him a small red book of Mao's poems, and as he talked he squared it on the table, aligned it with the table edge first vertically and then horizontally.  To understand who Michael Laski is you must have a feeling for that kind of compulsion."

— Joan Didion in the
Saturday Evening Post,
Nov. 18, 1967 (reprinted in
Slouching Towards Bethlehem)

"Or were you," I said.
He said nothing.
"Raised a Catholic," I said.
He aligned a square crystal paperweight with the edge of his desk blotter.

— Joan Didion in
The Last Thing He Wanted,
Knopf, 1996

"It was Plato who best expressed– who veritably embodied– the tension between the narrative arts and mathematics….

Plato clearly loved them both, both mathematics and poetry.  But he approved of mathematics, and heartily, if conflictedly, disapproved of poetry.  Engraved above the entrance to his Academy, the first European university, was the admonition: Oudeis ageometretos eiseto.  Let none ignorant of geometry enter.  This is an expression of high approval indeed, and the symbolism could not have been more perfect, since mathematics was, for Plato, the very gateway for all future knowledge.  Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason.  Mathematics is the threshold we cross to pass into the ideal, the truly real."

— Rebecca Goldstein,
Mathematics and
the Character of Tragedy

Sunday, December 12, 2004

Sunday December 12, 2004

Filed under: General — Tags: — m759 @ 7:59 PM

Ideas, Stories, Values:
Literati in Deep Confusion

Joan Didion, The White Album:

“We tell ourselves stories in order to live….

We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the ‘ideas‘ with which we have learned to freeze the shifting phantasmagoria which is our actual experience.

Or at least we do for a while. I am talking here about a time when I began to doubt the premises of all the stories I had ever told myself, a common condition but one I found troubling.”

Interview with Joseph Epstein:

“You can do in stories things that are above those in essays,” says Epstein.  “In essays and piecework, you are trying to make a point, whereas in stories you are not quite sure what the point is. T.S. Eliot once said of Henry James, ‘He had a mind so fine no idea could violate it,’ which, I think, is the ultimate compliment for an author. Stories are above ideas.”

Harvard President Lawrence H. Summers, Sept. 12, 2004:

“You are entering a remarkable community, the Harvard community. It is a community built on the idea of searching for truth… on the idea of respect for others….

… we practice the values we venerate. The values of seeking truth, the values of respecting others….”

Paul Redding on Hegel:

“… Hegel discusses ‘culture’ as the ‘world of self-alienated spirit.’ The idea seems to be that humans in society not only interact, but that they collectively create relatively enduring cultural products (stories, dramas, and so forth) within which they can recognise their own patterns of life reflected.”

The “phantasmagoria” of Didion seems related to the “phenomenology” of Hegel…

From Michael N. Forster,  Hegel’s Idea of a Phenomenology of Spirit:

“This whole system is conceived, on one level at least, as a defense or rational reworking of the Christian conception of God.  In particular, its three parts are an attempt to make sense of the Christian idea of a God who is three in one — the Logic depicting God as he is in himself, the Philosophy of Nature God the Son, and the Philosophy of Spirit God the Holy Spirit.”

and, indeed, to the phenomenology of narrative itself….

From Patrick Vert,
The Narrative of Acceleration:

“There are plenty of anecdotes to highlight the personal, phenomenological experience of railway passage…

… a unique study on phantasmagoria and the history of imagination. The word originates [in] light-projection, the so-called ghost-shows of the early 19th century….

… thought becomes a phantasmagorical process, a spectral, representative location for the personal imagination that had been marginalized by scientific rationalism….

Truly, ‘immediate experience is [or becomes] the phantasmagoria of the idler’ [Walter Benjamin, The Arcades Project.  Cambridge: Harvard University Press, 1999.  Page 801.]….

Thought as phantasm is a consequence of the Cartesian split, and… a further consequence to this is the broad take-over of perceptual faculty…. What better example than that of the American railway?  As a case-study it offers explanation to the ‘phantasmagoria of the idler’….

This phantasmagoria became more mediated over time…. Perception became increasingly visually oriented…. As this occurred, a narrative formed to encapsulate the phenomenology of it all….”

For such a narrative, see
the Log24.net entries of

November 5, 2002, 2:56 AM,
November 5, 2002, 6:29 AM,
January 3, 2003, 11:59 PM,
August 17, 2004, 7:29 PM,
August 18, 2004, 2:18 AM,
August 18, 2004, 3:00 AM, and
November 24, 2004, 10:00 AM.

Tuesday, April 6, 2004

Tuesday April 6, 2004

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

Ideas and Art, Part III

The first idea was not our own.  Adam
In Eden was the father of Descartes…

— Wallace Stevens, from
Notes Toward a Supreme Fiction

“Quaedam ex his tanquam rerum imagines sunt, quibus solis proprie convenit ideae nomen: ut cùm hominem, vel Chimaeram, vel Coelum, vel Angelum, vel Deum cogito.”

Descartes, Meditationes III, 5

“Of my thoughts some are, as it were, images of things, and to these alone properly belongs the name idea; as when I think [represent to my mind] a man, a chimera, the sky, an angel or God.”

Descartes, Meditations III, 5

Begin, ephebe, by perceiving the idea
Of this invention, this invented world,
The inconceivable idea of the sun.

You must become an ignorant man again
And see the sun again with an ignorant eye
And see it clearly in the idea of it.

— Wallace Stevens, from
Notes Toward a Supreme Fiction

“… Quinimo in multis saepe magnum discrimen videor deprehendisse: ut, exempli causâ, duas diversas solis ideas apud me invenio, unam tanquam a sensibus haustam, & quae maxime inter illas quas adventitias existimo est recensenda, per quam mihi valde parvus apparet, aliam verò ex rationibus Astronomiae desumptam, hoc est ex notionibus quibusdam mihi innatis elicitam, vel quocumque alio modo a me factam, per quam aliquoties major quàm terra exhibetur; utraque profecto similis eidem soli extra me existenti esse non potest, & ratio persuadet illam ei maxime esse dissimilem, quae quàm proxime ab ipso videtur emanasse.”

Descartes, Meditationes III, 11

“… I have observed, in a number of instances, that there was a great difference between the object and its idea. Thus, for example, I find in my mind two wholly diverse ideas of the sun; the one, by which it appears to me extremely small draws its origin from the senses, and should be placed in the class of adventitious ideas; the other, by which it seems to be many times larger than the whole earth, is taken up on astronomical grounds, that is, elicited from certain notions born with me, or is framed by myself in some other manner. These two ideas cannot certainly both resemble the same sun; and reason teaches me that the one which seems to have immediately emanated from it is the most unlike.”

Descartes, Meditations III, 11

“Et quamvis forte una idea ex aliâ nasci possit, non tamen hîc datur progressus in infinitum, sed tandem ad aliquam primam debet deveniri, cujus causa sit in star archetypi, in quo omnis realitas formaliter contineatur, quae est in ideâ tantùm objective.”

Descartes, Meditationes III, 15

“And although an idea may give rise to another idea, this regress cannot, nevertheless, be infinite; we must in the end reach a first idea, the cause of which is, as it were, the archetype in which all the reality [or perfection] that is found objectively [or by representation] in these ideas is contained formally [and in act].”

Descartes, Meditations III, 15

Michael Bryson in an essay on Stevens’s “Notes Toward a Supreme Fiction,”

The Quest for the Fiction of the Absolute:

“Canto nine considers the movement of the poem between the particular and the general, the immanent and the transcendent: “The poem goes from the poet’s gibberish to / The gibberish of the vulgate and back again. / Does it move to and fro or is it of both / At once?” The poet, the creator-figure, the shadowy god-figure, is elided, evading us, “as in a senseless element.”  The poet seeks to find the transcendent in the immanent, the general in the particular, trying “by a peculiar speech to speak / The peculiar potency of the general.” In playing on the senses of “peculiar” as particular and strange or uncanny, these lines play on the mystical relation of one and many, of concrete and abstract.”

Brian Cronin in Foundations of Philosophy:

“The insight is constituted precisely by ‘seeing’ the idea in the image, the intelligible in the sensible, the universal in the particular, the abstract in the concrete. We pivot back and forth between images and ideas as we search for the correct insight.”

— From Ch. 2, Identifying Direct Insights

Michael Bryson in an essay on Stevens’s “Notes Toward a Supreme Fiction“:

“The fourth canto returns to the theme of opposites. ‘Two things of opposite natures seem to depend / On one another . . . . / This is the origin of change.’  Change resulting from a meeting of opposities is at the root of Taoism: ‘Tao produced the One. / The One produced the two. / The two produced the three. / And the three produced the ten thousand things’ (Tao Te Ching 42) ….”

From an entry of March 7, 2004

From the web page

Introduction to the I Ching–
By Richard Wilhelm
:

“He who has perceived the meaning of change fixes his attention no longer on transitory individual things but on the immutable, eternal law at work in all change. This law is the tao of Lao-tse, the course of things, the principle of the one in the many. That it may become manifest, a decision, a postulate, is necessary. This fundamental postulate is the ‘great primal beginning’ of all that exists, t’ai chi — in its original meaning, the ‘ridgepole.’ Later Chinese philosophers devoted much thought to this idea of a primal beginning. A still earlier beginning, wu chi, was represented by the symbol of a circle. Under this conception, t’ai chi was represented by the circle divided into the light and the dark, yang and yin,

.

This symbol has also played a significant part in India and Europe. However, speculations of a gnostic-dualistic character are foreign to the original thought of the I Ching; what it posits is simply the ridgepole, the line. With this line, which in itself represents oneness, duality comes into the world, for the line at the same time posits an above and a below, a right and left, front and back-in a word, the world of the opposites.”

The t’ai chi symbol is also illustrated on the web page Cognitive Iconology, which says that

“W.J.T. Mitchell calls ‘iconology’
a study of the ‘logos’
(the words, ideas, discourse, or ‘science’)
of ‘icons’ (images, pictures, or likenesses).
It is thus a ‘rhetoric of images’
(Iconology: Image, Text, Ideology, p. 1).”

A variation on the t’ai chi symbol appears in a log24.net entry for March 5:

The Line,
by S. H. Cullinane

See too my web page Logos and Logic, which has the following:

“The beautiful in mathematics resides in contradiction. Incommensurability, logoi alogoi, was the first splendor in mathematics.”

— Simone Weil, Oeuvres Choisies, ed. Quarto, Gallimard, 1999, p. 100

 Logos Alogos,
by S. H. Cullinane 

In the conclusion of Section 3, Canto X, of “Notes,” Stevens says

“They will get it straight one day
at the Sorbonne.
We shall return at twilight
from the lecture
Pleased that
the irrational is rational….”

This is the logoi alogoi of Simone Weil.

In “Notes toward a Supreme Fiction,”
Wallace Stevens lists three criteria
for a work of the imagination:

It Must Be Abstract

The Line,
by S.H. Cullinane 

It Must Change

 The 24,
by S. H. Cullinane

It Must Give Pleasure

Puzzle,
by S. H. Cullinane

Related material:

Logos and Logic.

 

Sunday, September 22, 2002

Sunday September 22, 2002

Filed under: General,Geometry — Tags: , , , — m759 @ 8:02 PM

Force Field of Dreams

Metaphysics and chess in today’s New York Times Magazine:

  • From “Must-See Metaphysics,” by Emily Nussbaum:

    Joss Whedon, creator of a new TV series —

    “I’m a very hard-line, angry atheist” and
    “I want to invade people’s dreams.”

  • From “Check This,” by Wm. Ferguson:

    Garry Kasparov on chess —

    “When the computer sees forced lines,
    it plays like God.”

Putting these quotations together, one is tempted to imagine God having a little game of chess with Whedon, along the lines suggested by C. S. Lewis:

As Lewis tells it the time had come for his “Adversary [as he was wont to speak of the God he had so earnestly sought to avoid] to make His final moves.” (C. S. Lewis, Surprised by Joy, Harcourt, Brace, and World, Inc., 1955, p. 216) Lewis called them “moves” because his life seemed like a chess match in which his pieces were spread all over the board in the most disadvantageous positions. The board was set for a checkmate….

For those who would like to imagine such a game (God vs. Whedon), the following may be helpful.

George Steiner has observed that

The common bond between chess, music, and mathematics may, finally, be the absence of language.

This quotation is apparently from

Fields of Force:
Fischer and Spassky at Reykjavik
. by George Steiner, Viking hardcover, June 1974.

George Steiner as quoted in a review of his book Grammars of Creation:

“I put forward the intuition, provisional and qualified, that the ‘language-animal’ we have been since ancient Greece so designated us, is undergoing mutation.”

The phrase “language-animal” is telling.  A Google search reveals that it is by no means a common phrase, and that Steiner may have taken it from Heidegger.  From another review, by Roger Kimball:

In ”Grammars of Creation,” for example, he tells us that ”the classical and Judaic ideal of man as ‘language animal,’ as uniquely defined by the dignity of speech . . . came to an end in the antilanguage of the death camps.”

This use of the Holocaust not only gives the appearance of establishing one’s credentials as a person of great moral gravity; it also stymies criticism. Who wants to risk the charge of insensitivity by objecting that the Holocaust had nothing to do with the ”ideal of man as ‘language animal’ ”?

Steiner has about as clear an idea of the difference between “classical” and “Judaic” ideals of man as did Michael Dukakis. (See my notes of September 9, 2002.)

Clearly what music, mathematics, and chess have in common is that they are activities based on pure form, not on language. Steiner is correct to that extent. The Greeks had, of course, an extremely strong sense of form, and, indeed, the foremost philosopher of the West, Plato, based his teachings on the notion of Forms. Jews, on the other hand, have based their culture mainly on stories… that is, on language rather than on form. The phrase “language-animal” sounds much more Jewish than Greek. Steiner is himself rather adept at the manipulation of language (and of people by means of language), but, while admiring form-based disciplines, is not particularly adept at them.

I would argue that developing a strong sense of form — of the sort required to, as Lewis would have it, play chess with God — does not require any “mutation,” but merely learning two very powerful non-Jewish approaches to thought and life: the Forms of Plato and the “archetypes” of Jung as exemplified by the 64 hexagrams of the 3,000-year-old Chinese classic, the I Ching.

For a picture of how these 64 Forms, or Hexagrams, might function as a chessboard,

click here.

Other relevant links:

“As you read, watch for patterns. Pay special attention to imagery that is geometric…”

and


from Shakhmatnaia goriachka

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