Thursday, November 1, 2012

Theories of Truth

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

A review of two theories of truth described
by a clergyman, Richard J. Trudeau, in
The Non-Euclidean Revolution

The Story Theory of Truth:

"But, I asked, is there a difference
between fiction and nonfiction?
'Not much,' she said, shrugging."

New Yorker  profile of tesseract
     author Madeleine L'Engle

The Diamond Theory of Truth:

(Click image for some background.)

Spaces as Hypercubes

See also the links on a webpage at finitegeometry.org.

For All Saints’ Day

Filed under: General — Tags: , — m759 @ 5:31 AM

Conclusion of "The Storyteller," a story 
by Cynthia Zarin about author Madeleine L'Engle—

The New Yorker , April 12, 2004 —

Note the black diamond at the story's end.

Tuesday, November 1, 2011

For All Hallows Day

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

The following was suggested by the Sermon
of October 30 (the day preceding Devil's Night)
and by yesterday's Beauty, Truth, Halloween.

"The German language has itself been influenced by Goethe's Faust , particularly by the first part. One example of this is the phrase 'des Pudels Kern ,' which means the real nature or deeper meaning of something (that was not evident before). The literal translation of 'des Pudels Kern ' is 'the core of the poodle,' and it originates from Faust's exclamation upon seeing the poodle (which followed him home) turn into Mephistopheles." —Wikipedia

See also the following readings (click to enlarge)—

Hans Primas on Pauli's 'des Pudels Kern'

Suzanne Gieser on Pauli's 'des Pudels Kern'

Note particularly…

"The main enigma of any description of a patternless
unus mundus  is to find appropriate partitions which
create relevant patterns." —Hans Primas, above

"In general, the partition of into right cosets
can differ from its partition into left cosets. Galois
was the first to recognize the importance of when
these partitions agree. This happens when the
subgroup is normal." — David A. Cox,
Galois Theory , Wiley, 2004, p. 510

Monday, November 1, 2010

Seasons of…

Filed under: General — Tags: — m759 @ 5:24 AM

A Year of Magical Thinking

In memory of Theodore Chaikin Sorensen, who died at noon in New York on Halloween —

Two posts from All Saints' Day, 2009 —

October Endgame and Indignation and Laughter in Toronto.

Related material: New York Lottery on All Hallows' Eve this  year —

Midday 896,  Evening 384.

"Man is a system that transforms itself." (Paul Valéry, Cahiers , Vol. 2, page 896)

"There is  such a thing as a tesseract." (Madeleine L'Engle. See 384 on Halloween 2006.)

Sunday, November 1, 2009

Indignation and Laughter in Toronto

Filed under: General — Tags: — m759 @ 3:48 PM


St. Robertson Davies of Toronto on All Hallows' Eve, 1990— "Nevertheless, our forbears are deserving of tribute for one indisputable reason, if for no other: without them we should not be here. Let us recognize that we are not the ultimate triumph but rather we are beads on a string. Let us behave with decency to the beads that were strung before us, and hope modestly that the beads that come after us will not hold us of no account merely because we are dead. Today and tomorrow are the proper days for such reflection. It need not detain us for more than a few minutes, but it should be sincere. A few gentle thoughts or even — I hardly know how to put it without moving you to indignation or laughter — a brief prayer would not come amiss, and might turn your thoughts in a fruitful direction." Having had a few thoughts for the forbears, let us turn in the direction of Goldilocks.

Girl, you know who you are.

October Endgame

Filed under: General,Geometry — Tags: — m759 @ 8:28 AM

Suggested by the New York State lottery numbers on All Hallows' Eve–

430 (mid-day) and 168 (evening)…

From 430 as a date, 4/30Beyond Grief and Nothing: A Reading of Don DeLillo, by Joseph Dewey, University of South Carolina Press, 2006, page 123:

"It is as if DeLillo himself had moved to an endgame…."

For such an endgame, see yesterday's link to a Mira Sorvino drama. The number 168 suggested by the Halloween lottery deals with the properties of space itself and requires a more detailed exegesis… For the full picture, consider the Log24 entries of Feb. 16-28 this year, esp. the entries of Feb. 27 and the phrase they suggest–

Flores, Flores para los muertos.

Consider also Xinhua today, with its discussion of rocket science and seal-cutting:


Click image for context.

For space technology, see the above link to Feb. 16-28 this year as well as the following (click on image for details)–


As for seal-cutting, see the following seal from a Korean Christian site:


See Mizian Translation Service for some background on the seal's designer.

Wednesday, November 1, 2006

Wednesday November 1, 2006

Filed under: General — Tags: — m759 @ 9:48 PM
The Method

… "What did they tell you?"

"They told me that you had
gone totally insane and that
 your methods were unsound."

"Are my methods unsound?"


"I don't see
any method at all, sir."

Apocalypse Now, The Cage

Karl Rove
"Perfect, genuine,
complete, crystalline, pure."

Wednesday November 1, 2006

Filed under: General,Geometry — Tags: — m759 @ 8:24 AM

The image “http://www.log24.com/log/pix06B/061101-Geertz2.jpg” cannot be displayed, because it contains errors.

Clifford Geertz 

Professor Emeritus,
Institute for Advanced Study

Savage Logic

"Savage logic works like a kaleidoscope whose chips can fall into a variety of patterns while remaining unchanged in quantity, form, or color. The number of patterns producible in this way may be large if the chips are numerous and varied enough, but it is not infinite. The patterns consist in the disposition of the chips vis-a-vis one another (that is, they are a function of the relationships among the chips rather than their individual properties considered separately). And their range of possible transformations is strictly determined by the construction of the kaleidoscope, the inner law which governs its operation. And so it is too with savage thought. Both anecdotal and geometric, it builds coherent structures out of 'the odds and ends left over from psychological or historical process.'

These odds and ends, the chips of the kaleidoscope, are images drawn from myth, ritual, magic, and empirical lore. (How, precisely, they have come into being in the first place is one of the points on which Levi-Strauss is not too explicit, referring to them vaguely as the 'residue of events… fossil remains of the history of an individual or a society.') Such images are inevitably embodied in larger structures– in myths, ceremonies, folk taxonomies, and so on– for, as in a kaleidoscope, one always sees the chips distributed in some pattern, however ill-formed or irregular. But, as in a kaleidoscope, they are detachable from these structures and arrangeable into different ones of a similar sort. Quoting Franz Boas that 'it would seem that mythological worlds have been built up, only to be shattered again, and that new worlds were built from the fragments,' Levi-Strauss generalizes this permutational view of thinking to savage thought in general."

— Clifford Geertz, "The Cerebral Savage: the Structural Anthropology of Claude Levi-Strauss," in Encounter, Vol. 28 No. 4 (April 1967), pp. 25-32.

Today's New York Times
reports that
Geertz died on Monday,
October 30, 2006.

Related material:

Kaleidoscope Puzzle,

Being Pascal Sauvage,

and Up the River:


The Necessity For Story

by Frederick Zackel

While it's a story that's never been written, a suggested title– Indiana Jones Sails Up The River Of Death–

The image “http://www.log24.com/log/pix04B/041016-Poster2.jpg” cannot be displayed, because it contains errors.

shows how readily we as individuals or we as a culture can automatically visualize a basic story motif. We may each see the particular elements of the story differently, but almost instantaneously we catch its drift.

The hero sails up the river of death to discover what lies within his own heart: i.e., how much moral and physical strength he has.

Indiana Jones sails up the River of Death.

We are following Indiana Jones up the River of Death. We're going to visit with Colonel Kurtz. (You may not want to get off the boat.)

No, I am not mixing up metaphors.

These are the Story.



Tuesday, November 1, 2005

Tuesday November 1, 2005

Filed under: General,Geometry — Tags: , — m759 @ 9:00 PM
The image “http://www.log24.com/log/pix05B/051101-Seal.gif” cannot be displayed, because it contains errors.


The above seal is from an ad (pdf) for an Oct. 21 lecture, "The Nature of Space," by Sir Michael Atiyah, sponsored by the American Mathematical Society.

The picture in the seal is of Plato's Academy.

"The great philosopher Plato excluded from his Academy anyone who had not studied geometry.  He would have been delighted to admit Sir Michael Atiyah, who was for a time Savilian Professor of Geometry at Oxford…"


Would he?

Sir Michael Atiyah's

"Mathematics is an evolution from the human brain, which is responding to outside influences, creating the machinery with which it then attacks the outside world. It is our way of trying to reduce complexity into simplicity, beauty and elegance….

I tend to think that science and mathematics are ways the human mind looks and experiences– you cannot divorce the human mind from it. Mathematics is part of the human mind. The question whether there is a reality independent of the human mind, has no meaning– at least, we cannot answer it."

— Sir Michael Atiyah, interview in Oslo, May 2004

"For Plato, the Forms represent truth, or reality…. these Forms are independent of the mind: they are eternal, unchanging and perfect."

—  Roy Jackson (pdf)

Atiyah's denial of a reality independent of the human mind may have something to do with religion:

"Socrates and Plato were considered 'Christians before Christ'; they paved the way for the coming of Christianity by providing it with philosophical and theoretical foundations that would be acceptable to the western mind.
    In the analogy of the cave, the sun represents the Form of the Good. In the same way that the sun is the source of all things and gives light to them, the Form of the Good is over and above the other Forms, giving them light and allowing us to perceive them. Therefore, when you have awareness of the Form of the Good you have achieved true enlightenment. In Christianity, the Form of the Good becomes God: the source of all things."

— Roy Jackson, The God of Philosophy (pdf)

See also the previous entry.

Tuesday November 1, 2005

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

Antidote to Atiyah

In a recent talk, "The Nature of Space," Sir Michael Atiyah gave a misleading description of Plato's doctrine of "ideas," or "idealism."  Atiyah said that according to Plato, ideas reside in  "an imaginary world–  the world of the mind," and that what we see in the external world is "some pale reflection" of ideas in the mind.

An antidote to Atiyah's nonsense may be found in the Catholic Encyclopedia:

"So it came to pass that the word idea in various languages took on more and more the meaning of 'representation,' 'mental image,' and the like. Hence too, there was gradually introduced the terminology which we find in the writings of Berkeley, and according to which idealism is the doctrine that ascribes reality to our ideas, i.e. our representations, but denies the reality of the physical world. This sort of idealism is just the reverse of that which was held by the philosophers of antiquity and their Christian successors; it does away with the reality of ideal principles by confining them exclusively to the thinking subject; it is a spurious idealism…."

Atiyah contrasts his mistaken view of Plato with what he calls the "realism" of Hume.  He does not mention that Plato's doctrine of ideas is also known as "realism."  For details, see, again, the Catholic Encyclopedia:

"The conciliation of the one and the many, the changing and the permanent, was a favourite problem with the Greeks; it leads to the problem of universals. The typical affirmation of Exaggerated Realism, the most outspoken ever made, appears in Plato's philosophy; the real must possess the attributes of necessity, universality, unity, and immutability which are found in our intellectual representations. And as the sensible world contains only the contingent, the particular, the unstable, it follows that the real exists outside and above the sensible world. Plato calls it eîdos, idea. The idea is absolutely stable and exists by itself (ontos on; auta kath' auta), isolated from the phenomenal world, distinct from the Divine and human intellect…. The exaggerated Realism of Plato… is the principal doctrine of his metaphysics."
Atiyah's misleading remarks may appeal to believers in the contemptible religion of Scientism, but they have little to do with either historical reality or authentic philosophy.

Saturday, November 1, 2003

Saturday November 1, 2003

Filed under: General,Geometry — Tags: — m759 @ 1:05 PM

Symmetry in Diamond Theory:
Robbing Peter to Pay Paul

"Groups arise in most areas of pure and applied mathematics, usually as a set of operators or transformations of some structure. The appearance of a group generally reflects some kind of symmetry in the object under study, and such symmetry may be considered one of the fundamental notions of mathematics."

Peter Webb

"Counter-change is sometimes known as Robbing Peter to Pay Paul."

Helen Kelley Patchwork

Paul Robeson in
King Solomon's


For a look at the Soviet approach
to counterchange symmetry, see

The Kishinev School of Discrete Geometry.

The larger cultural context:

See War of Ideas (Oct. 24),
The Hunt for Red October (Oct. 25),
On the Left (Oct. 25), and
ART WARS for Trotsky's Birthday (Oct. 26).

Saturday November 1, 2003

Filed under: General — Tags: — m759 @ 8:48 AM

All Saints' Day:
The Song of Saint Ezra

Ezra Pound, imagist poet and fascist saint, died on this date in 1972.

 "But you, newest song of the lot,
  You are not old enough
     to have done much mischief.
will get you a green coat out of China
ith dragons worked upon it."

— "Further Instructions," 1913

For more on China and Christian Fascism, see the memorial to the wife of Generalissimo Chiang Kai-shek in TIME magazine, issue dated Nov. 3, 2003.

From Image in Poetry:

"Ezra Pound made perhaps the most widely used definition of image in the 20th century:

An ‘Image’ is that which presents an intellectual and emotional complex in an instant of time. "

— Ezra Pound, "A Few Don’ts by an Imagiste," Poetry, March 1913

For an excellent essay by Jungian James Hillman on the political implications of imagism, see

Egalitarian Typologies versus
the Perception of the Unique

A specific image that is a personal favorite of mine is found in the I Ching:

Note that in the West,
this Chinese character
is known as the "Pound sign."

"The Perception of the Unique," indeed.

Friday, November 1, 2002

Friday November 1, 2002

Filed under: General — Tags: — m759 @ 9:40 AM


Art Director of "Harvey" Dies at 95

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