Monday, February 26, 2018

The Unfolding

Filed under: Uncategorized — Tags: — m759 @ 9:20 AM

From the website of Richard P. Gabriel

" As part of my studies, I came up with a 'theory of poetry' 
based loosely on Christopher Alexander’s 'Nature of Order.' "
[The Alexander link is mine, not Gabriel’s.]

A phrase from this  journal a year ago today — "poetic order" —
links to the theory of Gabriel —

From Gabriel's "The Nature of Poetic Order" —

Positive Space

• Positive space is the characteristic of a center
that moves outward from itself, seemingly oozing life
rather than collapsing on itself
• An image that resonates is showing positive space
• A word that has many connotations that fit with the
other centers in the poem is showing positive space
• It is an expansion outward rather than a contraction
inward, and it shows that the poem is unfolding
in front of us and not dying

Related material —

From a post of April 26, 2017

Sunday, February 25, 2018

The Dark, Seductive Art of Groton

Filed under: Uncategorized — Tags: — m759 @ 9:26 AM

A sequel to Friday's "The Dark, Seductive Art of Phillips Exeter."

From Twitter today —

Groton School‏ @GrotonSchool  Feb 1

Groton School Theater Department Presents: CABARET
Friday, February 23rd at 7:30 pm
Saturday, February 24th at 7:30 pm
Sunday, February 25th at 3 pm
All performances are free to the public. Please make ticket
reservations in advance online: http://bit.ly/CABARET2018.

Friday, February 23, 2018

The Dark, Seductive Art of Phillips Exeter

Filed under: Uncategorized — Tags: — m759 @ 10:00 PM

From two pedagogues in Montana —


Related material from author Dan Brown's father,
a pedagogue who taught at Phillips Exeter Academy :

Click the above image for some background.

Related material from Log24 —


Compare and contrast with the above
Transformational Geometry  cover:

Related material from Vienna — The previous post and
Wittgenstein on Bewitchment.

See as well . . .

Click to enlarge.

Snow Games

Filed under: Uncategorized — Tags: — m759 @ 9:42 AM

'Origin' (NOT by Dan Brown)

Related material — (Click to enlarge) —

"Risin' up to the challenge of our rival"

Eye of the Tiger

Detail —

Thursday, November 30, 2017

The Matrix for Quantum Mystics

Filed under: 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: 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: Uncategorized — 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


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 

Lévi-Strauss vs. Propp

Filed under: Uncategorized — Tags: — m759 @ 12:25 PM

​Claude Lévi-Strauss

From "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  (Basic Books, 1976. and 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

Wednesday, November 22, 2017

Goethe on All Souls’ Day

Filed under: Uncategorized — Tags: — m759 @ 11:00 PM

David E. Wellbery on Goethe

From an interview published on 2 November 2017 at


as later republished in 



The logo at left above is that of The Point .
The menu icon at right above is perhaps better
suited to illustrate Verwandlungslehre .

Weyl on symmetry, the eightfold cube, the Fano plane, and trigrams of the I Ching

Tuesday, March 14, 2017


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

Wednesday, August 26, 2015

“The Quality Without a Name”

Filed under: Uncategorized — Tags: — m759 @ 8:00 AM

The title phrase, paraphrased without quotes in
the previous post, is from Christopher Alexander's book
The Timeless Way of Building  (Oxford University Press, 1979).

A quote from the publisher:

"Now, at last, there is a coherent theory
which describes in modern terms
an architecture as ancient as
human society itself."

Three paragraphs from the book (pp. xiii-xiv):

19. Within this process, every individual act
of building is a process in which space gets
differentiated. It is not a process of addition,
in which preformed parts are combined to
create a whole, but a process of unfolding,
like the evolution of an embryo, in which
the whole precedes the parts, and actualy
gives birth to then, by splitting.

20. The process of unfolding goes step by step,
one pattern at a time. Each step brings just one
pattern to life; and the intensity of the result
depends on the intensity of each one of these
individual steps.

21. From a sequence of these individual patterns,
whole buildings with the character of nature
will form themselves within your thoughts,
as easily as sentences.

Compare to, and contrast with, these illustrations of "Boolean space":

(See also similar illustrations from Berkeley and Purdue.)

Detail of the above image —

Note the "unfolding," as Christopher Alexander would have it.

These "Boolean" spaces of 1, 2, 4, 8, and 16 points
are also Galois  spaces.  See the diamond theorem —

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