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Friday, September 29, 2023

Annals of Mathematical Theology

Filed under: General — Tags: , , — m759 @ 12:23 pm

"As McCarthy peers through the screen, or veil,
of technological modernity to reveal the underlying
symbolic structures of human experience, 
The Making of Incarnation  weaves a set of stories
one inside the other, rings within rings, a perpetual
motion machine." — Amazon.com description
of a novel published on All Souls' Day (Dia de los
Muertos
), 2021.

The McCarthy novel is mentioned in The New York Times  today —

For a simpler perpetual motion machine, see T. S. Eliot's "Chinese jar."

Friday, May 3, 2019

“As a Chinese jar” — T. S. Eliot

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

 

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.

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

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