Sunday, December 10, 2017

Interlacing, Interweaving

Filed under: General — Tags: — m759 @ 2:00 PM

The above title should be sung to the following tune

"Right through hell
 there is a path…."
 — Malcolm Lowry,
Under the Volcano

Saturday, October 17, 2015

Contrapuntal Interweaving

Filed under: General — m759 @ 7:28 AM

(Continued from day before yesterday.)

"Sondheim's story is a dense contrapuntal interweaving
of four main fairy-tale stories…."

— Vladimir V. Zelevinsky, 1998 review
     in The Tech  at MIT

Related material: "Weaver's Tale" last Sunday,
and the novel Weaveworld  in this journal.

Thursday, October 15, 2015

Contrapuntal Interweaving

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

The title is a phrase from R. D. Laing's book The Politics of Experience .
(Published in the psychedelic year 1967. The later "contrapuntal interweaving"
below is of a less psychedelic nature.)

An illustration of the "interweaving' part of the title —
The "deep structure" of the diamond theorem:

IMAGE- A symplectic structure -- i.e. a structure that is symplectic (meaning plaited or woven).

The word "symplectic" from the end of last Sunday's (Oct. 11) sermon
describes the "interwoven" nature of the above illustration.

An illustration of the "contrapuntal" part of the title (click to enlarge):

The diamond-theorem correlation


Thursday, November 22, 2018

Geometric Incarnation

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

"The hint half guessed, the gift half understood, is Incarnation."

— T. S. Eliot in Four Quartets

Note also the four 4×4 arrays surrounding the central diamond
in the chi  of the chi-rho  page of the Book of Kells

From a Log24 post
of March 17, 2012

"Interlocking, interlacing, interweaving"

— Condensed version of page 141 in Eddington's
1939 Philosophy of Physical Science

Friday, January 19, 2018


Filed under: General — Tags: — m759 @ 4:04 AM

Sunday, December 10, 2017


Google search result for Plato + Statesman + interlacing + interweaving

See also Symplectic in this journal.

From Gotay and Isenberg, “The Symplectization of Science,”
Gazette des Mathématiciens  54, 59-79 (1992):

“… what is the origin of the unusual name ‘symplectic’? ….
Its mathematical usage is due to Hermann Weyl who,
in an effort to avoid a certain semantic confusion, renamed
the then obscure ‘line complex group’ the ‘symplectic group.’
… the adjective ‘symplectic’ means ‘plaited together’ or ‘woven.’
This is wonderfully apt….”

IMAGE- A symplectic structure -- i.e. a structure that is symplectic (meaning plaited or woven)

The above symplectic  figure appears in remarks on
the diamond-theorem correlation in the webpage
Rosenhain and Göpel Tetrads in PG(3,2). See also
related remarks on the notion of  linear  (or line ) complex
in the finite projective space PG(3,2) —

Anticommuting Dirac matrices as spreads of projective lines

Ron Shaw on the 15 lines of the classical generalized quadrangle W(2), a general linear complex in PG(3,2)

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.

Monday, June 26, 2017

Upgrading to Six

This post was suggested by the previous post — Four Dots —
and by the phrase "smallest perfect" in this journal.

Related material (click to enlarge) —

Detail —

From the work of Eddington cited in 1974 by von Franz —

See also Dirac and Geometry and Kummer in this journal.

Updates from the morning of June 27 —

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.

Saturday, October 22, 2016


Filed under: General — m759 @ 11:00 AM

From "The Magis way: Notes on the publishing culture,"
by Giampiero Bosoni, at http://www.magisdesign.com/magis-world/ —

" perhaps it is interesting to reflect further on the relationship between a design object and a literary work, by reading (in whatever interpretative key you choose) the illuminating definition given by the great semiologist Roland Barthes of the act of writing and of the literary value of a text. 'Writing,' Barthes tells us, 'is historically an action that involves constant contradiction, based on dual expectations. One aspect of writing is essentially commercial, a means of control and segregation, steeped in the most materialistic aspect of society. The other is an act of pleasure, connected to the deepest urges of the body and to the subtlest and most successful products of art. This is how the written text is woven. All I have done is to arrange and reveal the threads. Now each can add his own warp to the weft.' [3]

Magis’ long and highly advanced experience has given evidence, further confirmed by this latest publishing catalogue, of an ever-growing awareness of this necessary interweaving between warp and weft, between the culture of craftsmanship and that of industry, between design culture and business culture, between form and technique, between symbolic codes and practical functions, between poetry and everyday life." 

— Giampiero Bosoni

[3] Barthes R., Variations sur l’écriture  (1972), Editions du Seuil, Paris 1994, published in the second volume of the Oeuvres complètes  1966-1975 (freely translated from the Italian translation, Variazioni sulla scrittura seguite da Il piacere del testo , Ossola C. (editor) Einaudi, Turin 1999).

See as well "Interweaving" in this journal.

"Design is how it works." — Steve Jobs

Thursday, July 21, 2016

Image Search

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

Click to enlarge.

See also the word  "contrapuntal" in this journal. 

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