Log24

Friday, November 16, 2018

The Transposed Squares

Filed under: G-Notes,General,Geometry — m759 @ 9:12 pm
 
 

I.e. (click to enlarge) —

 

Wednesday, March 11, 2020

Visualizing Mathieu Group Generators

Filed under: General — Tags: — m759 @ 6:23 am

Marston Conder's M24 generators are illustrated by Cullinane's diamond-theorem (2x2 case) figures.

Update of March 17, 2020 —

The graphic images illustrate nicely Conder's six 4-cycles, but
their relationship, if any, to his eight 2-cycles is a mystery —

The Conder paper is at 
https://core.ac.uk/download/pdf/82622574.pdf.

 
 

Wednesday, December 12, 2018

Kummerhenge Continues.

Filed under: G-Notes,General,Geometry — Tags: , , — m759 @ 7:24 pm

Those pleased by what Ross Douthat today called
"The Return of Paganism" are free to devise rituals
involving what might be called "the sacred geometry
of the Kummer 166  configuration."

As noted previously in this journal, 

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

— T. S. Eliot in Four Quartets

Geometric incarnation and the Kummer configuration

See also earlier posts also tagged "Kummerhenge" and 
another property of the remarkable Kummer 166 

The Kummer 16_6 Configuration and the Nordstrom-Robinson Code

For some related literary remarks, see "Transposed" in  this journal.

Some background from 2001 —

Friday, November 16, 2018

Parable of India

Filed under: General — m759 @ 12:42 pm

See too  "When thou seekest me, seek towards India."

Thursday, September 28, 2017

The Last Word

Filed under: General — Tags: , , — m759 @ 6:00 am

Remarks suggested by the previous post

From Jeremy Biles, "Introduction: The Sacred Monster," in
Ecce Monstrum: Georges Bataille and the Sacrifice of Form

(Fordham University Press, 2007, page 3) —

Bataille’s insistent conjunction of the monstrous and the sacred is the subject of this book. Regarded by many as one of the most important thinkers of our time, and acknowledged as an important influence by such intellectuals as Michel Foucault, Julia Kristeva, Maurice Blanchot, and Jacques Derrida, Bataille produced a corpus of wide-ranging writings bearing the monstrous marks of the affective and intellectual contradictions he also sought to produce in his readers. In the following chapters, I will specify some of the ways in which Bataille evokes monstrosity to elicit in himself and his audience an experience of simultaneous anguish and joy—an experience that he calls sacred. In particular, Bataille is fascinated with the ‘‘left-hand’’ sacred. In contradistinction to its lucent and form-conferring ‘‘right-hand’’ counterpart, the left-hand sacred is obscure and formless—not transcendent, pure, and beneficent, but dangerous, filthy, and morbid. This sinister, deadly aspect of the sacred is at once embodied in, and communicated by, the monster. As we will see, it is in beholding the monster that one might experience the combination of ecstasy and horror that characterizes Bataille ’s notion of the sacred.

The dual etymology of ‘‘monster’’ reveals that aspect of the sacred that enticed Bataille. According to one vein of etymological study, the Latin monstrum  derives from monstrare  (to show or display). The monster is that which appears before our eyes as a sign of sorts; it is a demonstration. But another tradition emphasizes a more ominous point. Deriving from monere  (to warn), the monster is a divine omen, a portent; it heralds something that yet remains unexpected, unforeseeable—as a sudden reversal of fortune. In the writings of Bataille, the monster functions as a monstrance, putting on display the sinister aspect of the sacred that Bataille sees as the key to a ‘‘sovereign’’ existence. But in doing so the monster presents us with a portent of something that we cannot precisely foresee, but something that, Bataille claims, can be paradoxically experienced in moments of simultaneous anguish and ecstasy: death.

See as well

(Order of news items transposed for aesthetic effect.)

Monday, February 27, 2006

Monday February 27, 2006

Filed under: General — m759 @ 10:30 am

Point Counter Point

From the Encyclopaedia Britannica, 11th Edition, 1911:

COUNTERPOINT (Lat. contrapunctus, “point counter point,” “note against note”)

“In music, the art happily defined by Sir Frederick Gore Ouseley as that ‘of combining’ melodies….

Double Counterpoint is a combination of melodies so designed that either can be taken above or below the other. When this change of position is effected by merely altering the OCTAVE (from Lat. octavus, eighth, octo, eight) of either or both melodies (with or without transposition of the whole combination to another KEY), the artistic value of the device is simply that of the raising of the lower melody to the surface. The harmonic scheme remains the same, except in so far as some of the chords are not in their fundamental position, while others, not originally fundamental, have become so. But double counterpoint may be in other intervals than the octave; that is to say, while one of the parts remains stationary, the other may be transposed above or below it by some interval other than an octave, thus producing an entirely different set of harmonies.”

See also Sybille Bedford’s
biography of Aldous Huxley

The image “http://www.log24.com/log/pix06/060227-Huxley.jpg” cannot be displayed, because it contains errors.

and the entry below.
 
Related material:
A Contrapuntal Theme.

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