Log24

Thursday, January 17, 2019

The Dreaming Jewels’ Nightmares

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

Some Log24 posts related to Theodore Sturgeon's 1950 tale
of The Dreaming Jewels  have been tagged with that title.

For a purely mathematical approach to Sturgeon's concept see . . .

July 6, 2014, Amsterdam master's thesis on geometric models of the Golay code and Mathieu group

For some related nightmares, see July 2014 in this journal.

Wednesday, January 16, 2019

Permutahedron Dream

Filed under: General — Tags: , , , — m759 @ 3:21 PM

The geometric object of the title appears in a post mentioning Bourgain 
in this journal.  Bourgain appears also in today's online New York Times —

https://www.nytimes.com/2019/01/16/
obituaries/jean-bourgain-dead.html
 .

Bourgain reportedly died on December 22.

An image from this journal on that date

Related poetic meditations —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

The Dreaming Polyhedron

Filed under: General — Tags: , — m759 @ 5:32 AM

"Here is a recipe for preparing a copy of the Mathieu group M24.
The main ingredient is a genus-3 regular polyhedron X
with 56 triangular faces, 84 edges, and 24 vertices.
The most delicate part of this recipe is to hold the polyhedron
by the 24 vertices and immerse the rest of it in 3-dimensional space."

— "How to Make the Mathieu Group M24 ," undated webpage
by David A. Richter, Western Michigan University

Illustration from that page —

Illustration from a webpage by David A. Richter, Western Michigan University

"Another model of the (universal cover of the) polyhedron X"

Related fiction —

Cover of a 1971 British paperback edition of The Dreaming Jewels,  
a story by Theodore Sturgeon (first version published in 1950):

Discuss Richter's model and the Sturgeon tale 
in the context of posts tagged Aitchison.

Thursday, January 10, 2019

Archimedes at Hiroshima

Filed under: General,Geometry — Tags: , , , — m759 @ 7:35 PM

Two examples from the Wikipedia article  "Archimedean solid" —

Iain Aitchison said in a talk last year at Hiroshima that
the Mathieu group M24  can be represented as permuting
naturally the 24 edges  of the cuboctahedron.

The 24 vertices  of the truncated  octahedron are labeled 
naturally by the 24 elements of S4  in a permutahedron

Can M24  be represented as permuting naturally
the 24 vertices  of the truncated octahedron?

 
 

Sunday, January 6, 2019

For Broom Bridge*

Filed under: General,Geometry — Tags: — m759 @ 11:00 AM

GL(2,3) is not unrelated to GL(3,2).

See Quaternion Automorphisms 
and Spinning in Infinity.

* See Wikipedia.

Monday, December 7, 2015

Neon Joe, Werewolf Hunter

Filed under: General — Tags: , , — m759 @ 10:48 PM

For the title, see The New York Times  and the oeuvre  of Joseph Kosuth.

From The Dreaming Jewels , by Theodore Sturgeon:

"Oh. And the crystals make things — even complete things — like Tin Pan Alley makes songs."

"Something like it." Zena smiled. It was the first smile in a long while. "Sit down, honey; I'll bring the toast. Now — this is my guess — when two crystals mate, something different happens. They make a whole thing. But they don't make it from just anything the way the single crystals do. First they seem to die together. For weeks they lie like that. After that they begin a together-dream. They find something near them that's alive, and they make it over. They replace it, cell by cell. You can't see the change going on in the thing they're replacing. It might be a dog; the dog will keep on eating and running around; it will howl at the moon and chase cats. But one day — I don't know how long it takes — it will be completely replaced, every bit of it."

"Then what?"

"Then it can change itself — if it ever thinks of changing itself. It can be almost anything if it wants to be."

Bunny stopped chewing, thought, swallowed, and asked, "Change how?"

"Oh, it could get bigger or smaller. Grow more limbs. Go into a funny shape — thin and flat, or round like a ball. If it's hurt it can grow new limbs. And it could do things with thought that we can't even imagine. Bunny, did you ever read about werewolves?"

"Those nasty things that change from wolves to men and back again?"

Zena sipped coffee. "Mmm. Well, those are mostly legends, but they could have started when someone saw a change like that."

See as well The Dreaming Jewels 
and "Steven Universe" in this journal.

You can't make this stuff up.

Wittgenstein Illustrated

Filed under: General,Geometry — Tags: , , — m759 @ 1:17 PM

From "AMNESIA: VARIOUS, LUMINOUS, FIXED,"
An exhibition by Joseph Kosuth at
Sprüth Magers Gallery London,
NOVEMBER 26 2014 – FEBRUARY 14 2015 —

This journal, NOVEMBER 26 2014 –

Wednesday, November 26, 2014

Mathematics and Narrative

Filed under: Uncategorized — m759 @ 10:00 PM 

Mathematics:  Galois-Plane Models.

Narrative: "The Dreaming Jewels."

This journal, FEBRUARY 14 2015 —

Tuesday, April 14, 2015

Sacramental Geometry:

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

The Dreaming Jewels  continued

" the icosahedron and dodecahedron have the same properties
of symmetry. For the centres of the twenty faces of an icosahedron
may be joined to form a regular dodecahedron, and conversely, the
twelve vertices of an icosahedron can be placed at the centres
of the faces of a suitable dodecahedron. Thus the icosahedral and
dodecahedral groups are identical
 , and either solid may be used to
examine the nature of the group elements."

— Walter Ledermann, Introduction to the Theory
of Finite Groups
  (Oliver and Boyd, 1949, p. 93)

Salvador Dali, The Sacrament of the Last Supper

Omar Sharif and Gregory Peck in Behold a Pale Horse

Above: soccer-ball geometry.
              See also

             See as well
"In Sunlight and in Shadow."

Monday, December 29, 2014

Dodecahedron Model of PG(2,5)

Filed under: General,Geometry — Tags: , , — m759 @ 2:28 PM

Recent posts tagged Sagan Dodecahedron 
mention an association between that Platonic
solid and the 5×5 grid. That grid, when extended
by the six points on a "line at infinity," yields
the 31 points of the finite projective plane of
order five.  

For details of how the dodecahedron serves as
a model of this projective plane (PG(2,5)), see
Polster's A Geometrical Picture Book , p. 120:

For associations of the grid with magic rather than
with Plato, see a search for 5×5 in this journal.

Wednesday, November 26, 2014

Mathematics and Narrative

Filed under: General,Geometry — Tags: — m759 @ 10:00 PM

Mathematics:  Galois-Plane Models.

Narrative: "The Dreaming Jewels."

Tuesday, December 31, 2013

Christmas Ornaments

Filed under: General,Geometry — Tags: , — m759 @ 12:25 AM

Continued from December 25

IMAGE- Count rotational symmetries by rotating facets. Illustrated with 'Plato's Dice.'

A link from Sunday afternoon to Nov. 26, 2012,
suggests a review of one of the above structures.

The Dreaming Jewels  cover at left is taken from a review
by Jo Walton at Tor.com—

"This is a book that it’s clearly been difficult
for publishers to market. The covers have been
generally pretty awful, and also very different.
I own a 1975 Corgi SF Collectors Library
paperback that I bought new for 40p in the later
seventies. It’s purple, and it has a slightly grainy
cover, and it matches my editions of The Menace
From Earth
  and A Canticle for Leibowitz .
(Dear old Corgi SF Collectors Editions with their
very seventies fonts! How I imprinted on them at
an early age!) I mention this, however, because
the (uncredited) illustration actually represents and
illustrates the book much better than any of the other
cover pictures I’ve seen. It shows a hexagon with an
attempt at facets, a man, a woman, hands, a snake,
and stars, all in shades of green. It isn’t attractive,
but it wouldn’t put off people who’d enjoy what’s inside
either."

The "hexagon with an attempt at facets" is actually
an icosahedron, as the above diagram shows.
(The geometric part of the diagram is from a Euclid webpage.)

For Plato's dream about these jewels, see his Timaeus.

Saturday, March 30, 2013

Blackboard Jungle

Filed under: General — Tags: — m759 @ 10:30 AM

(Continued)

Harrowing of Hell (Catholic Encyclopedia )

"This is the Old English and Middle English term
for the triumphant descent of Christ into hell (or Hades)
between the time of His Crucifixion and His Resurrection,
when, according to Christian belief, He brought salvation
to the souls held captive there since the beginning of the world."

Through the Blackboard (Feb. 25, 2010)—

Physicist accelerated against his blackboard in 'A Serious Man'

See also The Dreaming Jewels and Colorful Tale.

Friday, March 29, 2013

The Dreaming Jewels (continued)

Filed under: General — Tags: , — m759 @ 8:00 AM

In Memoriam

"In the late ’60s, Williams became a friend and confidant
of science fiction writer Philip K. Dick and wrote about
the iconoclastic author in Rolling Stone  in 1974.
Williams eventually completed a biography on Dick
and became his literary executor after the writer’s death
in 1982. He also edited The Complete Stories of
Theodore Sturgeon, Vol. I-XII 
."

— Yesterday in the Hollywood Reporter —
Pioneering Rock Journalist Paul S. Williams Dies at 64
4:06 PM PDT 3/28/2013 by Mitch Myers

See also Crawdaddy Story and The Dreaming Jewels
in this journal.

Related reading: Yesterday's noon post and Puzzles.

Update of 8:20 AM Good Friday, 2013:

IMAGE- Daily Princetonian, Good Friday, 2013: James Diamond, rabbi and retired director of Princeton's University's Center for Jewish Life. Diamond was killed in a Princeton auto accident Thursday morning at about 9:42 AM ET.

Monday, November 26, 2012

“The Eight”…

Filed under: General — Tags: — m759 @ 2:18 PM

Meets "The Master"—

IMAGE- Joaquin Phoenix, corridor scene in 'The Master'

Today's midday NY Lottery: 333 and 5885.

"Continue a search for thirty-three and three." — The Eight  (1988)

"Make me young." — Kilgore Trout in
Breakfast of Champions . Trout was modeled after
author Theodore Sturgeon who died on 5/8/85.

(An example of Sturgeon's work: The Dreaming Jewels  (1950).)

Related illustrations from the eighth day of 2012—

See also "I'm sorry to be catechizing you like this."

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