Log24

Monday, April 23, 2018

Facets

Filed under: General — Tags: , — m759 @ 12:00 AM

Counting symmetries with the orbit-stabilizer theorem

See also the Feb. 17, 2017, post on Bertram Kostant
as well as "Mathieu Moonshine and Symmetry Surfing."

Thursday, December 8, 2016

Finite Groups and Their Geometric Representations

Filed under: General,Geometry — Tags: — m759 @ 8:06 AM

The title is that of a presentation by Arnold Emch
at the 1928 International Congress of Mathematicians:

See also yesterday's "Emch as a Forerunner of S(5, 8, 24)."

Related material: Diamond Theory in 1937.

Further remarks:  Christmas 2013 and the fact that
759 × 322,560 = the order of the large Mathieu group  M24 .

Sunday, December 6, 2015

Form and Idea

Filed under: General,Geometry — Tags: , , , — m759 @ 3:24 PM

"Those early works are succinct and uncompromising
in how they give shape to the philosophical perplexities
of form and idea…."

J. J. Charlesworth, artnet news, Dec. 16, 2014

"Form" and "idea" are somewhat synonymous, 
as opposed to "form" and "substance." A reading:

IMAGE- 'American Hustle' and Art Cube

Discuss.

Saturday, December 20, 2014

Dark Fields continued

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

A  Christmas  Ornament  for  Amy  Adams —

Tuesday, December 31, 2013

Objects of Beauty

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

(Continued)

"I am a town." — Mary Chapin Carpenter

"A town, huh?" — Sydney Prosser

Related material — "Put on your red dress, baby."

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.

Thursday, December 26, 2013

Dicey

Filed under: General — Tags: — m759 @ 7:00 PM

For fans of Hunger Games  and Elysium —

Roberta Smith in this evening's* online New York Times

"Especially with the gap between the wealthiest
and everyone else so wide, it is dicey
for a major museum to celebrate the often frivolous
objects on which the rich spend their ever increasing
surplus income. Such a show must be beyond reproach
in every way: transparent in organization, impeccable
in exhibition design, illuminating in catalog and labeling
and, most of all, self-evidently excellent in the quality of
the objects on display."

Da capo:  "I've heard of affairs that are strictly Platonic."

* 5:08 PM ET

How It Works

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

(Continued)

“Design is how it works.” — Steve Jobs

“By far the most important structure in design theory
is the Steiner system S(5, 8, 24).”

— “Block Designs,” by Andries E. Brouwer (Ch. 14 (pp. 693-746),
Section 16 (p. 716) of Handbook of Combinatorics, Vol. I ,
MIT Press, 1995, edited by Ronald L. Graham, Martin Grötschel,
and László Lovász)

For some background on that Steiner system, see the footnote to
yesterday’s Christmas post.

Wednesday, December 25, 2013

Rotating the Facets

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

Previous post

"… her mind rotated the facts…."

Related material— hypercube rotation,* in the context
of rotational symmetries of the Platonic solids:

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

"I've heard of affairs that are strictly Platonic"

Song lyric by Leo Robin

* Footnote added on Dec. 26, 2013 —

 See Arnold Emch, "Triple and Multiple Systems, Their Geometric 
 Configurations and Groups
," Trans. Amer. Math. Soc.  31 (1929),
 No. 1, 25–42. 

 On page 42, Emch describes the above method of rotating a
 hypercube's 8 facets (i.e., three-dimensional cubes) to count
 rotational symmetries —

See also Diamond Theory in 1937.

Also on p. 42, Emch mentions work of Carmichael on a
Steiner system with the Mathieu group M11 as automorphism
group, and poses the problem of finding such systems and
groups that are larger. This may have inspired the 1931
discovery by Carmichael of the Steiner system S(5, 8, 24),
which has as automorphisms the Mathieu group M24 .

Rotating the Facts

Filed under: General,Geometry — Tags: , , — m759 @ 4:00 AM

IMAGE- 'American Hustle' and Art Cube

"She never looked up while her mind rotated the facts,
trying to see them from all sides, trying to piece them
together into theory. All she could think was that she
was flunking an IQ test."

— Steve Martin, An Object of Beauty

"So you should not feel so all alone…"
— Adapted song lyric

Friday, June 14, 2013

Amy’s Shadow

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

Why knows what evil lurks…? — The Shadow

Backstory: "Amy Adams" + Shadow in this journal.

Related material —

Amy Adams as Lois Lane:

In the new Amy Adams version, Superman's Smallville mom
is played by Diane  Lane.

Lane also played George Reeves's sugar mommy
in the 2006 film Hollywoodland .

Ben Affleck and Diane Lane at the 2006 Venice Film Festival
premiere of  Hollywoodland :

See, too, today's previous post, and Amy Adams as Lacey Yeager
in the yet-to-be-made film version of An Object of Beauty .

Tuesday, July 12, 2011

An Object of Beauty and…

Filed under: General — Tags: — m759 @ 1:23 PM

http://www.log24.com/log/pix11B/110712-ObjectOfBeauty.jpg

 

The Usual Suspects

http://www.log24.com/log/pix11B/110712-NYnews.jpg

 

http://www.log24.com/log/pix11B/110711-ANDOR.jpg

http://www.log24.com/log/pix11B/110712-HotRock.jpg

For some background, click on the diamond above.

See also Harrison Ford in "Harvard Defeats Holy Cross."

Sunday, December 12, 2010

Brightness at Noon continued…

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

A picture one might view as
related to the novel An Object of Beauty
and the film "The Object of Beauty" —

The 3x3 square

Click for some background.

"If it's a seamless whole you want,
 pray to Apollo." — Margaret Atwood

Tuesday, November 23, 2010

Tale

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

A reviewer says Steve Martin finds in his new novel An Object of Beauty  "a sardonic morality tale."

From this journal on the day The Cube  was published (see today's Art Object ) —

Monday February 20, 2006

m759 @ 12:00 AM

The Past Revisited

From Log24 a year ago on this date, a quote from Many Dimensions  (1931), by Charles Williams:

“Lord Arglay had a suspicion that the Stone would be purely logical.  Yes, he thought, but what, in that sense, were the rules of its pure logic?”

For the rest of the story, see the downloadable version at Project Gutenberg of Australia.

See also a post on Mathematics and Narrative from Nov. 14, 2009.

That post compares characters in Many Dimensions  to those in Logicomix

Whitehead and Russell, 'Logicomix' page 181

Art Object

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

There is more than one way
to look at a cube.

http://www.log24.com/log/pix10B/101123-plain_cube_200x227.gif

 From Cambridge U. Press on Feb. 20, 2006 —

IMAGE- 'Cambridge Tracts in Mathematics 168: The Cube'

and from this journal on June 30, 2010 —

In memory of Wu Guanzhong, Chinese artist
who died in Beijing on June 25, 2010

Image-- The Dream of the Expanded Field

See also this journal on Feb. 20, 2006
(the day The Cube  was published).

Monday, November 22, 2010

Backstory

Filed under: General,Geometry — Tags: — m759 @ 8:48 AM

Steve Martin's new novel An Object of Beauty  will be released tomorrow.

"The most charmingly rendered female schemer since Truman Capote's Holly Golightly."
Elle  magazine

"Martin compresses the wild and crazy end of the millennium
 and finds in this piercing novel a sardonic morality tale….
 Exposes the sound and fury of the rarified Manhattan art world."
Publishers Weekly

"Like Steve Martin's Shopgirl , this very different novel will captivate your attention from start to finish."
— Joyce Carol Oates

Martin on his character Ray Porter in the novella Shopgirl  (published Oct. 11, 2000)—

http://www.log24.com/log/pix10B/101122-MartinShopgirl-loq.jpg

"He said, 'I wrote a piece of code
 that they just can’t seem to do without.'
 He was a symbolic logician. That was his career…."

As the above review notes, Martin's new book is about art at the end of the millennium.

See also Art Wars: Geometry as Conceptual Art
and some of my own notes from 2000 (March 9) in "Is Nothing Sacred?"

Some related material —

A paperback with a striking cover (artist unknown)—

http://www.log24.com/log/pix10B/101027-LangerSymbolicLogic.jpg

Note that the background may be constructed from
any of four distinct motifs. For another approach to these
motifs in a philosophical context, see June 8, 2010.

"Visual forms— lines, colors, proportions, etc.— are just as capable of articulation , i.e. of complex combination, as words. But the laws that govern this sort of articulation are altogether different from the laws of syntax that govern language. The most radical difference is that visual forms are not discursive . They do not present their constituents successively, but simultaneously, so the relations determining a visual structure are grasped in one act of vision."

Susanne K. Langer, Philosophy in a New Key

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