Log24

Monday, May 31, 2010

Memorial for Galois

Filed under: General,Geometry — m759 @ 7:16 pm

… and for Louise Bourgeois

Image-- Louise Bourgeois, sculptor of giant spiders, dies at 98

"The épateurs  were as boring as the bourgeois,
two halves of one dreariness."

— D. H. Lawrence, The Plumed Serpent

Image-- Google 5/31/2010 search for 'eightfold geometry' yields page on mother goddess as spider figure, also pages on some actual geometry

Thursday, February 17, 2022

Space Memorial

Filed under: General — m759 @ 1:27 pm

"FILE – Retired Sandinista Gen. Hugo Torres poses for portrait
at his home, in Managua, Nicaragua, May 2, 2018."

— Photo caption from a Feb. 12 Washington Post  obituary 

Also on May 2, 2018 —

Related theology —

Tuesday, February 23, 2016

Revolutionary

Filed under: General — m759 @ 7:14 PM 

From New York Times  obituary today —

"The Rev. Fernando Cardenal, a son of privilege
who embraced Latin America’s poor as a revolutionary
priest and brazenly defied Pope John Paul II’s order to
quit Nicaragua’s leftist cabinet in the 1980s, died on
Saturday in Managua. He was 82."

Photo caption from the same obituary —

"Fernando Cardenal in 1990. As education minister of
Nicaragua under the Sandinistas in the 1980s, he
oversaw a sweeping campaign credited with reducing
illiteracy to 13 percent from 51 percent."

This alleged literacy improvement makes him sound like
Protestant  revolutionary.

For a Catholic  view of literacy, see The Gutenberg Galaxy .

See also the post Being Interpreted (Aug. 14, 2015) — 

Saturday, June 27, 2020

Blank Memorial

Filed under: General — m759 @ 8:00 pm

This is a continuation of the “just seventeen” posts.

Saturday, August 6, 2011

Happy Web Day

Filed under: General,Geometry — m759 @ 9:00 pm

Today the World Wide Web turns 20.

http://www.log24.com/log/pix11B/110806-EightfoldGeometrySearch.jpg

See also Galois Memorial and Correspondences.

Monday, April 11, 2016

Like Decorations in a Cartoon Graveyard

Filed under: General,Geometry — Tags: , — m759 @ 10:48 pm

From Sunday evening's In Memoriam post —

The "from Princeton" remark in the previous post came  from
Princeton, but originated with a retired professor in Rochester,
NY, one Joseph Neisendorfer.

Another remark by Neisendorfer, from his weblog —

Those familiar with the chapter on Galois in the
Eric Temple Bell classic Men of Mathematics  
will know that the words quoted above by
Neisendorfer are definitely not  those of Albert Einstein.

Combinatorial Spider

Filed under: General,Geometry — Tags: , , , — m759 @ 1:16 pm

“Chaos is order yet undeciphered.”

— The novel The Double , by José Saramago,
on which the film "Enemy" was based

Some background for the 2012 Douglas Glover
"Attack of the Copula Spiders" book
mentioned in Sunday's Synchronicity Check

  • "A vision of Toronto as Hell" — Douglas Glover in the
    March 25, 2011, post Combinatorial Delight
  • For Louise Bourgeois — a post from the date of Galois's death—

http://www.log24.com/log/pix11B/110715-GaloisMemorial-Lg.jpg

  • For Toronto — Scene from a film that premiered there
    on Sept. 8, 2013:

Wednesday, November 26, 2014

Class Act

Filed under: General,Geometry — Tags: , — m759 @ 7:18 am

Update of Nov. 30, 2014 —

For further information on the geometry in
the remarks by Eberhart below, see
pp. 16-17 of A Geometrical Picture Book ,
by Burkard Polster (Springer, 1998). Polster
cites a different article by Lemay.

A search for background to the exercise in the previous post
yields a passage from the late Stephen Eberhart:

The first three primes p = 2, 3, and 5 therefore yield finite projective planes with 7, 13, and 31 points and lines, respectively. But these are just the numbers of symmetry axes of the five regular solids, as described in Plato's Timaeus : The tetrahedron has 4 pairs of face planes and corner points + 3 pairs of opposite edges, totalling 7 axes; the cube has 3 pairs of faces + 6 pairs of edges + 4 pairs of corners, totalling 13 axes (the octahedron simply interchanges the roles of faces and corners); and the pentagon dodecahedron has 6 pairs of faces + 15 pairs of edges + 10 pairs of corners, totalling 31 axes (the icosahedron again interchanging roles of faces and corners). This is such a suggestive result, one would expect to find it dealt with in most texts on related subjects; instead, while "well known to those who well know such things" (as Richard Guy likes to quip), it is scarcely to be found in the formal literature [9]. The reason for the common numbers, it turns out, is that the groups of symmetry motions of the regular solids are subgroups of the groups of collineations of the respective finite planes, a face axis being different from an edge axis of a regular solid but all points of a projective plane being alike, so the latter has more symmetries than the former.

[9] I am aware only of a series of in-house publications by Fernand Lemay of the Laboratoire de Didactique, Faculté des Sciences de I 'Éducation, Univ. Laval, Québec, in particular those collectively titled Genèse de la géométrie  I-X.

— Stephen Eberhart, Dept. of Mathematics,
California State University, Northridge, 
"Pythagorean and Platonic Bridges between
Geometry and Algebra," in BRIDGES: Mathematical
Connections in Art, Music, and Science 
, 1998,
archive.bridgesmathart.org/1998/bridges1998-121.pdf

Eberhart died of bone cancer in 2003. A memorial by his
high school class includes an Aug. 7, 2003, transcribed
letter from Eberhart to a classmate that ends…


… I earned MA’s in math (UW, Seattle) and history (UM, Missoula) where a math/history PhD program had been announced but canceled.  So 1984 to 2002 I taught math (esp. non-Euclidean geometry) at C.S.U. Northridge.  It’s been a rich life.  I’m grateful. 
 
Steve
 

See also another informative BRIDGES paper by Eberhart
on mathematics and the seven traditional liberal arts.

Wednesday, October 1, 2014

Big Time

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

The following post suggests the Spiders and Snakes of Fritz Leiber’s
Changewar , a mythology inspired by the hallucinations of delirium tremens .

Thursday, May 22, 2014

Visual Structure

Filed under: General,Geometry — Tags: — m759 @ 8:07 pm

“Chaos is order yet undeciphered.”

— The novel The Double , by José Saramago,
on which the recent film "Enemy" was based

For Louise Bourgeois — a post from the date of Galois's death—

http://www.log24.com/log/pix11B/110715-GaloisMemorial-Lg.jpg

For Toronto — Scene from a film that premiered there on Sept. 8, 2013:

Related material: This journal on that date, Sept. 8, 2013:

"I still haven't found what I'm looking for." — Bono

"In fact Surrealism found what it had been looking for
from the first in the 1920 collages [by Max Ernst],
which introduced an entirely original scheme of
visual structure…."

— Rosalind Krauss quoting André Breton*
in "The Master's Bedroom"

* "Artistic Genesis and Perspective of Surrealism"
(1941),
   in Surrealism and Painting  (New York,
Harper & Row, 1972, p. 64).

See also Damnation Morning in this journal.

Friday, July 15, 2011

Spider Women

Filed under: General,Geometry — Tags: — m759 @ 1:10 pm

"Of course, the aesthetic program
of cultural modernism
has long been summed up
by the maxim épater la bourgeoisie."

The New York Times
Sunday Book Review
, July 17

Examples:

"This Extreme and Difficult Sense of Spectacular Representation:
Antonin Artaud's Ontology of 'Live'
," by Deborah Levitt
of the New School (See the noon post of July 13), as well as…

http://www.log24.com/log/pix11B/110715-GaloisMemorial-Lg.jpg

and, from mathematician Ellen Gethner's home page

http://www.log24.com/log/pix11B/110715-GethnerSpiderSm.jpg

See also Sunday Dinner, A Link for Sunrise, and Inside CBS News.

Tuesday, August 10, 2010

A Problem

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

From Telegraph.co.uk (published: 5:56 PM BST 10 Aug 2010), a note on British-born Canadian journalist Bruce Garvey, who died at 70 on August 1—

In 1970, while reporting on the Apollo 13 mission at Nasa Mission Control for the Toronto Star, he was one of only two journalists— alongside Richard Killian of the Daily Express— to hear the famous message: "Houston we've had a problem."

See also Log24 posts of 10 AM and noon today.

The latter post poses the problem "You're dead. Now what?"

Again, as in this morning's post, applying Jungian synchronicity—

A check of this journal on the date of Garvey's death yields a link to 4/28's "Eightfold Geometry."

That post deals with a piece of rather esoteric mathematical folklore. Those who prefer easier problems may follow the ongoing struggles of Julie Taymor with "Spider-Man: Turn Off the Dark."

The problems of death, geometry, and Taymor meet in "Spider Woman" (April 29) and "Memorial for Galois" (May 31).

Friday, June 4, 2010

A Better Story

Filed under: General,Geometry — Tags: , — m759 @ 7:59 am

Continued from May 8
(Feast of Saint Robert Heinlein)

“Wells and trees were dedicated to saints.  But the offerings at many wells and trees were to something other than the saint; had it not been so they would not have been, as we find they often were, forbidden.  Within this double and intertwined life existed those other capacities, of which we know more now, but of which we still know little– clairvoyance, clairaudience, foresight, telepathy.”

— Charles Williams, Witchcraft, Faber and Faber, London, 1941

Why "Saint" Robert? See his accurate depiction of evil– the Eater of Souls in Glory Road.

For more on Williams's "other capacities," see Heinlein's story "Lost Legacy."

A related story– Fritz Leiber's "The Mind Spider." An excerpt:

The conference—it was much more a hyper-intimate
gabfest—proceeded.

"My static box bugged out for a few ticks this morning,"
Evelyn remarked in the course of talking over the
trivia of the past twenty-four hours.

The static boxes were an invention of Grandfather
Horn. They generated a tiny cloud of meaningless brain
waves. Without such individual thought-screens, there was
too much danger of complete loss of individual personality

—once Grandfather Horn had "become" his infant daughter
as well as himself for several hours and the unfledged
mind had come close to being permanently lost in its own
subconscious. The static boxes provided a mental wall be-
– hind which a mind could safely grow and function, similar
to the wall by which ordinary minds are apparently
always enclosed.

In spite of the boxes, the Horns shared thoughts and
emotions to an amazing degree. Their mental togetherness
was as real and as mysterious—and as incredible—as
thought itself . . . and thought is the original angel-cloud
dancing on the head of a pin. Their present conference
was as warm and intimate and tart as any actual family
gathering in one actual room around one actual table.
Five minds, joined together in the vast mental darkness
that shrouds all minds. Five minds hugged together for
comfort and safety in the infinite mental loneliness that
pervades the cosmos.

Evelyn continued, "Your boxes were all working, of
course, so I couldn't get your thoughts—just the blurs of
your boxes like little old dark grey stars. But this time
if gave me a funny uncomfortable feeling, like a spider
Crawling down my—Grayl! Don't feel so wildly! What
Is it?”

Then… just as Grayl started to think her answer…
something crept from the vast mental darkness and infinite
cosmic loneliness surrounding the five minds of the
Horns
.

Grayl was the first to notice. Her panicky thought had
ttie curling too-keen edge of hysteria. "There are six of
us now! There should only be five, but there are six.
Count! Count, I tell you! Six!"

To Mort it seemed that a gigantic spider was racing
across the web of their thoughts….

See also this journal on May 30– "720 in the Book"– and on May 31– "Memorial for Galois."

("Obnoxious nerds"— a phrase Martin Gardner recently applied to Galois— will note that 720 (= 6!) is one possible result of obeying Leiber's command "Count! Count, I tell you! Six!")

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