Log24

Saturday, February 27, 2021

Quarters

Filed under: General — Tags: , — m759 @ 1:58 PM

From posts tagged “The Empty Quarter” —

The image “http://www.log24.com/log/pix05B/050805-Rag.jpg” cannot be displayed, because it contains errors.

Related tune suggested today by Peter J. Cameron

The Beatles, “I Me Mine,” from the “Let It Be” album.

That album, and an image from Log24 on Feb. 23 —

The bond with reality is cut.

Tuesday, July 6, 2010

Window, continued

“Simplicity, simplicity, simplicity!
I say, let your affairs be as two or three,
and not a hundred or a thousand;
instead of a million count half a dozen,
and keep your accounts on your thumb-nail.”
— Henry David Thoreau, Walden

This quotation is the epigraph to
Section 1.1 of Alexandre V. Borovik’s
Mathematics Under the Microscope:
Notes on Cognitive Aspects of Mathematical Practice
(American Mathematical Society,
Jan. 15, 2010, 317 pages).

From Peter J. Cameron’s review notes for
his new course in group theory

http://www.log24.com/log/pix10A/100705-CameronExample.jpg

From Log24 on June 24

Geometry Simplified

Image-- The Four-Point Plane: A Finite Affine Space
(an affine  space with subsquares as points
and sets  of subsquares as hyperplanes)

Image-- The Three-Point Line: A Finite Projective Space
(a projective  space with, as points, sets
of line segments that separate subsquares)

Exercise

Show that the above geometry is a model
for the algebra discussed by Cameron.

Saturday, August 6, 2005

Saturday August 6, 2005

Filed under: General,Geometry — Tags: — m759 @ 1:25 PM

The Fugue

   "True joy is a profound remembering, and true grief is the same.
    Thus it was, when the dust storm that had snatched Cal up finally died, and he opened his eyes to see the Fugue spread out before him, he felt as though the few fragile moments of epiphany he'd tasted in his twenty-six years– tasted but always lost– were here redeemed and wed. He'd grasped fragments of this delight before. Heard rumour of it in the womb-dream and the dream of love; known it in lullabies. But never, until now, the whole, the thing entire.
    It would be, he idly thought, a fine time to die.
    And a finer time still to live, with so much laid out before him."

— Clive Barker,
Weaveworld,
 Book Two:
The Fugue

From Monday:

Weaveworld,
Book Three:
Out of the
Empty Quarter

"The wheels of its body rolled,
the visible mathematics
    of its essence turning on itself…."

From Friday:

The image “http://www.log24.com/log/pix05B/050806-Square.bmp” cannot be displayed, because it contains errors.

  For the meaning
of this picture, see
Geometry of the
4×4 Square.

For graphic designs
based on this geometry,
see Theme and Variations
and Diamond Theory.

For these designs in the
context of a Bach fugue,
see Timothy A. Smith's
essay (pdf) on

Fugue No. 21 in B-Flat Major
from Book II of
The Well-Tempered Clavier
by Johann Sebastian Bach.

Smith also offers a
Shockwave movie
that uses diamond theory
to illustrate this fugue.

Friday, August 5, 2005

Friday August 5, 2005

Filed under: General,Geometry — Tags: , , — m759 @ 4:23 PM

For Sir Alec

From Elegance:

"Philosophers ponder the idea of identity: what it is to give something a name on Monday and have it respond to that name on Friday…."

— Bernard Holland, page C12,
    The New York Times,
    Monday, May 20, 1996.

Holland was pondering the identity of the Juilliard String Quartet, which had just given a series of concerts celebrating its fiftieth anniversary.

"Elegant"

— Page one,
    The New York Times,
    Monday, August 7, 2000.
 
The Times was describing the work of Sir Alec Guinness, who died on 8/5/00.

An example of the Holland name problem:

Monday, August 1, 2005 — Visible Mathematics:

    "Earlier, there had been mapping projects in Saudi Arabia's Rub' al-Khali, the Empty Quarter in the south and west of the country….
   '
"Empty" is a misnomer…  the Rub' al-Khali contains many hidden riches.'"

Friday, August 5, 2005 —  

The image “http://www.log24.com/log/pix05B/050805-Rag.jpg” cannot be displayed, because it contains errors.

Related material:

Geometry for Prince Harry

Monday, August 1, 2005

Monday August 1, 2005

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

    "Earlier, there had been mapping projects in Saudi Arabia's Rub' al-Khali, the Empty Quarter in the south and west of the country….
     '
"Empty" is a misnomer…  the Rub' al-Khali contains many hidden riches.'"

Maps from the Sky,
   Saudi Aramco World, March/April 1995

From Weaveworld

Book Three:
Out of the Empty Quarter,
 by Clive Barker, 1987:


… As a child he'd learned the names of all the angels and archangels by heart: and among the mighty, Uriel was of the mightiest.  The archangel of salvation: called by some the flame of God…. What had he done, stepping into the presence of such power?  This was Uriel, of the principalities….
    Another of the angel's attributes rose from memory now, and with it a sudden shock of comprehension.  Uriel had been the angel left to stand guard at the gates of Eden.
    Eden.
    At the word, the creature blazed.  Though the ages had driven it to grief and forgetfulness, it was still an angel: its fires unquenchable.  The wheels of its body rolled, the visible mathematics of its essence turning on itself and preparing for new terrors.
    There were others here, the Seraph said, that called this place Eden.  But I never knew it by that name.
    "What, then?" Shadwell asked.
    Paradise, said the Angel, and at the word a new picture appeared in Shadwell's mind.  It was the garden, in another age….
    This was a place of making, the Angel said.  Forever and ever.  Where things came to be.
    "To be?"
    To find a form, and enter the world.

 

"The serpent's eyes shine
As he wraps around the vine
In the Garden of Allah."

Don Henley, 1995  
 

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