Saturday, August 17, 2019


Filed under: General — m759 @ 7:41 AM

See a Log24 search for "solid.html."

Friday, March 15, 2019

The Breach Report

Filed under: General — m759 @ 12:20 PM

See also two notes of my own, from Nov. 5 and Dec. 24, 1981.

Wednesday, April 27, 2016

Local and Global

Filed under: General,Geometry — m759 @ 1:00 PM

Three notes on local symmetries
that induce global symmetries

From July 1, 2011

Interplay of local symmetry with global symmetry

From November 5, 1981

Local symmetry groups induce global symmetry groups

From December 24, 1981

Local symmetry groups induce global symmetry groups

Monday, December 24, 2012

Post-Mortem for Quincy

Filed under: General,Geometry — m759 @ 11:59 PM

Raiders of the Lost Trunk, or:

Stars in the Attic

More »

See also A Glass for Klugman :

Context: Poetry and Truth,  Eternal Recreation,  
              Solid Symmetry, and Stevens's Rock.

Monday, December 3, 2012

The Revisiting

Filed under: General,Geometry — Tags: , — m759 @ 5:18 PM

Alan Cowell in the The New York Times ,
October 21, 2006— 

"Mr. Pinter played the role of Krapp,
a 69-year-old man revisiting
a tape recording he had made at 39…."

See also a weblog post by a 69-year-old man
revisiting a drawing he had made at 39.

The revisiting:

On Guy Fawkes Day 2011,
a return to Guy Fawkes day 2005—
Contrapuntal Themes in a Shadowland.

The drawing:

A clearer version, from 1981, of the central object below —

For commentary on the original 1981 drawing, see
Diamond-Faceted: Transformations of the Rock.

(A link in that page to "an earlier note from 1981
leads to remarks from exactly thirty years before
the 2011 post, made on another Guy Fawkes Day.)

Saturday, November 5, 2011


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

Between the idea
And the reality
Between the motion
And the act
Falls the Shadow

— T. S. Eliot, "The Hollow Men"

A passage quoted here on this date in 2005—

Douglas Hofstadter on his magnum opus:

“… I realized that to me,
Gödel and Escher and Bach
were only shadows
cast in different directions
by some central solid essence."

This refers to Hofstadter's cover image:

IMAGE- http://www.log24.com/log/pix11C/111105-GEBshadows.jpg

Also from this date in 2005:

IMAGE- www.log24.com/theory/images/GEB.jpg
BackgroundYesterday's link Change Logos,
and Solid Symmetry.

Midrash:         Hearts of Darkness.

Friday, July 1, 2011

Symmetry Review

Filed under: General,Geometry — Tags: , — m759 @ 5:01 AM

Popular novelist Dan Brown is to speak at Chautauqua Institution on August 1.

This suggests a review of some figures discussed here in a note on Brown from February 20, 2004

IMAGE- Like motions of a pattern's parts can induce motions of the whole. Escher-'Fishes and Scales,' Cullinane-'Invariance'

Related material: Notes from Nov. 5, 1981, and from Dec. 24, 1981.

For the lower figure in context, see the diamond theorem.

Thursday, January 20, 2011

Brightness at Noon, continued

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

"One wild rhapsody a fake for another."

– Wallace Stevens, "Arrival at the Waldorf," in Parts of a World  (1942)

"Camelot is an illusion.

That doesn't matter, according to Catherine.
Camelot is an artificial construction, a public perception.
The things that matter are closer, deeper, self-generated, unkillable.
You've got to grow up to discover what those things are."

— Dan Zak, Washington Post  movie review on Feb. 27, 2009. See also this journal on that date.

See as well a note on symmetry from Christmas Eve, 1981, and Verbum in this journal.

Some philosophical background— Derrida in the Garden.

Some historical background— A Very Private Woman  and Noland.

Saturday, May 10, 2008

Saturday May 10, 2008

Filed under: General,Geometry — Tags: , , , — m759 @ 8:00 AM
MoMA Goes to

"… the startling thesis of Mr. Brosterman's new book, 'Inventing Kindergarten' (Harry N. Abrams, $39.95): that everything the giants of modern art and architecture knew about abstraction they learned in kindergarten, thanks to building blocks and other educational toys designed by Friedrich Froebel, a German educator, who coined the term 'kindergarten' in the 1830's."

— "Was Modernism Born
     in Toddler Toolboxes?"
     by Trip Gabriel, New York Times,
     April 10, 1997


Figure 1 —
Concept from 1819:

Cubic crystal system
(Footnotes 1 and 2)

Figure 2 —
The Third Gift, 1837:

Froebel's third gift

Froebel's Third Gift

Froebel, the inventor of
kindergarten, worked as
an assistant to the
crystallographer Weiss
mentioned in Fig. 1.

(Footnote 3)

Figure 3 —
The Third Gift, 1906:

Seven partitions of the eightfold cube in a book from 1906

Figure 4 —
Solomon's Cube,
1981 and 1983:

Solomon's Cube - A 1981 design by Steven H. Cullinane

Figure 5 —
Design Cube, 2006:

Design Cube 4x4x4 by Steven H. Cullinane

The above screenshot shows a
moveable JavaScript display
of a space of six dimensions
(over the two-element field).

(To see how the display works,
try the Kaleidoscope Puzzle first.)

For some mathematical background, see

1. Image said to be after Holden and Morrison, Crystals and Crystal Growing, 1982
2. Curtis Schuh, "The Library: Biobibliography of Mineralogy," article on Mohs
3. Bart Kahr, "Crystal Engineering in Kindergarten" (pdf), Crystal Growth & Design, Vol. 4 No. 1, 2004, 3-9

Wednesday, May 7, 2008

Wednesday May 7, 2008

Filed under: General,Geometry — m759 @ 7:00 AM
Forms of the Rock

“point A / In a perspective
that begins again / At B”

— Wallace Stevens,
The Rock

See also

August 2, 2002

January 20, 2003

April 8, 2003

December 5, 2004

December 10, 2004

January 11, 2006

April 30, 2006

August 25, 2006

August 26, 2006

February 6, 2007

July 23, 2007

July 24, 2007

September 30, 2007

April 14, 2008

Christmas Eve, 1981

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