Sunday, September 29, 2019

Stage Direction: “Comments Off.”

Filed under: General — Tags: — m759 @ 11:29 AM

The previous post dealt with "magic" cubes, so called because of the
analogous "magic" squares. Douglas Hofstadter has written about a 
different, physical , object, promoted as "the  Magic Cube," that Hofstadter
felt embodied "a deep invariant":

Sunday, February 5, 2012


Filed under: General,Geometry — Tags: — m759 @ 5:15 PM

(Continued from January 11, 2012)

Wednesday, January 11, 2012


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

"Examples galore of this feeling must have arisen in the minds of the people who extended the Magic Cube concept to other polyhedra, other dimensions, other ways of slicing.  And once you have made or acquired a new 'cube'… you will want to know how to export a known algorithm , broken up into its fundamental operators , from a familiar cube.  What is the essence of each operator?  One senses a deep invariant lying somehow 'down underneath' it all, something that one can’t quite verbalize but that one recognizes so clearly and unmistakably in each new example, even though that example might violate some feature one had thought necessary up to that very moment.  In fact, sometimes that violation is what makes you sure you’re seeing the same thing , because it reveals slippabilities you hadn’t sensed up till that time….

… example: There is clearly only one sensible 4 × 4 × 4 Magic Cube.  It is the  answer; it simply has the right spirit ."

— Douglas R. Hofstadter, 1985, Metamagical Themas: Questing for the Essence of Mind and Pattern  (Kindle edition, locations 11557-11572)

See also Many Dimensions in this journal and Solomon's Cube.

Language Game

Filed under: General,Geometry — Tags: — m759 @ 8:08 AM

Tension in the Common Room

IMAGE- 'Launched from Cuber' scene in 'X-Men: First Class'

In memory of population geneticist James F. Crow,
who died at 95 on January 4th.

Saturday, August 27, 2011

Cosmic Cube*

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

IMAGE- Anthony Hopkins exorcises a Rubik cube

Prequel (Click to enlarge)

IMAGE- Galois vs. Rubik: Posters for Abel Prize, Oslo, 2008

Background —

IMAGE- 'Group Theory' Wikipedia article with Rubik's cube as main illustration and argument  by a cuber for the image's use

See also Rubik in this journal.

* For the title, see Groups Acting.

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