Nobel Flashback:
Wednesday, January 29, 2014
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Thursday, October 6, 2016
Cuber
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Wednesday, December 17, 2014
Launched from Cuber
Continued from Nobel Note (Jan. 29, 2014).
From Tradition in Action , "The Missal Crisis of '62,"
remarks on the revision of the Catholic missal in that year—
"Neither can the claim that none of these changes
is heretical in content be used as an argument
in favor of its use, for neither is the employment of
hula girls, fireworks, and mariachis strictly speaking
heretical in itself, but they belong to that class of novel
and profane things that do not belong in the Mass."
— Fr. Patrick Perez, posted Sept. 11, 2007
See also this journal on November 22, 2014…
… and on Bruce Springsteen's birthday this year —
Tuesday, September 23, 2014
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Friday, June 7, 2013
Rubric’s Cuber
From Night of Lunacy (Sunday, May 5, 2013):
Related posts: Rubric, Cuber, and Pound Sign.
Click image for some background.
See also Story Theory and Princeton Apocalypse.
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Wednesday, July 11, 2012
Cuber
For Pete Rustan, space recon expert, who died on June 28—
See also Galois vs. Rubik and Group Theory Template.
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Saturday, February 25, 2012
Cuber (continued)
Click images for further details.
See also Crimson Tide, Rubik, and Cuber.
For another monochromatic enigma without
guaranteed equality of results, see
Finite Geometry of the Square and Cube.
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Sunday, February 5, 2012
Wednesday, January 11, 2012
Cuber
“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.
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Friday, June 16, 2017
Rough Night at the Museum
See the previous three posts… and the Nobel flashback titled Cuber.
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Monday, December 29, 2014
Revolution of Forms
In memory of Cuban architect
Ricardo Porro, who died
on Christmas Day, 2014:
See also Rubik + Revolution
and Launched from Cuber.
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Thursday, October 9, 2014
Friday, June 13, 2014
It’s 10 PM
“The wind of change is blowing throughout the continent.
Whether we like it or not, this growth of national consciousness
is a political fact.”— Prime Minister Harold Macmillan,
South Africa, 1960
“Lord knows when the cold wind blows
it’ll turn your head around.” — James Taylor
From a Log24 post of August 27, 2011:
For related remarks on “national consciousness,” see Frantz Fanon.
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Wednesday, January 29, 2014
Nobel Note
"It's going to be accomplished in steps,
this establishment of the Talented
in the scheme of things."
— To Ride Pegasus ,
by Anne McCaffrey (Radcliffe '47)
From a post of Jan. 11, 2012 —
Tension in the Common Room—
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Tuesday, June 18, 2013
Multispeech
For those who prefer Trudeau's
"Story Theory" of truth to his "Diamond Theory"
Related material: Click images below for the original posts.
See as well the novel "Lexicon" at Amazon.com
and the word "lexicon" in this journal.
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Saturday, June 8, 2013
Multispeech (continued)
For this, the dies natalis of poet Gerard Manley Hopkins,
it seems apt to cite a 1973 master's thesis on what the author
calls multiguity in Hopkins.
See also multispeech in this journal.
Related material:
- Hopkins and tic-tac-toe in the above thesis, p. 20.
- Gail Collins's column today
- TIC
- tacto
See, too, the online front page of The New York Times
from 1:54 PM ET today, and, as an example of multispeech,
yesterday morning's post Rubric's Cuber.
Yesterday's noon post concerned a forthcoming novel
about poetry and intelligence services. Some related backstory:
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Monday, November 5, 2012
For the Hollow Men
"Remember, remember the Fifth of November."
Very well. See a post of Nov. 5, 2005, and the related posts
Shadows, Cuber, Cube Partitions, and Cube Review.
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Tuesday, October 16, 2012
Cube Review
Last Wednesday's 11 PM post mentioned the
adjacency-isomorphism relating the 4-dimensional
hypercube over the 2-element Galois field GF(2) to
the 4×4 array made up of 16 square cells, with
opposite edges of the 4×4 array identified.
A web page illustrates this property with diagrams that
enjoy the Karnaugh property— adjacent vertices, or cells,
differ in exactly one coordinate. A brief paper by two German
authors relates the Karnaugh property to the construction
of a magic square like that of Dürer (see last Wednesday).
In a similar way (search the Web for Karnaugh + cube ),
vertex adjacency in the 6-dimensional hypercube over GF(2)
is isomorphic to cell adjacency in the 4x4x4 cube, with
opposite faces of the 4x4x4 cube identified.
The above cube may be used to illustrate some properties
of the 64-point Galois 6-space that are more advanced
than those studied by enthusiasts of "magic" squares
and cubes.
See
- the 4x4x4 cube and An Invariance of Symmetry
- the 4x4x4 cube and the nineteenth-century
geometers' "Solomon's seal" - the 4x4x4 cube and the Kummer surface
- the 4x4x4 cube and the Klein quadric.
Those who prefer narrative to mathematics may
consult posts in this journal containing the word "Cuber."
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Thursday, April 12, 2012
Mythopoetic*
"Is Space Digital?"
— Cover story, Scientific American magazine, February 2012
"The idea that space may be digital
is a fringe idea of a fringe idea
of a speculative subfield of a subfield."
— Physicist Sabine Hossenfelder
at her weblog on Feb. 5, 2012
"A quantization of space/time
is a holy grail for many theorists…."
— Peter Woit in a comment at his physics weblog today
See also
* See yesterday's Steiner's Systems.
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Saturday, January 14, 2012
Damnation Morning*
The following is adapted from a 2011 post—
* The title, that of a Fritz Leiber story, is suggested by
the above picture of the symmetry axes of the square.
Click "Continued" above for further details. See also
last Wednesday's Cuber.
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Wednesday, January 11, 2012
Language Game
Tension in the Common Room—
In memory of population geneticist James F. Crow,
who died at 95 on January 4th.
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Saturday, August 27, 2011
Cosmic Cube*
Prequel — (Click to enlarge)
Background —
See also Rubik in this journal.
* For the title, see Groups Acting.
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