Log24

Monday, June 26, 2023

The Boole Tool  and The XOR Schism

Filed under: General — m759 @ 12:32 pm

'Galois Additions of Space Partitions'

Friday, December 29, 2023

A Wrinkle in Logic

Filed under: General — Tags: , — m759 @ 4:17 pm

Also on March 8, 2018

Barbara Johnson, Nothing Fails Like Success, detail

This post was suggested by the word "entanglement' in the previous post.

See as well "Galois (Xor) addition."

Sunday, July 7, 2019

Schoolgirl Problem

Filed under: General — Tags: , , , — m759 @ 11:18 pm

Anonymous remarks on the schoolgirl problem at Wikipedia —

"This solution has a geometric interpretation in connection with 
Galois geometry and PG(3,2). Take a tetrahedron and label its
vertices as 0001, 0010, 0100 and 1000. Label its six edge centers
as the XOR of the vertices of that edge. Label the four face centers
as the XOR of the three vertices of that face, and the body center
gets the label 1111. Then the 35 triads of the XOR solution correspond
exactly to the 35 lines of PG(3,2). Each day corresponds to a spread
and each week to a packing
."

See also Polster + Tetrahedron in this  journal.

There is a different "geometric interpretation in connection with
Galois geometry and PG(3,2)" that uses a square  model rather
than a tetrahedral  model. The square  model of PG(3,2) last
appeared in the schoolgirl-problem article on Feb. 11, 2017, just
before a revision that removed it.

Sunday, October 25, 2015

Celtic Cross

Filed under: General,Geometry — m759 @ 5:01 am

http://www.log24.com/log/pix11B/110714-Michelangelo.jpg

The above illustrations are
from posts tagged
"Universe of Discourse." 

Happy birthday to Évariste Galois, who may
prefer a mathematical, not religious,
interpretation of the above Celtic cross.

Tuesday, February 14, 2012

The Ninth Configuration

Filed under: General,Geometry — m759 @ 2:01 pm

The showmanship of Nicki Minaj at Sunday's
Grammy Awards suggested the above title, 
that of a novel by the author of The Exorcist .

The Ninth Configuration 

The ninth* in a list of configurations—

"There is a (2d-1)d  configuration
  known as the Cox configuration."

MathWorld article on "Configuration"

For further details on the Cox 326 configuration's Levi graph,
a model of the 64 vertices of the six-dimensional hypercube γ6  ,
see Coxeter, "Self-Dual Configurations and Regular Graphs,"
Bull. Amer. Math. Soc.  Vol. 56, pages 413-455, 1950.
This contains a discussion of Kummer's 166 as it 
relates to  γ6  , another form of the 4×4×4 Galois cube.

See also Solomon's Cube.

* Or tenth, if the fleeting reference to 113 configurations is counted as the seventh—
  and then the ninth  would be a 153 and some related material would be Inscapes.

Saturday, August 27, 2011

Cosmic Cube*

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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