Log24

Thursday, August 15, 2019

Schoolgirl Space — Tetrahedron or Square?

Filed under: General — Tags: , , — m759 @ 9:03 pm

The exercise in the previous post  was suggested by a passage
purporting to "use standard block design theory" that was written
by some anonymous author at Wikipedia on March 1, 2019:

Here "rm OR" apparently means "remove original research."

Before the March 1 revision . . .

The "original research" objected to and removed was the paragraph
beginning "To explain this further."  That paragraph was put into the
article earlier on Feb. 28 by yet another anonymous author (not  by me).

An account of my own (1976 and later) original research on this subject 
is pictured below, in a note from Feb. 20, 1986 —

'The relativity problem in finite geometry,' 1986

Friday, September 27, 2019

Algebra for Schoolgirls

Filed under: General — Tags: , , — m759 @ 8:37 am

The 15 points of the finite projective 3-space PG(3,2)
arranged in tetrahedral form:

The letter labels, but not the tetrahedral form,
are from The Axioms of Projective Geometry , by
Alfred North Whitehead (Cambridge U. Press, 1906).

The above space PG(3,2), because of its close association with
Kirkman's schoolgirl problem, might be called "schoolgirl space."

Screen Rant  on July 31, 2019:

A Google Search sidebar this morning:

Apocalypse Soon!

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.

Thursday, July 18, 2019

Avatar for Inspector Tennison

Filed under: General — Tags: — m759 @ 7:35 am

The image “http://www.log24.com/log/pix06B/061113-Mirren.jpg” cannot be displayed, because it contains errors. 

Image from a post of November 13, 2006.
See as well Schoolgirl Tetrahedron.

Related lyrics from Bruce Springsteen and
the Pointer Sisters

Well, Romeo and Juliet, Samson and Delilah
Baby you can bet a love they couldn't deny
My words say split, but my words they lie
Cause when we kiss, ooh, fire

{Bridge}

Oh fire
Kisses like fire…
Burn me up with fire
I like what you're doin now, fire
Touchin' me, fire
Touchin' me, burnin me, fire
Take me home

E is for Energy.

Monday, March 16, 2020

Mathematics and Narrative* Continues:

Filed under: General — Tags: — m759 @ 1:27 am

Expanding the Spielraum

Mathematics:  See Tetrahedron vs. Square in this journal
(Notes on two different models of schoolgirl space ).

Narrative:  Replacing the square  from the above posts by
a related cube 

… yields a merchandising inspiration

Dueling Holocrons: 

Jedi Cube vs. Sith Tetrahedron

.

* See also earlier posts on Mathematics and Narrative.

Wednesday, February 26, 2020

“Perfect”

Filed under: General — Tags: — m759 @ 9:59 pm

Usage example —

(Click to enlarge.)

See also the previous post as well as PG(3,2),
Schoolgirl Space, and Tetrahedron vs. Square.

Saturday, December 7, 2019

Canonicity* Illustrated: The Offensive Tet

Filed under: General — Tags: — m759 @ 8:56 pm

* “Canonicity” is a reference to the previous post.
See as well Tetrahedron vs. Square and Algebra for Schoolgirls.

Monday, August 19, 2019

A Couple of Tots

Filed under: General — Tags: , — m759 @ 10:15 pm

The title is from the post "Child's Play" of May 21, 2012 . . .

"It seems that only one course is open to the philosopher
who values knowledge and truth above all else. He must
refuse to accept from the champions of the forms the
doctrine that all reality is changeless [and exclusively
immaterial], and he must turn a deaf ear to the other party
who represent reality as everywhere changing [and as only
material]. Like a child begging for 'both', he must declare
that reality or the sum of things is both at once  [το όν τε και
το παν συναμφότερα] (Sophist  246a-249d)."

Related material —

"Schoolgirl Space: 1984 Revisited" (July 9, 2019) and
posts tagged Tetrahedron vs. Square.

Wednesday, July 17, 2019

The Artsy Quantum Realm

Filed under: General — Tags: , — m759 @ 6:38 pm
 

arXiv.org > quant-ph > arXiv:1905.06914 

Quantum Physics

Placing Kirkman's Schoolgirls and Quantum Spin Pairs on the Fano Plane: A Rainbow of Four Primary Colors, A Harmony of Fifteen Tones

J. P. Marceaux, A. R. P. Rau

(Submitted on 14 May 2019)

A recreational problem from nearly two centuries ago has featured prominently in recent times in the mathematics of designs, codes, and signal processing. The number 15 that is central to the problem coincidentally features in areas of physics, especially in today's field of quantum information, as the number of basic operators of two quantum spins ("qubits"). This affords a 1:1 correspondence that we exploit to use the well-known Pauli spin or Lie-Clifford algebra of those fifteen operators to provide specific constructions as posed in the recreational problem. An algorithm is set up that, working with four basic objects, generates alternative solutions or designs. The choice of four base colors or four basic chords can thus lead to color diagrams or acoustic patterns that correspond to realizations of each design. The Fano Plane of finite projective geometry involving seven points and lines and the tetrahedral three-dimensional simplex of 15 points are key objects that feature in this study.

Comments:16 pages, 10 figures

Subjects:Quantum Physics (quant-ph)

Cite as:arXiv:1905.06914 [quant-ph]

 (or arXiv:1905.06914v1 [quant-ph] for this version)

Submission history

From: A. R. P. Rau [view email] 
[v1] Tue, 14 May 2019 19:11:49 UTC (263 KB)

See also other posts tagged Tetrahedron vs. Square.

Life in Palermo

Filed under: General — Tags: , — m759 @ 9:55 am

See also other posts tagged Tetrahedron vs. Square, and a related
Log24 search for "Schoolgirl + Space."

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