Log24

Symplectic Macbeth

Lead on, McDuff:

( A sequel to Lux )

“By groping toward the light we are made to realize
how deep the darkness is around us.”

— Arthur Koestler, The Call Girls: A Tragi-Comedy ,
Random House, 1973, page 118

Robin Williams and the Stages of Math

i)   shock & denial
ii)  anger
iii) bargaining
iv) depression
v)  acceptance

A related description of the process —

“You know how sometimes someone tells you a theorem,
and it’s obviously false, and you reach for one of the many
easy counterexamples only to realize that it’s not a
counterexample after all, then you reach for another one
and another one and find that they fail too, and you begin
to concede the possibility that the theorem might not
actually be false after all, and you feel your world start to
shift on its axis, and you think to yourself: ‘Why did no one
tell me this before?’ “

— Tom Leinster yesterday at The n-Category Café

Syntactic  Structure —

See the Lightfoot of today’s previous post:

Symplectic  Structure —

See the plaited, or woven, structure of  August 6:

.

See also Deep  Structure  (Dec. 9, 2012).

From Wikipedia — Abuse of language —

“… in mathematics, a use of terminology in a way that is not formally correct
but that simplifies exposition or suggests the correct intuition.”

The phrase “symplectic structure” in the previous post
was a deliberate abuse of language. The real definition:

George Johnson, a science writer, in The New York Times
on July 21, 2014:

“New particles may yet be discovered, and even new laws.
But it is almost taken for granted that everything
from physics to biology, including the mind,
ultimately comes down to four fundamental concepts:
matter and energy interacting in an arena of space and time.”

Related material:

Ite, missa est.

(Continued from a private post of May 27, 2012)

From this morning’s post:

“Beyond Noplace, far into wide Nowhere” — John Hollander

Vide  Le Guin Geometry.

The date of a Vanity Fair  post on Hugh Jackman—
Sunday, June 8, 2014— suggests a review of the following
quotation from this journal on that date —

Zen ideal —

(Continued from yesterday’s noon post, from  “Block That Metaphor,”
and from “Mystery Box III: Inside, Outside“)

“In one corner are the advocates of the Common Core,
led by the Bill and Melinda Gates Foundation, which
helped develop the standards and has defended them
against efforts by some states to roll them back. In the
challengers’ corner, a lineup of foundations and
philanthropists…. Other funders in the opponents’ corner
read like a ‘who’s who’ of well-heeled conservative
philanthropists, including Pittsburgh media magnate
Richard Mellon Scaife….”

— “Meet the Funders Fighting the Common Core,”
from Inside Philanthropy , Feb. 10, 2014

Scaife reportedly died this morning.

The previous post told how user58512 at math.stackexchange.com
sought in 2013 a geometric representation of Q₈ , the quaternion group.
He ended up displaying an illustration that very possibly was drawn,
without any acknowledgement of its source, from my own work.

On the date that user58512 published that illustration, he further
pursued his March 1, 2013, goal of a “twisty” quaternion model.

On March 12, 2013,  he suggested that the quaternion group might be
the symmetry group of the following twisty-cube coloring:

Illustration by Jim Belk

Here is part of a reply by Jim Belk from Nov. 11, 2013, elaborating on
that suggestion:

Belk argues that the colored cube is preserved under the group
of actions he describes. It is, however, also preserved under a
larger group.  (Consider, say, rotation of the entire cube by 180
degrees about the center of any one of its checkered faces.)  The
group Belk describes seems therefore to be a  symmetry group,
not the  symmetry group, of the colored cube.

I do not know if any combination puzzle has a coloring with
precisely  the quaternion group as its symmetry group.

(Updated at 12:15 AM June 6 to point out the larger symmetry group
and delete a comment about an arXiv paper on quaternion group models.)

The webpage Galois.us, on Galois matrices , has been created as
a starting point for remarks on the algebra  (as opposed to the geometry)
underlying the rings of matrices mentioned in AMS abstract 79T-A37,
“Symmetry invariance in a diamond ring.”

See also related historical remarks by Weyl and by Atiyah.

“You’ve got to pick up every stitch…”
— Donovan, song on closing credits of  To Die For

“…’Supersymmetry’ was originally written
specifically for Her ….” — Pitchfork

“Eventually we see snow particles….”
— Her  screenplay by Spike Jonze

This journal on January 24, 2006:

Context:  See Free-Floating Signs.

Backstory:  Digital Member and  Uneven Break.

See the Field

“There have long been rumors of a mythical Ninth Element
that grants ultimate power to the Wizard who masters it.
The Order of Magick says there is no such thing. But….”

— Website of Magicka: The Ninth Element Novel

William Worthy in Beijing —

This journal on the date of Worthy’s death,
May 4, 2014, had a link to…

    The Holy Field

Or: Death Edit

See the above weblog post honoring a Swiss artist‘s
“wit, his perception, his genius, his horizon,
his determination, his humour, his friendship,
and his immeasurable kindness.”

Not a bad sendoff. Contrast with events at Harvard
on the date of the artist’s death.

Related material:  An album cover, and …

See also this  journal in September 2008.

As far as Swiss art goes, I personally prefer the work of, say,
Karl Gerstner and Paul Talman.

 Raven’s Progressive Matrices  intelligence test—

Wechsler Adult Intelligence Scale  test—  

Related art —  (Click images for further details.)

Patterns suggesting those of the Raven test:

Patterns suggesting those of the Wechsler test:

The latter patterns were derived from the former.

Yesterday’s online New York Times  has the following quote:

“The idea becomes a machine that makes the art.”
— Sol LeWitt

For instance, some conceptual art not  by LeWitt:

Diamond Theory Roulette (Feb. 2, 2014).

From The Ninth Element  website:

Cover of a Norwegian author’s forthcoming novel:

For some Norwegian non-fiction, see an Oslo artist’s Instagram page.

“For every kind of vampire, there is a kind of cross.” — Gravity’s Rainbow

“I don’t write exclusively on Jewish themes or about Jewish characters.
My collection of short stories, Strange Attractors , contained nine pieces,
five of which were, to some degree, Jewish, and this ratio has provided me
with a precise mathematical answer (for me, still the best kind of answer)
to the question of whether I am a Jewish writer. I am five-ninths a Jewish writer.”

— Rebecca Goldstein, “Against Logic”

Midrashim for Rebecca: 

The Diamond Theory vs.  the Story Theory (of truth)

Story Theory and the Number of the Beast

The Palm Sunday post “Gray Space”

For those who prefer the diamond theory of truth,
a “precise mathematical” view of a Gray code —

For those who prefer the story theory of truth,
Thursday with the Nashes —

The actors who portrayed Mr. and Mrs. John Nash in
‘A Beautiful Mind’ now portray Mr. and Mrs. Noah…

He “…believed the art to be real….”
— Lawyer for  Mosaic Miami Church pastor
accused of trying to sell forged Damien Hirst art

A Miami mosaic from this journal last Dec. 21—

The indicated link is to…

See also St. Ursula’s Day, 2010, and Emil Artin’s dies natalis  in 2003.

Geometer H. S. M. Coxeter died on this date in 2003.

This evening’s daily number from the Keystone state:   822.

The title is both a legal phrase and a phrase
used by Tom Wolfe in his writings on art.

See, too, the pattern of nine triangular half-squares
arranged in a 3×3 square used in the logo of  the
Jean Stephen art galleries in Minneapolis…

… and in a print at the Tate in London  (click to enlarge)—

See as well an obit of the print’s artist, Justin Knowles, who reportedly died
on Feb. 24, 2004.

Some instances of that date in this journal are related to Knowles’s aesthetics.

From an obituary for a Kennedy advisor
who reportedly died at 94 on February 23, 2014*—

“He favored withdrawing rural civilians
into what he called ‘strategic hamlets’
and spraying defoliants to cut off
the enemy’s food supply.”

Other rhetoric:  Hamlet and Infinite Space  in this journal,
as well as King of Infinite Space , Part I and Part II.

These “King” links, to remarks on Coxeter  and  Saniga ,
are about two human beings to whom Hamlet’s
phrase “king of infinite space” has been applied.

The phrase would, of course, be more accurately
applied to God.

* The date of the ‘God’s Architecture’ sermon
at Princeton discussed in this afternoon’s post.

From New World Encyclopedia —

See also Tetragrammaton in this journal.

For further context, see Solomon's Cube and Oct. 16, 2013.

Related material: 

For code  in a different sense, but related to the first passage above,
see Diamond Theory Roullete, a webpage by Radamés Ajna.

For "the method of the kaleidoscope" mentioned in the second
passage above, see both the Ajna page and a webpage of my own,
Kaleidoscope Puzzle.

(Continued)

"There is  such a thing as a tesseract."

— Saying from Crosswicks

See also March 5, 2011.

Adapted from the above passage —

"So did L'Engle understand four-dimensional geometry?"

No and Yes.

“… the object sets up a kind of 
 frame or space or field 
 within which there can be epiphany.”

— Charles Taylor

A frame or space or field —

Related material —

Star Wars (January 11, 2014),

The Lyche Gate Asterisk , from 10:31 AM ET on May 22, 2010,
the date of Martin Gardner's death —

— and the March 2014 issue of the
Notices of the American Mathematical Society  —

See as well Epiphany 2014 (Jan. 6) in this journal and the
March Notices  on the Shaw prize —

"Established under the auspices of Run Run Shaw
in November 2002, the prize is managed and
administered by the Shaw Prize Foundation
based in Hong Kong." 

(A sequel to yesterday's Raiders of the Lost Music Box)

See, in this book, "Walsh Functions: A Digital Fourier Series,"
by Benjamin Jacoby (BYTE , September 1977).  Some context:
Symmetry of Walsh Functions.

A sequel to last night's link Shear —

Some dead poet's words —

The "bride's chair" is the figure illustrating Euclid's proof
of the Pythagorean theorem (click image to enlarge) —

See also…

Not since Madeline Kahn in Blazing Saddles …

From this journal on Dec. 20, 2003 ("White, Geometric, and Eternal") —

Riddled:

The Absolutist Faith
of The New York Times

See also Dead Poets'  Word and  A Riddle for Davos, as well as…

"I don't like odd numbers, and I really don't like primes."

— Marissa Mayer

See Cube Symmetry Axes in this journal.

"And in the Master's chambers…" — Eagles

Related fiction — Amy + Dinner and today's previous post.

Related non-fiction — a page of pure mathematics —