See a University of Wisconsin obituary for Schneider,
a leading expert on linear algebra who reportedly died
at 87 on Tuesday, October 28, 2014.
Some background on linear algebra and “magic” squares:
tonight’s 3 AM (ET) post and a search in this
journal for Knight, Death, and the Devil.
Click image to enlarge.
Introducing a group of 322,560 affine transformations of Dürer’s ‘Magic’ Square
The four vector-space substructures of digits in 1st, 2nd, 3rd, 4th place,
together with the diamond theorem, indicate that Dürer’s square “minus one”
can be transformed by permutations of rows, columns, and quadrants to a
square with (decimal) digits in the usual numerical order, increasing from
top left to bottom right. Such permutations form a group of order 322,560.
(Continued from Vector Addition in a Finite Field, Twelfth Night, 2013.)
This journal Tuesday, Oct. 28, 2014, at 5 PM ET:
"What is a tai chi master, and what is it that he unfolds?"
From an earlier post, Hamlet's father's ghost
on "the fretful porpentine":
Hamlet , Act 1, Scene 5 —
Ghost:
“I could a tale unfold whose lightest word
Would harrow up thy soul, freeze thy young blood,
Make thy two eyes, like stars, start from their spheres,
Thy knotted and combinèd locks to part
And each particular hair to stand on end,
Like quills upon the fretful porpentine:
But this eternal blazon must not be
To ears of flesh and blood."
Galway Kinnell:
"I roll
this way and that in the great bed, under
the quilt
that mimics this country of broken farms and woods"
— "The Porcupine"
For quilt-block designs that do not mimic farms or woods,
see the cover of Diamond Theory . See also the quotations
from Wallace Stevens linked to in the last line of yesterday's
post in memory of Kinnell.
"… a bee for the remembering of happiness" — Wallace Stevens
For poet Galway Kinnell, Princeton ’48:
Kinnell was named "Tiger of the Week" in a
Princeton Alumni Weekly post of August 27, 2014.
See his obituary in today's New York Times
as well as posts here on August 27, 2014.
A print copy of next Sunday’s New York Times Book Review
arrived in today’s mail. From the front-page review:
Marcel Theroux on The Book of Strange New Things ,
a novel by Michel Faber —
“… taking a standard science fiction premise and
unfolding it with the patience and focus of a
tai chi master, until it reveals unexpected
connections, ironies and emotions.”
What is a tai chi master, and what is it that he unfolds?
Perhaps the taijitu symbol and related material will help.
The Origin of Change
“Two things of opposite natures seem to depend
On one another, as a man depends
On a woman, day on night, the imagined
On the real. This is the origin of change.
Winter and spring, cold copulars, embrace
And forth the particulars of rapture come.”
— Wallace Stevens,
“Notes Toward a Supreme Fiction,”
Canto IV of “It Must Change”
For Karl Pribram and Katherine Neville,
a sequel to this morning's Figural Processing —
See also Christmas 2013.
Part I:
Part II:
Click images for some context.
A post in honor of Évariste Galois (25 October 1811 – 31 May 1832)
From a book by Richard J. Trudeau titled The Non-Euclidean Revolution —
See also “non-Euclidean” in this journal.
One might argue that Galois geometry, a field ignored by Trudeau,
is also “non-Euclidean,” and (for those who like rhetoric) revolutionary.
The "Chern" of today's previous post is mathematician
Shiing-Shen Chern (b. Oct. 26, 1911, d. Dec. 3, 2004).
For an observance of the 2011 centennial of his birth,
see a website in China.
See also this journal on the centennial date —
Erlanger and Galois, a post of Oct. 26, 2011.
In the above illustration of the 3-4-5 Pythagorean triangle,
the grids on each side may be regarded as figures of
Euclidean geometry or of Galois geometry.
In Euclidean geometry, these grids illustrate a property of
the inner triangle.
In elementary Galois geometry, ignoring the connection with
the inner triangle, the grids may be regarded instead as
illustrating vector spaces over finite (i.e., Galois) fields.
Previous posts in this journal have dealt with properties of
the 3×3 and 4×4 grids. This suggests a look at properties of
the next larger grid, the 5×5 array, viewed as a picture of the
two-dimensional vector space (or affine plane) over the finite
Galois field GF(5) (also known as ℤ5).
The 5×5 array may be coordinatized in a natural way, as illustrated
in (for instance) Matters Mathematical , by I.N. Herstein and
Irving Kaplansky, 2nd ed., Chelsea Publishing, 1978, p. 171:
See Herstein and Kaplansky for the elementary Galois geometry of
the 5×5 array.
For 5×5 geometry that is not so elementary, see…
Hafner's abstract:
We describe the Hoffman-Singleton graph geometrically, showing that
it is closely related to the incidence graph of the affine plane over ℤ5.
This allows us to construct all automorphisms of the graph.
The remarks of Brouwer on graphs connect the 5×5-related geometry discussed
by Hafner with the 4×4 geometry related to the Steiner system S(5,8,24).
(See the Miracle Octad Generator of R. T. Curtis and the related coordinatization
by Cullinane of the 4×4 array as a four-dimensional vector space over GF(2).)
See Langer (Harvard U. Press, Third Edition, Jan. 31, 1957, pp. 3-4-5).
See also Old Key : Pythagoras, harmony, and the 3-4-5 triangle.
Robin Williams and the Stages of Math
i) shock & denial
ii) anger
iii) bargaining
iv) depression
v) acceptance
And then…
vi) checking
vii) Joan Rivers
See also
Continued from Day at the Museum, last Sunday, October 19, 2014.
This post was suggested by…
From The Catcher in the Rye , a passage just before the
museum passage quoted by Mendelsohn:
“She was having a helluva time tightening her skate.
She didn’t have any gloves on or anything and her hands
were all red and cold. I gave her a hand with it. Boy, I
hadn’t had a skate key in my hand for years. It didn’t feel
funny, though. You could put a skate key in my hand
fifty years from now, in pitch dark, and I’d still know
what it is. She thanked me and all when I had it tightened
for her. She was a very nice, polite little kid. God, I love it
when a kid’s nice and polite when you tighten their skate
for them or something. Most kids are. They really are.
I asked her if she’d care to have a hot chocolate or something
with me, but she said no, thank you. She said she had to meet
her friend. Kids always have to meet their friend. That kills me.
Even though it was Sunday and Phoebe wouldn’t be there
with her class or anything, and even though it was so damp
and lousy out, I walked all the way through the park over to
the Museum of Natural History. I knew that was the museum
the kid with the skate key meant.”
(Continued from Nov. 15, 2011)
Ben Bradlee, legendary Washington Post editor, dies at 93
See also a post of Jan. 20, 2011, and an earlier post on Twelfth Night, 2010.
A star figure and the Galois quaternion.
The square root of the former is the latter.
Two news items on art as a tool:
Two Log24 posts related to the 3×3 grid, the underlying structure for China’s
ancient Lo Shu “magic” square:
Finally, leftist art theorist Rosalind Krauss in this journal
on AntiChristmas, 2010:
Which is the tool here, the grid or Krauss?
(Night at the Museum continues.)
"Strategies for making or acquiring tools
While the creation of new tools marked the route to developing the social sciences,
the question remained: how best to acquire or produce those tools?"
— Jamie Cohen-Cole, “Instituting the Science of Mind: Intellectual Economies
and Disciplinary Exchange at Harvard’s Center for Cognitive Studies,”
British Journal for the History of Science vol. 40, no. 4 (2007): 567-597.
Obituary of a co-founder, in 1960, of the Center for Cognitive Studies at Harvard:
"Disciplinary Exchange" —
In exchange for the free Web tools of HTML and JavaScript,
some free tools for illustrating elementary Galois geometry —
The Kaleidoscope Puzzle, The Diamond 16 Puzzle,
The 2x2x2 Cube, and The 4x4x4 Cube
"Intellectual Economies" —
In exchange for a $10 per month subscription, an excellent
"Quilt Design Tool" —
This illustrates not geometry, but rather creative capitalism.
Related material from the date of the above Harvard death: Art Wars.
The online Harvard Crimson today:
“ ‘I don’t like how they check your bags
when you leave the library
even though you have to swipe your
student ID to get in.’
But what else would I be carrying in this
Gutenberg Bible-sized backpack? ”
Nicole Kidman at the end of “Hemingway & Gellhorn” (2012)
Or: The Long, Long Trailer
See also a Log24 post from the date of the above tweet: Welcome to the Ape Stuff.
“So it’s the laughter we will remember.” Speak for yourself, Barbra.
Barron's Educational Series (click to enlarge):
The Tablet of Ahkmenrah:
"With the Tablet of Ahkmenrah and the Cube of Rubik,
my power will know no bounds!"
— Kahmunrah in a novelization of Night at the Museum:
Battle of the Smithsonian , Barron's Educational Series
Another educational series (this journal):
Art theorist Rosalind Krauss and The Ninefold Square
On Walter Isaacson’s The Innovators :
“Yet as the book’s five hundred–plus pages unwind, Isaacson interrupts himself to present small bromides about what it means to innovate and what we might learn from these innovators, our presumed betters. “Innovation requires articulation,” he tells us, after explaining how the main strength of Grace Hopper, a trailblazing computer scientist for the US Navy, was her ability to speak in the languages of mathematicians, engineers, programmers, and soldiers alike. ‘One useful leadership talent is knowing when to push ahead against doubters and when to heed them,’ he offers later.
The book is peppered with these kinds of passages, which often intrude on the narrative, depriving us of moments of real emotional power.”
— Jacob Silverman in Bookforum , Sept/Oct/Nov 2014
From Isaacson’s book:
Related material:
In memory of T. S. Eliot…
… and in memory of Stanley Chase, producer of Colossus: The Forbin Project
and of Threepenny Opera :
Ninefold square from Colossus
(“There is another system”) —
Fourfold square introducing Brecht
in Dreigroschen Trifft Vierfarben —
Raiders of the Lost Archetype
“… an unexpected development: the discovery of a lost archetype….”
— “The Lost Theorem,” by Lee Sallows, Mathematical Intelligencer, Fall 1997
Related material:
A scene from the 1954 film:
A check of this journal on the above MetaFilter date — Jan. 24, 2012 —
yields a post tagged “in1954.” From another post with that tag:
Backstory: Posts tagged Root Circle.
Rebecca Newberger Goldstein, quoted in a webpage dated
October 7, 2014 (presumably according to Australian time):
"For the Athenians, kleos mattered more than anything,
according to Goldstein.
'Kleos is fame: it’s the deed that brings fame, it’s the poem
that sings your triumphs, it’s having your life replicated in
other minds, acquiring a kind of moreness, a kind of
secular immortality.' "
Related material:
A check of Goldstein's definition…
… and an image for Broomsday:
From Argument for the Existence of Rebecca (Feb. 6, 2010)
This post was suggested by today's previous posts, Broom Bridge Day
and Taking the Fork, as well as by Alyssa is Wonderland.
For the meaning of the title, see Serpent + Derrida and Symbology.
Powered by WordPress
