A meditation for Cyber Monday —
Impossible Missions Force
International Monetary Fund
Related image —
Cookies for Santa
Monday, November 30, 2015
Chiaroscuro
An image from Log24 on May 21, 2005 —
An image posted here on Saturday, November 28, 2015 —
http://www.martin-missfeldt.de/kontrast/hell-dunkel-kontrast.php
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Sunday, November 29, 2015
There the Dance Is
In memory of ballet designer
Yolanda Sonnabend, who
reportedly died at 80 on Nov. 9,
see posts on Apollo, Ballet Blanc,
maps of New Haven, etc., etc., etc.
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At the Still Point
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Cartography
Related material — Chemistry 101 (November 18, 2015).
See also the cover article from today's print version of
The New York Times Sunday Book Review —
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Saturday, November 28, 2015
11:30 in Dostoevsky
In memory of acoustic engineer Norman C. Pickering, who reportedly
died at 99 on November 18 —
Two readings from that date …
Another biblical quote relevant to the Nov. 17–18 tab icons above —
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Hell-Dunkel
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Friday, November 27, 2015
Once Upon a Matrix
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Einstein and Geometry
(A Prequel to Dirac and Geometry)
"So Einstein went back to the blackboard.
And on Nov. 25, 1915, he set down
the equation that rules the universe.
As compact and mysterious as a Viking rune,
it describes space-time as a kind of sagging mattress…."
— Dennis Overbye in The New York Times online,
November 24, 2015
Some pure mathematics I prefer to the sagging Viking mattress —
Readings closely related to the above passage —
Thomas Hawkins, "From General Relativity to Group Representations:
the Background to Weyl's Papers of 1925-26," in Matériaux pour
l'histoire des mathématiques au XXe siècle: Actes du colloque
à la mémoire de Jean Dieudonné, Nice, 1996 (Soc. Math.
de France, Paris, 1998), pp. 69-100.
The 19th-century algebraic theory of invariants is discussed
as what Weitzenböck called a guide "through the thicket
of formulas of general relativity."
Wallace Givens, "Tensor Coordinates of Linear Spaces," in
Annals of Mathematics Second Series, Vol. 38, No. 2, April 1937,
pp. 355-385.
Tensors (also used by Einstein in 1915) are related to
the theory of line complexes in three-dimensional
projective space and to the matrices used by Dirac
in his 1928 work on quantum mechanics.
For those who prefer metaphors to mathematics —
Rota fails to cite the source of his metaphor.
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Thursday, November 26, 2015
Charm School
"When the first Harry Potter book appeared, in 1997,
it was just a year before the universal search engine
Google was launched. And so Hermione Granger,
that charming grind, still goes to the Hogwarts library
and spends hours and hours working her way through
the stacks, finding out what a basilisk is or how to
make a love potion."
— Adam Gopnik in The New Yorker issue dated
St. Valentine's Day, 2011
More recently, Gopnik writes that …
"Arguing about non-locality went out of fashion, in this
account, almost the way 'Rock Around the Clock'
displaced Sinatra from the top of the charts."
— Adam Gopnik in The New Yorker issue dated
St. Andrew's Day, 2015
This journal on Valentine's Day, 2011 —
"One heart will wear a valentine." — Sinatra
"… she has written a love letter to Plato, whom
she regards as having given us philosophy.
He is, in her view, as relevant today as he ever
was — which is to say, very."
— New York Times review of a book by
Rebecca Newberger Goldstein, April 18, 2014
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Wednesday, November 25, 2015
Once Upon a Time
This post's title was suggested by the previous post
and by today's news of a notable sale of a one-copy
record album, "Once Upon a Time in Shaolin."
See as well posts from Tuesday, March 11, 2014,
the day Emma Watson unveiled a new trailer —
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Arkie
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Tuesday, November 24, 2015
Tools
In memory of economic historian Douglass C. North,
who reportedly died Monday, Nov. 23, 2015 —
“We needed new tools, but they simply did not exist.”
Related reading and viewing —
Beattyville, Kentucky and Log24 post About the People.
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Monday, November 23, 2015
Dirac and Line Geometry
Some background for my post of Nov. 20,
"Anticommuting Dirac Matrices as Skew Lines" —
His earlier paper that Bruins refers to, "Line Geometry
and Quantum Mechanics," is available in a free PDF.
For a biography of Bruins translated by Google, click here.
For some additional historical background going back to
Eddington, see Gary W. Gibbons, "The Kummer
Configuration and the Geometry of Majorana Spinors,"
pages 39-52 in Oziewicz et al., eds., Spinors, Twistors,
Clifford Algebras, and Quantum Deformations:
Proceedings of the Second Max Born Symposium held
near Wrocław, Poland, September 1992 . (Springer, 2012,
originally published by Kluwer in 1993.)
For more-recent remarks on quantum geometry, see a
paper by Saniga cited in today's update to my Nov. 20 post.
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Sunday, November 22, 2015
The Saint
Edith Stein, doctoral dissertation, 1916 —
"The goal of phenomenology is to clarify and thereby
to find the ultimate basis of all knowledge."*
"Ziel der Phänomenologie ist Klärung und damit
letzte Begründung aller Erkenntnis."
* A phrase echoed by Ong's words in the previous post.
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Overlook Video
CALIFORNIA, UNITED STATES – OCTOBER 1962:
People watching President John F. Kennedy’s
TV announcement of Cuban blockade during the
missile crisis in a department store. (Photo by
Ralph Crane/Life Magazine/The LIFE Picture
Collection/Getty Images)
A Sunday opinion column from 2011,
"The Enduring Cult of Kennedy" —
"In this landscape, the death of J.F.K. looms up
like the Overlook Hotel." — Ross Douthat
on November 27, 2011
From this journal on that date —
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Saturday, November 21, 2015
Visionary
Two figures to whom the word "visionary" has
recently been applied —
Paul Laffoley at news.artnet.com
William P. Thurston at AMS Notices (Dec. 2015)
A more classic example of a visionary is, of course, William Blake.
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The Undertaking
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Brightness at Noon*
A recent not-too-bright book from Princeton —
Some older, brighter books from Tony Zee —
Fearful Symmetry (1986) and
Quantum Field Theory in a Nutshell (2003).
* Continued.
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The Zero System
For the title phrase, see Encyclopedia of Mathematics .
The zero system illustrated in the previous post*
should not be confused with the cinematic Zero Theorem .
* More precisely, in the part showing the 15 lines fixed under
a zero-system polarity in PG(3,2). For the zero system
itself, see diamond-theorem correlation.
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Friday, November 20, 2015
Anticommuting Dirac Matrices as Skew Lines
(Continued from November 13)
The work of Ron Shaw in this area, ca. 1994-1995, does not
display explicitly the correspondence between anticommutativity
in the set of Dirac matrices and skewness in a line complex of
PG(3,2), the projective 3-space over the 2-element Galois field.
Here is an explicit picture —
References:
Arfken, George B., Mathematical Methods for Physicists , Third Edition,
Academic Press, 1985, pages 213-214
Cullinane, Steven H., Notes on Groups and Geometry, 1978-1986
Shaw, Ron, "Finite Geometry, Dirac Groups, and the Table of
Real Clifford Algebras," undated article at ResearchGate.net
Update of November 23:
See my post of Nov. 23 on publications by E. M. Bruins
in 1949 and 1959 on Dirac matrices and line geometry,
and on another author who gives some historical background
going back to Eddington.
Some more-recent related material from the Slovak school of
finite geometry and quantum theory —
The matrices underlying the Saniga paper are those of Pauli, not
those of Dirac, but these two sorts of matrices are closely related.
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The Wrench and the Circle*
Two Log24 posts from October 2, 2015 —
Source Code
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* The title is a reference to Quality Report (Aug. 24, 2015).
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Rhymes with Scary
"Gaitskill isn’t scary because she conjures monsters;
monsters, she points out, are almost always in fashion.
What makes her scary, and what makes her exciting,
is her ability to evoke the hidden life, the life unseen,
the life we don’t even know we are living. The critic
Greil Marcus, a champion of her work, calls her a
descendant of Nathaniel Hawthorne."
— "Mary Gaitskill and the Life Unseen,"
by Parul Sehgal
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Yogi’s Maxim
"When you come to a nexus in the time flow…."
See as well the recent post Tab Icons from the Clearing —
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Thursday, November 19, 2015
Rebecca Newberger Goldstein to Her Younger Self:
"Remember, Genesis IS Skynet."
Above: New York Times Book Review of Sunday, November 22, 2015.
Perhaps Goldstein, author of Plato at the Googleplex , was
"exposed to a nexus point in the time flow while she was in
a quantum field" ?
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