Log24

Wednesday, October 22, 2014

The Seventh Stage

Filed under: Uncategorized — m759 @ 7:01 PM

Robin Williams at Bunker Hill Community College

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

Claves Regni Caelorum

Filed under: Uncategorized — m759 @ 10:00 AM

Continued from Day at the Museum, last Sunday, October 19, 2014.

This post was suggested by…

  1.  A piece in the Bookends section of the New York Times
    Sunday Book Review
      (page BR31 last Sunday, Oct. 19):
    Daniel Mendelsohn on rereading The Catcher in the Rye .
  2. A detail in Day at the Museum— The New York Times ‘s
    appraisal of Joan Rivers: “A Comic Without a Shut-Off Switch.”
  3. A Sept. 7 Log24 post, Sunday School, in memory of Joan Rivers.

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.”

Tuesday, October 21, 2014

Eerie Twist

Filed under: Uncategorized — m759 @ 9:00 PM

(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.

Commentary:

http://www.log24.com/log/pix11/110219-SquareRootQuaternion.jpg

A star figure and the Galois quaternion.

The square root of the former is the latter.

Art as a Tool

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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 Anti-Christmas, 2010:

Which is the tool here, the grid or Krauss?

Tools

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(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.

Monday, October 20, 2014

The Library

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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)

Perhaps the I Ching ?

The Writing Desk

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Why is  a raven like a writing desk?

Sunday, October 19, 2014

Night at the Museum

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Or:  The Long, Long Trailer

See also a Log24 post from the date of the above tweet: Welcome to the Ape Stuff.

Day at the Museum

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IMAGE- 'The Final Cut,' 2004, at IMDb

“So it’s the laughter we will remember.”  Speak for yourself, Barbra.

Saturday, October 18, 2014

Elementary Galois Geometry

Filed under: Uncategorized — m759 @ 9:29 PM

The image search (2.26 MB).

Educational Series

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Barron’s Educational Series (click to enlarge):

The Tablet of Ahkmenrah:

IMAGE- The Tablet of Ahkmenrah, from 'Night at the Museum'

 “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):

Image-- Rosalind Krauss and The Ninefold Square

Art theorist Rosalind Krauss and The Ninefold Square

IMAGE- Elementary Galois Geometry over GF(3)

Friday, October 17, 2014

Raiders of the Inarticulate

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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:

IMAGE- Bletchley Park and the Colossus computer

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 —

Mathematics and Narrative, continued:

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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:

Medal of 9/15/06

Backstory:  Posts tagged Root Circle.

Thursday, October 16, 2014

Seeking Kleos

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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:

Rebecca Goldstein and a Cullinane quaternion

From Argument for the Existence of Rebecca (Feb. 6, 2010)

A Forkèd Tongue

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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.

Taking the Fork

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Related material:  Alyssa Milano in this journal —

IMAGE- Alyssa Milano as a child, with fork

Broom Bridge Day

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Wikipedia on Broom (or Broome, or Brougham) Bridge,
where on 16 October 1843 Hamilton discovered quaternions:

“The 16 October is sometimes referred to as
Broomsday (in reference to Broome Bridge)
and as a nod to the literary commemorations
on 16 June (Bloomsday in honour of James Joyce).”

See also, in this journal, The Craft.

Wednesday, October 15, 2014

Look Homeward, Dorothy

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For Dorothy Maharam Stone, mathematician, who reportedly
died on Sept. 27, 2014 (Gwyneth Paltrow’s birthday):

“When I die…. I want it to be Hollywood all the way.
I don’t want some rabbi rambling on; I want
Meryl Streep crying, in five different accents….”

Joan Rivers

How about Meryl Streep as Ethel Greenglass Rosenberg
saying Kaddish in Angels in America ?

Diabolically Complex

Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

The title is from a Log24 post, “Diabolically Complex Riddle,” of Sept. 27, 2014.

(See also a search for “Diabolic”  in this journal, which yields an application to
“magic” squares.)

Tuesday, October 14, 2014

The Judas Seat

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My own contribution to an event of the Mathematical Association of America:

Rick’s Tricky Six  and  The Judas Seat.

The Polster tetrahedral model of a finite geometry appears, notably,
in a Mathematics Magazine  article from April 2009—

IMAGE- Figure from article by Alex Fink and Richard Guy on how the symmetric group of degree 5 'sits specially' in the symmetric group of degree 6

Monday, October 13, 2014

Sallows on “The Lost Theorem”

Filed under: Uncategorized — Tags: — m759 @ 9:30 PM

Parallelograms and the structure of the 3×3 array —

Click to enlarge:

A different approach to parallelograms and arrays —

Click for original post:

Mathematics and Narrative, continued

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For those who prefer drama to mathematics:

See also Magic + Flute in this journal.

Raiders of the Lost Theorem

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(Continued from Nov. 16, 2013.)

The 48 actions of GL(2,3) on a 3×3 array include the 8-element
quaternion group as a subgroup. This was illustrated in a Log24 post,
Hamilton’s Whirligig, of Jan. 5, 2006, and in a webpage whose
earliest version in the Internet Archive is from June 14, 2006.

One of these quaternion actions is pictured, without any reference
to quaternions, in a 2013 book by a Netherlands author whose
background in pure mathematics is apparently minimal:

In context (click to enlarge):

Update of later the same day —

Lee Sallows, Sept. 2011 foreword to Geometric Magic Squares —

“I first hit on the idea of a geometric magic square* in October 2001,**
and I sensed at once that I had penetrated some previously hidden portal
and was now standing on the threshold of a great adventure. It was going
to be like exploring Aladdin’s Cave. That there were treasures in the cave,
I was convinced, but how they were to be found was far from clear. The
concept of a geometric magic square is so simple that a child will grasp it
in a single glance. Ask a mathematician to create an actual specimen and
you may have a long wait before getting a response; such are the formidable
difficulties confronting the would-be constructor.”

* Defined by Sallows later in the book:

“Geometric  or, less formally, geomagic  is the term I use for
a magic square in which higher dimensional geometrical shapes
(or tiles  or pieces ) may appear in the cells instead of numbers.”

** See some geometric  matrices by Cullinane in a March 2001 webpage.

Earlier actual specimens — see Diamond Theory  excerpts published in
February 1977 and a brief description of the original 1976 monograph:

“51 pp. on the symmetries & algebra of
matrices with geometric-figure entries.”

— Steven H. Cullinane, 1977 ad in
Notices of the American Mathematical Society

The recreational topic of “magic” squares is of little relevance
to my own interests— group actions on such matrices and the
matrices’ role as models of finite geometries.

Sunday, October 12, 2014

In Memoriam

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From the online Encyclopaedia Britannica:

Piero della Francesca, original name
Piero di Benedetto dei Franceschi
(born 
c. 1416/17, Sansepolcro, Republic of Florence [Italy]—
died Oct. 12, 1492, Sansepolcro),
painter whose serene, disciplined exploration of 
perspective
had little influence on his contemporaries but came to be
recognized in the 20th century as a major contribution to
the Italian 
Renaissance. The fresco cycle “The Legend of
the True Cross” (1452–66) and the diptych portrait of
Federico da Montefeltro, duke of 
Urbino, and his consort
(1465) are among his best known works.

A Passage from India

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(For Columbus Day.) See Con Vocation.

Saturday, October 11, 2014

The Code of Beauty

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Dialogue from “Django Unchained” —

“What’s a bounty?” “It’s like a reward.”

Today’s noon post links to posts on Tony Scott
that in turn lead to…

A post from June 27, 2005
the date of Domino Harvey‘s death.

A link at the end of that  post leads to…

“Dr. Chandra?” “Yes?” “Will I dream?”

See also…

Vikram Chandra, Geek Sublime:
The Beauty of Code, the Code of Beauty

Selfie Sequel

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This post is a sequel to Pythagorean Selfie (Sept. 30, 2014)
and October Nine: Lyche at Bodø.

Today’s Instagram photos from Josefine Lyche, still at Bodø:

The figure at left appears to be diving. This suggests a review of posts on
the late film director Tony Scott.

Friday, October 10, 2014

Cut to Stanley Chase

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Chase worked for years to make a movie of
‘The Threepenny Opera.’ He finally got it done in 1989 as
Mack the Knife,’ with Menahem Golan directing.”

— David Colker, LA Times  obituary, Oct. 9, 2014

See also, from Tuesday, Oct. 7, 2014, the date of Chase’s death,
the Log24 posts Grids and Space, Concepts of Space, and As Is.

High White Noon

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(The phrase is from Don DeLillo and Josefine Lyche.)

See “Complex Grid.”

See as well Bill O’Reilly’s remark, “Do not be a coxcomb,”
and an artist‘s self-portrait:

IMAGE- Jamie Foxx in 'Amazing Spider Man 2'

Grid Designer

Autistic Enchantment

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(Continued from Sept. 3, 2009)

George Steiner on chess:

“At the sight of a set, even the tawdriest of plastic pocket sets,
one’s fingers arch and a coldness as in a light sleep steals over
one’s spine. Not for gain, not for knowledge or reknown, but
in some autistic enchantment, pure as one of Bach’s inverted
canons or Euler’s formula for polyhedra.”

— George Steiner in “A Death of Kings,” The New Yorker,
issue dated September 7, 1968, page 133

A related remark from Dudeney:

See also a different context for 16 squares and 322,560 arrangements.

Both Hands and an Ass Map

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(Continued from Grids and Space and posts tagged Riddle for Caltech)

Thursday, October 9, 2014

Nine is a Vine

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See also Concepts of Space and  “Launched from Cuber.”

October Nine: Lyche at Bodø

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Click to enlarge.

See also Apollo in this  journal.

“Nine is a very powerful Nordic number.”

Katherine Neville, who deserves some sort of prize for literature.

IMAGE- Heidegger quote continued, ending with reference to Hölderlin's 'night of lunacy'

— Heidegger, “Hölderlin and the Essence of Poetry,”
translated by Douglas Scott, in Existence and Being  ,
Regnery, 1949

Tuesday, October 7, 2014

As Is

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“That simple operator, ‘as,’ turns out to carry within its philosophical grammar
a remarkable complex field* of operations….”

Charles Altieri,  Painterly Abstraction in Modernist American Poetry,
Cambridge University Press, 1989, page 343

See also Rota on Heidegger (What “As” Is, July 6, 2010), and Lead Belly
on the Rock Island Line — “You got to ride it like you find it.”

* Update of Oct. 10, 2014: See also “Complex + Grid” in this journal.

Ruler

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See also this  journal on Jan. 8, 2013:

Cards of Identity

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Or:  Plan 9 Continues

(Suggested by this afternoon’s post Concepts of Space.)

See also Card

… and Tick Tick Hash.

The image “http://www.log24.com/log/pix05B/051014-Tick.gif” cannot be displayed, because it contains errors.

Principles of Aesthetics

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Or:  Phantasmagoria Meets Pandemonium

Part I: Phantasmagoria

Rebecca Goldstein on first encountering Plato —

“I was reading Durant’s section on Plato, struggling to understand
his theory of the ideal Forms that lay in inviolable perfection
out beyond the phantasmagoria. (That was the first, and I think
the last, time that I encountered that word.)”

Screenwriter Joan Didion —

“We tell ourselves stories in order to live….We interpret
what we see, select the most workable of multiple choices.
We live entirely, especially if we are writers, by the imposition
of a narrative line upon disparate images, by the ‘ideas’
with which we have learned to freeze the shifting phantasmagoria
which is our actual experience.”

Part II: Pandemonium

Terry Teachout in Commentary  on Oct. 1, 2014:

“When making art or writing about it, the aesthete
tries never to moralize. Nor will he look with favor
upon artists who do so, no matter whether their
particular brand of moralizing is religious or secular.
But he can and must be fully, intensely alive to the
moral force of art whose creators aspire merely to
make the world around us more beautiful, and in
so doing to pierce the veil of the visible and give us
a glimpse of the permanently true. That is his job:
to help make sense of the pandemonium amid which
we live.”

Rivka Galchen in The New York Times Sunday Book Review
issue of October 5, 2014 (online Sept. 30):

“The story describes honestly something that is,
which is very different from proposing what ought to be.”

See also Pandemonium in this journal.

Concepts of Space

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(Continued)

IMAGE- Rubik's Cube in an ad, and some pure mathematics

Grids and Space

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In honor of the late Sidney Lumet

(See Makom Kadosh , April 9, 2011.)

IMAGE- Christopher Reeve in the 1982 film 'Deathtrap,' illustrating concepts of space

Monday, October 6, 2014

Exit Center Stage

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To note deaths on Samedi  and Dimanche :

IMAGE- German title of 'The Recruit' is 'Der Einsatz'; the MacGuffin is 'Ice 9.'

Reviews

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From the MacTutor biography of Otto Neugebauer:

“… two projects which would be among the most important
contributions anyone has made to mathematics. He persuaded
Springer-Verlag to publish a journal reviewing all mathematical
publications, which would complement their reviewing journals
in other topics. In 1931 the first issue of 
Zentralblatt für Matematik
appeared, edited by Neugebauer.” [Mathematical Reviews  was
the other project.]

Neugebauer appeared in Sunday morning’s post In Nomine Patris .

A review from Zentralblatt  appeared in the Story Creep link from
this morning’s post Mysterious Correspondences.

Arcs and Shards

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Ben Brantley in The New York Times  today on a Broadway opening:

“As Christopher navigates his way through an increasingly
unfamiliar landscape, both physical and emotional, the arcs
of his adventures are drawn into being.

So are the shards of sensory overload.”

Arc — See a search for Line at Infinity:

Shard — See Shard and Pythagorean Selfie:

Mysterious Correspondences

Filed under: Uncategorized — m759 @ 9:36 AM

(Continued from Beautiful Mathematics, Dec. 14, 2013)

“Seemingly unrelated structures turn out to have
mysterious correspondences.” — Jim Holt, opening
paragraph of 
a book review in the Dec. 5, 2013, issue
of 
The New York Review of Books

One such correspondence:

For bibliographic information and further details, see
the March 9, 2014, update to “Beautiful Mathematics.”

See as well posts from that same March 9 now tagged “Story Creep.”

Sunday, October 5, 2014

In Nomine Patris

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I.e., Neugebauer (See The Source, 9 PM Saturday, Oct. 4, 2014.)

See also Alms for Oblivion (January 22, 2006).

Sunday School

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With Sarah Silverman …

… Continued from The Story of N (October 15, 2010).

“I remember how the darkness doubled….”

Saturday, October 4, 2014

The Source

Filed under: Uncategorized — m759 @ 9:00 PM

“In ancient Greece, 9 was the number of
the Muses, patron goddesses of the arts.
They were the daughters of Mnemosyne (‘memory’),
the source of imagination, which in turn is
the carrier of archetypal, elementary ideas to
artistic realization in the field of space-time.”

— Joseph Campbell in The Inner Reaches of Outer Space

In memoriam:

 See also Raiders of the Lost Well and…

 The Eliot Omen 


Ground plan for a game of Noughts and Crosses

Watch the Trailer

Filed under: Uncategorized — m759 @ 3:09 PM

Nordic Number

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“Nine is a very powerful Nordic number.”

— Katherine Neville, The Magic Circle

See also Arcade Fire in this journal.

Thursday, October 2, 2014

The Christmas Theorem

Filed under: Uncategorized — m759 @ 7:29 PM

From the preface to Introduction to the Construction of Class Fields ,
by Harvey Cohn (Cambridge University Press, 1985):

“It is an elementary observation that an integral right triangle
has an even area. Suppose the hypotenuse is prime.

Q.  How do we determine from the prime value of the hypotenuse
when the area is divisible by 4, 8, 16, or any higher power of 2?

A.  We use class fields constructed by means of transcendental
functions, of course!

The question might have been asked by Pythagoras in about
500 BC….”

The question seems to assume something apparently not known to Pythagoras:

The area is determined uniquely by the prime hypotenuse.

Nontrivial exercise: Prove or disprove this assertion.

Background to the exercise: See Fermat’s Christmas Theorem  on the Web,
and a specific remark about prime hypotenuses in a letter from Fermat to
Mersenne on Christmas Day, 1640, quoted in The Mathematical Career
of Pierre de Fermat, 1601-1665
 
, by Michael Sean Mahoney (Princeton
University Press, 2nd ed,, 1994), pp. 316-317.

Titles

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From the title page of a book quoted here yesterday:

IMAGE- From title page of 1995 paperback edition of 'Group Theory and Physics,' by Shlomo Sternberg

Another title, in memory of a former mayor of Tel Aviv who reportedly died yesterday:

“President Reuven Rivlin called Lahat ‘Tel Aviv’s Herod,’
referring to the semi-mythical Jewish king whose epic
construction projects, including the Temple Mount,
Masada and Caesarea, remain standing 2,000 years after
his death.” — The Times of Israel

Wednesday, October 1, 2014

Misery

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The title is the usual pronunciation of MSRI,
the Mathematical Sciences Research Institute
at 17 Gauss Way, Berkeley, California.

The late Scandinavian novelist Stieg Larsson
might prefer to call this street Gardner Way.

I do not.

Big Time

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The following post suggests the Spiders and Snakes of Fritz Leiber’s
Changewar , a mythology inspired by the hallucinations of delirium tremens .

Good Question

Filed under: Uncategorized — m759 @ 11:00 AM

Related material:

Here “Lucifer’s temple” refers to Josefine Lyche’s Lynx 760 gallery in Oslo.

Mathematics for Tromsø

Filed under: Uncategorized — m759 @ 9:45 AM

Loren Olson, Harvard ’64, a professor of mathematics
at Norway’s Tromsø University,* died June 22, 2014.

In his memory, a search in this journal for Lie Group.

That search yields a post titled Lie Groups for Holy Week (March 30, 2010).

A quotation related to that post:

* The city of Tromsø hosted some art related to group theory in 2010.
Neither that art nor my own related remarks on group theory are very
relevant to physics (yet).

Tuesday, September 30, 2014

Pythagorean Selfie

Filed under: Uncategorized — m759 @ 5:01 PM

“Rarely is a TV show as brilliant and as terrible as Selfie .”

Kevin Fallon on a new ABC TV show that starts tonight at 8 PM ET

A recent selfie from Josefine Lyche’s Instagram page:

For some remarks related to Lyche’s pentagram, see
Lyche + Mathmagic* and also yesterday’s Michaelmas Mystery.

In today’s previous post, the late Harvey Cohn posed a question that
he said might have been asked by Pythagoras:

“It is an elementary observation that an integral right triangle
has an even area. Suppose the hypotenuse is prime.

Q.  How do we determine from the prime value of the hypotenuse
when the area is divisible by 4, 8, 16, or any higher power of 2?

A.  We use class fields constructed by means of transcendental
functions, of course!”

— From the preface to Introduction to the Construction of Class Fields ,
by Harvey Cohn (Cambridge University Press, 1985)

Illustration:

For a related song, see Prime Suspect (Dec. 13, 2007).

Footnote of 12:14 AM Oct. 1, 2014 —

* That search yields a link to…

This Lyche webpage’s pentagram  indicates an interest in Disney rather than
in SatanismOther Lyche webpages have been less reassuring.

Related material — Posts tagged Elegantly Packaged.

Pythagoras to Cohn

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Harvey Cohn on class field theory and a question that might have
been asked by Pythagoras:
IMAGE- Harvey Cohn on class field theory and a question that might have been asked by Pythagoras

See also yesterday’s Michaelmas Mystery and Michaelmas Texts.

Monday, September 29, 2014

Michaelmas Texts

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This morning’s previous post quoted a sort of
invitation to damnation
from Princeton University Press:

An alternative to damnation:

Michaelmas Mystery

Filed under: Uncategorized — m759 @ 9:30 AM

IMAGE- Pentagram from Arturo Sangalli's novel 'Pythagoras' Revenge'

Some related material in this journal: “Peter J. Cameron” + Magic.

Sunday, September 28, 2014

The Hades Factor

Filed under: Uncategorized — m759 @ 9:00 PM

Happy birthday to Mira Sorvino.

Related material:

Today’s posts Hitchcockian,  Darkness and Light,
and Requiem for Abse.

Some context for the last of these:

The conclusion of last night’s episode of Intruders .

Requiem for Abse

Filed under: Uncategorized — m759 @ 7:59 PM

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