Log24

Tuesday, March 22, 2016

The Barth Spielfeld

Filed under: Uncategorized — Tags: , — m759 @ 2:23 PM

For some backstory, search Log24 for "Wolf Barth."

Saturday, November 25, 2017

E-Elements

Filed under: Uncategorized — m759 @ 12:12 PM

German mathematician Wolf Barth reportedly died
on December 30, 2016.

Flashback to this journal on that date *

From "The Man Who Tried to Redeem the World with Logic" —

"The following June, 1945, von Neumann penned
what would become a historic document entitled
'First Draft of a Report on the EDVAC,' the first published
description of a stored-program binary computing machine—
the modern computer."

Image from von Neumann's report —

Version converted to text —


* And, of course, to the later post  Easy E for Cullinan  (Feb. 28, 2017).
    Cullinan, second from left below, is the now-famous Oscars accountant.

Wednesday, July 26, 2017

Icon Parking

Filed under: Uncategorized — m759 @ 9:00 AM

For the title, see Icon Parking in a search for 54th  in this journal.

For related iconic remarks, click on either image below.

  .

This post was suggested by the Dec. 30, 2016, date of the
death in Nuremberg of mathematician Wolf Barth.  The first
image above is from a mathematics-related work by
John von Neumann discussed here on that date.

See also Wolf Barth in this journal for posts that largely
concern not the above Barth, but an artist of the same name.
For posts on the mathematician only, see Barth + Kummer.

Tuesday, June 7, 2016

Art and Space…

Filed under: Uncategorized — Tags: — m759 @ 6:00 AM

Continues, in memory of chess grandmaster Viktor Korchnoi,
who reportedly died at 85 yesterday in Switzerland —

IMAGE- Spielfeld (1982-83), by Wolf Barth

The coloring of the 4×4 "base" in the above image
suggests St. Bridget's cross.

From this journal on St. Bridget's Day this year —

"Possible title: 

A new graphic approach 
to an old geometric approach
to a new combinatorial approach
to an old algebraic approach
to M24
"

The narrative leap from image to date may be regarded as
an example of "knight's move" thinking.

Sunday, August 30, 2015

Lines

Filed under: Uncategorized — Tags: , — m759 @ 11:01 AM

"We tell ourselves stories in order to live." — Joan Didion

A post from St. Augustine's day, 2015, may serve to
illustrate this.

The post started with a look at a painting by Swiss artist
Wolf Barth, "Spielfeld." The painting portrays two
rectangular arrays, of four and of twelve subsquares, 
that sit atop a square array of sixteen subsquares.

To one familiar with Euclid's "bride's chair" proof of the
Pythagorean theorem, "Spielfeld" suggests a right triangle
with squares on its sides of areas 4, 12, and 16.

That image in turn suggests a diagram illustrating the fact
that a triangle suitably inscribed in a half-circle is a right 
triangle… in this case, a right triangle with angles of 30, 60,
and 90 degrees… Thus —

In memory of screenwriter John Gregory Dunne (husband
of Joan Didion and author of, among other things, The Studio
here is a cinematric approach to the above figure.

The half-circle at top suggests the dome of an observatory.
This in turn suggests a scene from the 2014 film "Magic in
the Moonlight."  

As she gazes at the silent universe above
through an opening in the dome, the silent
Emma Stone is perhaps thinking, 
prompted by her work with Spider-Man

"Drop me a line."

As he  gazes at the crack in the dome,
Stone's costar Colin Firth contrasts the vastness 
of the Universe with the smallness of Man, citing 

"the tiny field F2 with two elements."

In conclusion, recall the words of author Norman Mailer
that summarized his Harvard education —

"At times, bullshit can only be countered
with superior bullshit."

Saturday, August 29, 2015

Quality Revisited

Filed under: Uncategorized — m759 @ 11:14 AM

From earlier this month —

Related material —

1991 Swiss commemorative stamp with painting by Wolf Barth

Friday, August 28, 2015

Art and Space

Filed under: Uncategorized — Tags: , — m759 @ 10:00 AM

IMAGE- Spielfeld (1982-83), by Wolf Barth
 

            Observatory scene from "Magic in the Moonlight"

"The sixteen nodes… can be parametrized
by the sixteen points in affine four-space
over the tiny field F2 with two elements."

Wolf Barth

Saturday, July 4, 2015

Context

Filed under: Uncategorized — Tags: , — m759 @ 10:00 AM

Some context for yesterday's post on a symplectic polarity —

This 1986 note may or may not have inspired some remarks 
of Wolf Barth in his foreword to the 1990 reissue of Hudson's
1905 Kummer's Quartic Surface .

See also the diamond-theorem correlation.  

Saturday, June 20, 2015

Conceptual Art for Basel

Filed under: Uncategorized — Tags: — m759 @ 7:59 PM

The previous post's link to The Lindbergh Manifesto
and Thursday's post on Basel-born artist Wolf Barth 
suggest the following —

See as well a June 14 New York Times
piece on Art Basel.

The logo of the University of Basel 

suggests a review of The Holy Field —

 .

Thursday, June 18, 2015

Expanding the Spielraum

Filed under: Uncategorized — Tags: — m759 @ 2:25 PM

(Continued from Feb. 3, 2015)

IMAGE- Spielfeld (1982-83), by Wolf Barth

The above artist  Wolf Barth is not the same person
as the mathematician  Wolf Barth quoted in the 
previous post.  For further background on the artist, see
an article in Neue Zürcher Zeitung  from Nov. 15, 2013.

Wednesday, June 17, 2015

Slow Art, Continued

Filed under: Uncategorized — Tags: — m759 @ 10:01 AM

The title of the previous post, "Slow Art," is a phrase
of the late art critic Robert Hughes.

Example from mathematics:

  • Göpel tetrads as subsets of a 4×4 square in the classic
    1905 book Kummer's Quartic Surface  by R. W. H. T. Hudson.
    These subsets were constructed as helpful schematic diagrams,
    without any reference to the concept of finite  geometry they
    were later to embody.
     
  • Göpel tetrads (not then named as such), again as subsets of
    a 4×4 square, that form the 15 isotropic projective lines of the
    finite projective 3-space PG(3,2) in a note on finite geometry
    from 1986 —

    Göpel tetrads in an inscape, April 1986

  • Göpel tetrads as these figures of finite  geometry in a 1990
    foreword to the reissued 1905 book of Hudson:

IMAGE- Galois geometry in Wolf Barth's 1990 foreword to Hudson's 1905 'Kummer's Quartic Surface'

Click the Barth passage to see it with its surrounding text.

Related material:

Saturday, September 21, 2013

Mathematics and Narrative (continued)

Filed under: Uncategorized — Tags: , — m759 @ 1:00 AM

Mathematics:

A review of posts from earlier this month —

Wednesday, September 4, 2013

Moonshine

Filed under: Uncategorized — m759 @ 4:00 PM

Unexpected connections between areas of mathematics
previously thought to be unrelated are sometimes referred
to as "moonshine."  An example—  the apparent connections
between parts of complex analysis and groups related to the
large Mathieu group M24. Some recent work on such apparent
connections, by Anne Taormina and Katrin Wendland, among
others (for instance, Miranda C.N. Cheng and John F.R. Duncan),
involves structures related to Kummer surfaces .
In a classic book, Kummer's Quartic Surface  (1905),
R.W.H.T. Hudson pictured a set of 140 structures, the 80
Rosenhain tetrads and the 60 Göpel tetrads, as 4-element
subsets of a 16-element 4×4 array.  It turns out that these
140 structures are the planes of the finite affine geometry
AG(4,2) of four dimensions over the two-element Galois field.
(See Diamond Theory in 1937.)

Thursday, September 5, 2013

Moonshine II

Filed under: Uncategorized — Tags:  — m759 @ 10:31 AM

(Continued from yesterday)

The foreword by Wolf Barth in the 1990 Cambridge U. Press
reissue of Hudson's 1905 classic Kummer's Quartic Surface
covers some of the material in yesterday's post Moonshine.

The distinction that Barth described in 1990 was also described, and illustrated,
in my 1986 note "Picturing the smallest projective 3-space."  The affine 4-space
over the the finite Galois field GF(2) that Barth describes was earlier described—
within a 4×4 array like that pictured by Hudson in 1905— in a 1979 American
Mathematical Society abstract, "Symmetry invariance in a diamond ring."

"The distinction between Rosenhain and Goepel tetrads
is nothing but the distinction between isotropic and
non-isotropic planes in this affine space over the finite field."

The 1990 paragraph of Barth quoted above may be viewed as a summary
of these facts, and also of my March 17, 2013, note "Rosenhain and Göpel
Tetrads in PG(3,2)
."

Narrative:

Aooo.

Happy birthday to Stephen King.

Thursday, September 5, 2013

Moonshine II

Filed under: Uncategorized — Tags: , , , , — m759 @ 10:31 AM

(Continued from yesterday)

The foreword by Wolf Barth in the 1990 Cambridge U. Press
reissue of Hudson's 1905 classic Kummer's Quartic Surface
covers some of the material in yesterday's post Moonshine.

The distinction that Barth described in 1990 was also described, and illustrated,
in my 1986 note "Picturing the smallest projective 3-space."  The affine 4-space
over the the finite Galois field GF(2) that Barth describes was earlier described—
within a 4×4 array like that pictured by Hudson in 1905— in a 1979 American
Mathematical Society abstract, "Symmetry invariance in a diamond ring."

"The distinction between Rosenhain and Goepel tetrads
is nothing but the distinction between isotropic and
non-isotropic planes in this affine space over the finite field."

The 1990 paragraph of Barth quoted above may be viewed as a summary
of these facts, and also of my March 17, 2013, note "Rosenhain and Göpel
Tetrads in PG(3,2)
."

Friday, May 18, 2018

Central Square

Filed under: Uncategorized — Tags: — m759 @ 11:54 AM

This  journal 10 years ago today  had a link to a post on
Tom Wolfe's "Sorry, but Your Soul Just Died."

Thursday, May 17, 2018

Leap

Filed under: Uncategorized — Tags: — m759 @ 9:45 PM

Quoted here on May 5, 2018

" Lying at the axis of everything, zero is both real and imaginary. Lovelace was fascinated by zero; as was Gottfried Leibniz, for whom, like mathematics itself, it had a spiritual dimension. It was this that let him to imagine the binary numbers that now lie at the heart of computers: 'the creation of all things out of nothing through God's omnipotence, it might be said that nothing is a better analogy to, or even demonstration of such creation than the origin of numbers as here represented, using only unity and zero or nothing.' He also wrote, 'The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and nonbeing.' "

— A footnote from page 229 of Sydney Padua's
    April 21, 2015, book on Lovelace and Babbage

The page number  229 may also be interpreted, cabalistically,
as the date  2/29, Leap Day.

See Leap Day 2016 among the posts tagged Mind Spider.

Speak, Memory

Filed under: Uncategorized — Tags: — m759 @ 6:29 PM

On the film "Anna" in the previous post

See also the above world premiere date in the posts of October 2013
esp. the post Conundrum.

Related material — An early scene in "Mindscape" . . .

. . . and "The Abacus Conundrum" in this journal.

DATA

Filed under: Uncategorized — Tags: — m759 @ 5:17 PM

Quoted here on May 7, 2018

Novelist George Eliot and programming pioneer Ada Lovelace —

PBS last night —

Trailer for last night's PBS program on artificial intelligence —

Piano roll for "I am sixteen going on seventeen" (see previous post) —

From yesterday evening's "Strong Women" post

"It's been dirty for dirty
Down the line . . ."

— Joni Mitchell,
"For the Roses" album (1972)

"… for the roses
Had the look of flowers that are looked at.”

— T. S. Eliot, Four Quartets

May 17

Filed under: Uncategorized — Tags: — m759 @ 3:45 PM

"Well, she was just 17 …" — Song lyric

See as well, from last Christmas Eve, Piano Roll.

Wednesday, May 16, 2018

Strong Women

Filed under: Uncategorized — Tags: — m759 @ 7:50 PM

Review

Filed under: Uncategorized — Tags: — m759 @ 5:52 PM

The title of the previous post, "Church and Temple," together
with today's online New York Times  obituaries for singer 
Lara Saint Paul (d. May 8) and playwright Leah Rose Napolin
(d. May 13), suggests a review

See as well a Log24 search for Isaac Singer.

Church and Temple

Filed under: Uncategorized — Tags: , — m759 @ 10:48 AM

Same Old Story

Filed under: Uncategorized — Tags: — m759 @ 9:00 AM

. . . as time goes by.

Tuesday, May 15, 2018

Space Revisited

Filed under: Uncategorized — Tags: — m759 @ 11:32 AM

"Well, let's see now "

— Tom Wolfe, July 18, 2009

Monday, May 14, 2018

Space

Filed under: Uncategorized — Tags: , — m759 @ 10:30 PM

"A generation lost in space" — Don McLean

See as well Varignon in the previous post.

Logos at Harvard

Filed under: Uncategorized — Tags: , — m759 @ 3:01 PM

In 2013, Harvard University Press changed its logo to an abstract "H."

Harvard University Press Logo, Before and After

Both logos now accompany a Harvard video first published in 2012,
"The World of Mathematical Reality." 

In the video, author Paul Lockhart discusses Varignon's theorem
without naming Varignon (1654-1722) . . .

Paul Lockhart on geometry

A related view of "mathematical reality" —

Note the resemblance to Plato's Diamond.

Saturday, May 12, 2018

The McLean Awakening

Filed under: Uncategorized — Tags: — m759 @ 4:14 PM

"Oh, and there we were all in one place
A generation lost in space"

— "American Pie" by Don McLean

Saturday, April 9, 2016

Expanding the Spielfeld (continued)

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

"Mr. Conrad was relentless and rigorous in expanding
the parameters of the fields in which he worked."

The New York Times  today

See also Spielfeld in this  journal, as well as Conrad Moonshine.

Wednesday, March 30, 2016

Romanesque

Filed under: Uncategorized — Tags: — m759 @ 12:20 PM

From New York Times  obituary
of Ellsworth Kelly by Holland Cotter —

"The anonymous role of
the Romanesque church artist
remained a model."

See as well 

Note the contradiction between the URL date (last Monday's)
and the printed date below it (that of Epiphany 2016).
 

Who's trolling whom?

Wednesday, January 6, 2016

Epiphany for Jews

Filed under: Uncategorized — Tags: — m759 @ 2:29 AM

A quarter to three

and a philosopher's Stone —

Sunday, December 27, 2015

Rigorous Imagist*

Filed under: Uncategorized — Tags: , , — m759 @ 11:00 PM

The death of a well-known artist today suggested
a search for Pythagorean Stone in this journal.

An image from that search, together with a sentence
from his obituary, may serve as a memorial.

From a New York Times  obituary
by Holland Cotter tonight —

"The anonymous role of
the Romanesque church artist
remained a model."

* For the title, see the two previous posts.

Wednesday, August 26, 2015

Ride

Filed under: Uncategorized — Tags: — m759 @ 3:01 PM

"Why don't you come with me, little girl,
on a magic carpet ride?" — Steppenwolf lyrics

Related material for fans of Christopher Alexander
(see previous post) — "The 'Life' of a Carpet."

Wednesday, September 4, 2013

Moonshine

Filed under: Uncategorized — Tags: , — m759 @ 4:00 PM

Unexpected connections between areas of mathematics
previously thought to be unrelated are sometimes referred
to as "moonshine."  An example—  the apparent connections
between parts of complex analysis and groups related to the 
large Mathieu group M24. Some recent work on such apparent
connections, by Anne Taormina and Katrin Wendland, among
others (for instance, Miranda C.N. Cheng and John F.R. Duncan),
involves structures related to Kummer surfaces .
In a classic book, Kummer's Quartic Surface  (1905),
R.W.H.T. Hudson pictured a set of 140 structures, the 80
Rosenhain tetrads and the 60 Göpel tetrads, as 4-element
subsets of a 16-element 4×4 array.  It turns out that these
140 structures are the planes of the finite affine geometry
AG(4,2) of four dimensions over the two-element Galois field.
(See Diamond Theory in 1937.) 

A Google search documents the moonshine
relating Rosenhain's and Göpel's 19th-century work
in complex analysis to M24  via the book of Hudson and
the geometry of the 4×4 square.

Thursday, February 17, 2011

Figure in the Carpet

Filed under: Uncategorized — Tags: — m759 @ 2:02 AM

"Why don't you come with me, little girl,
On a magic carpet ride?"

Steppenwolf lyrics

"I like to fold my magic carpet, after use,
in such a way as to superimpose
one part of the pattern upon another."

Vladimir Nabokov in Speak, Memory

http://www.log24.com/log/pix11/110217-IndexTo202.jpg

See also Nabokov at Harvard in today's Crimson
and the Russian boxes of Henry James.

Wednesday, February 9, 2011

An Abstract Power

Filed under: Uncategorized — Tags: — m759 @ 2:45 AM

Two characters named "Black" and "White" debate religion and the afterlife in the Cormac McCarthy play "The Sunset Limited."

The play opened in Chicago in a Steppenwolf Theatre production on May 18, 2006.

A New York Times  theater review from All Hallows' Eve, 2006—

"…there is an abstract power in the mysteriousness of Mr. McCarthy’s
vision’s allowing for a multitude of interpretations." –Jason Zinoman

The current New Yorker  (Feb.14) has a note
by Lillian Ross on the same play— "Two-Man Show: O Death"

http://www.log24.com/log/pix11/110209-TwoManShow.gif

Some purely visual black-and-white variations that are less dramatic, but have their own "abstract power"—

A book cover pictured here last November to contrast with
"the sound and fury of the rarified Manhattan art world"—

http://www.log24.com/log/pix10B/101027-LangerSymbolicLogic.jpg

and a web page with multiple interpretations of the book cover's pattern—

http://www.log24.com/log/pix11/110209-SymFrameBWPage.gif

A synchronicity— The first version of "Symmetry Framed" was done
on May 18, 2006— the day "The Sunset Limited" opened.

Another synchronicity relates the mathematics underlying
such patterns to the Halloween date of the above review.
See "To Announce a Faith," from October 31, 2006.

Monday, October 11, 2010

Venue

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

… Don't you know that when you play
at this level there's no ordinary venue?

— Lyrics from Chess

Why don't you come with me little girl
On a magic carpet ride?

Steppenwolf lyrics in Star Trek: First Contact

I like to fold my magic carpet, after use,
in such a way as to superimpose
one part of the pattern upon another.

Vladimir Nabokov in Speak, Memory

See also recent Log24 posts.

Friday, March 2, 2007

Friday March 2, 2007

Filed under: Uncategorized — m759 @ 7:00 AM
Today’s birthdays:

Jennifer Jones,
film star and arts patron;

Tom Wolfe, author of
The Painted Word.

“Hunt for the best.”
Norton Simon 

The image “http://www.log24.com/log/pix07/angel_angel_down_we_go2A.jpg” cannot be displayed, because it contains errors.

Cover detail,
soundtrack recording
of the Jennifer Jones film
“Angel, Angel, Down We Go”

The girl’s left eye in the above
portrait illustrates a remark
  in yesterday’s New York Times
on a figure in a painting:

“His head recedes into shadow, so you barely see his face. But a tiny fleck of white in his eye, a light that kindles his reawakening, brings him to life. It’s what Roland Barthes, the French critic, liked to call a punctum, the spot, marking time, that burns an image into memory.”

 (This remark, by Michael Kimmelman,
comes with a headline–

Lights! Darks! Action! Cut!  
Maestro of Mise-en-Scène
  

— that seems to have been inspired
by Tom Wolfe’s prose style.)

For further details, see
Barthes’s Punctum,
by Michael Fried.

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