Log24

Friday, November 7, 2014

The Missing ART

Filed under: General,Geometry — m759 @ 7:31 AM

IMAGE- Harvard art museum director: 'This is brand new museum.'

Back together, but missing an article.

“An article (abbreviated ART) is a word (or prefix or suffix)
that is used with a noun to indicate the type of reference
being made by the noun.” — Wikipedia

Perhaps Tommy Lee Jones has it.

Geometry was very important to us in this movie.”

Thursday, May 14, 2020

Art Issue*

Filed under: General — Tags: — m759 @ 11:25 AM

“… the beautiful object
that stood in
for something else.”

— Holland Cotter quoting an art historian
in The New York Times  on May 13

From a post of April 27, 2020 —

“The yarns of seamen have a direct simplicity,
the whole meaning of which lies within the shell
of a cracked nut. But Marlow was not typical
(if his propensity to spin yarns be excepted),
and to him the meaning of an episode was not inside
like a kernel but outside….”

— Joseph Conrad in Heart of Darkness

The beautiful object —

Something else —

* The title is a reference to other posts now also tagged Art Issue.

Tuesday, April 28, 2020

The Art Issue

Filed under: General — Tags: — m759 @ 10:47 AM

A sort of pointillist mosaic” 

— Author David Mitchell on the film adaptation of 
his novel Cloud Atlas .

See also the previous post, Cloud Atlas of Unknowing.

Art isn’t easy.” — Sondheim.

Friday, April 24, 2020

Art at Cologne

Filed under: General — Tags: — m759 @ 10:53 PM

This post was suggested by a New York Review of Books  article
on Cologne artist Gerhard Richter in the May 14, 2020, issue —

“The Master of Unknowing,” by Susan Tallman.

Some less random art

Wednesday, October 23, 2019

Art-Historical Narrative*

Filed under: General — Tags: , — m759 @ 9:25 PM

"Leonardo was something like what we now call a Conceptual artist,
maybe the original one.   Ideas —  experiments, theories —  were
creative ends in themselves."

— Holland Cotter in the online New York TImes  this evening

From other Log24 posts tagged Tetrahedron vs. Square —

* Phrase from the previous post, "Overarching Narrative."

Thursday, September 12, 2019

Art Logos …

Filed under: General — Tags: — m759 @ 10:19 AM

… Continued from previous posts now tagged Art Logos.

"Logos," a Greek word used in philosophy and theology,
is, in modern usage, also a brief form of "logotypes,"
a name for the branding symbols used by businesses.

For some less commercial aspects of the philosophical
concept, see Logo in this journal.

Saturday, January 5, 2019

Raiders of the Inarticulate

Filed under: General — Tags: — m759 @ 11:11 AM

Friday, December 7, 2018

The Angel Particle

Filed under: G-Notes,General,Geometry — Tags: , , — m759 @ 7:15 PM

(Continued from this morning)

Majorana spinors and fermions at ncatlab

The Gibbons paper on the geometry of Majorana spinors and the Kummer configuration

"The hint half guessed, the gift half understood, is Incarnation."

— T. S. Eliot in Four Quartets

Geometric incarnation and the Kummer configuration

See also other Log24 posts tagged Kummerhenge.

The Angel Particle

Filed under: General — Tags: — m759 @ 4:15 AM
 

https://newatlas.com/angel-particle-own-antiparticle/50579/

Scientists discover "angel particle"
that is its own antiparticle

Michael Irving
July 21st, 2017

. . . .

"Our team predicted exactly where to find the Majorana fermion and what to look for as its 'smoking gun' experimental signature," says Shoucheng Zhang, one of the senior authors of the research paper. "This discovery concludes one of the most intensive searches in fundamental physics, which spanned exactly 80 years."

. . . .

Zhang proposes that the team's discovery be named the "angel particle" after the Dan Brown novel Angels and Demons , which features a bomb powered by the meeting of matter and antimatter. In the long run, Majoranas could find practical application in making quantum computers more secure.

The research was published in the journal Science  . . . .

See as well Stanford News  yesterday  —

Shoucheng Zhang died on Dec. 1. He was 55. 

Zhang’s death was unexpected and followed
a “battle with depression,” according to his family. 

Friday, September 21, 2018

ABC Art

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 4:36 AM

Monday, June 11, 2018

Arty Fact

Filed under: General,Geometry — Tags: , , — m759 @ 10:35 PM

The title was suggested by the name "ARTI" of an artificial
intelligence in the new film 2036: Origin Unknown.

The Eye of ARTI

See also a post of May 19, "Uh-Oh" —

— and a post of June 6, "Geometry for Goyim" — 

Mystery box  merchandise from the 2011  J. J. Abrams film  Super 8 

An arty fact I prefer, suggested by the triangular computer-eye forms above —

IMAGE- Hyperplanes (square and triangular) in PG(3,2), and coordinates for AG(4,2)

This is from the July 29, 2012, post The Galois Tesseract.

See as well . . .

Wednesday, April 18, 2018

A Missing Link

Filed under: General — m759 @ 10:31 PM

Ben Brantley's review  tonight of an Irish Repertory Theater
production of "The Seafarer" suggests a look at an
earlier New York Times  article on the same play.

From that article  (Sunday, Nov. 11, 2007) —

The target of a link in this  journal on the above 2007 date —

Reflection groups in Wikipedia

"You've got to pick up every stitch . . . ." — Donovan

Thursday, April 27, 2017

Partner, Anchor, Decompose

Filed under: General,Geometry — Tags: — m759 @ 12:31 PM

See also a figure from 2 AM ET April 26 

" Partner, anchor, decompose. That's not math.
That's the plot to 'Silence of the Lambs.' "

Greg Gutfeld, September 2014

Wednesday, March 29, 2017

Art Space Illustrated

Filed under: General,Geometry — Tags: , — m759 @ 10:45 AM

Another view of the previous post's art space  —

IMAGE by Cullinane- 'Solomon's Cube' with 64 identical, but variously oriented, subcubes, and six partitions of these 64 subcubes

More generally, see Solomon's Cube in Log24.

See also a remark from Stack Exchange in yesterday's post Backstory,
and the Stack Exchange math logo below, which recalls the above 
cube arrangement from "Affine groups on small binary spaces" (1984).

IMAGE- Current math.stackexchange.com logo and a 1984 figure from 'Notes on Groups and Geometry, 1978-1986'

Art Space, Continued

Filed under: General — Tags: , — m759 @ 4:35 AM

"And as the characters in the meme twitch into the abyss
that is the sky, this meme will disappear into whatever
internet abyss swallowed MySpace."

—Staff writer Kamila Czachorowski, Harvard Crimson  today

From Log24 posts tagged Art Space

From a recent paper on Kummer varieties,
arXiv:1208.1229v3 [math.AG] 12 Jun 2013,
The Universal Kummer Threefold,” by
Qingchun Ren, Steven V Sam, Gus Schrader, and
Bernd Sturmfels —

IMAGE- 'Consider the 6-dimensional vector space over the 2-element field,' from 'The Universal Kummer Threefold'

Two such considerations —

IMAGE- 'American Hustle' and Art Cube

IMAGE- Cube for study of I Ching group actions, with Jackie Chan and Nicole Kidman 

Tuesday, June 7, 2016

Art and Space…

Filed under: General,Geometry — 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.

Tuesday, March 22, 2016

The Barth Spielfeld

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

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

Friday, August 28, 2015

Art and Space

Filed under: General,Geometry — 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

Wednesday, April 22, 2015

ART WARS continued

Filed under: General — Tags: — m759 @ 8:29 PM

The previous post mentioned a new mobile, "Triangle Constellation,"
commissioned for the Harvard Art Museums.

Related material (click to enlarge) —

The above review is of an exhibition by the "Constellation" artist,
Carlos Amorales, that opened on Sept. 26, 2008 — "just in time for
Halloween and the Day of the Dead."

See also this  journal on that date.

Saturday, November 29, 2014

Something Missing?

Filed under: General — m759 @ 7:59 AM

The title refers to this morning's previous post.

The above links from today's aldaily.com :  Cubism,  Bernstein,  Hell.

Wednesday, September 17, 2014

Raiders of the Lost Articulation

Tom Hanks as Indiana Langdon in Raiders of the Lost Articulation :

An unarticulated (but colored) cube:

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

A 2x2x2 articulated cube:

IMAGE- Eightfold cube with detail of triskelion structure

A 4x4x4 articulated cube built from subcubes like
the one viewed by Tom Hanks above:

Image-- Solomon's Cube

Solomon’s Cube

A Raid on the Inarticulate

Filed under: General — Tags: , — m759 @ 6:00 PM

                                “… And so each venture
Is a new beginning, a raid on the inarticulate….”

— T. S. Eliot, “East Coker V” in Four Quartets

Friday, March 28, 2014

Art School Confidential

Filed under: General — Tags: — m759 @ 4:01 AM

For Reba McEntire on her birthday:
Complex Reflection and Naturalized Epistemology.

Monday, October 28, 2013

Art at Midnight

Filed under: General — Tags: — m759 @ 12:00 AM

Art in America 

"After considering and dismissing a number of definitions,
Danto comes down on one that he thinks captures the
'artness of art': artworks are embodied meanings. As such,
they elicit from viewers acts of interpretation designed to
'grasp the intended meaning they embody.' " 

The New York Times —

"The critic Hilton Kramer, writing in The New Criterion
in 1987, likened Mr. Danto’s views to one of 'those
ingenious scenarios that are regularly concocted to
relieve the tedium of the seminar room and the
philosophical colloquium.' "

Sounds about right.

Sunday, February 3, 2013

The Gospel According to Cartier

Filed under: General — Tags: , , , — m759 @ 10:30 AM

Yesterday's 11 AM post Mad Day concluded
with a link to a 2001 American Mathematical Society
article by Pierre Cartier that sums up the religion and
politics of many mathematicians

"Here ends the infancy narrative of the gospel…."

"… while Simone Weil's Catholicism was violently
anti-Semitic (in 1942!), Grothendieck's Buddhism
bears a strong resemblance to the practices of
his Hasidic ancestors."

See also Simone Weil in this journal.

Note esp. a post of April 6, 2004 that provides
a different way of viewing Derrida's notion of
inscription .

Tuesday, September 15, 2015

Joyce’s Nightmare…

Filed under: General — m759 @ 2:42 PM

Continues.

Today's AP history notes


The above image suggests a search for Missing Art.

Thursday, April 9, 2015

Core Values

Filed under: General,Geometry — m759 @ 10:20 AM

"Yankee Doodle went to London" — Song lyric

  November Man

Geometry was very important to us in this movie.”

— The Missing ART   (Log24, November 7th, 2014)

ART —

"Faculty Approve Theater Concentration, Affirmation
of Integrity" — Recent Harvard Crimson  headline

Thursday, December 11, 2014

Stark and Bleak

Filed under: General,Geometry — m759 @ 3:33 PM

C. P. Snow on G. H. Hardy in the foreword to 
A Mathematician's Apology :

"… he had another favourite entertainment. 
'Mark that man we met last night,'
he said, and someone had to be marked
out of 100 in each of the categories
Hardy had long since invented and defined.  
STARK, BLEAK ('a stark man is not necessarily
bleak: but all bleak men without exception
want to be considered stark')…."

Related material :

Tommy Lee Jones in The New York Times  on Nov. 6th, 2014,
and Pierce Brosnan in the 2014 film "The November Man:

  

Geometry was very important to us in this movie.”

The Missing ART   (Log24, November 7th, 2014)

Tuesday, April 28, 2020

Cloud Atlas of Unknowing

Filed under: General — Tags: — m759 @ 10:15 AM

Darkness from the British Film Institute

Filed under: General — Tags: , — m759 @ 12:31 AM

Monday, April 27, 2020

Darkness Visible

Filed under: General — Tags: — m759 @ 2:48 PM

The Cracked Nut

Filed under: General — Tags: — m759 @ 1:25 PM

“At that instant he saw, in one blaze of light, an image of unutterable
conviction, the reason why the artist works and lives and has his being –
the reward he seeks –the only reward he really cares about, without which
there is nothing. It is to snare the spirits of mankind in nets of magic,
to make his life prevail through his creation, to wreak the vision of his life,
the rude and painful substance of his own experience, into the congruence
of blazing and enchanted images that are themselves the core of life, the
essential pattern whence all other things proceed, the kernel of eternity.”

— Thomas Wolfe, Of Time and the River

“… the stabiliser of an octad preserves the affine space structure on its
complement, and (from the construction) induces AGL(4,2) on it.
(It induces A8 on the octad, the kernel of this action being the translation
group of the affine space.)”

— Peter J. Cameron,
The Geometry of the Mathieu Groups (pdf)

“The yarns of seamen have a direct simplicity, the whole meaning
of which lies within the shell of a cracked nut. But Marlow was not
typical (if his propensity to spin yarns be excepted), and to him the
meaning of an episode was not inside like a kernel but outside….”

— Joseph Conrad in Heart of Darkness

Thursday, April 23, 2020

Octads and Geometry

Filed under: General — Tags: , , — m759 @ 10:11 PM

See the web pages octad.group and octad.us.

Related geometry (not the 759 octads, but closely related to them) —


The 4×6 rectangle of R. T. Curtis
illustrates the geometry of octads —

Counting symmetries with the orbit-stabilizer theorem

Curtis splits the 4×6 rectangle into three 4×2 “bricks” —

.

“In fact the construction enables us to describe the octads
in a very revealing manner. It shows that each octad,
other than Λ1, Λ2, Λ3, intersects at least one of these ‘ bricks’ —
the ‘heavy brick’ – in just four points.” . . . .

— R. T. Curtis (1976). “new combinatorial approach to M24,”
Mathematical Proceedings of the Cambridge Philosophical Society ,
79, pp 25-42.

Dead Poet Joke

Filed under: General — Tags: , , — m759 @ 8:42 PM

From the subtitles of the recent Kristen Stewart film “Underwater” —

427
00:30:26,144 –> 00:30:27,476
He’d always say
he had a new joke,

428
00:30:27,478 –> 00:30:29,445
and then he’d tell
the same stupid joke.

429
00:30:29,447 –> 00:30:32,785
I was… laughing at that joke.

430
00:30:34,053 –> 00:30:35,685
Yeah, what was it?

431
00:30:35,687 –> 00:30:38,654
What did the fish say when
it bumped into the brick wall?

April 11 was the dies natalis , in the Catholic sense, of John Horton Conway.
Related material: Other posts containing the phrase  “brick wall.”

Monday, February 17, 2020

Lines

Filed under: General — Tags: , — m759 @ 1:54 AM

"A fusion of all three" . . .

Voilà

(Illustration from Aug. 30, 2015)

Wednesday, October 23, 2019

Overarching Narrative

Filed under: General — Tags: , — m759 @ 8:13 PM

In memory of a retired co-director of Galerie St. Etienne
who reportedly died on October 17 . . .

"It is difficult to mount encyclopedic exhibitions
without an overarching art-historical narrative…."

—  Jane Kallir, director of Galerie St. Etienne, in
https://www.tabletmag.com/jewish-arts-and-culture/
visual-art-and-design/269564/the-end-of-middle-class-art

An overarching narrative from the above death date

See as well the previous post 
and "Dancing at Lughnasa."

Wednesday, September 11, 2019

The Logo

Filed under: General — Tags: — m759 @ 8:46 PM

The previous post suggests a review of . . .

“And after it rains . . .” — Paul Simon

Filed under: General — Tags: — m759 @ 11:15 AM

Black Feathers

Filed under: General — Tags: — m759 @ 10:44 AM

See also this morning's previous post, Peacock News.

"And all of the colors are black." — Paul Simon

Peacock* News

Filed under: General — Tags: — m759 @ 10:10 AM

* The title of course refers to the NBC logo. 
   See also other instances of "Peacock" in this  journal.

Tuesday, September 10, 2019

Sic Transit

Filed under: General — Tags: — m759 @ 12:46 PM

Neil Montanus, a Kodak Colorama Photographer, Dies at 92

His colossal pictures, depicting an idealized American life,
greeted travelers at Grand Central Terminal for decades.

Mr. Montanus was 92 when he died on Friday 
under hospice care in Rochester, his son Jim said.

Robert Frank Dies; Pivotal Documentary Photographer Was 94

Mr. Frank, who was best known for his groundbreaking book,
“The Americans,” had a visually raw and personally expressive
style that made him one of the most influential photographers
of the 20th century.

Robert Frank, one of the most influential photographers 
of the 20th century, whose visually raw and personally
expressive style was pivotal in changing the course of
documentary photography, died on Monday in Inverness,
Nova Scotia. He was 94.

"And everything looks worse in black and white." — Paul Simon

Saturday, July 27, 2019

The Stephen King Intelligence Test

Filed under: General — Tags: , — m759 @ 4:41 PM


Related images —

See also other posts tagged Arti Facts.

This  post was suggested by those posts and by the following
attempt at humor —

Tuesday, July 16, 2019

Morf Vandewalt, Social Prism

Filed under: General — Tags: , — m759 @ 8:38 AM

From the 2019 film "Velvet Buzzsaw" —

What is going on in this picture?
 

Friday, May 10, 2019

Desperately Seeking Resonance

Filed under: General — Tags: , , — m759 @ 10:46 AM

Continues

Also from Fall Equinox 2018 — Looney Tune for Physicists

Thursday, March 28, 2019

Eight and Seven

Filed under: General — Tags: — m759 @ 8:56 AM

'Knight' octad labeling by the 8 points of the projective line over GF(7)    

Wednesday, March 27, 2019

7-Up

Filed under: General — Tags: — m759 @ 1:00 PM

"Don't want to end up a cartoon
In a cartoon graveyard" 
— Paul Simon

Thursday, March 21, 2019

Rationalists

Filed under: General — Tags: , — m759 @ 2:46 PM

See also Eupalinos  in this journal.

Wednesday, March 20, 2019

Secret Characters

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

"Cell 461" quote from Curzio Malaparte superimposed on a scene from
the 1963 Godard film "Le Mépris " ("Contempt") —

"The architecture… beomes closely linked to the script…."

Malaparte's cell number , 461, is somewhat less closely  linked
to the phrase "eternal blazon" —

Irving was quoted here on Dec. 22, 2008

The Tale of
the Eternal Blazon

by Washington Irving

Blazon  meant originally a shield , and then
the heraldic bearings on a shield .
Later it was applied to the art of describing
or depicting heraldic bearings in the proper
manner; and finally the term came to signify 
ostentatious display  and also description or
record by words or other means 
. In Hamlet ,
Act I Sc. 5, the Ghost, while talking with
Prince Hamlet, says:

‘But this eternal blazon must not be
To ears of flesh and blood.’

Eternal blazon  signifies revelation or description
of things pertaining to eternity 
.”

— Irving’s Sketch Book , p. 461
 

Update of 6:25 PM ET —

"Self-Blazon of Edenic Plenitude"

(The Issuu text is taken from Speaking about Godard , by Kaja Silverman
and Harun Farocki, New York University Press, 1998, page 34.)

Tuesday, March 19, 2019

Architectural Note

Filed under: General — Tags: — m759 @ 11:00 PM

Casa Malaparte, also known as Villa Malaparte

Related film image with architectural quotation superimposed —

'Sincerity, order, logic and clarity above all' — Italian rationalist architecture philosophy.

Related art prose —

Friday, December 7, 2018

An Ark for Hanukkah

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

From religionnews.com

"The word 'Hanukkah' means dedication.
It commemorates the rededicating of the
ancient Temple in Jerusalem in 165 B.C. . . . ."

From The New York Times  this morning —

Related material —

From this  journal on Wednesday, December 5, 2018

Megan Fox in "Transformers" (2007) —

From a Google image search this morning —

The image search was suggested by recent posts tagged Aitchison
and by this morning's previous post.

Sunday, September 23, 2018

Three Times Eight

Filed under: General,Geometry — Tags: — m759 @ 9:21 AM

The New York Times 's Sunday School today —

I prefer the three bricks of the Miracle Octad Generator —

Image result for mog miracle octad bricks

Saturday, September 22, 2018

Minimalist Configuration

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 11:03 PM

From the previous post

From Wikipedia

From Log24

The Venturi Manifesto

Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 1:00 PM

Venturi reportedly died on Tuesday, September 18.*

See also this journal on that date.

* Fact check:

Symmetric Generation, by Curtis

Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 10:15 AM

Norwegian artist Josefine Lyche —

Lyche's shirt honors the late Kurt Cobain.

"Here we are now, entertain us."

Symmetric Generation, by Netflix

Filed under: General — Tags: , — m759 @ 5:05 AM

Suggested by the previous post . . .

'Out of nothing' opening of 'Maniac' at Netflix

"The pattern is the pattern."

Friday, September 21, 2018

Symmetric Generation, by Nao

Filed under: General — Tags: , — m759 @ 1:30 PM

"The creation of a new world
        starts now.
Once again I am tied
        to the logic of this
Hyper-symmetrical-dimension."

Bill Murray and Scarlett Johansson in 'Lost in Translation'

Thursday, September 20, 2018

Clash of the Titans

Filed under: General — Tags: , — m759 @ 6:18 PM

Saturday, September 1, 2018

Another 48 Hours

Filed under: General — Tags: — m759 @ 9:29 PM

http://www.log24.com/log/pix18/180901-Elliott-Gould-in-Oceans-8.jpg

Backstory:  See The Plaid Overnight Case in this journal.

Investigators: First 48 Hours Most Critical
In Locating Missing Children Who Entered
Portal To Fantastical World

See as well a post from 10:16 PM ET Thursday, August 30, 2018.

Sunday, July 22, 2018

Space

Filed under: General,Geometry — Tags: , , — m759 @ 10:29 AM

See also interality in the eightfold cube.

IMAGE- The Trinity Cube (three interpenetrating planes that split the eightfold cube into its eight subcubes)

Sunday, July 1, 2018

Deutsche Ordnung

Filed under: General,Geometry — Tags: , , — m759 @ 8:22 PM

The title is from a phrase spoken, notably, by Yul Brynner
to Christopher Plummer in the 1966 film "Triple Cross."

Related structures —

Greg Egan's animated image of the Klein quartic

For a smaller tetrahedral arrangement, within the Steiner quadruple
system of order 8 modeled by the eightfold cube, see a book chapter 
by Michael Huber of Tübingen

Steiner quadruple system in eightfold cube

For further details, see the June 29 post Triangles in the Eightfold Cube.

See also, from an April 2013 philosophical conference:

Abstract for a talk at the City University of New York:

The Experience of Meaning 
Jan Zwicky, University of Victoria 
09:00-09:40 Friday, April 5, 2013

Once the question of truth is settled, and often prior to it, what we value in a mathematical proof or conjecture is what we value in a work of lyric art: potency of meaning. An absence of clutter is a feature of such artifacts: they possess a resonant clarity that allows their meaning to break on our inner eye like light. But this absence of clutter is not tantamount to 'being simple': consider Eliot's Four Quartets  or Mozart's late symphonies. Some truths are complex, and they are simplified  at the cost of distortion, at the cost of ceasing to be  truths. Nonetheless, it's often possible to express a complex truth in a way that precipitates a powerful experience of meaning. It is that experience we seek — not simplicity per se , but the flash of insight, the sense we've seen into the heart of things. I'll first try to say something about what is involved in such recognitions; and then something about why an absence of clutter matters to them.

For the talk itself, see a YouTube video.

The conference talks also appear in a book.

The book begins with an epigraph by Hilbert

Saturday, June 23, 2018

Meanwhile …

Filed under: General,Geometry — Tags: , — m759 @ 9:00 PM

Backstory for fiction fans, from Log24 on June 11 —

Related non -fiction —

See as well the structure discussed in today's previous post.

Plan 9 from Inner Space

Filed under: General,Geometry — Tags: , — m759 @ 9:00 AM

From Nanavira Thera, "Early Letters," in Seeking the Path —

"nine  possibilities arising quite naturally" —

Compare and contrast with Hudson's parametrization of the
4×4 square by means of 0 and the 15  2-subsets of a 6-set —

Saturday, May 19, 2018

Uh-Oh.

Filed under: General — Tags: — m759 @ 2:27 AM

From the linked website —

The circle-in-a-triangle symbol is known as "the triangle of art" —

See as well a post of Feb. 27, 2018:  Raiders of the Lost Images.

Sunday, March 4, 2018

The Square Inch Space: A Brief History

Filed under: General,Geometry — Tags: , — m759 @ 11:21 AM

1955  ("Blackboard Jungle") —

1976 —

2009 —

2016 —

 Some small Galois spaces (the Cullinane models)

Wednesday, October 25, 2017

To the Egress

Filed under: General — Tags: — m759 @ 9:24 PM

The New York Times  at 8:22 PM ET

"Knight Landesman, a longtime publisher of Artforum magazine
and a power broker in the art world, resigned on Wednesday
afternoon, hours after a lawsuit was filed in New York accusing
him of sexually harassing at least nine women in episodes that
stretched back almost a decade."

See as well, in this  journal, Way to the Egress.

The Palo Alto Edge

Filed under: General,Geometry — Tags: — m759 @ 1:00 PM

From Stanford — The death on October 9, 2017, of a man who
"always wanted to be at the most cutting of cutting-edge technology."

Related material from Log24 on April 26, 2017

A sketch, adapted from Girl Scouts of Palo Alto —

Click the sketch for further details.

Friday, June 16, 2017

Chalkroom Jungle

Filed under: General — Tags: , , , — m759 @ 3:33 AM

At MASS MoCA, the installation "Chalkroom" quotes a lyric —

Oh beauty in all its forms
funny how hatred can also be a beautiful thing
When it's as sharp as a knife
as hard as a diamond

Perfect

— From "One Beautiful Evening," by Laurie Anderson.

See also the previous post and "Smallest Perfect" in this journal.

Thursday, June 15, 2017

Building Six

Filed under: General — Tags: , , — m759 @ 7:47 PM

Berkshire tales of May 25, 2017 —

See also, in this  journal from May 25 and earlier, posts now tagged
"The Story of Six."

Wednesday, April 26, 2017

A Tale Unfolded

Filed under: General,Geometry — Tags: , , — m759 @ 2:00 AM

A sketch, adapted tonight from Girl Scouts of Palo Alto

From the April 14 noon post High Concept

From the April 14 3 AM post Hudson and Finite Geometry

IMAGE- Geometry of the Six-Set, Steven H. Cullinane, April 23, 2013

From the April 24 evening post The Trials of Device

Pentagon with pentagram    

Note that Hudson's 1905 "unfolding" of even and odd puts even on top of
the square array, but my own 2013 unfolding above puts even at its left.

Monday, April 24, 2017

The Trials of Device

Filed under: General,Geometry — Tags: , , — m759 @ 3:28 PM

"A blank underlies the trials of device"
— Wallace Stevens, "An Ordinary Evening in New Haven" (1950)

A possible meaning for the phrase "the trials of device" —

See also Log24 posts mentioning particular device, the pentagram .

For instance —

Wittgenstein's pentagram and 4x4 'counting-pattern'

Related figures

Pentagon with pentagram    

Monday, April 17, 2017

Hatched

Filed under: General — Tags: , — m759 @ 9:00 AM

Related art

See also the previous post.

Saturday, April 15, 2017

Quanta Dating

Filed under: General — Tags: , — m759 @ 3:15 PM

From Quanta Magazine  —

For the Church of Synchronology

See also this  journal on July 17, 2014, and March 28, 2017.

Friday, April 14, 2017

Hudson and Finite Geometry

Filed under: General,Geometry — Tags: , — m759 @ 3:00 AM

IMAGE- Geometry of the Six-Set, Steven H. Cullinane, April 23, 2013

The above four-element sets of black subsquares of a 4×4 square array 
are 15 of the 60 Göpel tetrads , and 20 of the 80 Rosenhain tetrads , defined
by R. W. H. T. Hudson in his 1905 classic Kummer's Quartic Surface .

Hudson did not  view these 35 tetrads as planes through the origin in a finite
affine 4-space (or, equivalently, as lines in the corresponding finite projective
3-space).

In order to view them in this way, one can view the tetrads as derived,
via the 15 two-element subsets of a six-element set, from the 16 elements
of the binary Galois affine space pictured above at top left.

This space is formed by taking symmetric-difference (Galois binary)
sums of the 15 two-element subsets, and identifying any resulting four-
element (or, summing three disjoint two-element subsets, six-element)
subsets with their complements.  This process was described in my note
"The 2-subsets of a 6-set are the points of a PG(3,2)" of May 26, 1986.

The space was later described in the following —

IMAGE- Dolgachev and Keum, coordinatization of the 4x4 array in 'Birational Automorphisms of Quartic Hessian Surfaces,' AMS Transactions, 2002

Thursday, April 13, 2017

Space

Filed under: General — Tags: — m759 @ 7:00 PM

See "Smallest Perfect" in this journal.

Wednesday, April 12, 2017

Contracting the Spielraum

Filed under: General,Geometry — Tags: , , , — m759 @ 10:00 AM

The contraction of the title is from group actions on
the ninefold square  (with the center subsquare fixed)
to group actions on the eightfold cube.

From a post of June 4, 2014

At math.stackexchange.com on March 1-12, 2013:

Is there a geometric realization of the Quaternion group?” —

The above illustration, though neatly drawn, appeared under the
cloak of anonymity.  No source was given for the illustrated group actions.
Possibly they stem from my Log24 posts or notes such as the Jan. 4, 2012,
note on quaternion actions at finitegeometry.org/sc (hence ultimately
from my note “GL(2,3) actions on a cube” of April 5, 1985).

Expanding the Spielraum

Filed under: General,Geometry — Tags: , — m759 @ 9:48 AM

Cézanne's Greetings.

"Cézanne ignores the laws of classical perspective . . . ."

— Voorhies, James. “Paul Cézanne (1839–1906).”
In Heilbrunn Timeline of Art History .  New York:
The Metropolitan Museum of Art, 2000–. (October 2004)

Some others do not.

This is what I called "the large Desargues configuration
in posts of April 2013 and later.

Tuesday, April 4, 2017

White Cube

Filed under: General — Tags: , — m759 @ 12:21 PM

"Inside the White Cube" —

"We have now reached
a point where we see
not the art but the space first….
An image comes to mind
of a white, ideal space
that, more than any single picture,
may be the archetypal image
of 20th-century art."

http://www.log24.com/log/pix09/090205-cube2x2x2.gif

"Space: what you
damn well have to see."

— James Joyce, Ulysses  

Monday, April 3, 2017

Even Core

Filed under: General,Geometry — Tags: , — m759 @ 9:16 PM

4x4x4 gray cube

http://www.log24.com/log/pix11A/110625-CubeHypostases.gif

Odd Core

Filed under: General,Geometry — Tags: , — m759 @ 9:00 PM

 

3x3x3 Galois cube, gray and white

Wednesday, March 29, 2017

The Crimson Abyss

Filed under: General,Geometry — Tags: , — m759 @ 3:19 PM

"And as the characters in the meme twitch into the abyss
that is the sky, this meme will disappear into whatever
internet abyss swallowed MySpace."

—Staff writer Kamila Czachorowski, Harvard Crimson , March 29

1984

IMAGE- 'Affine Groups on Small Binary Spaces,' illustration

2010

Logo design for Stack Exchange Math by Jin Yang
 

Recent posts now tagged Crimson Abyss suggest
the above logo be viewed in light of a certain page 29

"… as if into a crimson abyss …." —

Update of 9 PM ET March 29, 2017:

Prospero's Children  was first published by HarperCollins,
London, in 1999. A statement by the publisher provides
an instance of the famous "much-needed gap." —

"This is English fantasy at its finest. Prospero’s Children 
steps into the gap that exists between The Lion, the Witch
and the Wardrobe
  and Clive Barker’s Weaveworld , and
is destined to become a modern classic."

Related imagery —

See also "Hexagram 64 in Context" (Log24, March 16, 2017).

Design Abyss

Filed under: General — Tags: , — m759 @ 1:00 PM


http://www.log24.com/images/IChing/hexagram29.gif  
Hexagram 29,
The Abyss (Water)

This post was suggested by an August 6, 2010, post by the designer
(in summer or fall, 2010) of the Stack Exchange math logo (see
the previous Log24 post, Art Space Illustrated) —

http://www.8164.org/☵☲/  .

In that post, the designer quotes the Wilhelm/Baynes I Ching  to explain
his choice of Hexagram 63, Water Over Fire, as a personal icon —

"When water in a kettle hangs over fire, the two elements
stand in relation and thus generate energy (cf. the
production of steam). But the resulting tension demands
caution. If the water boils over, the fire is extinguished
and its energy is lost. If the heat is too great, the water
evaporates into the air. These elements here brought in
to relation and thus generating energy are by nature
hostile to each other. Only the most extreme caution
can prevent damage."

See also this  journal on Walpurgisnacht (April 30), 2010 —

http://www.log24.com/images/IChing/hexagram29.gif

Hexagram 29:
Water

http://www.log24.com/log/pix10A/100430-Commentary.jpg

http://www.log24.com/images/IChing/hexagram30.gif

Hexagram 30:
Fire

"Hates California,
it's cold and it's damp.
"

Image--'The Fire,' by Katherine Neville

A thought from another German-speaking philosopher

"Die Philosophie ist ein Kampf gegen die Verhexung
unsres Verstandes durch die Mittel unserer Sprache."

See also The Crimson 's abyss in today's 4:35 AM post Art Space, Continued.

Tuesday, March 28, 2017

Bit by Bit

Filed under: General,Geometry — Tags: , , — m759 @ 11:45 AM

From Log24, "Cube Bricks 1984" —

An Approach to Symmetric Generation of the Simple Group of Order 168

Also on March 9, 2017 —

For those who prefer graphic  art

Broken Symmetries  in  Diamond Space  

Backstory

Filed under: General,Geometry — Tags: , — m759 @ 12:06 AM

Click here to enlarge.  Click the image for the source page.

The "this page" reference is to …

Finite Geometry of the Square and Cube.

Also from March 14, 2017 —

Related material

'Children of the Central Structure,' adapted from 'Children of the Damned'

Sunday, July 3, 2016

Another 48 Hours

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

The Onion  on Friday, July 1, 2016 —

Investigators: First 48 Hours Most Critical
In Locating Missing Children Who Entered
Portal To Fantastical World

From Friday afternoon —

Saturday, July 2, 2016

Not Even

Filed under: General — Tags: — m759 @ 11:29 AM

"At CERN the LHC has reached design luminosity,
and is breaking records with a fast pace of new
collisions. This may have something to do with the
report that the LHC is also about to tear open
a portal to another dimension
."

— Peter Woit, Thursday, June 30, 2016,
    at 1:01 PM ET 

See as well The Onion  yesterday (Friday, July 1) —

Investigators: First 48 Hours Most Critical
In Locating Missing Children Who Entered
Portal To Fantastical World

Friday, June 24, 2016

Contrast

Filed under: General — m759 @ 11:24 PM

From a work cited in the previous post —

"… representation of hell and the horrors
of the burial ground are missing."

— Page 384 of Joseph Campbell's The Mythic Image ,
    Princeton University Press, 1981
    (First published in 1974)

For those who regret the above omission

A review of a book published in 1977 —

"Its materials are fear and death, hallucination
and the burning of souls." 

The book's author reportedly died Thursday, June 23, 2016.

See also, from 11 AM ET that day, "Raiders of the Lost Code."

Friday, May 27, 2016

Raiders of the Lost Crucible…

Filed under: General — m759 @ 8:00 AM

Continues .

Number and Time, by Marie-Louise von Franz

For more on the modern physicist analyzed by von Franz,
see The Innermost Kernel , by Suzanne Gieser.

The above passage suggests a meditation on this morning's
New York Times * —

"When shall we three meet again?" — William Shakespeare

“We three have scattered, leaving only me behind
to clean up the scene,” Ms. Yang wrote.
“I am alone, missing us three.” — Amy Qin

Wednesday, March 30, 2016

Romanesque

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

quarter to three

and a philosopher's Stone —

Sunday, December 27, 2015

Rigorous Imagist*

Filed under: General — 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.

Sunday, December 6, 2015

Form and Idea

Filed under: General,Geometry — Tags: , , , — m759 @ 3:24 PM

"Those early works are succinct and uncompromising
in how they give shape to the philosophical perplexities
of form and idea…."

J. J. Charlesworth, artnet news, Dec. 16, 2014

"Form" and "idea" are somewhat synonymous, 
as opposed to "form" and "substance." A reading:

IMAGE- 'American Hustle' and Art Cube

Discuss.

Sunday, August 30, 2015

Lines

Filed under: General,Geometry — 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."

Thursday, June 18, 2015

Expanding the Spielraum

Filed under: General — 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.

Sunday, June 14, 2015

Autistic Enchantments

Filed under: General — m759 @ 12:45 PM

Continued )

Log24  on January 31, 2015 —
 

Spellbound (continued)

Filed under: Uncategorized — m759 @ 3:33 AM 

The New York Times  this morning, in an
obituary for a maker of crossword puzzles :

"… the first known crossword puzzle appeared in
an American newspaper. (Called a 'word-cross'
and shaped like a diamond, it was published in
The New York World  on Sunday, Dec. 21, 1913.)"

See St. Nicholas  magazine, November 1874, p. 59 :

For the answer, see this  journal on Aug. 29, 2002
(with a scene from Spellbound ) and on July 15, 2004.

On that same date 

The Seattle Times , Feb. 8, 2015, updated Feb. 12—

How to solve the puzzle:

"… you begin by filling in the missing words 
for the limericks. 

Dice, yAhtzee, woN, yahTzee, twicE; 
Wall, dRawl, geOrgia’s, staTe, minnEsota; 
Truck, rEd, fiReman’s, blaZe, hydrAnt; 
Bob, sLob, prAy, saiNt, thanK. 

The capital letters help to show what comes next, 
as clued by the 1,2,3,4,5 in the title. 

You take the first letter of the first inserted word, 
the second of the second and so on. The resulting 
message is ‘Dante wrote terza blank.’ The blank 
is RIMA, as terza rima was the rhyme scheme 
Dante used in the Divine Comedy."

See also two other dates, June 3, 2015, and June 10, 2015,
in this  journal and in the life of the puzzle author.

The date of the puzzle's answer, Feb. 8, 2015, is also
not without interest.

IMAGE- Art Jeffries (Bruce Willis) and Simon Lynch (Miko Hughes), 'Mercury Rising' (1998)

“Click on fanciful .”

Tuesday, May 5, 2015

Harvard Cinco de Mayo

Filed under: General — Tags: , — m759 @ 1:00 PM

… And Some Not So Live —

"Here was finality indeed, and cleavage!" — Under the Volcano

Sunday, May 3, 2015

In Memoriam

Filed under: General — Tags: — m759 @ 11:30 AM

For the author of Dances with Wolves —

'Winter Count,' by Barry Holstun Lopez, cover with shades of gray

Saturday, May 2, 2015

Die Scheinung

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

See also Die Scheinung  in this journal.

Wednesday, April 22, 2015

Purely Aesthetic

Filed under: General,Geometry — Tags: , — m759 @ 11:00 AM

G. H. Hardy in A Mathematician's Apology —

What ‘purely aesthetic’ qualities can we distinguish in such theorems as Euclid’s or Pythagoras’s?

I will not risk more than a few disjointed remarks. In both theorems (and in the theorems, of course, I include the proofs) there is a very high degree of unexpectedness, combined with inevitability and economy. The arguments take so odd and surprising a form; the weapons used seem so childishly simple when compared with the far-reaching results; but there is no escape from the conclusions. There are no complications of detail—one line of attack is enough in each case; and this is true too of the proofs of many much more difficult theorems, the full appreciation of which demands quite a high degree of technical proficiency. We do not want many ‘variations’ in the proof of a mathematical theorem: ‘enumeration of cases’, indeed, is one of the duller forms of mathematical argument. A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way. 

Related material:

Tuesday, February 3, 2015

Expanding the Spielraum

Filed under: General — Tags: , — m759 @ 11:00 AM

A short poem by several authors:

"The role of
the 16 singular points
on the Kummer surface
is now played by
the 64 singular points
on the Kummer threefold."

— From Remark 2.4 on page 9 of
"The Universal Kummer Threefold,"
by Qingchun Ren, Steven V Sam,
Gus Schrader, and Bernd Sturmfels,
http://arxiv.org/abs/1208.1229v3,
August 6, 2012 — June 12, 2013.

See also "Expanded Field" in this journal.

IMAGE- Concepts of Space

Illustration from "Sunday School," July 20, 2014.

Other Log24 background:  Kummer, Spielraum, Art Space.

Wednesday, September 17, 2014

HaShem

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

The Horse

Filed under: General — Tags: — m759 @ 10:23 AM

A New York Times  piece today on author Donald Antrim:

“The next project is a novel ‘about’ (having loosely to do with)
his father, Harry, a T. S. Eliot scholar who wrote a well-regarded
monograph on the poet.”

— John Jeremiah Sullivan

From Harry T. Antrim’s 1967 thesis on Eliot:

“That words can be made to reach across the void
left by the disappearance of God (and hence of all
Absolutes) and thereby reestablish some basis of
relation with forms existing outside the subjective
and ego-centered self has been one of the chief
concerns of the first half of the twentieth century.”

An epigraph selected by Sullivan for a 2002 Harper’s Magazine
article, “Horseman, Pass By“—

Far back, far back in our dark soul
the horse prances.

— D. H. Lawrence

A related image from pure mathematics
(a source of Absolutes unrelated to theology):

See April 9, 2004, for a post on the “Horseman” article.

Tuesday, September 16, 2014

Where the Joints Are

Filed under: General,Geometry — Tags: , , — m759 @ 10:00 AM

An image related to the recent posts Sense and Sensibility:

A quote from yesterday's post The Eight:

A possible source for the above phrase about phenomena "carved at their joints":

See also the carving at the joints of Plato's diamond from the Meno :

Image-- Plato's diamond and a modern version from finite geometry

Related material: Phaedrus on Kant as a diamond cutter
in Zen and the Art of Motorcycle Maintenance .

Monday, August 11, 2014

Syntactic/Symplectic

(Continued from August 9, 2014.)

Syntactic:

Symplectic:

"Visual forms— lines, colors, proportions, etc.— are just as capable of
articulation , i.e. of complex combination, as words. But the laws that govern
this sort of articulation are altogether different from the laws of syntax that
govern language. The most radical difference is that visual forms are not
discursive 
. They do not present their constituents successively, but
simultaneously, so the relations determining a visual structure are grasped
in one act of vision."

– Susanne K. LangerPhilosophy in a New Key

For examples, see The Diamond-Theorem Correlation
in Rosenhain and Göpel Tetrads in PG(3,2).

This is a symplectic  correlation,* constructed using the following
visual structure:

IMAGE- A symplectic structure -- i.e. a structure that is symplectic (meaning plaited or woven).

* Defined in (for instance) Paul B. Yale, Geometry and Symmetry ,
Holden-Day, 1968, sections 6.9 and 6.10.

Saturday, July 26, 2014

OOPs

Filed under: General — m759 @ 2:01 PM

Or:  Two Rivets Short of a Paradigm

Detail from an author photo:

IMAGE- 'House of Cards,' book on Bear Stearns, author photo, with two missing rivets

From rivet-rivet.net:

The philosopher Graham Harman is invested in re-thinking the autonomy of objects and is part of a movement called Object-Oriented-Philosophy (OOP). Harman wants to question the authority of the human being at the center of philosophy to allow the insertion of the inanimate into the equation. With the aim of proposing a philosophy of objects themselves, Harman puts the philosophies of Bruno Latour and Martin Heidegger in dialogue. Along these lines, Harman proposes an unconventional reading of the tool-being analysis made by Heidegger. For Harman, the term tool does not refer only to human-invented tools such as hammers or screwdrivers, but to any kind of being or thing such as a stone, dog or even a human. Further, he uses the terms objects, beings, tools and things, interchangeably, placing all on the same ontological footing. In short, there is no “outside world.”

Harman distinguishes two characteristics of the tool-being: invisibility and totality. Invisibility means that an object is not simply used but is: “[an object] form(s) a cosmic infrastructure of artificial and natural and perhaps supernatural forces, power by which our last action is besieged.” For instance, nails, wooden boards and plumbing tubes do their work to keep a house “running” silently (invisibly) without being viewed or noticed. Totality means that objects do not operate alone but always in relation to other objects–the smallest nail can, for example, not be disconnected from wooden boards, the plumbing tubes or from the cement. Depending on the point of view of each entity (nail, tube, etc.) a different reality will emerge within the house. For Harman, “to refer to an object as a tool-being is not to say that it is brutally exploited as a means to an end, but only that it is torn apart by the universal duel between the silent execution of an object’s reality and the glistening aura of its tangible surface.”

— From “The Action of Things,” an M.A. thesis at the Center for Curatorial Studies, Bard College, by Manuela Moscoso, May 2011, edited by Sarah Demeuse

From Wikipedia, a programming paradigm:

See also posts tagged Turing’s Cathedral, and Alley  Oop (Feb. 11, 2003).

Friday, March 28, 2014

Musement

Filed under: General — Tags: — m759 @ 7:00 PM

(The title is from a work by Charles Sanders Peirce.)

For LYNX 760 —

IMAGE- Image search for 'the clean crystalline work'

For more beauty and strangeness, see Strange McEntire.

Chinese Rune

Filed under: General,Geometry — Tags: — m759 @ 12:00 PM

"The Geometry of the I Ching introduces something called the Cullinane sequence
for the hexagrams, and uses a notation based on the four sides and two diagonals
in a square to indicate the yin and yang lines. The resulting rune-like symbols
are intriguing…."

— Andreas Schöter's  I Ching  home page

Actually, the geometry is a bit deeper than the rune-like symbols.

" 'Harriet Burden has been really great to me,'
Rune says in an interview, 'not only as a collector
of my work but as a true supporter. And I think of her
as a muse for the project … ' "

— In The Blazing World , the artist known as Rune

Nabokovian

Filed under: General — Tags: — m759 @ 11:16 AM

"Constructed as a Nabokovian cat’s cradle, the novel
purports to be the work of a professor of aesthetics…."

— Fernanda Eberstadt in a book review now online

Blazing Thule

Filed under: General — Tags: — m759 @ 10:20 AM

The title is suggested by a new novel (see cover below),
and by an unwritten book by Nabokov —

Siri Hustvedt, 'The Blazing World'.

Related material:

Symbol

Filed under: General — Tags: — m759 @ 12:00 AM

For Josefine Lyche, by fellow artist  Nuno Borges:

Related material:

Recent remarks by Lyche and
a recurring image from this journal.

Friday, March 7, 2014

Kummer Varieties

Filed under: General,Geometry — Tags: , , — m759 @ 11:20 AM

The Dream of the Expanded Field continues

Image-- The Dream of the Expanded Field

From Klein's 1893 Lectures on Mathematics —

"The varieties introduced by Wirtinger may be called Kummer varieties…."
E. Spanier, 1956

From this journal on March 10, 2013 —

From a recent paper on Kummer varieties,
arXiv:1208.1229v3 [math.AG] 12 Jun 2013,
"The Universal Kummer Threefold," by
Qingchun Ren, Steven V Sam, Gus Schrader, and Bernd Sturmfels —

IMAGE- 'Consider the 6-dimensional vector space over the 2-element field,' from 'The Universal Kummer Threefold'

Two such considerations —

IMAGE- 'American Hustle' and Art Cube

IMAGE- Cube for study of I Ching group actions, with Jackie Chan and Nicole Kidman 

Update of 10 PM ET March 7, 2014 —

The following slides by one of the "Kummer Threefold" authors give
some background related to the above 64-point vector space and
to the Weyl group of type E7(E7):

The Cayley reference is to "Algorithm for the characteristics of the
triple ϑ-functions," Journal für die Reine und Angewandte
Mathematik  87 (1879): 165-169. <http://eudml.org/doc/148412>.
To read this in the context of Cayley's other work, see pp. 441-445
of Volume 10 of his Collected Mathematical Papers .

Monday, February 3, 2014

Designs

Filed under: General — Tags: , — m759 @ 7:00 AM

This journal a year ago yesterday

“Some designs work subtly.
Others are successful through sheer force.”

Penelope Green

Subtly:

Sheer force:

IMAGE- The Cartier diamond ring from 'Inside Man'

Tuesday, January 21, 2014

Class of 64

Filed under: General — Tags: — m759 @ 7:31 AM

NY Times  researcher from this morning’s previous post
tweeted last fall about art forgery and China.

Related material — Art Cube.

IMAGE- 'American Hustle' and Art Cube

Illustration from December 25, 2013.

Wednesday, December 25, 2013

Rotating the Facts

Filed under: General,Geometry — Tags: , , — m759 @ 4:00 AM

IMAGE- 'American Hustle' and Art Cube

"She never looked up while her mind rotated the facts,
trying to see them from all sides, trying to piece them
together into theory. All she could think was that she
was flunking an IQ test."

— Steve Martin, An Object of Beauty

"So you should not feel so all alone…"
— Adapted song lyric

Thursday, September 5, 2013

Moonshine II

Filed under: General,Geometry — 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)
."

Wednesday, September 4, 2013

Moonshine

Filed under: General,Geometry — 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, August 8, 2013

Heaven’s Gate

Filed under: General — m759 @ 3:01 PM

Yesterday's post Devil's Gate provided a dark view of life and culture.

A more cheerful view is provided by the late Gail Levin,
a maker of PBS "American Masters" documentaries
that included, notably, Jeff Bridges and Marilyn Monroe.

Levin reportedly died at 67 on July 31, 2013.*

An image from an interview with Levin —

The date in the image, July 19th, 2006, is the broadcast
date of the PBS "American Masters" program on Monroe.
A check for synchronicity shows there was no Log24 post
on that date.

See, however, posts for the day before— "Sacred Order"—
and the day after— "Bead Game."

A related quote from an article linked to in the latter—

"First world culture, which is 'pagan and in the majority
everywhere,' has as its defining characteristic
a 'primacy of possibility,' or pop— a broadly inclusive
concept that covers everything from the Aboriginal
dreamtime to Plato’s Forms."

Review by Jess Castle of Philip Rieff’s 
Sacred Order/Social Order, Vol. 1: My Life among the
Deathworks: Illustrations of the Aesthetics of Authority
,
University of Virginia Press, 2006. 256 pages, $34.95.

This quote may serve as the missing July 19, 2006, post.

Related material:  Dreamtime,  Possibility,  and Plato's Forms.

* See that date in this journal for two less famous American
  masters, artist Edward Valigursky and writer Robert Silverberg.

Saturday, February 2, 2013

Mad Day

Filed under: General — Tags: , , , — m759 @ 11:00 AM

A perceptive review of Missing Out: In Praise of the Unlived Life

IMAGE- The perception of doors

"Page 185: 'Whatever else we are, we are also mad.' "

Related material— last night's Outside the Box and, from Oct. 22 last year

"Some designs work subtly.
Others are successful through sheer force."

Par exemple—

IMAGE- The Cartier diamond ring from 'Inside Man'

See also Cartier in this journal.

The Cartier link leads to, among other things

A Mad Day’s Work: From Grothendieck to Connes and Kontsevich.
The Evolution of Concepts of Space and Symmetry
,”
by Pierre Cartier, Bulletin of the American Mathematical Society ,
Vol. 38 (2001) No. 4, pages 389-408

Tuesday, January 22, 2013

Raven Light

Filed under: General — Tags: , — m759 @ 11:40 AM

"…a fundamental cognitive ability known as 'fluid' intelligence: the capacity to solve novel problems, to learn, to reason, to see connections and to get to the bottom of things. …

…matrices are considered the gold standard of fluid-intelligence tests. Anyone who has taken an intelligence test has seen matrices like those used in the Raven’s: three rows, with three graphic items in each row, made up of squares, circles, dots or the like. Do the squares get larger as they move from left to right? Do the circles inside the squares fill in, changing from white to gray to black, as they go downward? One of the nine items is missing from the matrix, and the challenge is to find the underlying patterns— up, down and across— from six possible choices. Initially the solutions are readily apparent to most people, but they get progressively harder to discern. By the end of the test, most test takers are baffled."

— Dan Hurley, "Can You Make Yourself Smarter?," NY Times , April 18, 2012

See also "Raven Steals the Light" in this  journal.

Related material:

Plan 9 from MIT and, perhaps exemplifying crystallized  rather than fluid  intelligence, Black Diamond.

Wednesday, November 14, 2012

Group Actions

Filed under: General,Geometry — Tags: , — m759 @ 4:30 PM

The December 2012 Notices of the American
Mathematical Society  
has an ad on page 1564
(in a review of two books on vulgarized mathematics)
for three workshops next year on “Low-dimensional
Topology, Geometry, and Dynamics”—

(Only the top part of the ad is shown; for further details
see an ICERM page.)

(ICERM stands for Institute for Computational
and Experimental Research in Mathematics.)

The ICERM logo displays seven subcubes of
a 2x2x2 eight-cube array with one cube missing

The logo, apparently a stylized image of the architecture
of the Providence building housing ICERM, is not unlike
a picture of Froebel’s Third Gift—

 

Froebel's third gift, the eightfold cube

© 2005 The Institute for Figuring

Photo by Norman Brosterman from the Inventing Kindergarten
exhibit at The Institute for Figuring (co-founded by Margaret Wertheim)

The eighth cube, missing in the ICERM logo and detached in the
Froebel Cubes photo, may be regarded as representing the origin
(0,0,0) in a coordinatized version of the 2x2x2 array—
in other words the cube invariant under linear , as opposed to
more general affine , permutations of the cubes in the array.

These cubes are not without relevance to the workshops’ topics—
low-dimensional exotic geometric structures, group theory, and dynamics.

See The Eightfold Cube, A Simple Reflection Group of Order 168, and
The Quaternion Group Acting on an Eightfold Cube.

Those who insist on vulgarizing their mathematics may regard linear
and affine group actions on the eight cubes as the dance of
Snow White (representing (0,0,0)) and the Seven Dwarfs—

.

Thursday, October 13, 2011

The Lost Cornerstone

Filed under: General — m759 @ 6:29 AM

This post was suggested by this morning's New York Times  story on the missing cornerstone of St. Patrick's Cathedral and by the recent design for an official T-shirt celebrating Harvard's 375th anniversary—

http://www.log24.com/log/pix11C/111011-HtshirtSm.jpg

In Harvard's case, the missing piece beneath the cathedral-like spire* is the VERITAS on the college shield.

Possible sources for a shield image representing VERITAS—

1. "Patrick Blackburn" in this journal, which might be combined with

2. Reflections on Kurt Gödel ** by Hao Wang, Chapter 9, "To Fit All the Parts Together"—

"The metaphor of fitting parts together readily suggests
  the concrete image of solving a picture puzzle…." (p. 243)

Or the image of a Wang tiles puzzle.

A graphic image, colorful but garish, that summarizes these two sources—

http://www.log24.com/log/pix11C/111013-WangShield.bmp

  Shield with matching Wang tiles

* The Lowell House bell tower
** MIT Press, first published in 1987

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