Log24

Tuesday, May 9, 2017

Art Space at Princeton

Filed under: General — m759 @ 9:00 PM

A recent book on mathematics and art
from Princeton University Press, with a
foreword by Neil deGrasse Tyson —

Not to put too fine a point on it —

From an earlier post

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 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

Friday, July 20, 2018

Starting Over

Filed under: General — m759 @ 10:32 AM

See also "Smallest Perfect" in this journal.

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 . . .

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 

Monday, October 24, 2016

Princeton Space

Filed under: General — m759 @ 12:00 PM
 

From the Thursday, Oct. 13, 2016, Daily Princetonian —
The opening paragraphs of an article by Andie Ayala,
"In Pursuit of Space":

The ever-elusive “space” is a word spoken into a great expanse of hopes and fears and delusions: “safe spaces,” “inclusive spaces,” “open spaces,” “green spaces,” “learning spaces.” In this space, words float around abstractly, almost effortlessly, seemingly without the weight of any gravity; appearing to be a distant glimmer of an idea, a once bright and assuring light, which— without much definition— easily fades into obscurity.

Coming to Princeton, it’s tempting to feel as though the rhetoric surrounding the term “space” stretches the word out, magnifies it, and tacks it onto well-designed brochures and anonymous invitations. Yet the question remains— how do you comfortably situate yourself within the incredibly abstruse concept of “space,” especially when you happen to exist in a territory that has been occupied and claimed by an endless sea of others, and which has been upheld by an impregnable and deeply rooted history?

In the process of interviewing various members of the University, one thing has become clear; the question of space is an issue that is pertinent to all members of the Princeton community.

For greater depth on this topic, see the previous post.

For less depth, see a post of January 18, 2005.

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.

Monday, April 11, 2016

Like Decorations in a Cartoon Graveyard

Filed under: General,Geometry — Tags: , — m759 @ 10:48 PM

From Sunday evening's In Memoriam post —

The "from Princeton" remark in the previous post came  from
Princeton, but originated with a retired professor in Rochester,
NY, one Joseph Neisendorfer.

Another remark by Neisendorfer, from his weblog —

Those familiar with the chapter on Galois in the
Eric Temple Bell classic Men of Mathematics  
will know that the words quoted above by
Neisendorfer are definitely not  those of Albert Einstein.

Tuesday, March 22, 2016

The Barth Spielfeld

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

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

Tuesday, November 10, 2015

Princeton Symmetry

Filed under: General — m759 @ 9:37 AM

From this journal nine years ago today, on the
anniversary of Stanley finding Livingstone —

Click on the image for the Princeton connection.

Related art — Search Log24 for Time + Eternity.

See as well the theater producer pictured in last night's post
and a Princeton-related* review of one of his productions.

Footnote of November 11, 2015:

* Related, that is, only by the "Princeton connection" mentioned above.
For another Princeton connection of interest, see a symposium at
Princeton University on May Day, 2015 —

THE PEDAGOGY OF IMAGES:  
 DEPICTING  COMMUNISM  FOR  CHILDREN

A sample symposium participant:

Thursday, November 5, 2015

ABC Art or: Guitart Solo

Filed under: General,Geometry — Tags: — m759 @ 5:55 PM

"… the A B C of being…." — Wallace Stevens

Scholia —

Compare to my own later note, from March 4, 2010 —

"It seems that Guitart discovered these 'A, B, C' generators first,
though he did not display them in their natural setting,
the eightfold cube." — Borromean Generators (Log24, Oct. 19)

See also Raiders of the Lost Crucible (Halloween 2015)
and "Guitar Solo" from the 2015 CMA Awards on ABC.

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

Thursday, August 27, 2015

The Space of Art

Filed under: General — m759 @ 3:18 PM

"Thinking Outside the Square:
Support for Landscape and Portrait
Formats on Instagram
"

Related material from March 18, 2015 —

Play Is Not Playing Around

— m759 @ 1:00 PM 

(A saying of Friedrich Fröbel)

 

See also the previous two posts,
Dude!  and Focus! .

Tuesday, June 9, 2015

Princeton Flashback

Filed under: General — m759 @ 1:00 PM

From The Daily Princetonian  on May 29, 2015:

"… well, isn’t that what Reunions is all about?
  Making memories?"

"Try to remember the kind of September ."

From this  journal on May 29, 2015:

Openings

Filed under: Uncategorized — m759 @ 7:29 AM 

The film "Pawn Sacrificereportedly opened in Toronto 
on September 11, 2014. 

See as well Log24 posts of that day and Autistic Enchantment.

 

The Dark Horse Rises

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.

Monday, April 6, 2015

Springtime for Princeton*

Filed under: General — m759 @ 11:00 PM

Continues.

* And the late Julie Wilson.
  For the title, see a Log24 search.

Thursday, January 15, 2015

Princeton Music continues…

Filed under: General — Tags: — m759 @ 2:22 AM

A post yesterday linked to a discussion
of the Faustian music of Milton Babbitt,
a serial composer who reportedly died
in Princeton on Saturday, Jan. 29, 2011.

Related material from this journal in
January 2005:

See also "me into you, you into me"
("Taking Lucifer Seriously," Jan. 24, 2004)
and the Saturday night "cold open" in this
journal on the date of Babbitt's death.

Tuesday, January 13, 2015

Princeton Requiem

Filed under: General — m759 @ 5:45 PM

Angel Eyes

From The Daily Princetonian ,
a story dated Monday, Jan. 12, 2015:

U. community gathers to
remember Dantzlerward '16

BY JACOB DONNELLY

Students, faculty, staff and community members circled around a table supporting a single lit candle in the lobby of Murray-Dodge Hall on Monday night as they remembered the life of Audrey Dantzlerward ’16, who was found dead in her room in Edwards Hall today. The gathering, led by Dean of Religious Life and the Chapel Alison Boden, was moved to the lobby after a room reserved for the meeting overflowed.

Participants spoke commonly of Dantzlerward’s contributions to campus life, sharp intellect, supportive gestures and friendly demeanor, and the Wildcats, an a cappella group of which Dantzlerward was a member, sang the song “Angel Eyes,” which is traditionally the first and last song Wildcats members sing upon joining the group and graduating. ….

See a YouTube video, uploaded on May 26, 2014,
of the Princeton Wildcats singing "Angel Eyes."

See also "Angel Eyes" and "Proginoskes" in this journal.

Wednesday, September 17, 2014

Raiders of the Lost Articulation

Filed under: General,Geometry — Tags: , , , — m759 @ 6:14 PM

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

Sunday, July 13, 2014

Useful Princeton

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

See…

"Numbers themselves are fictions, abstractions humans invented
to gain more control over the world." — Keith Devlin

Related material:

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.

Friday, January 10, 2014

Department of Corrections

Filed under: General,Geometry — m759 @ 5:01 AM

The reference to David Justice at the beginning of
yesterday afternoon's post does not imply an
endorsement of all his writings. For instance, a
Justice post from yesterday contains the following—

Correction—

The above author name and page number are wrong.

Related to the above "fundamental theme" — 

Midsummer Geometry.

Monday, June 3, 2013

New Yorker Art

Filed under: General — m759 @ 7:59 PM

New Yorker  editor David Remnick at Princeton today
(from a copy of his prepared remarks):

"Finally, speaking of fabric design…."

I prefer Tom and Harold:

Tom Wolfe in The Painted Word 

"I am willing (now that so much has been revealed!)
to predict that in the year 2000, when the Metropolitan
or the Museum of Modern Art puts on the great
retrospective exhibition of American Art 1945-75,
the three artists who will be featured, the three seminal
figures of the era, will be not Pollock, de Kooning, and
Johns-but Greenberg, Rosenberg, and Steinberg.
Up on the walls will be huge copy blocks, eight and a half
by eleven feet each, presenting the protean passages of
the period … a little 'fuliginous flatness' here … a little
'action painting' there … and some of that 'all great art
is about art' just beyond. Beside them will be small
reproductions of the work of leading illustrators of
the Word from that period…."

Harold Rosenberg in The New Yorker 

(Click to enlarge.)

Tom's book seems to be repeating, in 1975, what Harold said better in 1969.

"Finally, speaking of fabric design…."

Note "fabric design" in Rosenberg's words on philistine views of the art of Noland.

For Princeton’s Class Day

Filed under: General — m759 @ 10:30 AM

Triple Threat

"'Mr. Remnick's work is smart, funny and insightful —
a triple threat Class Day speaker!' said Class Day
co-chair Lily Alberts." — News at Princeton

Related material: David Remnick on Miss Gould.

See also Remnick and Miss Gould in this journal.

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 .

Saturday, March 3, 2012

Big Art

Filed under: General — m759 @ 1:00 PM

For Women's History Month—

The Beam of Pink Light

Beam of pink light in Philip K. Dick's 'VALIS'

Video by Josefine Lyche ('Jo Lyxe')

From a post linked to on Lyxe's upload date, Feb. 6, 2012

“… with primitives the beginnings of art, science, and religion
coalesce in the undifferentiated chaos of the magical mentality….”

— Carl G. Jung, “On the Relation of Analytical Psychology to Poetry,”
     Collected Works, Vol. 15, The Spirit in Man, Art, and Literature,
     Princeton University Press, 1966, excerpted in
    Twentieth Century Theories of Art, edited by James M. Thompson.

See also the NY Lottery for St. Luke's Day, 2011, publication date
of the new edition of Philip K. Dick's VALIS  quoted above.

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

Wednesday, August 28, 2019

Tiger’s Leap  to 1905

Filed under: General — Tags: , — m759 @ 3:03 PM

Walter Benjamin on 'a tiger's leap into the past'

See other posts
now tagged
Crosswicks Curse.

 

Click to enlarge:

Block Designs?

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

Monday, May 6, 2019

In Memoriam Goro Shimura (d. May 3, 2019)

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

From Richard Taylor, "Modular arithmetic:  driven by inherent beauty
and human curiosity
," The Letter of the Institute for Advanced Study  [IAS],
Summer 2012, pp. 6– 8 (links added) :

"Stunningly, in 1954, Martin Eichler (former IAS Member)
found a totally new reciprocity law . . . .

Within less than three years, Yutaka Taniyama and Goro Shimura
(former IAS Member) proposed a daring generalization of Eichler’s
reciprocity law to all cubic equations in two variables. A decade later,
André Weil (former IAS Professor) added precision to this conjecture,
and found strong heuristic evidence supporting the Shimura-Taniyama
reciprocity law. This conjecture completely changed the development of
number theory."

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 —

Saturday, March 16, 2019

Multifaceted Narrative

Filed under: General — Tags: — m759 @ 2:40 PM

"Here, modernism is defined as an autonomous body
of ideas, having little or no outward reference, placing
considerable emphasis on formal aspects of the work
and maintaining a complicated—indeed, anxious—
rather than a naïve relationship with the day-to-day
world, which is the de facto view of a coherent group
of people, such as a professional or discipline-based
group that has a high sense of the seriousness and
value of what it is trying to achieve. This brisk definition…."

— Jeremy Gray, Plato's Ghost: The Modernist
Transformation of Mathematics
 , Princeton, 2008 

"Even as the dominant modernist narrative was being written,
there were art historians who recognized that it was inaccurate.
The narrative was too focused on France . . . . Nor was it
correct to build the narrative so exclusively around formalism;
modernism was far messier, far more multifaceted than that."

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

quoted here on the above date — Sept. 11, 2018.
 

From some related Log24 posts

Wednesday, March 6, 2019

The Relativity Problem and Burkard Polster

Filed under: General,Geometry — Tags: — m759 @ 11:28 AM
 

From some 1949 remarks of Weyl—

"The relativity problem is one of central significance throughout geometry and algebra and has been recognized as such by the mathematicians at an early time."

— Hermann Weyl, "Relativity Theory as a Stimulus in Mathematical Research," Proceedings of the American Philosophical Society , Vol. 93, No. 7, Theory of Relativity in Contemporary Science: Papers Read at the Celebration of the Seventieth Birthday of Professor Albert Einstein in Princeton, March 19, 1949  (Dec. 30, 1949), pp. 535-541

Weyl in 1946—:

"This is the relativity problem: to fix objectively a class of equivalent coordinatizations and to ascertain the group of transformations S mediating between them."

— Hermann Weyl, The Classical Groups , Princeton University Press, 1946, p. 16

For some context, see Relativity Problem  in this journal.

In the case of PG(3,2), there is a choice of geometric models 
to be coordinatized: two such models are the traditional
tetrahedral model long promoted by Burkard Polster, and
the square model of Steven H. Cullinane.

The above Wikipedia section tacitly (and unfairly) assumes that
the model being coordinatized is the tetrahedral model. For
coordinatization of the square model, see (for instance) the webpage
Finite Relativity.

For comparison of the two models, see a figure posted here on
May 21, 2014 —

Labeling the Tetrahedral Model  (Click to enlarge) —

"Citation needed" —

The anonymous characters who often update the PG(3,2) Wikipedia article
probably would not consider my post of 2014, titled "The Tetrahedral
Model of PG(3,2)
," a "reliable source."

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

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 tetrahedral key to the arrangement of the 56 triangles within the above
structure, see a book chapter by Michael Huber of Tübingen

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 —

Tuesday, June 19, 2018

Death on Father’s Day

Filed under: General — m759 @ 8:45 PM

From the University of Notre Dame in an obituary dated June 17

Timothy O’Meara, provost emeritus, Kenna Professor of Mathematics Emeritus and Trustee Emeritus at the University of Notre Dame, died June 17. He was 90.

A member of the Notre Dame faculty since 1962, O’Meara twice served as chairman of the University’s mathematics department and served as its first lay provost from 1978 to 1996.
. . . .         

He was graduated from the University of Cape Town in 1947 and earned a master’s degree in mathematics there the following year.  Earning his doctoral degree from Princeton University in 1953, he taught at the University of Otago in New Zealand from 1954 to 1956 before returning to Princeton where he served on the mathematics faculty and as a member of the Institute for Advanced Study for the next six years.  
. . . .

In addition to his mathematical teaching and scholarship, he published magisterial works, including “Introduction to Quadratic Forms,” “Lectures on Linear Groups,” “Symplectic Groups” and “The Classical Groups and K-Theory,” co-authored with Alexander J. Hahn, professor of mathematics emeritus at Notre Dame and a former O’Meara doctoral student.
. . . .

Related material (update of 9:20 PM ET on June 19) —

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.

Tuesday, April 24, 2018

Alma Maman

Filed under: General — m759 @ 1:16 PM

"Almost 9 meters tall, Maman  is one of the most ambitious
of a series of sculptures by Bourgeois that take as their subject
the spider, a motif that first appeared in several of the artist's
drawings in the 1940s and came to assume a central place in
her work during the 1990s. Intended as a tribute to her mother,
who was a weaver, Bourgeois's spiders are highly contradictory
as emblems of maternity: they suggest both protector and predator—
the silk of a spider is used both to construct cocoons and to bind prey—
and embody both strength and fragility."

A Guggenheim Bilbao page

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)

Saturday, February 17, 2018

Frosties: A Sequel to “Frozen”

Filed under: General — m759 @ 11:48 AM

See as well a search in this  journal for Frost at Wanganui.

Friday, February 16, 2018

Two Kinds of Symmetry

Filed under: General,Geometry — m759 @ 11:29 PM

The Institute for Advanced Study (IAS) at Princeton in its Fall 2015 Letter 
revived "Beautiful Mathematics" as a title:

This ugly phrase was earlier used by Truman State University
professor Martin Erickson as a book title. See below. 

In the same IAS Fall 2015 Letter appear the following remarks
by Freeman Dyson —

". . . a special case of a much deeper connection that Ian Macdonald 
discovered between two kinds of symmetry which we call modular and affine.
The two kinds of symmetry were originally found in separate parts of science,
modular in pure mathematics and affine in physics. Modular symmetry is
displayed for everyone to see in the drawings of flying angels and devils
by the artist Maurits Escher. Escher understood the mathematics and got the
details right. Affine symmetry is displayed in the peculiar groupings of particles
created by physicists with high-energy accelerators. The mathematician
Robert Langlands was the first to conjecture a connection between these and
other kinds of symmetry. . . ." (Wikipedia link added.)

The adjective "modular"  might aptly be applied to . . .

The adjective "affine"  might aptly be applied to . . .

From 'Beautiful Mathematics,' by Martin Erickson, an excerpt on the Cullinane diamond theorem (with source not mentioned)

The geometry of the 4×4 square combines modular symmetry
(i.e., related to theta functions) with the affine symmetry above.

Hudson's 1905 discussion of modular symmetry (that of Rosenhain
tetrads and Göpel tetrads) in the 4×4 square used a parametrization
of that square by the digit 0 and the fifteen 2-subsets of a 6-set, but 
did not discuss the 4×4 square as an affine space.

For the connection of the 15 Kummer modular 2-subsets with the 16-
element affine space over the two-element Galois field GF(2), see my note
of May 26, 1986, "The 2-subsets of a 6-set are the points of a PG(3,2)" —

— and the affine structure in the 1979 AMS abstract
"Symmetry invariance in a diamond ring" —

For some historical background on the symmetry investigations by
Dyson and Macdonald, see Dyson's 1972 article "MIssed Opportunities."

For Macdonald's own  use of the words "modular" and "affine," see
Macdonald, I. G., "Affine Lie algebras and modular forms," 
Séminaire N. Bourbaki , Vol. 23 (1980-1981), Talk no. 577, pp. 258-276.

Saturday, February 10, 2018

Into the Upside Down

Filed under: General — m759 @ 10:45 AM

(Title suggested by the TV series Stranger Things )

" 'Untitled' (2016) is the most recent painting in the show
and includes one of Mr. Johns’s recurring images of a ruler."

— Image caption in an article by Deborah Solomon
     in The New York Times  online, Feb. 7, 2018
 

From a Log24 search for "Ruler"

Related art

See also, in this journal, Magic Mountain and Davos.

Einstein and Thomas Mann, Princeton, 1938

Friday, November 10, 2017

Annals of Rarefied Scholarship

Filed under: General,Geometry — m759 @ 3:00 PM

From Cambridge Core, suggested by a reference to
that website in the previous post and by the following
bibliographic data . . .

https://doi.org/10.1017/fmp.2016.5

Downloaded from https://www.cambridge.org/core
on 10 Nov 2017 at 19:06:19 

See Conwell + Princeton in this journal.

Related art

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.

Tuesday, October 3, 2017

Show Us Your Wall

Filed under: General,Geometry — m759 @ 12:10 PM

From Monday morning's post Advanced Study

"Mathematical research currently relies on
a complex system of mutual trust
based on reputations."

— The late Vladimir Voevodsky,
Institute for Advanced Study, Princeton,
The Institute Letter , Summer 2014, p. 8

Related news from today's online New York Times

A heading from the above screenshot: "SHOW US YOUR WALL."

This suggests a review of a concept from Galois geometry

On the wall— A Galois-geometry 'inscape'

(On the wall — a Galois-geometry inscape .)

Tuesday, September 5, 2017

Florence 2001

Filed under: General,Geometry — Tags: — m759 @ 4:44 AM

Or:  Coordinatization for Physicists

This post was suggested by the link on the word "coordinatized"
in the previous post.

I regret that Weyl's term "coordinatization" perhaps has
too many syllables for the readers of recreational mathematics —
for example, of an article on 4×4 magic squares by Conway, Norton,
and Ryba to be published today by Princeton University Press.

Insight into the deeper properties of such squares unfortunately
requires both the ability to learn what a "Galois field" is and the
ability to comprehend seven-syllable words.

Thursday, August 31, 2017

A Conway-Norton-Ryba Theorem

Filed under: General,Geometry — m759 @ 1:40 PM

In a book to be published Sept. 5 by Princeton University Press,
John Conway, Simon Norton,  and Alex Ryba present the following
result on order-four magic squares —

A monograph published in 1976, "Diamond Theory," deals with 
more general 4×4 squares containing entries from the Galois fields
GF(2), GF(4), or GF(16).  These squares have remarkable, if not 
"magic," symmetry properties.  See excerpts in a 1977 article.

See also Magic Square and Diamond Theorem in this  journal.

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."

Thursday, May 18, 2017

Bit Plot

Filed under: General — Tags: — m759 @ 1:40 AM

From a May 15 review of a new book by Douglas Coupland, author of
the 1991 book Generation X: Tales for an Accelerated Culture .

"Minimalists are actually extreme hoarders:
 they hoard space." — Douglas Coupland

The title of Coupland's new book suggests a review of Schmeikal 
in this  journal

Coupland's above remark on hoarders suggests a look at
a wealthy California collector whom, were he not wealthy,
some might call a hoarder.

“I buy things because they strike an emotional bell,
they appeal to my curiosity, to the thrill of discovery
of the extraordinary in the ordinary,” Mr. Cotsen told
The Denver Post in 1998. “They appeal to my sense
of humor, and to my search for the beauty in simplicity.”

He added, “I decided I had a collection when there was
no more space to put anything.”

By the time he died at 88 on May 8 in Beverly Hills, Calif.,
Mr. Cotsen (pronounced COAT-zen) had donated about
half of the material in his collections to institutions like the
Asian Art Museum in San Francisco, Princeton University
and the Museum of International Folk Art in Santa Fe, N.M.

Richard Sandomir in the online New York Times , May 17

Cotsen reportedly died at 88 on May 8. 

See also this  journal on that date —

Monday, May 8, 2017

New Pinterest Board

Filed under: Uncategorized — m759 @ 9:29 PM 

https://www.pinterest.com/stevenhcullinane/art-space/

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, March 26, 2017

Four-Year* Date

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

"Eigenvalues. Fixed points. Stable equilibria.
Mathematicians like things that stay put.
And if they can't stay put, the objects of study
should at least repeat themselves on a regular basis. . . ."

— Barry Cipra, "A Moveable Feast," SIAM News , Jan. 14, 2006

Tuesday, March 18, 2014

Class of 64 continues…

Uncategorized — m759 @ 12:00 PM 

Mathematician Norbert Wiener reportedly
died on this date in 1964.

“Mathematics is too arduous and uninviting a field
to appeal to those to whom it does not give great rewards.
These rewards are of exactly the same character as
those of the artist. To see a difficult uncompromising material
take living shape and meaning is to be Pygmalion,
whether the material is stone or hard, stonelike logic."
. . . .

Wednesday, March 18, 2015

Play Is Not Playing Around

Uncategorized — m759 @ 1:00 PM

(A saying of Friedrich Fröbel)


. . . .

Friday, March 18, 2016

Southwestern Noir

Uncategorized — m759 @ 2:56 PM 

Kyle Smith on April 15, 2015, in the New York Post —

"The ludicrous action thriller 'Beyond the Reach'
fails to achieve the Southwestern noir potency
of 'No Country for Old Men,' but there’s no denying
it brings to mind another Southwestern classic
about malicious pursuit: the Road Runner cartoons."
. . . .

Saturday, March 18, 2017

Back to the Past

Uncategorized — Tags:  — m759 @ 7:35 PM 

"Old men ought to be explorers" — T. S. Eliot

. . . .

* For a full  four years, see also March 18, 2013.

Monday, March 6, 2017

Bullshit Studies

Filed under: General — m759 @ 1:19 AM

From The Chronicle of Higher Education  on March 2, 2017 —

These days, in a world totally dependent on microprocessors, lasers, and nanotechnology, it has been estimated that 30 percent of the U.S. gross national product is based on inventions made possible by quantum mechanics. With the booming high-tech industry and the expected advent of quantum computers, this percentage will only grow. Within a hundred years, an esoteric theory of young physicists became a mainstay of the modern economy.

It took nearly as long for Einstein’s own theory of relativity, first published in 1905, to be used in everyday life in an entirely unexpected way. The accuracy of the global positioning system, the space-based navigation system that provides location and time information in today’s mobile society, depends on reading time signals of orbiting satellites. The presence of Earth’s gravitational field and the movement of these satellites cause clocks to speed up and slow down, shifting them by 38 milliseconds a day. In one day, without Einstein’s theory, our GPS tracking devices would be inaccurate by about seven miles.

Robbert Dijkgraaf, Director, Institute for Advanced Study, Princeton

The above paragraphs are clearly propaganda, not physics.

For "It has been estimated," see

The "without Einstein 's theory" statement may or may not be correct.
See the lengthy discussion at

http://physics.stackexchange.com/questions/1061/
why-does-gps-depend-on-relativity
.

See also Princeton's March of Mediocrity Continues.

Sunday, February 12, 2017

Colorful Tales

Filed under: General — m759 @ 1:23 PM

“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”

— Hermann Weyl, Philosophy of  Mathematics and
    Natural Science 
, Princeton, 1949, p. 237

Harvard University Press on the late Angus Fletcher, author of
The Topological Imagination  and Colors of the Mind

From the Harvard webpage for Colors of the Mind

Angus Fletcher is one of our finest theorists of the arts,
the heir to I. A. Richards, Erich Auerbach, Northrop Frye.
This… book…  aims to open another field of study:
how thought— the act, the experience of thinking—
is represented in literature.

. . . .

Fletcher’s resources are large, and his step is sure.
The reader samples his piercing vision of Milton’s

Satan, the original Thinker,
leaving the pain of thinking
as his legacy for mankind.

A 1992 review by Vinay Dharwadker of Colors of the Mind —

See also the above word "dianoia" in The Echo in Plato's Cave.
Some context 

This post was suggested by a memorial piece today in
the Los Angeles Review of Books

A Florilegium for Angus Fletcher

By Kenneth Gross, Lindsay Waters, V. N. Alexander,
Paul Auster, Harold Bloom, Stanley Fish, K. J. Knoespel,
Mitchell Meltzer, Victoria Nelson, Joan Richardson,
Dorian Sagan, Susan Stewart, Eric Wilson, Michael Wood

Fletcher reportedly died on November 28, 2016.

"I learned from Fletcher how to apprehend
the daemonic element in poetic imagination."

— Harold Bloom in today's Los Angeles florilegium

For more on Bloom and the daemonic, see a Log24 post,
"Interpenetration," from the date of Fletcher's death.

Some backstory:  Dharwadker in this journal.

Thursday, December 22, 2016

Constructivist Witness

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

The title refers to a philosophy of mathematics.

For those who prefer metaphor Folk Etymology.

See also Stages of Math at Princeton's  
Institute for Advanced Study in March 2013 —

— and in this journal starting in August 2014.

Wednesday, December 14, 2016

Graveyard Roses

Filed under: General — m759 @ 2:35 AM

Two deaths on Tuesday, Dec. 13, 2016 —

In memory of game show figure Alan Thicke —

Minimal ABC Art.

In memory of game theory author Thomas Schelling —

Barbara Rose in a Log24 search for Princeton + Art.

Tuesday, November 15, 2016

A Paris Review

Filed under: General — Tags: — m759 @ 4:56 PM

The half-hour referred to here was from 12 PM ET
to 12:30 PM ET on Friday, April 4, 2014

12 PM at Log24 —

12:30 PM at Princeton

The New York Times  on an art lecturer who died on Nov. 9 —

She became a Vogue  correspondent in postwar Paris
and worked for art magazines before starting her own,
the celebrated L’Oeil  (The Eye).

See also Obituary Metaphysics from November 11th —

Tuesday, October 25, 2016

Head Space

Filed under: General — m759 @ 7:23 PM

"When logic and proportion
Have fallen sloppy dead" 

See Princeton,  Alice,  and Breitbart.

Tuesday, August 23, 2016

Puritan Contemplation:

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

For an authority on Japanese art

Text Tiles*

Res ipsa loquitur.

Compare to and contrast with 

Remarks on art, contemplation. and Puritanism 
from a recent Princeton University Press book —

"Lucy Lippard distinguished Asian art
(ego-less and contemplative)
from New York Minimalism
(moralistic and puritanical)."
Mathematics and Art ,
     Princeton U. Press, Fall 2015

* Update of Aug. 24, 2016 — See also Nov. 2, 2014.

Friday, August 12, 2016

Dustbucket Physics

Filed under: General,Geometry — m759 @ 3:00 PM

Peter Galison, a Harvard professor, is a defender of
the Vienna Circle and the religion of Scientism.

From Galison's “Structure of Crystal, Bucket of Dust,” in
Circles Disturbed: The Interplay of Mathematics and Narrative ,
edited by Apostolos Doxiadis and Barry Mazur, pp. 52-78 
(Princeton: Princeton U. Press, 2012) 

Galison's final paragraph —

"Perhaps, then, it should not surprise us too much if,
as Wheeler approaches the beginning-end of all things,
there is a bucket of Borelian dust. Out of this filth,
through the proposition machine of quantum mechanics
comes pregeometry; pregeometry makes geometry;
geometry gives rise to matter and the physical laws
and constants of the universe. At once close to and far
from the crystalline story that Bourbaki invoked,
Wheeler’s genesis puts one in mind of Genesis 3:19:
'In the sweat of thy face shalt thou eat bread, till thou
return unto the ground; for out of it wast thou taken:
for dust thou art, and unto dust shalt thou return.' "

For fans of Scientism who prefer more colorful narratives —

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."

Tuesday, April 12, 2016

The Remnick Remark

Filed under: General — m759 @ 12:12 AM

A remark by New Yorker  editor David Remnick
at Princeton on June 3, 2013 —

"Finally, speaking of fabric design. . . ."

Monday, April 11, 2016

Gospel of the Nobodies

Filed under: General — Tags: , — m759 @ 2:56 PM

"Principles before personalities" — AA saying

Principles

From an April 8 Princeton obituary of a mathematician —

" Moore embodied a 'Princeton style' that made him
a challenging and influential presence in the careers
of his students, said Joseph Neisendorfer, a professor
of mathematics at the University of Rochester who
received his Ph.D. in mathematics from Princeton in
1972. Because of Moore's style, his students would
write theses that 'almost without exception' were
significant advances in mathematics, Neisendorfer said.

'There's a certain Princeton style that focuses on
precision, centrality and simplicity. He was a superb
mathematician and he exercised a lot of influence
by imparting his style to his students,' Neisendorfer said.
'He epitomized the Princeton style.' "

Personalities 

Gospel of the Nobodies 

Tuesday, April 5, 2016

Spring Play

Filed under: General — Tags: , , — m759 @ 4:24 PM

The spring play this March at Princeton's McCarter Theatre Center
was Agatha Christie's "The Mousetrap."

In related news —

See as well, in this  journal, a post from the date pictured above,
that of the Disneyland Diamond Celebration on May 22, 2015 —

Donald Duck with pentagram

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?

Monday, February 1, 2016

The Hiroshima Preprint

Filed under: General,Geometry — m759 @ 2:00 PM

This morning at 11:44 I happened upon

This was published as

Toshiyuki Katsura, Shigeyuki Kondo, Ichiro Shimada,
"On the supersingular K3 surface in characteristic 5 with Artin invariant 1,"
Michigan Mathematical Journal , vol. 63, issue 4 (Dec. 2014), 803–844.

Related material from later today —

See also earlier Log24 remarks on the Hoffman-Singleton graph
and a remark on geometry for Princeton.

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.

Saturday, November 21, 2015

Brightness at Noon*

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

A recent not-too-bright book from Princeton

Some older, brighter books from Tony Zee

Fearful Symmetry  (1986) and
Quantum Field Theory in a Nutshell  (2003).

* Continued.

Thursday, November 5, 2015

The Monster

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

In memory of Princeton mathematician John Nash

"For the past six years all over the world 
experts in the branch of abstract algebra
called group theory have been struggling
to capture a group known as the monster."

Martin Gardner, Scientific American ,  June 1980

"When the Hawkline Monster moved to get a better view
of what was happening, the shadow, after having checked
all the possibilities of light, had discovered a way that it
could shift itself in front of the monster, so that the monster
at this crucial time would be blinded by darkness for a few
seconds, did so, causing confusion to befall the monster.

This was all that the shadow could do and it hoped that this
would give Greer and Cameron the edge they would need
to destroy the Hawkline Monster using whatever plan they
had come up with, for it seemed that they must have a plan
if they were to have any chance at all with the monster and
they did not seem like fools.

When Cameron yelled at Greer, the shadow interpreted this
as the time to move and did so. It obscured the vision of the
Hawkline Monster for a few seconds, knowing full well that if
the monster were destroyed it would be destroyed, too, but
death was better than going on living like this, being a part of
this evil."

— Richard Brautigan, The Hawkline Monster , 1974

From the post For Scientific Witch Hunters of October 30,
an illustration from The Boston Globe —

From the post Colorful Story (All Souls' Day),  
an Illustration from Google Book Search —

Earlier in Brautigan's tale

" Everybody started to leave the parlor to go downstairs
and pour out the Hawkline Monster but just as
they reached the door and one of the Hawkline women
had her hand on the knob, Cameron said, 'Hold it for a
second. I want to get myself a little whiskey.' "

Wednesday, November 4, 2015

Tony Strikes Again

Filed under: General — m759 @ 10:09 AM

Princeton's march of mediocrity continues:

Saturday, October 24, 2015

Tightrope

Filed under: General — m759 @ 9:00 PM

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."

Sunday, August 16, 2015

Sunday School

Filed under: General — m759 @ 9:00 AM

The title of the previous post, "For Quantum Mystics,"
suggests a search in this journal for Quantum + Mystic.

That search in turn suggests, in particular, a review of
a post of October 16, 2007 — a discussion of the 
P.T. Barnum-like phrase "deep beauty" used to describe
a topic under discussion at Princeton by physicists.

Princeton, by the way, serves to illustrate the "gutter"
mentioned by Sir Laurence Olivier in a memorable
classroom scene from 1962

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.

Tuesday, June 2, 2015

Point of View

Filed under: General — m759 @ 5:45 PM

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