Log24

Saturday, November 16, 2019

Red and Gray

Filed under: General — m759 @ 11:29 AM

Oh, the red leaf looks to the hard gray stone
To each other, they know what they mean

— Suzanne Vega, “Songs in Red and Gray

Monday, October 21, 2019

Algebra and Space… Illustrated.

Filed under: General — Tags: , — m759 @ 4:26 PM

Related entertainment —

Detail:

   George Steiner

"Perhaps an insane conceit."

 

Perhaps.

 

See Quantum Tesseract Theorem .

 

Perhaps Not.

 

 See Dirac and Geometry .

Tuesday, August 20, 2019

Ice Giants and Fire Gods: Mind the Gap

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

From my reading Monday morning —

From the online New York Times  this afternoon —

Related literature —

For the Church of Synchronology

The Gigantomachia page above is dated September 20, 2003.
See as well my own webpage from that date: "The Form, the Pattern."

Monday, August 19, 2019

Gods and Giants

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

For "the Pergamum altar," see Pergamon in this journal.

See also . . .

Tuesday, June 25, 2019

Medium and Message

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

Wednesday, May 1, 2019

The Medium and the Message

Filed under: General — Tags: — m759 @ 6:45 PM

In memory of Quentin Fiore — from a Log24 search for McLuhan,
an item related to today's previous post . . .

Related material from Log24 on the above-reported date of death —

See also, from a search for Analogy in this journal . . .

 .

Sunday, August 26, 2018

Mathematics and Narrative: Queensland

Filed under: General — Tags: — m759 @ 3:56 AM

Mathematics —

http://www.log24.com/log/pix18/180826-Cameron-on-U_of_Queensland-slide-500w.jpg

Narrative —

http://www.log24.com/log/pix18/180826-Huntsman-Winters-War-Billboard-Art-500w.jpg

See also other recent posts tagged Queensland.

Thursday, June 21, 2018

Dirac and Geometry (continued)

"Just fancy a scale model of Being 
made out of string and cardboard."

Nanavira Thera, 1 October 1957,
on a model of Kummer's Quartic Surface
mentioned by Eddington

"… a treatise on Kummer's quartic surface."

The "super-mathematician" Eddington did not see fit to mention
the title or the author of the treatise he discussed.

See Hudson + Kummer in this  journal.

See also posts tagged Dirac and Geometry.

Wednesday, May 16, 2018

Church and Temple

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

Friday, June 23, 2017

Annals of Art and Design

Filed under: General — Tags: — m759 @ 10:12 PM

The life of Mr. Breder is not unrelated to that of Carl Andre.

See also, in this  journal, Bulk Apperception.

Wednesday, May 10, 2017

In the Park with Yin and Yang

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

In memory of an art dealer who 
reportedly died on Sunday, May 7—

Decorations for a Cartoon Graveyard

Tuesday, May 9, 2017

Text and Context

Filed under: General,Geometry — Tags: — m759 @ 2:11 PM

Some context for the previous post, which was about
a new Art Space  Pinterest board

Monday, March 13, 2017

Gray Space

Filed under: General — Tags: — m759 @ 8:35 PM


Image in Log24 from the date of the architecture writer's death —

See also the post Gray Space of Palm Sunday, 2014.

Tuesday, July 12, 2016

Group Elements and Skew Lines

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

The following passage by Igor Dolgachev (Good Friday, 2003
seems somewhat relevant (via its connection to Kummer's 166 )
to previous remarks here on Dirac matrices and geometry

Note related remarks from E. M. Bruins in 1959 —

First page of 'Configurations in Quantum Mechanics,' by E.M. Bruins, 1959

Friday, June 3, 2016

Bruins and van Dam

Filed under: General,Geometry — Tags: , — m759 @ 8:00 AM

A review of some recent posts on Dirac and geometry,
each of which mentions the late physicist Hendrik van Dam:

The first of these posts mentions the work of E. M. Bruins.
Some earlier posts that cite Bruins:

Wednesday, May 25, 2016

Kummer and Dirac

From "Projective Geometry and PT-Symmetric Dirac Hamiltonian,"
Y. Jack Ng  and H. van Dam, 
Physics Letters B , Volume 673, Issue 3,
23 March 2009, Pages 237–239

(http://arxiv.org/abs/0901.2579v2, last revised Feb. 20, 2009)

" Studies of spin-½ theories in the framework of projective geometry
have been undertaken before. See, e.g., Ref. [4]. 1 "

1 These papers are rather mathematical and technical.
The authors of the first two papers discuss the Dirac equation
in terms of the Plucker-Klein correspondence between lines of
a three-dimensional projective space and points of a quadric
in a five-dimensional projective space. The last paper shows
that the Dirac equation bears a certain relation to Kummer’s
surface, viz., the structure of the Dirac ring of matrices is 
related to that of Kummer’s 166 configuration . . . ."

[4]

O. Veblen
Proc. Natl. Acad. Sci. USA , 19 (1933), p. 503
Full Text via CrossRef

E.M. Bruins
Proc. Nederl. Akad. Wetensch. , 52 (1949), p. 1135

F.C. Taylor Jr., Master thesis, University of North Carolina
at Chapel Hill (1968), unpublished


A remark of my own on the structure of Kummer’s 166 configuration . . . .

See that structure in this  journal, for instance —

See as well yesterday morning's post.

Tuesday, May 24, 2016

Rosenhain and Göpel Revisited

The authors Taormina and Wendland in the previous post
discussed some mathematics they apparently did not know was
related to a classic 1905 book by R. W. H. T. Hudson, Kummer's
Quartic Surface
.

"This famous book is a prototype for the possibility
of explaining and exploring a many-faceted topic of
research, without focussing on general definitions,
formal techniques, or even fancy machinery. In this
regard, the book still stands as a highly recommendable,
unparalleled introduction to Kummer surfaces, as a
permanent source of inspiration and, last but not least, 
as an everlasting symbol of mathematical culture."

— Werner Kleinert, Mathematical Reviews ,
     as quoted at Amazon.com

Some 4×4 diagrams from that book are highly relevant to the
discussion by Taormina and Wendland of the 4×4 squares within
the 1974 Miracle Octad Generator of R. T. Curtis that were later,
in 1987, described by Curtis as pictures of the vector 4-space over
the two-element Galois field GF(2).

Hudson did not think of his 4×4 diagrams as illustrating a vector space,
but he did use them to picture certain subsets of the 16 cells in each
diagram that he called Rosenhain and Göpel tetrads .

Some related work of my own (click images for related posts)—

Rosenhain tetrads as 20 of the 35 projective lines in PG(3,2)

IMAGE- Desargues's theorem in light of Galois geometry

Göpel tetrads as 15 of the 35 projective lines in PG(3,2)

Anticommuting Dirac matrices as spreads of projective lines

Related terminology describing the Göpel tetrads above

Ron Shaw on symplectic geometry and a linear complex in PG(3,2)

Monday, December 14, 2015

Dirac and Geometry

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

(Continued)

See a post by Peter Woit from Sept. 24, 2005 — Dirac's Hidden Geometry.

The connection, if any, with recent Log24 posts on Dirac and Geometry
is not immediately apparent.  Some related remarks from a novel —

From Broken Symmetries by Paul Preuss
(first published by Simon and Schuster in 1983) —

"He pondered the source of her fascination with the occult, which sooner or later seemed to entangle a lot of thoughtful people who were not already mired in establishmentarian science or religion. It was  the religious impulse, at base. Even reason itself could function as a religion, he supposed— but only for those of severely limited imagination. 

He’d toyed with 'psi' himself, written a couple of papers now much quoted by crackpots, to his chagrin. The reason he and so many other theoretical physicists were suckers for the stuff was easy to understand— for two-thirds of a century an enigma had rested at the heart of theoretical physics, a contradiction, a hard kernel of paradox. Quantum theory was inextricable from the uncertainty relations. 

The classical fox knows many things, but the quantum-mechanical hedgehog knows only one big thing— at a time. 'Complementarity,' Bohr had called it, a rubbery notion the great professor had stretched to include numerous pairs of opposites. Peter Slater was willing to call it absurdity, and unlike some of his older colleagues who, following in Einstein’s footsteps, demanded causal explanations for everything (at least in principle), Peter had never thirsted after 'hidden variables' to explain what could not be pictured. Mathematical relationships were enough to satisfy him, mere formal relationships which existed at all times, everywhere, at once. It was a thin nectar, but he was convinced it was the nectar of the gods. 

The psychic investigators, on the other hand, demanded to know how  the mind and the psychical world were related. Through ectoplasm, perhaps? Some fifth force of nature? Extra dimensions of spacetime? All these naive explanations were on a par with the assumption that psi is propagated by a species of nonlocal hidden variables, the favored explanation of sophisticates; ignotum per ignotius

'In this connection one should particularly remember that the human language permits the construction of sentences which do not involve any consequences and which therefore have no content at all…' The words were Heisenberg’s, lecturing in 1929 on the irreducible ambiguity of the uncertainty relations. They reminded Peter of Evan Harris Walker’s ingenious theory of the psi force, a theory that assigned psi both positive and negative values in such a way that the mere presence of a skeptic in the near vicinity of a sensitive psychic investigation could force null results. Neat, Dr. Walker, thought Peter Slater— neat, and totally without content. 

One had to be willing to tolerate ambiguity; one had to be willing to be crazy. Heisenberg himself was only human— he’d persuasively woven ambiguity into the fabric of the universe itself, but in that same set of 1929 lectures he’d rejected Dirac’s then-new wave equations with the remark, 'Here spontaneous transitions may occur to the states of negative energy; as these have never been observed, the theory is certainly wrong.' It was a reasonable conclusion, and that was its fault, for Dirac’s equations suggested the existence of antimatter: the first antiparticles, whose existence might never have been suspected without Dirac’s crazy results, were found less than three years later. 

Those so-called crazy psychics were too sane, that was their problem— they were too stubborn to admit that the universe was already more bizarre than anything they could imagine in their wildest dreams of wizardry."

Particularly relevant

"Mathematical relationships were enough to satisfy him,
mere formal relationships which existed at all times,
everywhere, at once."

Some related pure  mathematics

Anticommuting Dirac matrices as spreads of projective lines

Friday, November 27, 2015

Einstein and Geometry

Filed under: General,Geometry — Tags: — m759 @ 2:01 PM

(A Prequel to Dirac and Geometry)

"So Einstein went back to the blackboard.
And on Nov. 25, 1915, he set down
the equation that rules the universe.
As compact and mysterious as a Viking rune,
it describes space-time as a kind of sagging mattress…."

— Dennis Overbye in The New York Times  online,
     November 24, 2015

Some pure  mathematics I prefer to the sagging Viking mattress —

Readings closely related to the above passage —

Thomas Hawkins, "From General Relativity to Group Representations:
the Background to Weyl's Papers of 1925-26
," in Matériaux pour
l'histoire des mathématiques au XXe siècle:
Actes du colloque
à la mémoire de Jean Dieudonné
, Nice, 1996  (Soc. Math.
de France, Paris, 1998), pp. 69-100.

The 19th-century algebraic theory of invariants is discussed
as what Weitzenböck called a guide "through the thicket
of formulas of general relativity."

Wallace Givens, "Tensor Coordinates of Linear Spaces," in
Annals of Mathematics  Second Series, Vol. 38, No. 2, April 1937, 
pp. 355-385.

Tensors (also used by Einstein in 1915) are related to 
the theory of line complexes in three-dimensional
projective space and to the matrices used by Dirac
in his 1928 work on quantum mechanics.

For those who prefer metaphors to mathematics —

"We acknowledge a theorem's beauty
when we see how the theorem 'fits' in its place,
how it sheds light around itself, like a Lichtung ,
a clearing in the woods." 
— Gian-Carlo Rota, Indiscrete Thoughts ,
Birkhäuser Boston, 1997, page 132

Rota fails to cite the source of his metaphor.
It is Heidegger's 1964 essay, "The End of Philosophy
and the Task of Thinking" —

"The forest clearing [ Lichtung ] is experienced
in contrast to dense forest, called Dickung  
in our older language." 
— Heidegger's Basic Writings 
edited by David Farrell Krell, 
Harper Collins paperback, 1993, page 441

Monday, November 23, 2015

Dirac and Line Geometry

Some background for my post of Nov. 20,
"Anticommuting Dirac Matrices as Skew Lines" —

First page of 'Configurations in Quantum Mechanics,' by E.M. Bruins, 1959

His earlier paper that Bruins refers to, "Line Geometry
and Quantum Mechanics," is available in a free PDF.

For a biography of Bruins translated by Google, click here.

For some additional historical background going back to
Eddington, see Gary W. Gibbons, "The Kummer
Configuration and the Geometry of Majorana Spinors,"
pages 39-52 in Oziewicz et al., eds., Spinors, Twistors,
Clifford Algebras, and Quantum Deformations:
Proceedings of the Second Max Born Symposium held
near Wrocław, Poland, September 1992
 . (Springer, 2012,
originally published by Kluwer in 1993.)

For more-recent remarks on quantum geometry, see a
paper by Saniga cited in today's update to my Nov. 20 post

Friday, November 13, 2015

A Connection between the 16 Dirac Matrices and the Large Mathieu Group



Note that the six anticommuting sets of Dirac matrices listed by Arfken
correspond exactly to the six spreads in the above complex of 15 projective
lines of PG(3,2) fixed under a symplectic polarity (the diamond theorem
correlation
 
). As I noted in 1986, this correlation underlies the Miracle
Octad Generator of R. T. Curtis, hence also the large Mathieu group.

References:

Arfken, George B., Mathematical Methods for Physicists , Third Edition,
Academic Press, 1985, pages 213-214

Cullinane, Steven H., Notes on Groups and Geometry, 1978-1986

Related material:

The 6-set in my 1986 note above also appears in a 1996 paper on
the sixteen Dirac matrices by David M. Goodmanson —

Background reading:

Ron Shaw on finite geometry, Clifford algebras, and Dirac groups 
(undated compilation of publications from roughly 1994-1995)—

Sunday, October 25, 2015

Buyers and Sellers of Children

Filed under: General — Tags: — m759 @ 6:45 AM

(Continued.)

Featured on this morning's online front page of
The New York Times

Some further details —

An example of New York Times  culture is shown above —

"… Mondrian paintings at the Museum of Modern Art
blend symmetry with a tensile volatility."

(To be fair, this contemptible bullshit is from a picture caption,
not from the art review being summarized.)

Related cultural observations —

Math for Child Buyers  and  Fiction for Child Sellers.

Thursday, October 8, 2015

Redemption

Filed under: General — Tags: — m759 @ 9:48 PM

(Continued)

“I need a photo opportunity, I want a shot at redemption.
 Don’t want to end up a cartoon in a cartoon graveyard.”
 — Paul Simon

A portion of the above photo appeared on the cover of
a German edition of a book by the winner of the 2015 Nobel
Prize in Literature, Svetlana Alexievich. The German title, 
Der Krieg hat kein weibliches Gesicht , is closer to the Russian
original than is the title of an English translation, War's Unwomanly Face .  
Further book and photo information —

Friday, May 22, 2015

Mathmagic Land

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

Donald Duck with Pythagorean pentagram on hand

Donald in Mathmagic Land

Manly P. Hall

Saturday, February 7, 2015

Words and Pictures, continued

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

Word and Object

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

From actor James Spader, whose birthday is today —

"… my father taught English. My mother taught art…."

— Spader in a 2014 interview

See as well the 2013 film "Words and Pictures"
and Log24 posts on a 2007 film, "The Last Mimzy."

Above: A scene from Spader's TV series "The Blacklist"
that was aired on Thursday, February 5, 2015.

Monday, November 3, 2014

Gods and Giants

Filed under: General — Tags: — m759 @ 2:01 PM

A weblog reports Chris Rock's remarks
on Saturday Night Live this past weekend:

"It’s America, we commercialize everything.
Look at what we did to Christmas.
Christmas.  Christmas is Jesus’ birthday.
It’s Jesus’ birthday.  Now, I don’t know Jesus
but from what I’ve read, Jesus is the least
materialistic person to ever roam the earth.
No bling on Jesus.
Jesus kept a low profile and we turned his
birthday into the most materialistic day of the
year.  Matter of fact, we have the Jesus birthday
season.  It’s a whole season of materialism.
Then, at the end of the Jesus birthday season
we have the nerve to have an economist come
on TV and tell you how horrible the Jesus birthday
season was this year.  Oh, we had a horrible Jesus’
birthday this year.  Hopefully, business will pick up
by his Crucifixion.”

Related music and image:

"Show us the way to the next little girl …"

Natalie Wood in "Miracle on 34th Street" (1947)

Related non-materialistic meditations:
The Rhetoric of Abstract Concepts and Gods and Giants.

Friday, October 10, 2014

Both Hands and an Ass Map

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

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

IMAGE- Scene from 'Deathtrap,' with subtitle

Tuesday, September 9, 2014

Smoke and Mirrors

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

This post is continued from a March 12, 2013, post titled
"Smoke and Mirrors" on art in Tromsø, Norway, and from
a June 22, 2014, post on the nineteenth-century 
mathematicians Rosenhain and Göpel.

The latter day was the day of death for 
mathematician Loren D. Olson, Harvard '64.

For some background on that June 22 post, see the tag 
Rosenhain and Göpel in this journal.

Some background on Olson, who taught at the
University of Tromsø, from the American Mathematical
Society yesterday:

Olson died not long after attending the 50th reunion of the
Harvard Class of 1964.

For another connection between that class (also my own) 
and Tromsø, see posts tagged "Elegantly Packaged."
This phrase was taken from today's (print) 
New York Times  review of a new play titled "Smoke."
The phrase refers here  to the following "package" for 
some mathematical objects that were named after 
Rosenhain and Göpel — a 4×4 array —

For the way these objects were packaged within the array
in 1905 by British mathematician R. W. H. T. Hudson, see
a page at finitegometry.org/sc. For the connection to the art 
in Tromsø mentioned above, see the diamond theorem.

Thursday, July 24, 2014

Death in Mathmagic Land

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

(Continued from May 14, 2014.)

See also consciousness growth and the previous post.

Sunday, June 22, 2014

Göpel and Rosenhain

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

(Continued)

Some bizarre remarks on “purity” in the previous post
suggest a review of some pure  mathematics.

Wednesday, May 14, 2014

Death in Mathmagic Land

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

"It was our old friend Pythagoras who discovered
that the pentagram was full of mathematics."

— Narrator, "Donald in Mathmagic Land," Disney, 1959

and it was Peter J. Cameron who discovered that
mathematics was full of pentagrams.

From Log24 on May 3:  Gray Space —

Robert J. Stewart (left) andpentagram photo posted May 2
by Oslo artist Josefine Lyche. See also Lyche in this journal.

From Log24 on May 13:  An Artist's Memorial —

The death mentioned in the above May 13 post occurred on
May 12, the date of a scheduled Black Mass at Harvard.

Related material:

Sunday, April 20, 2014

Gray Space

Filed under: General — m759 @ 10:17 PM

(Continued from Palm Sunday)

From Richard Wilbur’s “Walking to Sleep” —

Try to remember this: what you project
Is what you will perceive; what you perceive
With any passion, be it love or terror,
May take on whims and powers of its own.
Therefore a numb and grudging circumspection
Will serve you best, unless you overdo it,
Watching your step too narrowly, refusing
To specify a world, shrinking your purview
To a tight vision of your inching shoes—
Which may, as soon you come to think, be crossing
An unseen gorge upon a rotten trestle.
What you must manage is to bring to mind
A landscape not worth looking at, some bleak
Champaign at dead November’s end, its grass
As dry as lichen, and its lichens grey….

See also —

Sunday, April 13, 2014

Gray Space

Filed under: General — m759 @ 9:48 PM

Art Wars  view —
image from a post at noon on Saturday, April 12:

Kansas City view:

Review of Seeing Gray , a book by pastor Adam Hamilton
of the United Methodist Church of the Resurrection
in Leawood, Kansas, a suburb of Kansas City—

“Adam Hamilton invites us to soulful gray space
between polarities, glorious gray space that is holy,
mysterious, complex, and true. Let us find within
our spirits the courage and humility to live and learn
in this faithful space, to see gray, to discern a more
excellent way.”

Review by United Methodist Bishop Hope Morgan Ward

The above quotation was suggested by the following from today’s
online Kansas City Star :

“Two of the victims were 14-year-old Reat Griffin Underwood
and his grandfather, William Lewis Corporon, who attended the
United Methodist Church of the Resurrection in Leawood.

The Rev. Adam Hamilton, the church’s senior pastor, shared
the news with church members at the beginning of the evening
Palm Sunday service.”

Update of 10:48 PM — A related photo:

Wednesday, March 5, 2014

Rosenhain and Göpel Again

Filed under: General — Tags: , — m759 @ 8:25 PM

IMAGE- Rosenhain, Göpel, and hyperelliptic curves

See also Rosenhain and Göpel in the Wikipedia
article Kummer surface, and in this journal.

Related material: user @hyperelliptic on Twitter.

Thursday, February 27, 2014

Sacred Space, continued

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

"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."

— Brian O'Doherty, "Inside the White Cube"

Cube  spaces exist also in mathematics.

Saturday, February 15, 2014

Rosenhain and Göpel

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

(Continued)

See The Oslo Version in this journal and the New Year’s Day 2014 post.
The pictures of the 56 spreads in that post (shown below) are based on
the 20 Rosenhain and 15 Göpel tetrads that make up the 35 lines of
PG(3,2), the finite projective 3-space over the 2-element Galois field.

IMAGE- The 56 spreads in PG(3,2)

Click for a larger image.

Saturday, September 21, 2013

Mathematics and Narrative (continued)

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

Mathematics:

A review of posts from earlier this month —

Wednesday, September 4, 2013

Moonshine

Filed under: Uncategorized — m759 @ 4:00 PM

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

Thursday, September 5, 2013

Moonshine II

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

(Continued from yesterday)

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

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

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

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

Narrative:

Aooo.

Happy birthday to Stephen King.

Friday, July 5, 2013

Mathematics and Narrative (continued)

Filed under: General,Geometry — Tags: , , — m759 @ 6:01 PM

Short Story — (Click image for some details.)

IMAGE- Andries Brouwer and the Galois Tesseract

Parts of a longer story —

The Galois Tesseract and Priority.

Thursday, April 25, 2013

Rosenhain and Göpel Revisited

Filed under: General,Geometry — Tags: , — m759 @ 5:24 PM

Some historical background for today's note on the geometry
underlying the Curtis Miracle Octad Generator (MOG):

IMAGE- Bateman in 1906 on Rosenhain and Göpel tetrads

The above incidence diagram recalls those in today's previous post
on the MOG, which is used to construct the large Mathieu group M24.

For some related material that is more up-to-date, search the Web
for Mathieu + Kummer .

Tuesday, March 19, 2013

Mathematics and Narrative (continued)

Filed under: General,Geometry — Tags: , — m759 @ 10:18 AM

Angels & Demons meet Hudson Hawk

Dan Brown's four-elements diamond in Angels & Demons :

IMAGE- Illuminati Diamond, pp. 359-360 in 'Angels & Demons,' Simon & Schuster Pocket Books 2005, 448 pages, ISBN 0743412397

The Leonardo Crystal from Hudson Hawk :

Hudson:

Mathematics may be used to relate (very loosely)
Dan Brown's fanciful diamond figure to the fanciful
Leonardo Crystal from Hudson Hawk 

"Giving himself a head rub, Hawk bears down on
the three oddly malleable objects. He TANGLES 
and BENDS and with a loud SNAP, puts them together,
forming the Crystal from the opening scene."

— A screenplay of Hudson Hawk

Happy birthday to Bruce Willis.

Saturday, October 6, 2012

Red October, continued*

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

"At Cambridge, where he studied in the 30s, he had
a reputation for omniscience. Running the local
Communist party cell from the set of college rooms
beneath Wittgenstein's, the youthful Hobsbawm was
invited to join the exclusive Apostles society."

Mark Mazower  in The Guardian , Oct. 1, 2012

* See related posts from Oct. 1, 2, and 5, 2012.

Tuesday, October 2, 2012

Red October

Filed under: General — Tags: — m759 @ 10:00 PM

(Continued)

IMAGE- Klein-group picture by Rosalind Krauss in essay titled 'In the Master's Bedroom'

"In the master's bedroom, they gathered for the feast…."
— Suggested by the current film Hotel Transylvania

"For every kind of vampire, there is a kind of cross."
– Thomas Pynchon, Gravity's Rainbow

Related material— the Feast of Saint Patrick in 2009.

Saturday, February 25, 2012

The Rock

Filed under: General — m759 @ 9:26 PM

(Continued. See previous post and Red and Gray in this journal.)

"Give faith a fighting chance." —Country song

From a post of June 3, 2007—

Related illustration relevant to theology—

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

For some background, see Cube Trinity in this journal.

For greater depth, see Levering's Scripture and Metaphysics:
Aquinas and the Renewal of Trinitarian Theology 
,
Blackwell, 2004, page 150.

Saturday, March 12, 2011

A Songwriter’s Apology

Filed under: General — m759 @ 7:59 PM

From this evening's online New York Times , a death from yesterday

Mr. Hardy’s song “St. Clare” was covered by Ms. Vega
and appears on her 2001 album “Songs in Red and Gray.”

[Lyrics here.]

See also "red and gray" and "The Eye" in this journal.

Tuesday, March 1, 2011

Women’s History Month

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

Susanne for Suzanne

From pages 7-8 of William York Tindall’s Literary Symbolism  (Columbia U. Press, 1955)—

                                     ... According to Cassirer's Essay 
on Man, as we have seen, art is a symbolic form, parallel in respect 
of this to religion or science. Each of these forms builds up a universe 
that enables man to interpret and organize his experience; and each 
is a discovery, because a creation, of reality. Although similar in func- 
tion, the forms differ in the kind of reality built. Whereas science
builds it of facts, art builds it of feelings, intuitions of quality, and 
the other distractions of our inner life— and in their degrees so do 
myth and religion. What art, myth, and religion are, Cassirer con- 
fesses, cannot be expressed by a logical definition. 

Nevertheless, let us see what Clive Bell says about art. He calls 
it "significant form," but what that is he is unable to say. Having 
no quarrel with art as form, we may, however, question its signifi- 
cance. By significant he cannot mean important in the sense of 
having import, nor can he mean having the function of a sign; 
for to him art, lacking reference to nature, is insignificant. Since, 
however, he tells us that a work of art "expresses" the emotion of 
its creator and "provokes" an emotion in its contemplator,he seems 
to imply that his significant means expressive and provocative. The 
emotion expressed and provoked is an "aesthetic emotion," contem- 
plative, detached from all concerns of utility and from all reference. 

Attempting to explain Bell's significant form, Roger Fry, equally 
devoted to Whistler and art for art's sake, says that Flaubert's "ex- 
pression of the idea" is as near as he can get to it, but neither Flaubert 
nor Fry tells what is meant by idea. To "evoke" it, however, the artist 
creates an "expressive design" or "symbolic form," by which the 
spirit "communicates its most secret and indefinable impulses." 

Susanne Langer,who occupies a place somewhere between Fry 
and Cassirer, though nearer the latter, once said in a seminar that a 
work of art is an "unassigned syntactical symbol." Since this defini- 

End of page 7 

tion does not appear in her latest book, she may have rejected it, but 
it seems far more precise than Fry's attempt. By unassigned she prob- 
ably intends insignificant in the sense of lacking sign value or fixed 
reference; syntactical implies a form composed of parts in relation- 
ship to one another; and a symbol, according to Feeling and Form, 
is "any device whereby we are enabled to make an abstraction." Too 
austere for my taste, this account of symbol seems to need elaboration, 
which, to be sure, her book provides. For the present, however, taking 
symbol to mean an outward device for presenting an inward state, 
and taking unassigned and syntactical as I think she uses them, let 
us tentatively admire her definition of the work of art.

http://www.log24.com/log/pix11/110301-VegaSongsSm.jpg

http://www.log24.com/log/pix11/110301-Diamond-RedOnGray.bmp

Oh, the red leaf looks to the hard gray stone
To each other, they know what they mean

— Suzanne Vega, “Song in Red and Gray

Saturday, July 11, 2009

Saturday July 11, 2009

Filed under: General,Geometry — m759 @ 7:28 AM
Mercilessly Tasteful

Diamond logo

Suzanne Vega, 'Songs in Red and Gray'


Related material:

The Literary Symbol
by William York Tindall

(Columbia University Press,
Epiphany 1955)

Friday, May 18, 2007

Friday May 18, 2007

Filed under: General — Tags: — m759 @ 6:29 AM
Devil in the Details

Today’s Harvard Crimson:

“Paul B. Davis ’07-’08, who contributed to a collection of student essays written in 2005 on the purpose and structure of a Harvard education, said that ‘the devil is in the details’….”

From the weblog of Peter Woit
:

The New Yorker keeps its physics theme going this week with cover art that includes a blackboard full of basic equations from quantum mechanics.”

The image “http://www.log24.com/log/pix07/070518-Cover2.jpg” cannot be displayed, because it contains errors.
May 21, 2007
New Yorker cover

The image “http://www.log24.com/log/pix07/070518-CoverDetail.jpg” cannot be displayed, because it contains errors.
 
Detail

The detail suggests
the following
religious images from
Twelfth Night 2003:

Devil’s Claws, or
Hourglass Var. 3

Yankee Puzzle, or
Hourglass Var. 5

 
“Mercilessly tasteful”
 
Andrew Mueller,
review of Suzanne Vega’s
Songs in Red and Gray

Sunday, December 11, 2005

Sunday December 11, 2005

Filed under: General — m759 @ 6:00 PM

Classic Sixties

The image “http://www.log24.com/log/pix05B/051211-Collins.jpg” cannot be displayed, because it contains errors.

And Jesus was a sailor
When he walked
   upon the water…”
Leonard Cohen   

meets the timeless
Satori at Pearl Harbor:

“Mercilessly tasteful.”
 — Andrew Mueller,
review of Suzanne Vega’s
Songs in Red and Gray

Related material:

The image “http://www.log24.com/log/pix05B/051211-SpiritWhole.jpg” cannot be displayed, because it contains errors.

Philosophy in
Blue and Green

Sunday, December 19, 2004

Sunday December 19, 2004

Filed under: General — Tags: — m759 @ 2:56 PM
Sunday Sermon
on Saturday’s Numbers

Today’s New York Times on a rabbi who died in Jerusalem on Sunday, Dec. 5:

“In the 1950’s, he was a vocal advocate for the relaxation of New York City’s blue laws, which forbade many kinds of commerce on Sundays but not on Saturdays. The laws were repealed in the 1970’s. Solomon Joseph Sharfman was born on Nov. 1, 1915, in Treblinka, Poland; his family immigrated to the United States five years later. His father, Rabbi Label Sharfman, worked as a shochet, or ritual slaughterer….”

Saturday’s lottery numbers from Pennsylvania, the State of Grace:

Saturday Midday:  144
Saturday Evening: 360

A Sunday Sermon:

“Once upon a time there was a sensible straight line who was hopelessly in love with a beautiful dot. But the dot, though perfect in every way, only had eyes for a wild and unkempt squiggle. All of the line’s romantic dreams were in vain, until he discovered . . . angles! Now, with newfound self-expression, he can be anything he wants to be–a square….”

Related material:

The image “http://www.log24.com/log/pix04B/041219-Line.jpg” cannot be displayed, because it contains errors.

(See Song in Red and Gray
and The Dot and the Line.)

Friday, December 17, 2004

Friday December 17, 2004

Filed under: General — Tags: — m759 @ 12:05 PM

Song in Red and Gray

The image “http://www.log24.com/log/pix04B/041217-WaterFlower2.jpg” cannot be displayed, because it contains errors.   The image “http://www.log24.com/log/pix04B/041217-Agnes.jpg” cannot be displayed, because it contains errors.

From today's New York Times:

Agnes Martin, Abstract Painter, Dies at 92

Background: entry of 7 PM Wednesday.

Wednesday, December 15, 2004

Wednesday December 15, 2004

Filed under: General — m759 @ 7:00 PM

Judeo-Christian Heritage:
The Wiener Kreis

The meditation below was suggested by this passage:

“… the belief that any sensible discourse had to be formulated within the rules of the scientific language, avoiding the non sense of the ordinary language. This belief, initially expressed by Wittgenstein as aphorisms, was later formalized by the Wiener Kreis [Vienna Circle] as a ‘logical construction of the world’….”

“Deeply Vulgar”

— Epithet applied in 2003 to
Harvard President Lawrence Summers.

“Examples are the stained-glass
windows of knowledge.”
— Vladimir Nabokov

 

In today’s Crimson:
The image “http://www.log24.com/log/pix04B/041215-Crimson.jpg” cannot be displayed, because it contains errors.

 

Only moderately vulgar, with its sniggering pop-culture reference. But it  should be
Frankfurter
Professor of Law.

 

 

The image “http://www.log24.com/log/pix04B/041215-Frankfort.gif” cannot be displayed, because it contains errors.

 

Those seeking relief from
Judeo-Christian vulgarity may enjoy
the Buddhist Suzanne Vega’s

Songs in Red and Gray.”

“Mercilessly tasteful”
Andrew Mueller

Sunday, January 5, 2003

Sunday January 5, 2003

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

Whirligig

Thus the whirligig of time brings in his revenges.
Twelfth Night. Act v. Sc. 1.

Twelfth night is the night of January 5-6.

Tonight is twelfth night in Australia; 4 AM Jan. 5
in New York City is 8 PM Jan. 5 in Sydney.


An October 6 entry:

Twenty-first Century Fox

On Sunday, October 6, 1889, the Moulin Rouge music hall opened in Paris, an event that to some extent foreshadowed the opening of Fox Studios Australia in Sydney on November 7, 1999.  The Fox ceremonies included, notably, Kylie Minogue singing "Diamonds are a Girl's Best Friend." 

 

Red Windmill

Kylie Minogue

For the mathematical properties of the red windmill (moulin rouge) figure at left, see Diamond Theory.

An October 5 entry:

The Message from Vega

"Mercilessly tasteful"
 — Andrew Mueller,
review of Suzanne Vega's
"Songs in Red and Gray"


In accordance with the twelfth-night
"whirligig of time" theme,
here are two enigmatic quilt blocks:

Devil's Claws, or
Hourglass Var. 3

Yankee Puzzle, or
Hourglass Var. 5

 
One can approach these symbols in either a literary or a mathematical fashion. For a purely mathematical discussion of the differences in the two symbols' structure, see Diamond Theory. Those who prefer literary discussions may make up their own stories.
 
"Plato is wary of all forms of rapture other than reason's. He is most deeply leery of, because himself so susceptible to, the literary imagination. He speaks of it as a kind of holy madness or intoxication and goes on to link it to Eros, another derangement that joins us, but very dangerously, with the gods."
 
Rebecca Goldstein in The New York Times,
    December 16, 2002 
 
"It's all in Plato, all in Plato; bless me,
what do they teach them at these schools?"
 
— C. S. Lewis in the Narnia Chronicles 

Saturday, December 7, 2002

Saturday December 7, 2002

Filed under: General — m759 @ 4:01 PM

Satori at Pearl Harbor

The following old weblog entry seems
relevant both to the Zen concept of satori,
or “awakening,” and to Pearl Harbor Day.

Saturday, October 5, 2002… 11:30 PM

The Message from Vega

“Mercilessly tasteful”
 — Andrew Mueller,
review of Suzanne Vega’s
Songs in Red and Gray

The appropriate response to Vega’s Buddhism today seems to be the following classic by James Taylor:

“Won’t you look down upon me, Jesus?
You’ve got to help me make a stand…”

This is today’s new site background music.

For more log entries relevant to today, see 

Satori at Pearl Harbor.

Saturday, October 5, 2002

Saturday October 5, 2002

Filed under: General — m759 @ 11:30 PM

The Message from Vega

“Mercilessly tasteful”
 — Andrew Mueller,
review of Suzanne Vega’s
Songs in Red and Gray

 

Wednesday, October 9, 2019

The Joy of Six

Note that in the pictures below of the 15 two-subsets of a six-set,
the symbols 1 through 6 in Hudson's square array of 1905 occupy the
same positions as the anticommuting Dirac matrices in Arfken's 1985
square array. Similarly occupying these positions are the skew lines
within a generalized quadrangle (a line complex) inside PG(3,2).

Anticommuting Dirac matrices as spreads of projective lines

Related narrative The "Quantum Tesseract Theorem."

Tuesday, August 27, 2019

Tiger Leaps

Filed under: General — Tags: , — m759 @ 10:33 AM

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

See also Tiger in this journal, esp.

The image “http://www.log24.com/log/pix05/050123-Tiger.JPG” cannot be displayed, because it contains errors.   and . . .

other "Death and the Spirit" posts.

Monday, August 19, 2019

A Couple of Tots

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

The title is from the post "Child's Play" of May 21, 2012 . . .

"It seems that only one course is open to the philosopher
who values knowledge and truth above all else. He must
refuse to accept from the champions of the forms the
doctrine that all reality is changeless [and exclusively
immaterial], and he must turn a deaf ear to the other party
who represent reality as everywhere changing [and as only
material]. Like a child begging for 'both', he must declare
that reality or the sum of things is both at once  [το όν τε και
το παν συναμφότερα] (Sophist  246a-249d)."

Related material —

"Schoolgirl Space: 1984 Revisited" (July 9, 2019) and
posts tagged Tetrahedron vs. Square.

Sunday, August 18, 2019

Structure at Pergamon

Filed under: General — Tags: — m759 @ 2:35 AM

Some background for The Epstein Chronicles

"What modern painters
are trying to do,
if they only knew it,
is paint invariants."

— James J. Gibson, Leonardo,
    Vol. 11, pp. 227-235.
    Pergamon Press Ltd., 1978

See also Robert Maxwell,
Frank Oppenheimer,
and the history of Leonardo .

Click the above Pergamon Press image
for Pergamon-related material.

Wednesday, August 14, 2019

Double Veil

Filed under: General — Tags: , , — m759 @ 9:48 PM

"If you want to win, you need to know just one thing and not to waste your time
on anything else: the pleasures of erudition are reserved for losers. The more
a person knows, the more things have gone wrong."

— Eco, Umberto. Numero Zero  (p. 9). HMH Books. Kindle Edition. 

"All this notwithstanding, I dreamed what all losers dream, about one day writing
a book that would bring me fame and fortune. To learn how to become a great
writer, I became what in the last century was called the nègre  (or ghostwriter,
as they say today, to be politically correct) for an author of detective stories who
gave himself an American name to improve sales, like the actors in spaghetti
westerns. But I enjoyed working in the shadows, hidden behind a double veil
(the Other’s and the Other’s other name)."

— Eco, Umberto. Numero Zero  (pp. 9-10). HMH Books. Kindle Edition. 

How's this for a double veil, Umberto?

Boeing/Being Meets the Flying Spaghetti Monster . . .

The Mask of Zero

Filed under: General — Tags: , — m759 @ 12:55 PM

For the title, see Zero: Both Real and Imaginary (a Log24 search).

The title was suggested by the previous post, by Zorro Ranch,
by the classic 1967 film The Producers , and by . . .

Related material —

Vanity Fair  on Sept. 8, 2017, celebrated the young actress
who played Beverly Marsh in the 2017 film version of
Stephen King's IT . See a post from her 12th birthday —
"Winter's Game" — that touches upon Maori themes.

More generally, see Bester + Deceivers in this  journal.

And for the Church of Synchronology . . .
See posts related to the above Vanity Fair  date.

Sunday, July 14, 2019

Old Pathways in Science:

Filed under: General — Tags: , — m759 @ 12:37 PM

The Quantum Tesseract Theorem Revisited

From page 274 — 

"The secret  is that the super-mathematician expresses by the anticommutation
of  his operators the property which the geometer conceives as  perpendicularity
of displacements.  That is why on p. 269 we singled out a pentad of anticommuting
operators, foreseeing that they would have an immediate application in describing
the property of perpendicular directions without using the traditional picture of space.
They express the property of perpendicularity without the picture of perpendicularity.

Thus far we have touched only the fringe of the structure of our set of sixteen E-operators.
Only by entering deeply into the theory of electrons could I show the whole structure
coming into evidence."

A related illustration, from posts tagged Dirac and Geometry —

Anticommuting Dirac matrices as spreads of projective lines

Compare and contrast Eddington's use of the word "perpendicular"
with a later use of the word by Saniga and Planat.

Tuesday, June 25, 2019

Analogy

Filed under: General — Tags: — m759 @ 6:36 AM

Monday, June 24, 2019

Ex Fano Apollinis

Filed under: General — Tags: — m759 @ 11:57 PM

Sunday, May 19, 2019

The Building Blocks of Geometry

Filed under: General — Tags: , — m759 @ 10:21 PM

From "On the life and scientific work of Gino Fano
by Alberto Collino, Alberto Conte, and Alessandro Verra,
ICCM Notices , July 2014, Vol. 2 No. 1, pp. 43-57 —

" Indeed, about the Italian debate on foundations of Geometry, it is not rare to read comments in the same spirit of the following one, due to Jeremy Gray13. He is essentially reporting Hans Freudenthal’s point of view:

' When the distinguished mathematician and historian of mathematics Hans Freudenthal analysed Hilbert’s  Grundlagen he argued that the link between reality and geometry appears to be severed for the first time in Hilbert’s work. However, he discovered that Hilbert had been preceded by the Italian mathematician Gino Fano in 1892. . . .' "

13 J. Gray, "The Foundations of Projective Geometry in Italy," Chapter 24 (pp. 269–279) in his book Worlds Out of Nothing , Springer (2010).


Restoring the severed link —

Structure of the eightfold cube

See also Espacement  and The Thing and I.
 

Related material —

 
 

Saturday, December 22, 2018

Cremona-Richmond

Filed under: General,Geometry — Tags: , — m759 @ 12:34 PM

The following are some notes on the history of Clifford algebras
and finite geometry suggested by the "Clifford Modules" link in a
Log24 post of March 12, 2005

A more recent appearance of the configuration —

Wednesday, December 12, 2018

An Inscape for Douthat

Some images, and a definition, suggested by my remarks here last night
on Apollo and Ross Douthat's remarks today on "The Return of Paganism" —

Detail of Feb. 20, 1986, note by Steven H. Cullinane on Weyl's 'relativity problem'

Kibler's 2008 'Variations on a theme' illustrated.

In finite geometry and combinatorics,
an inscape  is a 4×4 array of square figures,
each figure picturing a subset of the overall 4×4 array:


 

Related material — the phrase
"Quantum Tesseract Theorem" and  

A.  An image from the recent
      film "A Wrinkle in Time" — 

B.  A quote from the 1962 book —

"There's something phoney
in the whole setup, Meg thought.
There is definitely something rotten
in the state of Camazotz."

Sunday, November 18, 2018

Space Music

Filed under: General,Geometry — Tags: , , — m759 @ 9:27 AM

'The Eddington Song,' based on 'The Philosophy of Physical Science,' p. 141 (1939)

Update of Nov. 19 —

"Design is how it works." — Steve Jobs

See also www.cullinane.design.

Tuesday, September 25, 2018

Trinity

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

See some posts related to three names
associated with Trinity College, Cambridge —

Atiyah + Shaw + Eddington .

Saturday, September 1, 2018

Ron Shaw — D. 21 June 2016

The date of Ron Shaw's 2016 death appears to be June 21:

http://www.log24.com/log/pix18/180901-Ron_Shaw-d_21_June_2016-LMS-500w.jpg

All other Internet sources I have seen omit the June 21 date.

This  journal on that date —

http://www.log24.com/log/pix18/180901-The_Central_Structure-21_June_2016.jpg

Wednesday, August 22, 2018

Castle Rock

Filed under: General — Tags: — m759 @ 2:03 PM

See the title in a TV review* from io9 this morning and in
this  journal.

http://www.log24.com/log/pix18/180822-io9-URL-and-logo.jpg

* Spoiler alert

Apple

Filed under: General — Tags: — m759 @ 1:06 PM

http://www.log24.com/log/pix18/180822-Mirror_Mirror-ad-One_Bad_Apple-2012.jpg

Tuesday, August 21, 2018

Purported Endgame

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

http://www.log24.com/log/pix18/180821-NYT-Corrections-Japanese-IMA-NOW.jpg

A search for "IMA" yields, at ima.org.au . . .

"Since 1975, the Institute of Modern Art (IMA) has been Queensland’s 
leading independent forum for art and its discourses." And

http://www.log24.com/log/pix18/180821-IMA-Brisbane-Mirror_Mirror_Then_and_Now-text.jpg

http://www.log24.com/log/pix18/180821-IMA-Brisbane-Mirror_Mirror_Then_and_Now-500wide.jpg

"Clog, therefore, purple Jack and crimson Jill."

— Wallace Stevens

Available Light

Filed under: General — Tags: — m759 @ 12:16 PM

http://www.log24.com/log/pix18/180821-Jesse_Harris-AKA_Playland-co-writer.jpg

Click the image above for an interview dated Nov. 9, 2015.
Also on that date —

http://www.log24.com/log/pix18/180821-Nov_9_2015-Forever_Now-500w.jpg

Wednesday, August 1, 2018

Abschattungen*

Filed under: General — Tags: — m759 @ 2:00 PM

“… I realized that to me, Gödel and Escher and Bach
were only shadows cast in different directions
by some central solid essence.
I tried to reconstruct the central object . . . ."

— Douglas Hofstadter (1979)

See also posts of July 23, 2007, and April 7, 2018.

* Term from a visual-culture lexicon —

“Ready Player One” Mnemonic:

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

O AS IS

 

See also other posts tagged "Is and As."

Tuesday, July 31, 2018

A is for Abschattungen

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

Max Bialystock discovers a new playwright

Lexicon

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

"A blank underlies the trials of device." — Wallace Stevens

IMAGE- The ninefold square .

Wednesday, May 16, 2018

Review

Filed under: General — Tags: , — m759 @ 5:52 PM

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

See as well a Log24 search for Isaac Singer.

Same Old Story

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

. . . as time goes by.

Friday, April 13, 2018

Philosophy 101

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

See also Log24 posts now tagged "Is and As."

Monday, March 12, 2018

“Quantum Tesseract Theorem?”

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

Remarks related to a recent film and a not-so-recent film.

For some historical background, see Dirac and Geometry in this journal.

Also (as Thas mentions) after Saniga and Planat —

The Saniga-Planat paper was submitted on December 21, 2006.

Excerpts from this  journal on that date —

A Halmos tombstone and the tale of HAL and the pod bay doors

     "Open the pod bay doors, HAL."

Thursday, March 8, 2018

Stories

Filed under: General — m759 @ 7:00 PM

"We tell ourselves stories . . . ." — Joan Didion

New York Times Wire, 6:40 PM ET Thursday, March 8, 2018 

3h ago
GRAY MATTER
How Lies Spread Online

They diffuse farther, faster and more broadly than the truth does.

4h ago
It’s True: False News Spreads Faster and Wider.
And Humans Are to Blame.

False claims posted on Twitter were 70 percent more likely
to be shared than the truth, researchers at M.I.T. found.
And people appear to prefer false news.

Monday, February 26, 2018

The Unfolding

Filed under: General,Geometry — Tags: — m759 @ 9:20 AM

From the website of Richard P. Gabriel

" As part of my studies, I came up with a 'theory of poetry' 
based loosely on Christopher Alexander’s 'Nature of Order.' "
[The Alexander link is mine, not Gabriel’s.]

A phrase from this  journal a year ago today — "poetic order" —
links to the theory of Gabriel —

From Gabriel's "The Nature of Poetic Order" —

Positive Space

• Positive space is the characteristic of a center
that moves outward from itself, seemingly oozing life
rather than collapsing on itself
• An image that resonates is showing positive space
• A word that has many connotations that fit with the
other centers in the poem is showing positive space
• It is an expansion outward rather than a contraction
inward, and it shows that the poem is unfolding
in front of us and not dying

Related material —

From a post of April 26, 2017

Sunday, February 25, 2018

The Dark, Seductive Art of Groton

Filed under: General — Tags: — m759 @ 9:26 AM

A sequel to Friday's "The Dark, Seductive Art of Phillips Exeter."

From Twitter today —

Groton School‏ @GrotonSchool  Feb 1

Groton School Theater Department Presents: CABARET
Friday, February 23rd at 7:30 pm
Saturday, February 24th at 7:30 pm
Sunday, February 25th at 3 pm
All performances are free to the public. Please make ticket
reservations in advance online: http://bit.ly/CABARET2018.

Friday, February 23, 2018

The Dark, Seductive Art of Phillips Exeter

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

From two pedagogues in Montana —

https://www.nctm.org/Publications/
Mathematics-Teaching-in-Middle-School/
2016/Vol22/Issue1/Quilt-Block-Symmetries/

Related material from author Dan Brown's father,
a pedagogue who taught at Phillips Exeter Academy :

Click the above image for some background.

Related material from Log24 —
 

Verwandlungslehre.
 

Compare and contrast with the above
Transformational Geometry  cover:

Related material from Vienna — The previous post and
Wittgenstein on Bewitchment.

See as well . . .

Click to enlarge.

Snow Games

Filed under: General — Tags: — m759 @ 9:42 AM

'Origin' (NOT by Dan Brown)

Related material — (Click to enlarge) —

"Risin' up to the challenge of our rival"

Eye of the Tiger

Detail —

Saturday, February 17, 2018

The Binary Revolution

Filed under: General,Geometry — Tags: , — m759 @ 5:00 PM

Michael Atiyah on the late Ron Shaw

Phrases by Atiyah related to the importance in mathematics
of the two-element Galois field GF(2) —

  • "The digital revolution based on the 2 symbols (0,1)"
  • "The algebra of George Boole"
  • "Binary codes"
  • "Dirac's spinors, with their up/down dichotomy"

These phrases are from the year-end review of Trinity College,
Cambridge, Trinity Annual Record 2017 .

I prefer other, purely geometric, reasons for the importance of GF(2) —

  • The 2×2 square
  • The 2x2x2 cube
  • The 4×4 square
  • The 4x4x4 cube

See Finite Geometry of the Square and Cube.

See also today's earlier post God's Dice and Atiyah on the theology of 
(Boolean) algebra vs. (Galois) geometry:

God’s Dice

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

On a Trinity classmate of Ian Macdonald (see previous post)—

Atiyah's eulogy of Shaw in Trinity Annual Record 2017 
is on pages 137 through 146.  The conclusion —

 

Sunday, December 10, 2017

Geometry

Google search result for Plato + Statesman + interlacing + interweaving

See also Symplectic in this journal.

From Gotay and Isenberg, “The Symplectization of Science,”
Gazette des Mathématiciens  54, 59-79 (1992):

“… what is the origin of the unusual name ‘symplectic’? ….
Its mathematical usage is due to Hermann Weyl who,
in an effort to avoid a certain semantic confusion, renamed
the then obscure ‘line complex group’ the ‘symplectic group.’
… the adjective ‘symplectic’ means ‘plaited together’ or ‘woven.’
This is wonderfully apt….”

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

The above symplectic  figure appears in remarks on
the diamond-theorem correlation in the webpage
Rosenhain and Göpel Tetrads in PG(3,2). See also
related remarks on the notion of  linear  (or line ) complex
in the finite projective space PG(3,2) —

Anticommuting Dirac matrices as spreads of projective lines

Ron Shaw on the 15 lines of the classical generalized quadrangle W(2), a general linear complex in PG(3,2)

Thursday, November 30, 2017

The Matrix for Quantum Mystics

Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 10:29 PM

Scholia on the title — See Quantum + Mystic in this journal.

The Matrix of Lévi-Strauss

"In Vol. I of Structural Anthropology , p. 209, I have shown that
this analysis alone can account for the double aspect of time
representation in all mythical systems: the narrative is both
'in time' (it consists of a succession of events) and 'beyond'
(its value is permanent)." — Claude Lévi-Strauss, 1976

I prefer the earlier, better-known, remarks on time by T. S. Eliot
in Four Quartets , and the following four quartets (from
The Matrix Meets the Grid) —

.

From a Log24 post of June 26-27, 2017:

A work of Eddington cited in 1974 by von Franz

See also Dirac and Geometry and Kummer in this journal.

Ron Shaw on Eddington's triads "associated in conjugate pairs" —

For more about hyperbolic  and isotropic  lines in PG(3,2),
see posts tagged Diamond Theorem Correlation.

For Shaw, in memoriam — See Contrapuntal Interweaving and The Fugue.

Friday, November 24, 2017

The Matrix Meets the Grid

Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 2:00 PM

The Matrix —

  The Grid —

  Picturing the Witt Construction

     "Read something that means something." — New Yorker  ad

Thursday, November 23, 2017

The Matrix

Filed under: General — Tags: — m759 @ 10:00 PM

David Brooks in The New York Times  today

"We once had a unifying national story, celebrated each Thanksgiving.
It was an Exodus story. Americans are the people who escaped oppression,
crossed a wilderness and are building a promised land. The Puritans brought
this story with them. Each wave of immigrants saw themselves in this story.
The civil rights movement embraced this story.

But we have to admit that many today do not resonate with this story. . . .

Today, we have no common national narrative, no shared way
of interpreting the flow of events. Without a common story,
we don’t know what our national purpose is. We have no
common set of goals or ideals.

We need a new national narrative."

From a post of August 15, 2010

http://www.log24.com/log/pix10B/100815-NeoAndOracle.jpg

For some background, see Java Jive and Today's Theology.

Related readings —

From 1928:

From the previous post:

"Thus, instead of Propp's chronological scheme,
in which the order of succession of events
is a feature of the structure . . .
another scheme should be adopted, which would present
a structural model defined as the group of transformations
of a small number of elements. This scheme would appear
as a matrix . . . ."

Claude Lévi-Strauss, 1960 

Lévi-Strauss vs. Propp

Filed under: General,Geometry — Tags: , — m759 @ 12:25 PM
 

​Claude Lévi-Strauss

From his "Structure and Form:
Reflections on a Work by Vladimir Propp
" *

To maintain. as I have done. that the permutability of contents is not arbitrary amounts to saying that, if the analysis is carried to a sufficiently deep level, behind diversity we will discover constancy. And, of course. the avowed constancy of form must not hide from us that functions are also permutable.

The structure of the folktale as it is illustrated by Propp presents a chronological succession of qualitatively distinct functions. each constituting an independent genre. One can wonder whether—as with dramatis personae and their attributes— Propp does not stop too soon, seeking the form too close to the level of empirical observation. Among the thirty-one functions that he distinguishes, several are reducible to the same  function reappearing at different  moments of the narrative but after undergoing one or a number of transformations . I have already suggested that this could be true of the false hero (a transformation of the villain), of assigning a difficult task (a transformation of the test), etc. (see p. 181 above), and that in this case the two parties  constituting the fundamental tale would themselves be transformations of each other.

Nothing prevents pushing this reduction even further and analyzing each separate partie  into a small number of recurrent functions, so that several of Propp's functions would constitute groups of transformations of one and the same function. We could treat the "violation" as the reverse of the "prohibition" and the latter as a negative transformation of the "injunction." The "departure" of the hero and his "return" would appear as the negative and positive expressions of the same disjunctive function. The "quest" of the hero (hero pursues someone or something) would become the opposite of "pursuit" (hero is pursued by something or someone), etc.

In Vol. I of Structural Anthropology , p. 209, I have shown that this analysis alone can account for the double aspect of time representation in all mythical systems: the narrative is both "in time" (it consists of a succession of events) and "beyond" (its value is permanent). With regard to Propp's theories my analysis offers another advantage: I can reconcile much better than Propp himself  his principle of a permanent order of wondertale elements with the fact that certain functions or groups of functions are shifted from one tale to the next (pp. 97-98. p. 108) If my view is accepted, the chronological succession will come to be absorbed into an atemporal matrix structure whose form is indeed constant. The shifting of functions is then no more than a mode of permutation (by vertical columns or fractions of columns).

These critical remarks are certainly valid for the method used by Propp and for his conclusions. However. it cannot be stressed enough that Propp envisioned them and in several places formulated with perfect clarity the solutions I have just suggested. Let us take up again from this viewpoint the two essential themes of our discussion: constancy of the content (in spite of its permutability) and permutability of functions (in spite of their constancy).

* Translated from a 1960 work in French.  It appeared in English as Chapter VIII
of Structural Anthropology, Volume 2  (U. of Chicago Press, 1976).  Chapter VIII
was originally published in Cahiers de l'Institut de Science 
Économique Appliquée , 
No. 9 (Series M, No. 7) (Paris: ISEA, March 1960).

See also "Lévi-Strauss" + Formula  in this journal.

Some background related to the previous post

Wednesday, November 22, 2017

Goethe on All Souls’ Day

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

David E. Wellbery on Goethe

From an interview published on 2 November 2017 at

http://literaturwissenschaft-berlin.de/interview-with-david-wellbery/

as later republished in 

https://thepointmag.com/2017/dialogue/
irreducible-significance-david-wellbery-literature-goethe-cavell
 —

 

The logo at left above is that of The Point .
The menu icon at right above is perhaps better
suited to illustrate Verwandlungslehre .

Weyl on symmetry, the eightfold cube, the Fano plane, and trigrams of the I Ching

Sunday, October 29, 2017

Sunday in the Park

Filed under: General — Tags: — m759 @ 1:18 PM

http://www.abc.net.au/news/2017-10-29/
mexico-city-day-of-dead-parade-honours-quake-rescuers/
9097134

Scholium —

Related material —  Sunday in the Park  in this  journal.

Damnation… Or Not?

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

Related material —

Faust Vivifies Death with Wit and Humor
by April H. N. Yee, Harvard Crimson , Feb. 7, 2008.

See as well all posts now tagged Willow and Mandorla.

Tuesday, October 17, 2017

The Movement of Analogy

Filed under: General,Geometry — Tags: , — m759 @ 4:20 PM

The title is a phrase by Octavio Paz from today's post
"Status Symbols."

Other phrases from a link target in Sunday's post 
The Strength at the Centre

                                a single world
In which he is and as and is are one.

See also Four Dots in this journal.

Status Symbols

Filed under: General,Geometry — Tags: — m759 @ 2:02 PM

"Status: Defunct"  

As is now its owner, who reportedly
died at 80 on Sunday, October 15, 2017.

In memoriam —

Excerpts from Log24 posts on Sunday night 
and yesterday evening

http://www.log24.com/log/pix11/110203-Scholia.jpg.

" … listen: there's a hell
of a good universe next door; let's go"

— e. e. cummings

Some literary background —

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by Helen Lane 

Sunday, October 15, 2017

The Strength at the Centre

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

The title, a phrase from a poem by Wallace Stevens,
was suggested by the previous post, "Center."

See posts tagged May 19 Gestalt in particular, 
May 19, 2007 — "Point of View."

Saturday, October 14, 2017

Center

Rosalind Krauss in 1978

"To get inside the systems of this work,
whether LeWitt's or Judd's or Morris's,
is precisely to enter
a world without a center,
a world of substitutions and transpositions
nowhere legitimated by the revelations
of a transcendental subject. This is the strength
of this work, its seriousness, and its claim to modernity." 

Wikipedia

"The center of
the quaternion group,
Q8 = {1, −1, i, −i, j, −j, k, −k} ,
is {1, −1}."

Illustration from a post of Feb. 3,  2011

http://www.log24.com/log/pix11/110203-Scholia.jpg.

Tuesday, October 10, 2017

Another 35-Year Wait

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

The title refers to today's earlier post "The 35-Year Wait."

A check of my activities 35 years ago this fall, in the autumn
of 1982, yields a formula I prefer to the nonsensical, but famous,
"canonical formula" of Claude Lévi-Strauss.

The Lévi-Strauss formula

My "inscape" formula, from a note of Sept. 22, 1982 —

S = f ( f ( X ) ) .

Some mathematics from last year related to the 1982 formula —

Koen Thas, 'Unextendible Mututally Unbiased Bases' (2016)

See also Inscape in this  journal and posts tagged Dirac and Geometry.

Monday, July 3, 2017

Award Gala

Filed under: General — m759 @ 12:31 PM

Monday, June 26, 2017

Upgrading to Six

This post was suggested by the previous post — Four Dots —
and by the phrase "smallest perfect" in this journal.

Related material (click to enlarge) —

Detail —

From the work of Eddington cited in 1974 by von Franz —

See also Dirac and Geometry and Kummer in this journal.

Updates from the morning of June 27 —

Ron Shaw on Eddington's triads "associated in conjugate pairs" —

For more about hyperbolic  and isotropic  lines in PG(3,2),
see posts tagged Diamond Theorem Correlation.

For Shaw, in memoriam — See Contrapuntal Interweaving and The Fugue.

Four Dots

Analogies — "A : B  ::  C : D"  may be read  "A is to B  as  C is to D."

Gian-Carlo Rota on Heidegger…

"… The universal as  is given various names in Heidegger's writings….

The discovery of the universal as  is Heidegger's contribution to philosophy….

The universal 'as' is the surgence of sense in Man, the shepherd of Being.

The disclosure of the primordial as  is the end of a search that began with Plato….
This search comes to its conclusion with Heidegger."

— "Three Senses of 'A is B' in Heideggger," Ch. 17 in Indiscrete Thoughts
 

See also Four Dots in this journal. 

Some context:  McLuhan + Analogy.

Friday, June 23, 2017

A Kind of Cross

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

"For every kind of vampire, there is a kind of cross."

Gravity's Rainbow

See also Heidegger + Rift in this  journal.

“Information from the Middle of the Night”

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

The title is from an obituary in tonight's online New York Times.

Information —

See also another art publication cover from 1976 —

Thursday, May 11, 2017

Reopening the Tesseract

Filed under: General,Geometry — Tags: — m759 @ 11:27 AM

Dialogue from the film "Interstellar" —

Cooper: Did it work?

TARS: I think it might have.

Cooper: How do you know?

TARS: Because the bulk beings
            are closing the tesseract.

Related material — "Bulk apperception"
in this journal, and

Monday, May 8, 2017

New Pinterest Board

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

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

Sunday, May 7, 2017

Art Space

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

Detail of an image in the previous post

This suggests a review of a post on a work of art by fashion photographer
Peter Lindbergh, made when he was younger and known as "Sultan."

The balls in the foreground relate Sultan's work to my own.

Linguistic backstory —

The art space where the pieces by Talman and by Lindbergh
were displayed is Museum Tinguely in Basel.

As the previous post notes, the etymology of "glamour" (as in
fashion photography) has been linked to "grammar" (as in 
George Steiner's Grammars of Creation ). A sculpture by 
Tinguely (fancifully representing Heidegger) adorns one edition
of Grammars .

Yale University Press, 2001:

Tinguely, "Martin Heidegger,
Philosopher," sculpture, 1988

Saturday, April 8, 2017

A Perfect Nonentity

Filed under: General,Geometry — Tags: , — m759 @ 8:25 AM

The title is from Hume:

 "And were all my perceptions removed by death,
and could I neither think, nor feel, nor see, nor love,
nor hate, after the dissolution of my body, I should
be entirely annihilated, nor do I conceive what is
further requisite to make me a perfect nonentity."

— Book I, Part IV, Section vi  of  
    A Treatise of Human Nature

"What is further requisite" — Perhaps  

This four-dot notation ("as") is from a search for Lévi-Strauss in this journal.

See also "That I Am."

Friday, April 7, 2017

Personal Identity

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

From "The Most Notorious Section Phrases," by Sophie G. Garrett
in The Harvard Crimson  on April 5, 2017 —

This passage reminds me of (insert impressive philosophy
that was not in the reading).

This student is just being a show off. We get that they are smart
and well read. Congrats, but please don’t make the rest of the us
look bad in comparison. It should be enough to do the assigned
reading without making connections to Hume’s theory of the self.

Hume on personal identity (the "self")

For my part, when I enter most intimately into what I call myself, I always stumble on some particular perception or other, of heat or cold, light or shade, love or hatred, pain or pleasure. I never can catch myself at any time without a perception, and never can observe any thing but the perception. When my perceptions are removed for any time, as by sound sleep, so long am I insensible of myself, and may truly be said not to exist. And were all my perceptions removed by death, and could I neither think, nor feel, nor see, nor love, nor hate, after the dissolution of my body, I should be entirely annihilated, nor do I conceive what is further requisite to make me a perfect nonentity.
. . . .

I may venture to affirm of the rest of mankind, that they are nothing but a bundle or collection of different perceptions, which succeed each other with an inconceivable rapidity, and are in a perpetual flux and movement. Our eyes cannot turn in their sockets without varying our perceptions. Our thought is still more variable than our sight; and all our other senses and faculties contribute to this change: nor is there any single power of the soul, which remains unalterably the same, perhaps for one moment. The mind is a kind of theatre, where several perceptions successively make their appearance; pass, repass, glide away, and mingle in an infinite variety of postures and situations. There is properly no simplicity in it at one time, nor identity in different, whatever natural propension we may have to imagine that simplicity and identity. The comparison of the theatre must not mislead us. They are the successive perceptions only, that constitute the mind; nor have we the most distant notion of the place where these scenes are represented, or of the materials of which it is composed.

Related material —
Imago Dei  in this journal.

The Ring of the Diamond Theorem

Backstory —
The previous post
and The Crimson Abyss.

Wednesday, April 5, 2017

Dem Bones

Filed under: General — Tags: , — m759 @ 12:15 PM

A note at the end of an article on architecture historian
Christopher Gray in the current online New Yorker  —

This article appears in other versions
of the April 10, 2017, issue, with
the headline “Dem Bones.”

"Defeated, you will rise to your feet as is said of Dry Bones .
These bones will rise again." — Agnes Martin, 1973

Accounting for Taste —

Faye Dunaway and Warren Beatty at the Oscars:

Ben Affleck, star of "The Accountant," at the Oscars:

See also Prisoner + Bones in this  journal.

Tuesday, April 4, 2017

Plan 9 Continues

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

"Plan 9 deals with the resurrection of the dead."

— Bill Murray in "Ed Wood"
 

For The Church of Plan 9

(The plan , as well as the elevation ,
of the above structure is a 3×3 grid.)

Making Science Come Alive

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

From a post on March 13, 2017


Shafarevich was not the only one with a legacy . . .

See also posts in this  journal
now tagged The Gray Legacy.

Tuesday, March 14, 2017

Review

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

Monday, March 13, 2017

Pragmatism at the Church of the Transformers*

Filed under: General — Tags: — m759 @ 9:17 PM

"I would drop the keystone into my arch . . . ."

Click the Auto Body image for some backstory.

* For the church, see Transformers in this journal.

Saturday, February 11, 2017

The God Identity

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

The previous post suggests a related concept, in which
"I Am that I Am" is replaced by "I am as  I am." —

Sunday, December 11, 2016

Stark to Parker in New Trailer

Filed under: General — m759 @ 9:28 AM

Literature marches on

"Don't do anything I would  do.
And definitely don't do anything I wouldn't do.
There's a little gray area in there
and that's where you operate."

See as well "Spirit and Space" (Nov. 25, 2016) —

Monday, October 17, 2016

Groundhog Day for Hindus

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

Live, Die, Repeat.

Older Posts »

Powered by WordPress