Log24

Monday, December 17, 2018

Signs

Filed under: General — m759 @ 12:58 PM

The diamond signs of Donald Knuth

“When there’s nothing to believe in 
Still you’re coming back,
you’re running back 
You’re coming back for more
 
So put me on a highway….”
— Eagles, 1975  

See also …

See as well Knuth in this  journal.

"Spirit-guide of the algorithmic realm"

— Description of Donald Knuth by Siobhan Roberts, Dec. 17, 2018.

There are spirit guides and spirit  guides.

"One of These Nights  is the fourth studio album
by the Eagles, released in 1975." — Wikipedia

Sunday, December 16, 2018

Interlocking

Filed under: General — m759 @ 2:30 PM

http://m759.net/wordpress/?s=Eddington+Song

'The Eddington Song'

Inaction Illustrated

Filed under: General — m759 @ 12:06 PM

See "Inaction Film," a Log24 post of August 21, 2012 —
the date of death for one William P. Thurston.

Sunday School News

Filed under: General — Tags: — m759 @ 9:41 AM

Promotional news from Google: Bullock's Bird Box.

See as well Friday night's post "Lone Star Wars."

Saturday, December 15, 2018

Bee Season continues.

Filed under: General — m759 @ 3:30 PM

" … this beautiful love story . . . ."

See as well Bee Season in this  journal.

Casting

Filed under: General — m759 @ 2:23 PM

"When you cast a spell . . . ."

See Lily Collins in The Telegraph  today.  A related tale —

"On August 30, 2017, Lily Collins was cast … as Edith Tolkien,
love and later wife of Tolkien, who was also the inspiration of
the princess characters in The Lord of the Rings ."

https://en.wikipedia.org/wiki/Tolkien_(film)

The Log24  posts of August 30, 2017, are now tagged Verbum 2017.

A Very Belated Happy Birthday…

Filed under: General — m759 @ 12:00 AM

To Chloë Grace Moretz ("Brain on Fire" (US release June 22, 2018),
and "Clouds of Sils Maria" (2014-15 in various film festivals)).

From a post of Feb. 10, 2018, when Moretz turned 21 —

Friday, December 14, 2018

Lone Star Wars

Filed under: General — m759 @ 10:46 PM



   "Learn more."

  — University of Texas at Austin

Starbird Variations

Filed under: General — m759 @ 4:56 PM

The reference in the previous post's image to "Starbird No. 2,"
the single on the flip side of Manfred Mann's 1976 version of
"Blinded by the Light," suggests a review —

A professor named Starbird

From the above YouTube date,
a bird of a different color

The Blinded Ear

Filed under: General — m759 @ 1:00 PM

The Aug. 6, 1976, single of 
Manfred Mann's Earth Band version of
Springsteen's 1972 "Blinded by the Light"—

See also two posts of Oct. 29, 2015.

Small Space Odyssey

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

References in recent posts to physical space and 
to mathematical space suggest a comparison.

Physical space is well known, at least in the world
of mass entertainment.

Mathematical space, such as the 12-dimensional
finite space of the Golay code, is less well known.

A figure from each space —

The source of the Conway-Sloane brick —

Quote from a mathematics writer —

“Looking carefully at Golay’s code is like staring into the sun.”

— Richard Evan Schwartz

The former practice yields reflections like those of Conway and Sloane.
The latter practice is not recommended.

Thursday, December 13, 2018

Big Space Odyssey

Filed under: General — m759 @ 9:09 PM

From The New York Times  this evening —

For a small  space odyssey, see this  journal's Sunday posts.

Dirty Deeds

Filed under: General — m759 @ 1:00 PM

The title was suggested by headlines in today's news
and by the classic film "Dirty Computer."

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

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

Space Art

Filed under: General — m759 @ 12:15 PM

For Oslo artist Josefine Lyche, excerpts
from a Google image search today —

Material related to Lyche's experience as an adolescent with a ZX Spectrum computer —

Click "Hello World" for a larger image.

Wednesday, December 12, 2018

Kummerhenge Continues.

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 7:24 PM

Those pleased by what Ross Douthat today called
"The Return of Paganism" are free to devise rituals
involving what might be called "the sacred geometry
of the Kummer 166  configuration."

As noted previously in this journal, 

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

— T. S. Eliot in Four Quartets

Geometric incarnation and the Kummer configuration

See also earlier posts also tagged "Kummerhenge" and 
another property of the remarkable Kummer 166 

The Kummer 16_6 Configuration and the Nordstrom-Robinson Code

For some related literary remarks, see "Transposed" in  this journal.

Some background from 2001 —

An Inscape for Douthat

Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 9:41 AM

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."

Tuesday, December 11, 2018

Review

Filed under: General — m759 @ 11:00 PM

See also a theater review of a Walpurgisnacht 2008
Brooklyn Academy of Music production —

The New York Times  on the Walpurgisnacht production —

"Specifically grim but never merely glum, the production fully taps
the self-conscious theatricality of the play ('I’m warming up for
my last soliloquy,' Hamm announces toward the end) without
letting us forget that its strange figures are appallingly real,
enacting a grotesque pantomime of humanity’s hungry need to
distract itself by wresting order, meaning and a sliver of satisfaction —
just one more sugarplum, please, or maybe a Vicodin — from
the formless, aimless, timeless nothingness of life."

— Charles Isherwood

The Epstein Exit

Filed under: General — m759 @ 4:48 PM

A New York Times  obituary photo caption this afternoon —

"Alvin Epstein, center, with Elaine Stritch and John Turturro
in a production of Samuel Beckett’s 'Endgame' at the
Brooklyn Academy of Music in 2008. Mr. Epstein played all
three male roles in 'Endgame' at various stages in his career . . . ."

— https://www.nytimes.com/2018/12/11/obituaries/alvin-epstein-dead.html

Epstein reportedly died yesterday, Dec. 10, in Newton, Mass., at 93.

Carried Away

Filed under: General — m759 @ 7:00 AM

"The word 'ablative' derives from the Latin ablatus ,
the (irregular) perfect passive participle of auferre 'to carry away'.[1]"

Example —

See as well Cicero, In Verrem II. 1. 46

He reached Delos. There one night he secretly 46 
carried off, from the much-revered sanctuary of 
Apollo, several ancient and beautiful statues, and 
had them put on board his own transport. Next 
day, when the inhabitants of Delos saw their sanc- 
tuary stripped of its treasures, they were much 
distressed . . . .
Delum venit. Ibi ex fano Apollinis religiosissimo 
noctu clam sustulit signa pulcherrima atque anti- 
quissima, eaque in onerariam navem suam conicienda 
curavit. Postridie cum fanum spoliatum viderent ii 
qui Delum incolebant, graviter ferebant . . . .

Sunday, December 9, 2018

Quaternions in a Small Space

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

The previous post, on the 3×3 square in ancient China,
suggests a review of group actions on that square
that include the quaternion group.

Click to enlarge

Three links from the above finitegeometry.org webpage on the
quaternion group —

Related material —

Iain Aitchison on the 'symmetric generation' of R. T. Curtis

See as well the two Log24 posts of December 1st, 2018 —

Character and In Memoriam.

A Small Space

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

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

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.

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.

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. 

Thursday, December 6, 2018

The Mathieu Cube of Iain Aitchison

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

This journal ten years ago today —

Surprise Package

Santa and a cube
 

From a talk by a Melbourne mathematician on March 9, 2018 —

The Mathieu group cube of Iain Aitchison (2018, Hiroshima)

The source — Talk II below —

Search Results

pdf of talk I  (March 8, 2018)

www.math.sci.hiroshima-u.ac.jp/branched/…/Aitchison-Hiroshima-2018-Talk1-2.pdf

Iain Aitchison. Hiroshima  University March 2018 … Immediate: Talk given last year at Hiroshima  (originally Caltech 2010).

pdf of talk II  (March 9, 2018)  (with model for M24)

www.math.sci.hiroshima-u.ac.jp/branched/files/…/Aitchison-Hiroshima-2-2018.pdf

Iain Aitchison. Hiroshima  University March 2018. (IRA: Hiroshima  03-2018). Highly symmetric objects II.

Abstract

www.math.sci.hiroshima-u.ac.jp/branched/files/2018/abstract/Aitchison.txt

Iain AITCHISON  Title: Construction of highly symmetric Riemann surfaces , related manifolds, and some exceptional objects, I, II Abstract: Since antiquity, some …

Related material — 

The 56 triangles of  the eightfold cube . . .

The Eightfold Cube: The Beauty of Klein's Simple Group

   Image from Christmas Day 2005.

Wednesday, December 5, 2018

The Hassenfeld Legacy

Filed under: General — m759 @ 11:30 AM

The Finkelstein Talisman —

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

"Before time began, there was the Cube."

— Optimus Prime in "Transformers" (Paramount, 2007)
 

Wikipedia on Hasbro

Three American Jewish brothers,[6] Herman, Hillel, and Henry Hassenfeld[7] 
founded Hassenfeld Brothers in Providence, Rhode Island in 1923 . . . .
 

The Hassenfeld Auction — 

Also on September 16, 2015 —


 

The Hindman Image —

The Hood Warenkorb —

Under the Hood —

Megan Fox in "Transformers" (2007) —


 

This Way to the Egress —

Caesarian (continued)

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

Later editions of a book first published on New Year's Day 2002
by Bantam in Australia —

Tuesday, December 4, 2018

Melbourne Noir

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 11:30 AM

 March 8, 2018, was the date of death for Melbourne author Peter Temple.

Monday, December 3, 2018

Ruthless

Filed under: General — m759 @ 8:29 PM

In memory of Ruth Haring, a former president of the United States
Chess Federation who reportedly died at 63 on Thursday,
November 29, 2018 —

A search for Ruthless  in this journal yields the tag Mythologem Day.

For Quantum Mystics

Filed under: General — m759 @ 7:00 PM

See a Quanta Magazine  article published today and
https://www.chapman.edu/our-faculty/matt-leifer.

From the article —

Leifer, for his part, is holding out for something new. “I think the correct interpretation of quantum mechanics is none of the above,” he said.

He likens the current situation with quantum mechanics to the time before Einstein came up with his special theory of relativity. Experimentalists had found no sign of the “luminiferous ether” — the medium through which light waves were thought to propagate in a Newtonian universe. Einstein argued that there is no ether. Instead he showed that space and time are malleable. “Pre-Einstein I couldn’t have told you that it was the structure of space and time that was going to change,” Leifer said.

Quantum mechanics is in a similar situation now, he thinks. “It’s likely that we are making some implicit assumption about the way the world has to be that just isn’t true,” he said. “Once we change that, once we modify that assumption, everything would suddenly fall into place. That’s kind of the hope. Anybody who is skeptical of all interpretations of quantum mechanics must be thinking something like this. Can I tell you what’s a plausible candidate for such an assumption? Well, if I could, I would just be working on that theory.”

See as well this  journal on the Feast of the Assumption, 2018.

The Relativity Problem at Hiroshima

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 6:21 PM

“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

Iain Aitchison's 'dice-labelled' cuboctahedron at Hiroshima, March 2018

See also Relativity Problem and Diamonds and Whirls.

We See Your Documents.

Filed under: General — m759 @ 11:45 AM

Review

Filed under: General — m759 @ 8:58 AM
 

Tuesday, March 31, 2015

Würfel-Märchen

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

  See also Würfel in this journal.

Sunday, December 2, 2018

Iacta Est.

Filed under: General — m759 @ 5:48 PM

Altizer reportedly died on Wednesday, November 28.
See also this  journal on that date

 .

Symmetric Generation …

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

Continued .   See as well a Log24 search for "Symmetric Generation."

Iain Aitchison on symmetric generation of M24

Iain Aitchison on symmetric generation of M24

Update of 2 PM ET —

Symmetry at Hiroshima

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 6:43 AM

A search this morning for articles mentioning the Miracle Octad Generator
of R. T. Curtis within the last year yielded an abstract for two talks given
at Hiroshima on March 8 and 9, 2018

http://www.math.sci.hiroshima-u.ac.jp/
branched/files/2018/abstract/Aitchison.txt

Iain AITCHISON

Title:

Construction of highly symmetric Riemann surfaces, related manifolds, and some exceptional objects, I, II

Abstract:

Since antiquity, some mathematical objects have played a special role, underpinning new mathematics as understanding deepened. Perhaps archetypal are the Platonic polyhedra, subsequently related to Platonic idealism, and the contentious notion of existence of mathematical reality independent of human consciousness.

Exceptional or unique objects are often associated with symmetry – manifest or hidden. In topology and geometry, we have natural base points for the moduli spaces of closed genus 2 and 3 surfaces (arising from the 2-fold branched cover of the sphere over the 6 vertices of the octahedron, and Klein's quartic curve, respectively), and Bring's genus 4 curve arises in Klein's description of the solution of polynomial equations of degree greater than 4, as well as in the construction of the Horrocks-Mumford bundle. Poincare's homology 3-sphere, and Kummer's surface in real dimension 4 also play special roles.

In other areas: we have the exceptional Lie algebras such as E8; the sporadic finite simple groups; the division algebras: Golay's binary and ternary codes; the Steiner triple systems S(5,6,12) and S(5,8,24); the Leech lattice; the outer automorphisms of the symmetric group S6; the triality map in dimension 8; and so on. We also note such as: the 27 lines on a cubic, the 28 bitangents of a quartic curve, the 120 tritangents of a sextic curve, and so on, related to Galois' exceptional finite groups PSL2(p) (for p= 5,7,11), and various other so-called `Arnol'd Trinities'.

Motivated originally by the `Eightfold Way' sculpture at MSRI in Berkeley, we discuss inter-relationships between a selection of these objects, illustrating connections arising via highly symmetric Riemann surface patterns. These are constructed starting with a labeled polygon and an involution on its label set.

Necessarily, in two lectures, we will neither delve deeply into, nor describe in full, contexts within which exceptional objects arise. We will, however, give sufficient definition and detail to illustrate essential inter-connectedness of those exceptional objects considered.

Our starting point will be simplistic, arising from ancient Greek ideas underlying atomism, and Plato's concepts of space. There will be some overlap with a previous talk on this material, but we will illustrate with some different examples, and from a different philosophical perspective.

Some new results arising from this work will also be given, such as an alternative graphic-illustrated MOG (Miracle Octad Generator) for the Steiner system S(5,8,24), and an alternative to Singerman – Jones' genus 70 Riemann surface previously proposed as a completion of an Arnol'd Trinity. Our alternative candidate also completes a Trinity whose two other elements are Thurston's highly symmetric 6- and 8-component links, the latter related by Thurston to Klein's quartic curve.

See also yesterday morning's post, "Character."

Update: For a followup, see the next  Log24 post.

Saturday, December 1, 2018

Character

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

"What we do may be small, but it has
a certain character of permanence."

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

In Memoriam

Filed under: General — m759 @ 10:06 AM

From today's print New York Times  obituary for a screenwriter
who reportedly died last Sunday —

“Indiana Jones and the Temple of Doom,”
a 1984 follow-up to “Raiders of the Lost Ark”
made an estimated $333 million worldwide.

Friday, November 30, 2018

Latin-Square Structure

Filed under: G-Notes,General,Geometry — m759 @ 2:56 AM

Continued from March 13, 2011

"…as we saw, there are two different Latin squares of order 4…."
— Peter J. Cameron, "The Shrikhande Graph," August 26, 2010

Cameron counts Latin squares as the same if they are isotopic .
Some further context for Cameron's remark—

A new website illustrates a different approach to Latin squares of order 4 —

https://shc7596.wixsite.com/website .

Thursday, November 29, 2018

Icons . . .

Filed under: General — m759 @ 12:05 PM

For the People's Temple of Doom —

Suggested by the oeuvre  of Steven Spielberg —

The Fortune Cookie

Filed under: General — m759 @ 10:54 AM

The mathematician Chuanming Zong in the previous post
has also written about  Aristotle's pyramid scheme

The White Cube

Filed under: G-Notes,General,Geometry — m759 @ 9:57 AM

Clicking on Zong in the above post leads to a 2005 article
in the Bulletin of the American Mathematical Society .

See also the eightfold  cube and interality .

Wednesday, November 28, 2018

Geometry and Experience

Filed under: G-Notes,General,Geometry — m759 @ 9:18 AM

Einstein, "Geometry and Experience," lecture before the
Prussian Academy of Sciences, January 27, 1921–

This view of axioms, advocated by modern axiomatics, purges mathematics of all extraneous elements, and thus dispels the mystic obscurity, which formerly surrounded the basis of mathematics. But such an expurgated exposition of mathematics makes it also evident that mathematics as such cannot predicate anything about objects of our intuition or real objects. In axiomatic geometry the words "point," "straight line," etc., stand only for empty conceptual schemata. That which gives them content is not relevant to mathematics.

Yet on the other hand it is certain that mathematics generally, and particularly geometry, owes its existence to the need which was felt of learning something about the behavior of real objects. The very word geometry, which, of course, means earth-measuring, proves this. For earth-measuring has to do with the possibilities of the disposition of certain natural objects with respect to one another, namely, with parts of the earth, measuring-lines, measuring-wands, etc. It is clear that the system of concepts of axiomatic geometry alone cannot make any assertions as to the behavior of real objects of this kind, which we will call practically-rigid bodies. To be able to make such assertions, geometry must be stripped of its merely logical-formal character by the coordination of real objects of experience with the empty conceptual schemata of axiomatic geometry. To accomplish this, we need only add the proposition: solid bodies are related, with respect to their possible dispositions, as are bodies in Euclidean geometry of three dimensions. Then the propositions of Euclid contain affirmations as to the behavior of practically-rigid bodies.

Geometry thus completed is evidently a natural science; we may in fact regard it as the most ancient branch of physics. Its affirmations rest essentially on induction from experience, but not on logical inferences only. We will call this completed geometry "practical geometry," and shall distinguish it in what follows from "purely axiomatic geometry." The question whether the practical geometry of the universe is Euclidean or not has a clear meaning, and its answer can only be furnished by experience.  ….

Later in the same lecture, Einstein discusses "the theory of a finite
universe." Of course he is not using "finite" in the sense of the field
of mathematics known as "finite geometry " — geometry with only finitely
many points.

Nevertheless, his remarks seem relevant to the Fano plane , an
axiomatically defined entity from finite geometry, and the eightfold cube ,
a physical object embodying the properties of the Fano plane.

 I want to show that without any extraordinary difficulty we can illustrate the theory of a finite universe by means of a mental picture to which, with some practice, we shall soon grow accustomed.

First of all, an observation of epistemological nature. A geometrical-physical theory as such is incapable of being directly pictured, being merely a system of concepts. But these concepts serve the purpose of bringing a multiplicity of real or imaginary sensory experiences into connection in the mind. To "visualize" a theory therefore means to bring to mind that abundance of sensible experiences for which the theory supplies the schematic arrangement. In the present case we have to ask ourselves how we can represent that behavior of solid bodies with respect to their mutual disposition (contact) that corresponds to the theory of a finite universe. 

Tuesday, November 27, 2018

The Saints — Claus, Fe; Fe, Claus.

Filed under: General — m759 @ 1:59 PM

See The Saints in this journal, as well as Claus and Fe.

Organizing the Mine Workers

Filed under: General — m759 @ 11:17 AM

(Continued from August 8th, 2011) —

See also Sunday evening's post At Eternity's Gate.

Fe

Filed under: General — m759 @ 10:38 AM

http://www.log24.com/log/pix18/180808-Cosima_drank_the_purple_kool-aid-500w.jpg

Sunday, November 25, 2018

At Eternity’s Gate

Filed under: General — m759 @ 10:42 PM

A New York Times  theater review from 2002
is now accompanied by an ad for a current film,
"At Eternity's Gate." (Click to enlarge.)

"At Eternity's Gate" opened November 16th, 2018.

From this  journal on that date —

"Right through hell there is a path." — Malcolm  Lowry

Artifacts

Filed under: General — m759 @ 2:00 PM

The word "artifacts" in the above obituary summary
suggests three Log24 posts now tagged with that word.

See as well . . .

"Bad news on the doorstep…." — American Pie

Ricky Jay

Filed under: General — m759 @ 2:05 AM

See also Ricky Jay in this  journal.

Saturday, November 24, 2018

Portfolio

Filed under: G-Notes,General,Geometry — m759 @ 6:29 PM

A new portfolio site:

Portfolio on art and geometry of Steven H. Cullinane

Friday, November 23, 2018

Artfield Studio

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

The title is that of an new Internet domain, artfield.studio,
that is used only to store branded links  such as . . .

artfield.studio/trinity-dice

artfield.studio/dirac-and-geometry

artfield.studio/eddington

artfield.studio/kummerhenge

artfield.studio/pinterest .

Some context —

artfield.studio/patrick-blackburn.

Thursday, November 22, 2018

Rosenhain and Göpel Meet Kummer in Projective 3-Space

Filed under: General,Geometry — Tags: — m759 @ 2:07 PM

For further details, see finitegeometry.org/sc/35/hudson.html.

Geometric Incarnation

Filed under: General,Geometry — Tags: — m759 @ 6:00 AM

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

— T. S. Eliot in Four Quartets

Note also the four 4×4 arrays surrounding the central diamond
in the chi  of the chi-rho  page of the Book of Kells

From a Log24 post
of March 17, 2012

"Interlocking, interlacing, interweaving"

— Condensed version of page 141 in Eddington's
1939 Philosophy of Physical Science

Wednesday, November 21, 2018

Opening Credits

Filed under: General — m759 @ 7:47 PM

From Log24 on Friday, Nov. 16

This evening's New York Times  on an opening-credits designer, 
Pablo Ferro, who reportedly died at 83 on Friday, Nov. 16 —

An example of Ferro's later work in film —

Musical accompaniment from Sunday morning —

'The Eddington Song'

Tuesday, November 20, 2018

Logos

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

(Continued)

Musical accompaniment from Sunday morning

'The Eddington Song'

Update of Nov. 21 —

The reader may contrast the above Squarespace.com logo
(a rather serpentine version of the acronym SS) with a simpler logo
for a square space (the Galois window ):

Claremont Noir

Filed under: General — m759 @ 11:00 AM

From the Claremont Review of Books

From elsewhere —

See as well posts from Log24 related to
the McClay date above — June 8, 2007.

Lincoln’s Commedia

Filed under: General — m759 @ 2:29 AM

A November 19th story by one Ross A. Lincoln

See as well Commedia  in this  journal.

Monday, November 19, 2018

Pleasure Paradise

Filed under: General — m759 @ 9:34 AM

The title refers to an image reproduced here in
a post of August 1st, 2017. That post also included
the following quotation —

"Remembering speechlessly we seek
the great forgotten language,
the lost lane-end into heaven,
a stone, a leaf, an unfound door.
Where? When?" — Thomas Wolfe 

— From "All the stuff we'd like to buy at
the Back To The Future prop auction
,"
by Meredith Woerner, 11/04/10, 9:30 am

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.

Diamond Theorem Symmetry

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

The title is a useful search phrase:

Saturday, November 17, 2018

Representation

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

See as well . . .

. . . and posts tagged Alperin.

On its current homepage, the American Mathematical Society  
links to a Nov. 15 blog post illustrating the Stan Lee approach
to mathematics:

Stories: "Math needs more stories. All kinds of stories…" 

See too Mathematics and Narrative in this  journal.

Friday, November 16, 2018

The Transposed Squares

Filed under: G-Notes,General,Geometry — m759 @ 9:12 PM
 
 

I.e. (click to enlarge) —

 

Parable of India

Filed under: General — m759 @ 12:42 PM

See too  "When thou seekest me, seek towards India."

William Goldman

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

From the above source —

See as well the author Les Daniels in this  journal.

On All Souls’ Day 2018

Filed under: General — m759 @ 2:40 AM

See as well Under the Volcano  and All Souls in this  journal.

Related material —

Thursday, November 15, 2018

Mathematics and Narrative

Filed under: General,Geometry — m759 @ 9:08 PM

Mathematics —

See (for instance) a research group at Ghent University.

For those who prefer narrative . . .

See also . . .

Nocciolo

Filed under: General — m759 @ 8:15 AM

"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

From the previous post

From a cartoon graveyard —

See also, in this  journal, Smallest Perfect and Nocciolo .

Wednesday, November 14, 2018

Phase Space

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

"Open the pod bay doors, Bernard."

Tuesday, November 13, 2018

Blackboard Jungle Continues.

Filed under: G-Notes,General,Geometry — m759 @ 6:19 PM

From the 1955 film "Blackboard Jungle" —

From a trailer for the recent film version of A Wrinkle in Time

Detail of the phrase "quantum tesseract theorem":

From the 1962 book —

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

Related mathematics from Koen Thas that some might call a
"quantum tesseract theorem" —

Some background —

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

See also posts tagged Dirac and Geometry. For more
background on finite  geometry, see a web page
at Thas's institution, Ghent University.

Monday, November 12, 2018

Half Crazy

Filed under: General — m759 @ 10:42 PM

Douglas Rain, the voice of HAL in Kubrick's 2001 , reportedly
died at 90 on Sunday, Nov. 11, 2018. A piece from the Sunday,
April 1, 2018, print  edition of The New York Times  recalls that . . .

When HAL says, “I know I’ve made some very poor decisions recently, but I can give you my complete assurance that my work will be back to normal,” Mr. Rain somehow manages to sound both sincere and not reassuring. And his delivery of the line “I think you know what the problem is just as well as I do” has the sarcastic drip of a drawing-room melodrama and also carries the disinterested vibe of a polite sociopath.

Kubrick had Mr. Rain sing the 1892 love song “Daisy Bell” (“I’m half crazy, all for the love of you”) almost 50 times, in uneven tempos, in monotone, at different pitches and even just by humming it. In the end, he used the very first take. Sung as HAL’s brain is being disconnected, it’s from his early programming days, his computer childhood. It brings to an end the most affecting scene in the entire film.

— Gerry Flahive in the online New York Times 
 

"A version of this article appears in print on , on Page AR13 of the New York edition with the headline: HAL 9000 Wasn’t Always So Eerily Calm."

This  journal on the above online date, March 30, 2018 —

"Program or be programmed."
— A saying by Douglas Rushkoff

See as well the following link from this journal
on Armistice Day, the reported date of Mr. Rain's death —

"Halmos + Tombstone."

Raum und Zwischenraum*

Filed under: General — m759 @ 8:42 AM

An Internet search for "Raum und Zwischenraum " this morning
led to a Munich artist who reportedly died on Nov. 11, 2012.

Related material —

Desert Cross, in Log24 on that date, and . . .

* See Zwischenraum  in this journal.

Sunday, November 11, 2018

Zwischenraum

Filed under: General — m759 @ 11:00 PM

Warburg at Cornell U. Press

See also Warburg + Cornell in this journal.

"Yet if this Denkraum ,  this 'twilight region,'  is where the artist and
emblem-maker invent, then, as Gombrich well knew, Warburg also
constantly regrets the 'loss' of this 'thought-space,' which he also
dubs the Zwischenraum  and Wunschraum ."

Memory, Metaphor, and Aby Warburg's Atlas of Images ,
     Christopher D. Johnson, Cornell University Press, 2012, p. 56

Tombstone

Filed under: General — m759 @ 3:33 AM

Search for 'Catch-22' + 'Also sprach'

See also this journal on the above Catch-22 date — July 16, 2014 —
and a search in this journal for "Halmos + Tombstone."

Thursday, November 8, 2018

Reality vs. Axiomatic Thinking

Filed under: G-Notes,General,Geometry — m759 @ 11:16 PM

From https://blogs.scientificamerican.com/…

A  Few  of  My  Favorite  Spaces:
The Fano Plane

The intuition-challenging Fano plane may be
the smallest interesting configuration
of points and lines.

By Evelyn Lamb on October 24, 2015

"…finite projective planes seem like
a triumph of purely axiomatic thinking
over any hint of reality. . . ."

For Fano's axiomatic  approach, see the Nov. 3 Log24 post
"Foundations of Geometry."

For the Fano plane's basis in reality , see the eightfold cube
at finitegeometry.org/sc/ and in this journal.

See as well "Two Views of Finite Space" (in this journal on the date 
of Lamb's remarks — Oct. 24, 2015).

Some context:  Gödel's Platonic realism vs. Hilbert's axiomatics
in remarks by Manuel Alfonseca on June 7, 2018. (See too remarks
in this journal on that date, in posts tagged "Road to Hell.")

Geometry Lesson

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

From "The Trials of Device" (April 24, 2017) —

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

Pentagon with pentagram    

See also Wittgenstein in a search for "Ein Kampf " in this journal.

Wednesday, November 7, 2018

The Fact-Checker

Filed under: General — m759 @ 9:43 PM

http://www.log24.com/log/pix18/180831-NYer-back-cover-ad-Lifespan_of_a_Fact.jpg

In memory of Christopher Lehmann-Haupt, who reportedly died
today (Wed., Nov. 7, 2018) at 84 —

See Lehmann-Haupt in this journal on May 23, 2012:

On author Paul Fussell, who died today —

"Vincent B. Sherry, writing in The Cambridge Companion to the Literature of the First World War , called Mr. Fussell’s book 'the fork in the road for Great War criticism.'"  — Christopher Lehmann-Haupt in The New York Times

Actually, the writing was by James Campbell. Sherry was the book's editor. See Campbell's "Interpreting the War," pp. 261-279 of the 2005 (first) printing. The fork is on page 267.

Update of 9:26 PM— In the latest  version of Lehmann-Haupt's article, the fork has disappeared. But Campbell's writing is still misidentified as Sherry's.

Defense Against the Dark Arts

Filed under: General — m759 @ 6:19 AM

"What is the Necropastoral?" was published on April 29th, 2014.
Also on April 29th, 2014 —

See as well Christianity and Culture  by T. S. Eliot.

Tuesday, November 6, 2018

Four Quartets Prize

Filed under: General — m759 @ 9:00 PM

On a poem sequence that won this year's Four Quartets Prize —

"Decomposing and reconstituting bodies and landforms
feed the evolution of Smith’s afrofuturist necropastoral."

Bait and Tackle

Filed under: General — Tags: — m759 @ 1:13 PM

The Bait —

For the tackle, see a 1988 album from The Residents.

Settings and Tools

Filed under: General — m759 @ 11:02 AM

Desert Notes*

Filed under: General — Tags: — m759 @ 3:13 AM

A November 1 LA Times  article about a book to be published today —

Why did Jonathan Lethem
turn toward the desert
in 'The Feral Detective'?

See also searches in this  journal for Desert and, more particularly,
Point Omega and Mojave.

* The title of a book by Barry Holstun Lopez.

On Mathematical Beauty

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 2:18 AM

A phrase from the previous post —
"a size-eight dame in a size-six dress" —
suggests a review . . .

See as well the diamond-theorem correlation and . . .

Why PSL(2,7) is isomorphic to GL(3.2)

Monday, November 5, 2018

Eyes on the Prize

Filed under: General — Tags: , — m759 @ 7:04 PM

High Life at Sils Maria

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

Related art —

Sunday, November 4, 2018

Kristen vs. the Space Witch*

Filed under: General — Tags: — m759 @ 11:59 PM

* We know the former. There is no shortage of candidates for the latter.

“Look Up” — The Breakthrough Prize* Theme This Evening

Filed under: General — Tags: — m759 @ 10:45 PM

Looking up images for "The Space Theory of Truth" this evening —

Detail  (from the post "Logos" of Oct. 14)

http://www.spaceref.com/news/viewpr.html?pid=53323

Dead Poet

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

The New York Times  today on a poet, Judith Kazantzis,
"who died on Sept. 18 at 78" —

"Judith’s oldest sister is Antonia Fraser, the biographer
and novelist and widow of the playwright Harold Pinter."

"Her [Judith’s] death was confirmed by Andy Croft, who runs
Smokestack Books, the publisher of 'Sister Intervention' [sic* ]
(2014), Ms. Kazantzis’ last collection of poetry. He did not
specify the cause or where she died."

Notable lines from that book's poem "In the Garden" —

Two trees of life, not in the woods,
but in the garden.

See also the post "Death Day" in this  journal on Sept. 18.

* The title is actually "Sister Invention ."

Saturday, November 3, 2018

For St. Anselm

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

"… at his home in San Anselmo . . . ."

See also Anselm in this journal, as well as the Devil's Night post Ojos.

The Space Theory of Truth

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

Earlier posts have discussed the "story theory of truth"
versus the "diamond theory of truth," as defined by 
Richard Trudeau in his 1987 book The Non-Euclidean Revolution.

In a New York Times  opinion piece for tomorrow's print edition,*
novelist Dara Horn touched on what might be called 
"the space theory of truth."

When they return to synagogue, mourners will be greeted
with more ancient words: “May God comfort you
among the mourners of Zion and Jerusalem.”
In that verse, the word used for God is hamakom 
literally, “the place.” May the place comfort you.

[Link added.]

The Source —

See Dara Horn in this  journal, as well as Makom.

* "A version of this article appears in print on ,
on Page A23 of the New York edition with the headline: 
American Jews Know This Story."

Foundations of Geometry

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

"costruire (o, dirò meglio immaginare) un ente" — Fano, 1892

"o, dirò meglio, costruire" — Cullinane, 2018

Friday, November 2, 2018

Day of the Dead

Filed under: General — m759 @ 9:00 AM

From Wikipedia

Day of the Dead
Observed by Mexico, and regions with large Hispanic populations
Type Cultural 
Syncretic Christian
Significance Prayer and remembrance of friends and family members who have died
Celebrations Creation of altars to remember the dead, traditional dishes for the Day of the Dead
Begins October 31
Ends November 2
Date October 31
Next time 31 October 2019
Frequency Annual
Related to All Saints' Day

"The Day of the Dead (Spanish: Día de Muertos ) is
a Mexican holiday celebrated throughout Mexico,
in particular the Central and South regions,
and by people of Mexican heritage elsewhere.
The multi-day holiday focuses on gatherings
of family and friends to pray for and remember
friends and family members who have died, and
help support their spiritual journey. . . .

The holiday is sometimes called Día de los Muertos 
in Anglophone countries, a back-translation of its
original name, Día de Muertos .

Gradually, it was associated with October 31,
November 1, and November 2 to coincide with the
Western Christianity triduum of Allhallowtide: 
All Saints' EveAll Saints' Day, and All Souls' Day."

—————————————————————————-

The previous post concerned a poet who reportedly
died on October 23, 2018.  This journal on that date —

Elevation of the Hostess

Filed under: General — m759 @ 1:27 AM

Or:  Netflix and Chill on All Souls' Day

Midrash from Huffington Post  (click to enlarge) —

Thursday, November 1, 2018

Formation, Transformation . . . . Solution, Dissolution

Filed under: General,Geometry — m759 @ 8:40 PM

Literary Doodles

Filed under: General — m759 @ 11:59 AM

The Great Doodle of Northrop Frye —

Shown below is a "Story Circle" based on the work of Joseph Campbell.
The author of this particular version is unknown.  

Note that there are 12 steps in the above Story Circle. This suggests
some dialogue from a recent film . . .

Donnie —"We can't ask for help if we don't think there's anyone out there to give it. You have to grasp this concept. And that doesn't have to be fucking Jesus Christ or Buddha or Vanna White."
John — "So, can I choose the genitalia of Raquel Welch?"
Donnie — "I would advise against that, Callahan."
John — "Why?"
Donnie — "'Cause it's not a fucking joke. If you can't look outside yourself and you can't find a higher power, you're fucked."

Read more: https://www.springfieldspringfield.co.uk/movie_script.php?movie=dont-worry-he-wont-get-far-on-foot

The Albee Box

Filed under: General — m759 @ 3:00 AM

See also Albee + Box in this  journal.

Wednesday, October 31, 2018

The Crucible of Death

Filed under: General — m759 @ 7:00 PM

This journal yesterday

On a new Netflix series:

We don’t yet have a story structure that allows witches to be powerful for long stretches of time without men holding them back. And what makes the new Sabrina  so exciting is that it seems to be trying to build that story structure itself, in real time, to find a way to let Sabrina have her power and her freedom.

It might fail. But if it does, it will be a glorious and worthwhile failure — the type that comes with trying to pioneer a new kind of story.

—  Constance Grady at Vox, the morning before
      Devil's Night (Oct. 30-31), 2018

A playwright who reportedly died yesterday

"Attention must be paid."

Tuesday, October 30, 2018

Ojos

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

From the Hulu series 'The Path,' the Eye logo

A better term than "phase space" might be "story space."

The Quantum Space Story

Filed under: General — m759 @ 2:00 PM

Finkelstein reportedly died on Sunday, January 24, 2016.

"A Serious Man  kicks off with a Yiddish-language frame story that takes place in a 19th-century Eastern European shtetl, where a married couple has an enigmatic encounter with an old acquaintance who may be a dybbuk , or malevolent spirit (and who's played by the Yiddish theater actor Fyvush Finkel). The import of this parable is cryptic to the point of inscrutability, making it a perfect introduction to the rest of the movie."

— Dana Stevens at Slate.com on Oct. 1, 2009

See also Finkelstein in this  journal.

See as well posts now tagged Oct. 4, 2018,
in the context of today's previous post.

Story Structure, Story Space

Filed under: General — m759 @ 1:00 PM

Constance Grady at Vox  today on a new Netflix series —

We don’t yet have a story structure that allows witches to be powerful for long stretches of time without men holding them back. And what makes the new Sabrina  so exciting is that it seems to be trying to build that story structure itself, in real time, to find a way to let Sabrina have her power and her freedom.

It might fail. But if it does, it will be a glorious and worthwhile failure — the type that comes with trying to pioneer a new kind of story.

See also Story Space  in this  journal.

Monday, October 29, 2018

For the Church of Synchronology*

Filed under: General — m759 @ 9:21 PM

* See that term in this journal.

Sunday, October 28, 2018

Commonwealth Tales, or “Lost in Physics”

Filed under: General — m759 @ 11:00 PM

From Ulysses , by James Joyce —

John Eglinton, frowning, said, waxing wroth:

—Upon my word it makes my blood boil to hear anyone compare Aristotle with Plato.

—Which of the two, Stephen asked, would have banished me from his commonwealth?

Compare and contrast:

Plato's diamond in Jowett's version of the Meno dialogue

Fans of Plato might enjoy tales of Narnia, but fans of
James Joyce and Edgar Allan Poe might prefer
a tale by Michael Chabon from April 2001 about a
"doleful little corner of western Pennsylvania."

Outreach

Filed under: General — m759 @ 4:56 PM

From a New York Times  obituary today —

“Centering prayer is all about heartfulness, which
is a little different from mindfulness,” the Rev. Carl Arico,
a co-founder of Contemplative Outreach, said in a
telephone interview. “It goes to the relationship with God,
who is already there. It’s not sitting in a void.”

Windows 10 lockscreen image

For the Sabine Women

Filed under: General — m759 @ 3:12 PM

Sunday Dinner

Filed under: General — m759 @ 2:11 PM

History 101

Filed under: General — Tags: — m759 @ 1:01 PM

 181028-Interrobang-Wikipedia.jpg (229×524)

'Pinter's hallmark,' according to Harlan Ellison

Friday, October 26, 2018

Saying More: Pathmark, Hallmark, Waymark

Filed under: General — m759 @ 2:11 PM

The previous post (Pathmark Meets Hallmark) suggests
a review of the Waymark Prize in mathematics.

Pathmark Meets Hallmark

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

From earlier posts now tagged Pathmark

From earlier posts tagged Black Diamond

A source for the above Ellison quote —

'Pinter's hallmark,' according to Harlan Ellison

See also A Christmas Carol.

Thursday, October 25, 2018

Breaking the Stranglehold

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

George Soros

Postscript

When I wrote this article I was troubled by drawing an overly sharp distinction between the natural and social sciences. Beinhocker’s (2013) article in this symposium and a workshop at the Central European University on 8 October 2013 led me to modify my views on separating the two. I still think that the methodological convention I proposed is needed in the near term in order to break the stranglehold of rational choice theory, but . . . .

The above postscript is from . . .

See also this  journal on 8 October 2013 —

Clerisy

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

Two images from a post of April 11, 2014

Tom Cruise at the Vatican in MI3

_____________________________________________________________________

Michelle Monaghan, star of "The Path," in MI3 —

Hickory Dickory.

Aesthetic Requiem

Filed under: General — Tags: , — m759 @ 12:01 AM

See also Aesthetics (Oct. 17, 2018).

Wednesday, October 24, 2018

Raiders of the Lost Crucible Continues

Filed under: General — Tags: , , — m759 @ 10:22 PM

Mystery Box

Filed under: General — Tags: , — m759 @ 3:38 PM

". . . humanity battling an unseen force . . . ." —

Quantum Space Elements?

The Cracked Potter

Filed under: General — Tags: , — m759 @ 1:52 PM

See also an embedded ad in The Atlantic  magazine, Sept. 2017.

Shadowlands

Filed under: General — Tags: , — m759 @ 4:38 AM

The previous post suggests a review.

Following the above reference to March 30, 2016 —

Following the above reference to Lovasz —

The Path of Logic

Filed under: General — Tags: , — m759 @ 3:05 AM

Ay Que Bonito

Filed under: General — m759 @ 2:00 AM

(Continued)

"Ay que bonito es bailar
a las dos de la mañana"

— Adapted from a song lyric

See also . . .

Shadi Bartsch-Zimmer, Helen A. Regenstein
Distinguished Service Professor of Classics
at the University of Chicago,

"currently the lead editor of the journal 
KNOW: A Journal on the Formation of Knowledge."

Tuesday, October 23, 2018

Simplicity Versus Complexity

Filed under: General — m759 @ 7:13 PM

Simplicity  (Click for some complexity.)

Complexity  (Click for some simplicity.)

A passage from the 2011 book Idea Man  that was suggested by
a recent New Yorker  article on the book's author, the late Paul Allen —

Left-click image to enlarge.

Plan 9 from Inner Space

Filed under: G-Notes,General,Geometry — m759 @ 9:57 AM

Click the image for some context.

Monday, October 22, 2018

Story Space

Filed under: General — m759 @ 4:48 PM

A better term than "phase space" might be "story space."

See as well Expanding the Spielraum.

For Connoisseurs of Conceptual Art

Filed under: General — Tags: — m759 @ 1:32 PM

In related news . . .

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