Log24

Thursday, June 21, 2018

Cavell’s Matrix

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

From an obituary for Stanley Cavell, Harvard philosopher
who reportedly died at 91 on Tuesday,  June 19:

The London Review of Books  weblog yesterday —

"Michael Wood reviewed [Cavell’s] 
Philosophy the Day after Tomorrow  in 2005:

'The ordinary slips away from us. If we ignore it, we lose it.
If we look at it closely, it becomes extraordinary, the way
words or names become strange if we keep staring at them.
The very notion turns into a baffling riddle.' "

See also, in this  journal, Tuesday morning's Ici vient M. Jordan  and
this  morning's previous post.

Update of 3:24 AM from my RSS feed —

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

Sunday, March 5, 2017

The Omega Matrix

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

Richard Evan Schwartz on
the mathematics of the 4×4 square

See also Priority in this journal.

Monday, June 15, 2015

Omega Matrix

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

See that phrase in this journal.

See also last night's post.

The Greek letter Ω is customarily used to
denote a set that is acted upon by a group.
If the group is the affine group of 322,560
transformations of the four-dimensional
affine space over the two-element Galois
field, the appropriate Ω is the 4×4 grid above.

See the Cullinane diamond theorem.

Friday, August 15, 2014

The Omega Matrix

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

(Continued)

The webpage Rosenhain and Göpel Tetrads in PG(3,2)
has been updated to include more material on symplectic structure.

Sunday, August 3, 2014

The Omega Matrix

Filed under: General,Geometry — Tags: , , — m759 @ 10:31 PM

Shown below is the matrix Omega from notes of Richard Evan Schwartz.
See also earlier versions (1976-1979) by Steven H. Cullinane.

IMAGE- The matrix Omega from notes of Richard Evan Schwartz. See also earlier versions (1977-1979) by Steven H. Cullinane.

Backstory:  The Schwartz Notes (June 1, 2011), and Schwartz on
the American Mathematical Society's current home page:

(Click to enlarge.)

Thursday, October 25, 2012

Bunker Bingo*

Filed under: General — Tags: — m759 @ 11:09 AM

Mathematics and Narrative continues…

IMAGE- In 'Downfall,' Hitler says that 'Steiner's assault will bring it under control.'

Steiner's version of "classical functional analysis"—

"Mein Führer Steiner"

IMAGE- Classical functional analysis according to Moscow State University

* See the story by Kilgore Trout. See also On Linguistic Creation,
   The Matrix of Abraham, and The Thoreau Foundation.

Thursday, October 14, 2010

Diamond Theory and Magic Squares

Filed under: General,Geometry — Tags: , — m759 @ 6:19 PM

"A world of made
is not a world of born— pity poor flesh
and trees, poor stars and stones, but never this
fine specimen of hypermagical
ultraomnipotence."

— e. e. cummings, 1944

For one such specimen, see The Matrix of Abraham
a 5×5 square that is hypermagical… indeed, diabolical.

Related material on the algebra and geometry underlying some smaller structures
that have also, unfortunately, become associated with the word "magic"—

  1. Finite Geometry of the Square and Cube
  2. Clifford Pickover on a 4×4 square
  3. Christopher J. Henrich on the geometry of 4×4 magic squares
    (without any mention of  [1] above or related work dating back to 1976)

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

— e. e. cummings

Happy birthday, e. e.

Tuesday, August 17, 2004

Tuesday August 17, 2004

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

The Zen of Abraham

Today’s Zen Chautauqua, prompted by the fact that this is Abrahamic week at the real Chautauqua, consists of links to

The Matrix of Abraham,

Matrix of the Death God, and

Happy Birthday, Kate and Kevin.

The real Chautauqua’s program this week is, of course, Christian rather than Zen.  Its theme is “Building a Global Neighborhood: The Abrahamic Vision 2004.”  One of the featured performers is Loretta Lynn; in her honor (and, of course, that of Sissy Spacek), I will try to overcome the fear and loathing that the Semitic (i. e., “Abrahamic”) religions usually inspire in me.

To a mathematician, the phrase “global neighborhood” sounds like meaningless politico-religious bullshit —  a phrase I am sure accurately characterizes most of the discourse at Chautauqua this week.  But a Google search reveals an area of research — “particle swarm optimization” in which the phrase “global neighborhood” actually means something.  See

A Hybrid Particle Swarm
and Neural Network Approach
for Reactive Power Control,
by Paulo F. Ribeiro and
W. Kyle Schlansker
(pdf).

This article includes the following:

Given the sophistication of his writing, I am surprised at Schlansker’s Christian background:

A good omen for the future is the fact that Schlansker balances the looney Semitic (or “Abrahamic”) teachings of Christianity with good sound Aryan religion, in the form of the goddess Themis.

 Themis, often depicted as “Justice”

For those who must have an Abraham, Schlansker’s paper includes the following:

A Themis figure I prefer to the above:

For more on religious justice
at midnight in the garden of
good and evil, see the Log24
entries of Oct. 1-15, 2002.

For material on Aryan religion that is far superior to the damned nonsense at Chautauqua, New York, this week, see

Jane Ellen Harrison’s Themis: a Study of the Social Origins of Greek Religion, with an excursus on the ritual forms preserved in Greek tragedy by Gilbert Murray and a chapter on the origin of the Olympic games by F. M. Cornford.  Rev. 2nd ed., Cambridge, Cambridge U.P., 1927.

Those who prefer the modern religion of Scientism will of course believe that Themis is purely imaginary, and that truth is to be found in modern myths like that of Carl Sagan’s novel Contact, illustrated below.

Jodie Foster (an admirer of
Leni Riefenstahl) and the
opening of the 1936 Olympics

“Heraclitus…. says: ‘The ruler whose prophecy occurs at Delphi oute legei oute kryptei, neither gathers nor hides, alla semainei, but gives hints.'”
An Introduction to Metaphysics, by Martin Heidegger, Yale University Press paperback, 1959, p. 170

“The lord whose oracle is in Delphi neither indicates clearly nor conceals, but gives a sign.”
Adolf Holl, The Left Hand of God, Doubleday, 1998, p. 50

Tuesday, July 1, 2003

Tuesday July 1, 2003

Filed under: General — Tags: — m759 @ 5:37 PM

Jew’s on First

This entry is dedicated to those worshippers of Allah who have at one time or another cried
Itbah al-Yahud!” … Kill the Jew!
(See June 29 entries).

Dead at 78

Comedian Buddy Hackett died on Tuesday, July First, 2003, according to the New York Times.  According to Bloomberg.com, he died Sunday or Monday.

Associated Press

Buddy Hackett,
on the set of
“It’s a Mad, Mad,
Mad, Mad
World”
in 1962.

Whatever.  We may imagine he has now walked, leading a parade of many other stand-up saints, into a bar.


Hepburn at Chaillot

MIDRASH
for Buddy Hackett

From my May 25 entry,

Matrix of the Death God:

R. M. Abraham’s Diversions and Pastimes, published by Constable and Company, London, in 1933, has the following magic square:

The Matrix of Abraham

A summary of the religious import of the above from Princeton University Press:

“Moslems of the Middle Ages were fascinated by pandiagonal squares with 1 in the center…. The Moslems thought of the central 1 as being symbolic of the unity of Allah.  Indeed, they were so awed by that symbol that they often left blank the central cell on which the 1 should be positioned.”

— Clifford A. Pickover, The Zen of Magic Squares, Circles, and Stars, Princeton U. Press, 2002, pp. 71-72

Other appearances of this religious icon on the Web include:

On Linguistic Creation

Picasso’s Birthday

1991 Yearbook
Rolling Stone



Hackett

In the Picasso’s Birthday version, 22 of the 25 magic square cells are correlated with pictures on the “Class of ’91” cover of Rolling Stone magazine.  Number 7 is Rod Stewart.  In accordance with the theological rhyme “Seven is heaven, eight is a gate,” our site music for today is “Forever Young,” a tune made famous by Stewart.

Roderick, actually   the name of the hero in “Madwoman of Chaillot”

Sunday, May 25, 2003

Sunday May 25, 2003

Filed under: General,Geometry — Tags: — m759 @ 7:11 PM

ART WARS

Mental Health Month, Day 25:

Matrix of the Death God

Having dealt yesterday with the Death Goddess Sarah, we turn today to the Death God Abraham.  (See Jacques Derrida, The Gift of Death, University of Chicago Press, 1996.)  For a lengthy list of pictures of this damned homicidal lunatic about to murder his son, see The Text This Week.

 

See, too, The Matrix of Abraham, illustrated below.  This is taken from a book by R. M. Abraham, Diversions and Pastimes, published by Constable and Company, London, in 1933.

The Matrix of Abraham

A summary of the religious import of the above from Princeton University Press:

“Moslems of the Middle Ages were fascinated by pandiagonal squares with 1 in the center…. The Moslems thought of the central 1 as being symbolic of the unity of Allah.  Indeed, they were so awed by that symbol that they often left blank the central cell on which the 1 should be positioned.”

— Clifford A. Pickover, The Zen of Magic Squares, Circles, and Stars, Princeton U. Press, 2002, pp. 71-72

Other appearances of this religious icon on the Web:

On Linguistic Creation

Picasso’s Birthday

A less religious approach to the icon may be found on page 393 of R. D. Carmichael’s Introduction to the Theory of Groups of Finite Order (Ginn, Boston, 1937, reprinted by Dover, 1956).

This matrix did not originate with Abraham but, unlike Neo, I have not yet found its Architect.

Wednesday, September 23, 2020

Geometry of Even Subsets

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

Various posts here on the geometry underlying the Mathieu group M24
are now tagged with the phrase “Geometry of Even Subsets.”

For example, a post with this diagram . . .

Wednesday, August 12, 2020

Dry Humor

Filed under: General — Tags: , — m759 @ 1:24 PM

Hidden Figure: Type Design at the East Village Other

Filed under: General — Tags: , — m759 @ 12:59 PM

    I.e.  . . . 

Tuesday, August 11, 2020

Consensual Objectification… Continued

Filed under: General — Tags: , — m759 @ 9:30 PM

Here’s to Consensual Objectification

Filed under: General — Tags: , — m759 @ 4:52 PM
New Woke Stance

“The new Playboy claims to have moved away from the male gaze, but no matter how tasteful it may be, it is still relying on nudity.

‘We talk a lot about when something is objectification versus when it is consensual objectification versus when it is art,’ Singh said. ‘I think objectification removes the agency of the subject.

‘Consensual objectification is the idea of someone feeling good about themselves and wanting someone to look at them. Art means, O.K., we can hang this on a wall. And if it’s both, for us, that’s the major win.’ ”

— Erica Tempesta for DailyMail.com, 2 Aug. 2019

Monday, June 1, 2020

The Gefter Boundary

Filed under: General — Tags: , — m759 @ 5:09 PM

“The message was clear: having a finite frame of reference
creates the illusion of a world, but even the reference frame itself
is an illusion. Observers create reality, but observers aren’t real.
There is nothing ontologically distinct about an observer, because
you can always find a frame in which that observer disappears:
the frame of the frame itself, the boundary of the boundary.”

— Amanda Gefter in 2014, quoted here on Mayday 2020.

Image- Josefine Lyche work (with 1986 figures by Cullinane) in a 2009 exhibition in Oslo

See as well the previous post.

Wednesday, May 20, 2020

Cue the Violins

Filed under: General — Tags: , — m759 @ 11:36 PM

In memory of a music editor.

Blangsted reportedly died on May 1.
See also that date in this journal, among
other posts tagged The Next Level.

Mathematics as a Black Art

Filed under: General — Tags: , , — m759 @ 11:34 AM

Wednesday, April 8, 2020

A Midrash for Steiner

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

(The late Mark  Steiner, not the late George  Steiner.)

See Katherine Neville’s novel The Eight ,
Log24  posts tagged Crucible Raiders, and
St. Isidore, whose feast day is April 4 —

Mark Steiner’s book The Applicability of Mathematics
as a Philosophical Problem  (Harvard University Press, 2002,
$36.50) is available for free at a website named for St. Isidore.)

Ereignis ereignet.

Sunday, March 1, 2020

Notes Towards the Ministry of Culture

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

Same Staircase, Different Day

Filed under: General — Tags: , , — m759 @ 2:18 PM

Freeman Dyson on his staircase at Trinity College
(University of Cambridge) and on Ludwig Wittgenstein:

“I held him in the highest respect and was delighted
to find him living in a room above mine on the same
staircase. I frequently met him walking up or down
the stairs, but I was too shy to start a conversation.”

Frank Close on Ron Shaw:

“Shaw arrived there in 1949 and moved into room K9,
overlooking Jesus Lane. There is nothing particularly
special about this room other than the coincidence that
its previous occupant was Freeman Dyson.”

— Close, Frank. The Infinity Puzzle  (p. 78).
Basic Books. Kindle Edition.

See also other posts now tagged Trinity Staircase.

Illuminati enthusiasts  may enjoy the following image:

'Ex Fano Apollinis'- Fano plane, eightfold cube, and the two combined.

Friday, February 7, 2020

Correspondences

Filed under: General — Tags: , , — m759 @ 1:05 PM

The 15  2-subsets of a 6-set correspond to the 15 points of PG(3,2).
(Cullinane, 1986*)

The 35  3-subsets of a 7-set correspond to the 35 lines of PG(3,2).
(Conwell, 1910)

The 56  3-subsets of an 8-set correspond to the 56 spreads of PG(3,2).
(Seidel, 1970)

Each correspondence above may have been investigated earlier than
indicated by the above dates , which are the earliest I know of.

See also Correspondences in this journal.

* The above 1986 construction of PG(3,2) from a 6-set also appeared
in the work of other authors in 1994 and 2002 . . .

Addendum at 5:09 PM suggested by an obituary today for Stephen Joyce:

See as well the word correspondences  in
James Joyce and the Hermetic Tradition,” by William York Tindall
(Journal of the History of Ideas , Jan. 1954).

Saturday, December 28, 2019

Caballo Blanco

Filed under: General — Tags: , , , — m759 @ 9:02 AM

The key  is the cocktail that begins the proceedings.”

– Brian Harley, Mate in Two Moves

http://www.log24.com/log/pix18/180809-The_EIght-and-coordinates-for-PSL(2,7)-actions-500w.jpg

“Just as these lines that merge to form a key
Are as chess squares . . . .” — Katherine Neville, The Eight

“The complete projective group of collineations and dualities of the
[projective] 3-space is shown to be of order [in modern notation] 8! ….
To every transformation of the 3-space there corresponds
a transformation of the [projective] 5-space. In the 5-space, there are
determined 8 sets of 7 points each, ‘heptads’ ….”

— George M. Conwell, “The 3-space PG (3, 2) and Its Group,”
The Annals of Mathematics , Second Series, Vol. 11, No. 2 (Jan., 1910),
pp. 60-76.

“It must be remarked that these 8 heptads are the key  to an elegant proof….”

— Philippe Cara, “RWPRI Geometries for the Alternating Group A8,” in
Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference
(July 16-21, 2000), Kluwer Academic Publishers, 2001, ed. Aart Blokhuis,
James W. P. Hirschfeld, Dieter Jungnickel, and Joseph A. Thas, pp. 61-97.

Sunday, December 22, 2019

M24 from the Eightfold Cube

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

Exercise:  Use the Guitart 7-cycles below to relate the 56 triples
in an 8-set (such as the eightfold cube) to the 56 triangles in
a well-known Klein-quartic hyperbolic-plane tiling. Then use
the correspondence of the triples with the 56 spreads of PG(3,2)
to construct M24.

Click image below to download a Guitart PowerPoint presentation.

See as well earlier posts also tagged Triangles, Spreads, Mathieu.

Friday, December 20, 2019

Triangles, Spreads, Mathieu…

Filed under: General — Tags: , — m759 @ 1:38 AM

Continued.

An addendum for the post “Triangles, Spreads, Mathieuof Oct. 29:

Wednesday, December 11, 2019

Miracle Octad Generator Structure

Filed under: General — Tags: , , — m759 @ 11:44 PM

Miracle Octad Generator — Analysis of Structure

(Adapted from Eightfold Geometry, a note of April 28, 2010.
See also the recent post Geometry of 6 and 8.)

Sunday, December 8, 2019

Geometry of 6 and 8

Filed under: General — Tags: , , — m759 @ 4:03 AM

Just as
the finite space PG(3,2) is
the geometry of the 6-set, so is
the finite space PG(5,2)
the geometry of the 8-set.*

Selah.

* Consider, for the 6-set, the 32
(16, modulo complementation)
0-, 2-, 4-, and 6-subsets,
and, for the 8-set, the 128
(64, modulo complementation)
0-, 2-, 4-, 6-, and 8-subsets.

Update of 11:02 AM ET the same day:

See also Eightfold Geometry, a note from 2010.

Friday, November 22, 2019

Triangles, Spreads, Mathieu …

Filed under: General — Tags: , — m759 @ 4:39 PM

Continued from October 29, 2019.

More illustrations (click to enlarge) —

Thursday, October 31, 2019

56 Triangles

Filed under: General — Tags: , — m759 @ 8:09 AM

The post “Triangles, Spreads, Mathieuof October 29 has been
updated with an illustration from the Curtis Miracle Octad Generator.

Related material — A search in this journal for “56 Triangles.”

Tuesday, October 29, 2019

Triangles, Spreads, Mathieu

Filed under: General — Tags: , — m759 @ 8:04 PM

There are many approaches to constructing the Mathieu
group M24. The exercise below sketches an approach that
may or may not be new.

Exercise:

It is well-known that

 There are 56 triangles in an 8-set.
There are 56 spreads in PG(3,2).
The alternating group An is generated by 3-cycles.
The alternating group Ais isomorphic to GL(4,2).

Use the above facts, along with the correspondence
described below, to construct M24.

Some background —

A Log24 post of May 19, 2013, cites

Peter J. Cameron in a 1976 Cambridge U. Press
book — Parallelisms of Complete Designs .
See the proof of Theorem 3A.13 on pp. 59 and 60.

See also a Google search for “56 triangles” “56 spreads” Mathieu.

Update of October 31, 2019 — A related illustration —

Update of November 2, 2019 —

See also p. 284 of Geometry and Combinatorics:
Selected Works of J. J. Seidel
  (Academic Press, 1991).
That page is from a paper published in 1970.

Update of December 20, 2019 —

Wednesday, July 31, 2019

Broadway* News

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

* … and off-Broadway —

Prince reportedly died today in Reykjavik.

Tuesday, July 9, 2019

Schoolgirl Space: 1984 Revisited

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

Cube Bricks 1984 —

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

From "Tomorrowland" (2015) —

From John Baez (2018) —

See also this morning's post Perception of Space 
and yesterday's Exploring Schoolgirl Space.

Perception of Space

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

(Continued)

The three previous posts have now been tagged . . .

Tetrahedron vs. Square  and  Triangle vs. Cube.

Related material —

Tetrahedron vs. Square:

Labeling the Tetrahedral Model  (Click to enlarge) —

Triangle vs. Cube:

and, from the date of the above John Baez remark —

Monday, July 8, 2019

Exploring Schoolgirl Space

See also "Quantum Tesseract Theorem" and "The Crosswicks Curse."

Wednesday, June 5, 2019

The Tigerman Kaballah

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

See also Life of Pi   in this  journal.

Tuesday, June 4, 2019

Zen and the Art

Filed under: General — Tags: , , — m759 @ 6:13 PM

Or:  Burning Bright

A post in memory of Chicago architect Stanley Tigerman,
who reportedly died at 88 on Monday.

“Hello the Camp”

Filed under: General — Tags: , — m759 @ 12:20 AM

The title is a quotation from the 2015 film "Mojave."

Thursday, February 7, 2019

Geometry of the 4×4 Square: The Kummer Configuration

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

From the series of posts tagged Kummerhenge

A Wikipedia article relating the above 4×4 square to the work of Kummer —

A somewhat more interesting aspect of the geometry of the 4×4 square
is its relationship to the 4×6 grid underlying the Miracle Octad Generator
(MOG) of R. T. Curtis.  Hudson's 1905 classic Kummer's Quartic Surface
deals with the Kummer properties above and also foreshadows, without
explicitly describing, the finite-geometry properties of the 4×4 square as
a finite affine 4-space — properties that are of use in studying the Mathieu
group M24  with the aid of the MOG.

Thursday, December 6, 2018

The Mathieu Cube of Iain Aitchison

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.

Saturday, October 13, 2018

Location: Endor

Filed under: General — Tags: — m759 @ 2:26 PM

See also Space Writer in this  journal.

Space 101

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

Screenshot of a tweet by space writer Shannon Stirone
posted at 10:57 PM ET October 12 —

See also NASA + Wiig.

Stirone has an opinion piece in today's online New York Times  promoting NASA.

Discussing the Hubble Space Telescope, she claims that . . .

"Hubble peers deep into space, patiently collecting the universe’s traveling light,
then delivering it to us in never before seen images: galaxies, supernovas and
nebulae. It is a time machine. And without it we wouldn’t know we are inside
a galaxy that is just one of possibly trillions."

Thursday, September 20, 2018

Clash of the Titans

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

Thursday, July 12, 2018

The Bell

Filed under: General — Tags: , , — m759 @ 6:11 PM

Three hidden keys open three secret gates
Wherein the errant will be tested for worthy traits
And those with the skill to survive these straits
Will reach The End where the prize awaits

— Ready Player One , by Ernest Cline

“Look, my favorite expression is,
‘When you go up to the bell, ring it,
or don’t go up to the bell.’
We’ve gone too far. We have to ring the bell.”

Mel Brooks on “The Producers”
in The New York Times  today.

A 2016 Scribner edition of Stephen King’s IT —

Related material —

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

Kummerhenge Illustrated

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

      

“… the utterly real thing in writing is the only thing that counts…."

— Maxwell Perkins to Ernest Hemingway, Aug. 30, 1935

"Omega is as real  as we need it to be."

— Burt Lancaster in "The Osterman Weekend"

Wednesday, July 11, 2018

Titans

Filed under: General — Tags: — m759 @ 5:01 PM

"By The Boston Globe

July 10, 2018

The private jets have begun clogging the jetways
in Sun Valley, Idaho, which can only mean one thing:
'Billionaire summer camp’' has begun.

The annual Allen & Company conference, the investment
firm’s invite-only gathering of some of the world’s most
powerful corporate titans, officially begins on Wednesday."

In other news —

"NASHVILLE, Tenn. 

Get ready to see the Titans in training camp."

See also another  post now tagged "Clash of the Titans."

Sunday, July 1, 2018

Deutsche Ordnung

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

Related structures —

Greg Egan’s animated image of the Klein quartic —

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

Steiner quadruple system in eightfold cube

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

See also, from an April 2013 philosophical conference:

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

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

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

For the talk itself, see a YouTube video.

The conference talks also appear in a book.

The book begins with an epigraph by Hilbert

Friday, June 29, 2018

Triangles in the Eightfold Cube

Filed under: General,Geometry — Tags: , — m759 @ 9:10 PM

From a post of July 25, 2008, “56 Triangles,” on the Klein quartic
and the eightfold cube

Baez’s discussion says that the Klein quartic’s 56 triangles
can be partitioned into 7 eight-triangle Egan ‘cubes’ that
correspond to the 7 points of the Fano plane in such a way
that automorphisms of the Klein quartic correspond to
automorphisms of the Fano plane. Show that the
56 triangles within the eightfold cube can also be partitioned
into 7 eight-triangle sets that correspond to the 7 points of the
Fano plane in such a way that (affine) transformations of the
eightfold cube induce (projective) automorphisms of the Fano plane.”

Related material from 1975 —

More recently

Monday, June 25, 2018

The Trials of Device

Filed under: General — Tags: — m759 @ 9:34 AM

"A blank underlies the trials of device."

Wallace Stevens

"Designing with just a blank piece of paper is very quiet."

Kate Cullinane

Related material —

An image posted at 12 AM ET December 25, 2014:

The image stands for the
phrase "five by five,"
meaning "loud and clear."

Other posts featuring the above 5×5 square with some added structure:

Thursday, June 21, 2018

Kummerhenge

Filed under: General,Geometry — Tags: , — m759 @ 2:19 AM

See also the Omega Matrix in this  journal.

Tuesday, June 19, 2018

Ici vient M. Jordan

Filed under: General,Geometry — Tags: , — m759 @ 2:13 AM

NY Times correction, online June 16, about 'Here Comes Mr. Jordan' and 'Heaven Can Wait'

See also this  journal on Saturday morning, June 16.

Monday, April 23, 2018

Facets

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

Counting symmetries with the orbit-stabilizer theorem

See also the Feb. 17, 2017, post on Bertram Kostant
as well as "Mathieu Moonshine and Symmetry Surfing."

Friday, February 2, 2018

For Plato’s Cave

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

"Plato's allegory of the cave describes prisoners,
inhabiting the cave since childhood, immobile,
facing an interior wall. A large fire burns behind
the prisoners, and as people pass this fire their
shadows are cast upon the cave's wall, and
these shadows of the activity being played out
behind the prisoner become the only version of
reality that the prisoner knows."

— From the Occupy Space gallery in Ireland

IMAGE- Patrick McGoohan as 'The Prisoner,' with lapel button that says '6.'

Monday, November 27, 2017

The Golay Code via Witt’s Construction

Filed under: General,Geometry — Tags: — m759 @ 2:08 PM

Reference

Hansen, Robert Peter, "Construction and Simplicity of
the Large Mathieu Groups" (2011). Master's Theses. 4053. 
http://scholarworks.sjsu.edu/etd_theses/4053.

See also The Matrix Meets the Grid (Log24, Nov. 24).
More generally, see SPLAG in this journal.

Sunday, August 27, 2017

Profiling

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

See also earlier posts tagged Profiling Trump.

Friday, August 11, 2017

Symmetry’s Lifeboat

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

A post suggested by the word tzimtzum  (see Wednesday)
or tsimtsum  (see this morning) —

Lifeboat from the Tsimtsum  in Life of Pi  —

Another sort of tsimtsum, contracting infinite space to a finite space —

IMAGE- Desargues's theorem in light of Galois geometry

Thursday, May 25, 2017

Presidential Address of November 19, 1976

Filed under: General — Tags: — m759 @ 2:14 PM

Deep Problems in the Faculty Lounge

Filed under: General — Tags: — m759 @ 7:14 AM

The Story of Six Continues

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

A post of March 22, 2017, was titled "The Story of Six."

Related material from that date —

"I meant… a larger map." — Number Six in "The Prisoner"

Wednesday, April 26, 2017

A Tale Unfolded

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

A sketch, adapted tonight from Girl Scouts of Palo Alto

From the April 14 noon post High Concept

From the April 14 3 AM post Hudson and Finite Geometry

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

From the April 24 evening post The Trials of Device

Pentagon with pentagram    

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

Wednesday, March 22, 2017

The Story of Six

Filed under: General,Geometry — Tags: , , — m759 @ 8:01 PM

On a psychotherapist who died at 86 on Monday —

"He studied mathematics and statistics at the Courant Institute,
a part of New York University — he would later write   a
mathematical fable, Numberland  (1987)."

The New York Times  online this evening
 


 

From Publishers Weekly

This wry parable by a psychotherapist contains one basic message: though death is inevitable, each moment in life is to be cherished. In the orderly but sterile kingdom of Numberland, digits live together harmoniously under a rigid president called The Professor. Their stable society is held intact by the firm conviction that they are immortal: When has a number ever died? This placid universe is plunged into chaos when the inquisitive hero SIX crosses over into the human world and converses with a young mathematician. This supposedly impossible transition convinces the ruling hierarchy that if SIX can talk to a mortal, then the rest of the numbers are, after all, mortal. The digits conclude that any effort or achievement is pointless in the face of inevitable death, and the cipher society breaks down completely. The solution? Banish SIX to the farthest corners of kingdom. Weinberg (The Heart of Psychotherapy ) uses his fable to gently satirize the military, academics, politicians and, above all, psychiatrists. But his tale is basically inspirational; a triumphant SIX miraculously returns from exile and quells the turmoil by showing his fellow digits that knowledge of one's mortality should enrich all other experiences and that death ultimately provides a frame for the magnificent picture that is life. 

Copyright 1987 Reed Business Information, Inc.

See also The Prisoner in this journal.

Tuesday, March 7, 2017

Signature Backdrop

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

"The Bitter End’s signature stage backdrop —
a bare 150-year-old brick wall — helped distinguish it from
other popular bohemian hangouts like the Village Gate  
and the Village Vanguard. It appeared on the cover of
Peter, Paul and Mary’s first album."

The New York Times  this evening on a Sunday death

Commentary

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

— Richard Evan Schwartz

See also Schwartz in "The Omega Matrix," a post of 5 PM ET Sunday:

Thursday, December 8, 2016

Finite Groups and Their Geometric Representations

Filed under: General,Geometry — Tags: — m759 @ 8:06 AM

The title is that of a presentation by Arnold Emch
at the 1928 International Congress of Mathematicians:

See also yesterday's "Emch as a Forerunner of S(5, 8, 24)."

Related material: Diamond Theory in 1937.

Further remarks:  Christmas 2013 and the fact that
759 × 322,560 = the order of the large Mathieu group  M24 .

Wednesday, December 7, 2016

Spreads and Conwell’s Heptads

Filed under: General,Geometry — Tags: — m759 @ 7:11 PM

For a concise historical summary of the interplay between
the geometry of an 8-set and that of a 16-set that is
involved in the the Miracle Octad Generator approach
to the large Mathieu group M24, see Section 2 of 

Alan R. Prince
A near projective plane of order 6 (pp. 97-105)
Innovations in Incidence Geometry
Volume 13 (Spring/Fall 2013).

This interplay, notably discussed by Conwell and
by Edge, involves spreads and Conwell’s heptads .

Update, morning of the following day (7:07 ET) — related material:

See also “56 spreads” in this  journal.

Wednesday, November 30, 2016

Language Game

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

Tuesday, September 27, 2016

Chomsky and Lévi-Strauss in China

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

Or:  Philosophy for Jews

From a New Yorker  weblog post dated Dec. 6, 2012 —

"Happy Birthday, Noam Chomsky" by Gary Marcus—

"… two titans facing off, with Chomsky, as ever,
defining the contest"

"Chomsky sees himself, correctly, as continuing
a conversation that goes back to Plato, especially
the Meno dialogue, in which a slave boy is
revealed by Socrates to know truths about
geometry that he hadn’t realized he knew."

Socrates and the slave boy discussed a rather elementary "truth
about geometry" — A diamond inscribed in a square has area 2
(and side the square root of 2) if the square itself has area 4
(and side 2).

Consider that not-particularly-deep structure from the Meno dialogue
in the light of the following…

The following analysis of the Meno diagram from yesterday's
post "The Embedding" contradicts the Lévi-Strauss dictum on
the impossibility of going beyond a simple binary opposition.
(The Chinese word taiji  denotes the fundamental concept in
Chinese philosophy that such a going-beyond is both useful
and possible.)

The matrix at left below represents the feminine yin  principle
and the diamond at right represents the masculine yang .

      From a post of Sept. 22,
  "Binary Opposition Illustrated" —

A symbol of the unity of yin and yang —

Related material:

A much more sophisticated approach to the "deep structure" of the
Meno diagram —

The larger cases —

The diamond theorem

Monday, September 12, 2016

The Kummer Lattice

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

The previous post quoted Tom Wolfe on Chomsky's use of
the word "array." 

An example of particular interest is the 4×4  array
(whether of dots or of unit squares) —

      .

Some context for the 4×4 array —

The following definition indicates that the 4×4 array, when
suitably coordinatized, underlies the Kummer lattice .

Further background on the Kummer lattice:

Alice Garbagnati and Alessandra Sarti, 
"Kummer Surfaces and K3 surfaces
with $(Z/2Z)^4$ symplectic action." 
To appear in Rocky Mountain J. Math.

The above article is written from the viewpoint of traditional
algebraic geometry. For a less traditional view of the underlying
affine 4-space from finite  geometry, see the website
Finite Geometry of the Square and Cube.

Some further context

"To our knowledge, the relation of the Golay code
to the Kummer lattice is a new observation."

— Anne Taormina and Katrin Wendland,
"The overarching finite symmetry group of
Kummer surfaces in the Mathieu group M24 
"

As noted earlier, Taormina and Wendland seem not to be aware of
R. W. H. T. Hudson's use of the (uncoordinatized*) 4×4 array in his
1905 book Kummer's Quartic Surface.  The array was coordinatized,
i.e. given a "vector space structure," by Cullinane eight years prior to
the cited remarks of Curtis.

* Update of Sept. 14: "Uncoordinatized," but parametrized  by 0 and
the 15 two-subsets of a six-set. See the post of Sept. 13.

The Kingdom of Arrays

Filed under: General — Tags: — m759 @ 11:07 AM

Chomsky and arrays, from Tom Wolfe's 'The Kingdom of Speech'

See also Array  in this journal.

Thursday, September 1, 2016

Bedtime Story

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

For midnight retirees —

See also Leibniz medal in this journal.

Friday, August 26, 2016

Wolfe vs. Chomsky

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

1.  Tom Wolfe has a new book on Chomsky, "The Kingdom of Speech."

2.  This suggests a review of a post of Aug. 11, 2014, Syntactic/Symplectic.

To paraphrase Wittgenstein, sentence 1 above is about "correlating in real life"
(cf. Crooked House and Wolfe's From Bauhaus to Our House ), and may be 
compared to sentence 2 above, which links to a sort of "correlating in
mathematics" that is a particular example of the more general sort of
mathematical correlating mentioned by Wittgenstein in 1939.

Thursday, August 4, 2016

Routine

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

Peter Gelzinis in the Boston Herald  today

"What has become painfully clear this week
is that there is no Republican campaign for
the presidency. There is only The Donald,
his 
reflex tweets, the folded pieces of paper
he pulls out of his coat pocket and a crazy
stand-up routine that is part Lenny Bruce
and part professor Irwin Corey."

APPLAUSE

Another Diagnostic Jew

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

"Take that baby,  please! "

See also the previous post.

The Soltan Diagnosis

Filed under: General — Tags: — m759 @ 2:26 PM

Prof. Margaret Soltan's psychiatric diagnosis of Donald Trump

Professor Soltan, a fan of James Joyce, would do well
to apply her diagnostic powers to Finnegans Wake , 
a word salad if ever there was one.

Related recommended reading:

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)

Sunday, December 27, 2015

Rigorous

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

A death on Xmas Day

Artist Josefine Lyche

IMAGE- Josefine Lyche bowling, from her Facebook page

Symbol

Monday, November 7, 2011

The X Box

Filed under: Uncategorized — m759 @ 10:30 AM 

"Design is how it works." — Steve Jobs, quoted in
The New York Times Magazine  on St. Andrew's Day, 2003.

The X-Box Sum .

For some background on this enigmatic equation,
see Geometry of the I Ching.

Saturday, December 26, 2015

Midnight Reflection

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

Mirror, Mirror, on the wall,
Robbing Peter, paying Paul

Friday, December 25, 2015

At Play in the Fields

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

See Fields of Force  and recent posts.

From PR Newswire  in July 2011 —

Campus Crusade for Christ Adopts New Name: Cru
60-year-old Int'l Ministry Aims to Increase
Relevance and Global Effectiveness

Related material:

Yin + Yang —

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

Dark Symbol

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

Related material:

The previous post (Bright Symbol) and
a post from Wednesday,
December 23, 2015, that links to posts
on Boolean algebra vs. Galois geometry.

“An analogy between mathematics and religion is apposite.”

— Harvard Magazine  review by Avner Ash of
Mathematics without Apologies
(Princeton University Press, January 18, 2015)

Bright Symbol

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

Detail:

Thursday, December 24, 2015

Group Actions…

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

On the Eight

Sunday, December 6, 2015

Form and Idea

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

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

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

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

IMAGE- 'American Hustle' and Art Cube

Discuss.

Monday, November 16, 2015

Good Question.

Filed under: General — Tags: — m759 @ 4:00 PM

YouTube 

Uploaded on Sep 17, 2009

Who'll love the devil?
Who'll sing his song?
Who will love the devil and his song?

"The pictures are understood to have been taken
just a few minutes before three gunmen burst into
the venue at 9.40pm (8.40pm GMT) as the
Californian rock band were launching into one of
their favourites, Kiss The Devil."

Read more: DailyMail.com.

The End of the Tour

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

From this date four years ago —

Click the following image for other examples of "complex style."

Sunday, August 9, 2015

The Cauldron

Filed under: General — Tags: — m759 @ 7:19 AM

From a review of the 2013 film "The Wolverine" —

"The rituals, culture and hierarchies of Japan
have intrigued and baffled the typical Westerner
for centuries …."

Not to mention those of China 

 Hexagram 50:
         
Ding
The Cauldron

Nine is a Vine

Filed under: General — Tags: — m759 @ 6:50 AM

Backstory:  That phrase in this journal.

““The serpent’s eyes shine
As he wraps around the vine….”
– Don Henley

With Derrida, as usual, playing the role of
the serpent, see a philosophical meditation from
October 9, 2014, by a perceptive and thoughtful Eve
that includes the following passage:

“But, before this and first of all, there is
the resistance posed by the work itself,
the hard kernel formed when the intelligibility
of a universal ‘message’ is joined to the
unintelligible secret of a singularity.”

See as well the word “kernel” here.

Cryptomorphisms

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

Backstory:  Other posts tagged “Cryptomorphisms,”
and the word itself in Wikipedia.

Compare and contrast:

Baez and Baez

Hegel and Genet

Heaven and Hell.

Knell

Filed under: General — Tags: , — m759 @ 5:19 AM

From a French dictionary

Tintement lent, sur une seule note,
d’une cloche d’église pour annoncer
l’agonie, la mort ou les obsèques de
quelqu’un.
 

” I go, and it is done: the bell invites me.
Hear it not, Duncan, for it is a knell
That summons thee to heaven, or to hell. “

Wednesday, July 22, 2015

Harvard Death

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

Bloomberg.com —
July 21, 2015 — 3:51 PM EDT
Updated on July 21, 2015 — 6:04 PM EDT —

James Rothenberg of Capital Group
Dies at 69 of Heart Attack

"He was  chairman of Harvard Management Co.,
which invests the university’s $36.4 billion endowment."

See also  
The Harvard Crimson —
UPDATED: July 22, 2015, at 1:28 a.m.

"Rothenberg’s death, reportedly of a heart attack,
was unexpected."

He reportedly "chaired Harvard Management Company’s
board of directors from 2004 until his death."

Tuesday, July 21, 2015

“Ragtime” Author Dies at 84

Filed under: General — Tags: — m759 @ 11:55 PM

“…right through hell
     there is a path…”
 
  — Malcolm Lowry

E!

Filed under: General — Tags: — m759 @ 6:19 PM

Monday, June 15, 2015

Slow Art

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

Slowness is sometimes in the eye of the beholder.

See this journal on Slow Art Day 2015.

Related material: Epistemic States in this journal.

Wednesday, May 27, 2015

The Coffee Detective

Filed under: General — Tags: , — m759 @ 7:01 AM

See also this morning's earlier posts.

Voiced

Filed under: General — Tags: , — m759 @ 6:06 AM

"J.A.R.V.I.S. (Stands for Just A Rather Very Intelligent System),
also stylized as JARVIS, or Jarvis, is a highly advanced
computerized A.I. developed by Tony Stark, and was voiced
by actor Paul Bettany, to manage almost everything, especially
matters related to technology, in Tony's life."

Happy birthday, Mr. Bettany.

View from the intersection of U.S. Routes 6 and 62.

Grindhouse

Filed under: General — Tags: , — m759 @ 5:12 AM

For Madonna —

Mainlining

Filed under: General — Tags: , — m759 @ 4:45 AM

"Looking for what was, where it used to be" —Wallace Stevens

A section of Route 6 at the former location of an A&P store —

"Wake up and smell the coffee" —

Tuesday, May 26, 2015

Colorful Tales

Filed under: General — Tags: , — m759 @ 9:50 PM

See also the Log24 post from May 18,
the date of Eric Caidin's reported death,
as well as Hexagram 50 and May 14, 2014—
Death in Mathmagic Land.

Thursday, April 16, 2015

National Library Week

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

"Celebrate National Library Week 2015 (April 12-18, 2015)
with the theme "Unlimited possibilities @ your library®."

See also Library of Hell.

A page from Princeton University Press on March 18, 2012:

IMAGE- 'Circles Disturbed: The Interplay of Mathematics and Narrative,' p. xvi

… "mathematics and narrative…." (top of page xvii).

I prefer the interplay of Euclidean  and Galois  mathematics.

Forms of Luminosity

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

"Visibilities are not forms of objects, nor even forms
that would show up under light, but rather forms of
luminosity which are created by the light itself and
allow a thing or object to exist only as a flash, sparkle
or shimmer."

— Deleuze, Foucault

Clap if you believe in Plotnitsky .

From his "Teaching" page

Capitalism and Paranoia, Capitalism and Schizophrenia: Foucault, Deleuze, and Modernist Novel. The course offers a comprehensive examination of the works of Michel Foucault and Gilles Deleuze, and of the relationships between their ideas and the culture of modernity and, then, postmodernity, as the culture of capitalism. The course also considers, through the optics of Foucault's and Deleuze's work, how this culture is reflected in modernist and postmodernist novels of the twentieth century, and in the genre of the novel itself, which has been the dominant and indeed defining literary genre of this culture, from early to late capitalism. While Foucault's and Deleuze's work may be seen as a radical philosophical critique of modernity and capitalism by the philosophical means, the novel enacts an analogous and often equally radical literary critique. The works to be discussed include selections from Marx, Nietzsche, and Freud; Foucault's The Order of ThingsDiscipline and Punish, History of Sexuality, vol.1, and selected essays; and substantive selections from such works by Deleuze (and Deleuze and Guattari) as Anti-OedipusA Thousand Plateaus, and Foucault, as well as several shorter essays. Among the works of fiction to be considered are Joyce's A Portrait of the Artist as a Young Man; Kafka's The Trial; Woolf's Orlando; and Pynchon's The Crying of Lot 49.

Monday, April 13, 2015

Is That a Fish in Your Ear?*

Filed under: General — Tags: — m759 @ 7:24 PM

(Continued from April 9)

*… Or a Spearhead?

Hermeneutics for Academics

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

Würfel-Märchen  continued 

"Again, you are free to interpret these symbols
 as you like."

See also

Through the Looking Glass: A Sort of Eternity —

and The Library of Hell.

Unorthodox Easter

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

(A sequel to yesterday's Orthodox Easter posts)

This morning's Google News —

The New York Times  on the late Günter Grass —

"Many of Mr. Grass’s books are phantasmagorical
mixtures of fact and fantasy, some of them inviting
comparison with the Latin American style known as
magical realism. His own name for this style was
'broadened reality.'"

From p. xii of the 2005 second edition of a book discussed
in yesterday's Orthodox Easter posts —

(Click image to enlarge.)

Early editions of The Heart of Mathematics  include 
Gary Larson's legendary Hell's Library "Far Side" cartoon. 
Books in Hell's Library include Big Book of Story Problems ,
More Story Problems , and Even More Story Problems .

— Adapted from a review of the 2000 first edition

See also Mathematics and Narrative in this journal.

Wednesday, April 8, 2015

For Students of the Forked Tongue

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

IMAGE- Daily Princetonian- U. acquires personal library of philosopher Jacques Derrida

See also "Derrida + Serpent" in this journal.

Tuesday, March 31, 2015

Würfel-Märchen

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

See also Würfel in this journal.

Saturday, December 20, 2014

Dark Fields continued

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

A  Christmas  Ornament  for  Amy  Adams —

Wednesday, August 13, 2014

Stranger than Dreams*

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

Illustration from a discussion of a symplectic structure 
in a 4×4 array quoted here on January 17, 2014 —

See symplectic structure in this journal.

* The final words of Point Omega , a 2010 novel by Don DeLillo.
See also Omega Matrix in this journal.

Thursday, August 7, 2014

The Omega Mystery

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

See a post,  The Omega Matrix, from the date of her death.

Related material:

"When Death tells a story, you really have to listen."
— Cover of The Book Thief

A scene from the film of the above book —

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

— Richard Evan Schwartz

Some context — "Mathematics, Magic, and Mystery" —
See posts tagged April Awareness 2014.

Tuesday, August 5, 2014

The Omega Story

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

"We tell ourselves stories in order to live…. We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the 'ideas' with which we have learned to freeze the shifting phantasmagoria which is our actual experience."

Joan Didion

See also a post from May 4, 2011 (the date, according to a Google
search, of untitled notes regarding a matrix called Omega).

Monday, August 4, 2014

A Wrinkle in Space

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

"There is  such a thing as a tesseract." — Madeleine L'Engle

An approach via the Omega Matrix:

http://www.log24.com/log/pix10A/100619-TesseractAnd4x4.gif

See, too, Rosenhain and Göpel as The Shadow Guests .

Tuesday, December 31, 2013

Objects of Beauty

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

(Continued)

"I am a town." — Mary Chapin Carpenter

"A town, huh?" — Sydney Prosser

Related material — "Put on your red dress, baby."

Christmas Ornaments

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

Continued from December 25

IMAGE- Count rotational symmetries by rotating facets. Illustrated with 'Plato's Dice.'

A link from Sunday afternoon to Nov. 26, 2012,
suggests a review of one of the above structures.

The Dreaming Jewels  cover at left is taken from a review
by Jo Walton at Tor.com—

"This is a book that it’s clearly been difficult
for publishers to market. The covers have been
generally pretty awful, and also very different.
I own a 1975 Corgi SF Collectors Library
paperback that I bought new for 40p in the later
seventies. It’s purple, and it has a slightly grainy
cover, and it matches my editions of The Menace
From Earth
  and A Canticle for Leibowitz .
(Dear old Corgi SF Collectors Editions with their
very seventies fonts! How I imprinted on them at
an early age!) I mention this, however, because
the (uncredited) illustration actually represents and
illustrates the book much better than any of the other
cover pictures I’ve seen. It shows a hexagon with an
attempt at facets, a man, a woman, hands, a snake,
and stars, all in shades of green. It isn’t attractive,
but it wouldn’t put off people who’d enjoy what’s inside
either."

The "hexagon with an attempt at facets" is actually
an icosahedron, as the above diagram shows.
(The geometric part of the diagram is from a Euclid webpage.)

For Plato's dream about these jewels, see his Timaeus.

Thursday, December 26, 2013

Dicey

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

For fans of Hunger Games  and Elysium —

Roberta Smith in this evening's* online New York Times

"Especially with the gap between the wealthiest
and everyone else so wide, it is dicey
for a major museum to celebrate the often frivolous
objects on which the rich spend their ever increasing
surplus income. Such a show must be beyond reproach
in every way: transparent in organization, impeccable
in exhibition design, illuminating in catalog and labeling
and, most of all, self-evidently excellent in the quality of
the objects on display."

Da capo:  "I've heard of affairs that are strictly Platonic."

* 5:08 PM ET

How It Works

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

(Continued)

“Design is how it works.” — Steve Jobs

“By far the most important structure in design theory
is the Steiner system S(5, 8, 24).”

— “Block Designs,” by Andries E. Brouwer (Ch. 14 (pp. 693-746),
Section 16 (p. 716) of Handbook of Combinatorics, Vol. I ,
MIT Press, 1995, edited by Ronald L. Graham, Martin Grötschel,
and László Lovász)

For some background on that Steiner system, see the footnote to
yesterday’s Christmas post.

Wednesday, December 25, 2013

Rotating the Facets

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

Previous post

“… her mind rotated the facts….”

Related material— hypercube rotation,* in the context
of rotational symmetries of the Platonic solids:

IMAGE- Count rotational symmetries by rotating facets. Illustrated with 'Plato's Dice.'

“I’ve heard of affairs that are strictly Platonic”

Song lyric by Leo Robin

* Footnote added on Dec. 26, 2013 —

 See Arnold Emch, “Triple and Multiple Systems, Their Geometric
Configurations and Groups
,” Trans. Amer. Math. Soc.  31 (1929),
No. 1, 25–42.

 On page 42, Emch describes the above method of rotating a
hypercube’s 8 facets (i.e., three-dimensional cubes) to count
rotational symmetries —

See also Diamond Theory in 1937.

Also on p. 42, Emch mentions work of Carmichael on a
Steiner system with the Mathieu group M11 as automorphism
group, and poses the problem of finding such systems and
groups that are larger. This may have inspired the 1931
discovery by Carmichael of the Steiner system S(5, 8, 24),
which has as automorphisms the Mathieu group M24 .

Rotating the Facts

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

IMAGE- 'American Hustle' and Art Cube

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

— Steve Martin, An Object of Beauty

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

A Midnight Clear

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

Click image for a meditation.

Sunday, October 6, 2013

Sunday Dinner (continued)

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

Judith Shulevitz in The New York Times
on Sunday, July 18, 2010
(quoted here Aug. 15, 2010) —

“What would an organic Christian Sabbath look like today?”

One possibility —

See also The Pride of Lowell  (Oct. 3, 2012)
and, a year later, The Hunt for Green October .

Friday, September 6, 2013

Space

Filed under: General,Geometry — Tags: — m759 @ 9:15 PM

"A vast space that travels down to the bedrock
upon which the towers were built, the museum
winds its way deeper and deeper underground,
taking visitors on a journey to the very bottom."

— The Associated Press in
this evening's Washington Post

This suggests a review of a different sort of
bedrock:—

IMAGE- Right 3-4-5 triangle with squares on sides and hypotenuse as base

"If you have built castles in the air, 
your work need not be lost;
that is where they should be.
Now put the foundations under them.”

— Henry David Thoreau

Saturday, August 17, 2013

The Story of N…

Filed under: General — Tags: — m759 @ 8:28 PM

Continues.

IMAGE- Marissa Mayer on numbers in Vogue magazine

— Marissa Mayer in the current Vogue  online

Tuesday, August 13, 2013

The Story of N

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

(Continued from this morning)

http://www.log24.com/log/pix11/110107-The1950Aleph-Sm.jpg

The above stylized "N," based on
an 8-cycle in the 9-element Galois field
GF(9), may also be read as
an Aleph.

Graphic designers may prefer a simpler,
bolder version:

Plan 9

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

(Continued from August 28 last year)

Backstory— 

Reflections from today's date, August 13, in 2003, that included
the following remark by Aldous Huxley on an artist's work:

"All the turmoil, all the emotions of the scenes
have been digested by the mind into a
grave intellectual whole. It is as though
Bach had written the 1812 Overture."

Related art—

Josefine Lyche, from her 2013 Crackquarelle  series:

IMAGE- From the 2013 Josefine Lyche 'Crackquarelle' series

Steven H. Cullinane, The Story of N ,
from The Misalignment of Mars and Venus series:

http://www.log24.com/log/pix11B/110720-Misaligned.jpg

See, too, previous posts on The Story of N.

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