Friday, August 31, 2012


Filed under: General — Tags: — m759 @ 6:08 AM

"Translation in the direction
conceptual -> concrete and symbolic
is much easier than
translation in the reverse direction…."

The late William P. Thurston

(See also "Atlas to the Text," Harvard Crimson , March 8, 2011).

Related cinematic imagery

Conceptual  (thanks to Don DeLillo and The New York Times )—

IMAGE- NY Times headline 'A Wrinkle in Time' with 24 Hour Psycho and Point Omega scene

Concrete and symbolic (thanks to Amy Adams and Emily Blunt, as well as
Frederick Seidel in the September 3, 2012, New Yorker )

"Biddies still cleaned the student rooms."

IMAGE- Shower wall in 'Sunshine Cleaning'

Thursday, August 30, 2012

The Cruelest Month

Filed under: General — Tags: — m759 @ 6:08 AM

Last night's 10 PM post linked to an April 7, 2012,
post that through a series of further links leads
to Columbia Film Theory .

For other film-related remarks, by a
Columbia alumnus,* see last night's post.

See also the 1.3 MB image from Aug. 16, the night 
of Elvis's Wrap Party. An excerpt from that image
stars Amy Adams—

Images, including the late Richard Zanuck

For Amy, from the current New Yorker

The Master

* N.O.C.D.

Wednesday, August 29, 2012

It’s 10 PM…

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

Do you know where your children are?

Continued from Plan 9 , a Log24 post of  9 PM Monday

See another weblog's April 7, 2012, post on
God and Horror Movies.

See also this  weblog's post on that date.

Hexagram 18

Filed under: General — Tags: — m759 @ 9:14 AM

(Continued from June 14, 2007)

The late William P. Thurston on how mathematical knowledge may decay:

"There are several obvious mechanisms of decay. The experts in a subject retire and die, or simply move on to other subjects and forget. Mathematics is commonly explained and recorded in symbolic and concrete forms that are easy to communicate, rather than in conceptual forms that are easy to understand once communicated. Translation in the direction conceptual -> concrete and symbolic is much easier than translation in the reverse direction, and symbolic forms often replaces [sic ] the conceptual forms of understanding. And mathematical conventions and taken-for-granted knowledge change, so older texts may become hard to understand.

In short, mathematics only exists in a living community of mathematicians that spreads understanding and breaths [sic ] life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others. All of us have clear understanding of a few things and murky concepts of many more. There is no way to run out of ideas in need of clarification. The question of who is the first person to ever set foot on some square meter of land is really secondary. Revolutionary change does matter, but revolutions are few, and they are not self-sustaining — they depend very heavily on the community of mathematicians."

At mathoverflow.net, October 30, 2010.
     The discussion has been "closed as no longer relevant."
     For another Thurston quote of interest, see a more recent
     mathoverflow discussion "closed as not a real question."

Tuesday, August 28, 2012

Dark and Stormy

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

It  was a  dark and stormy night.

A Wrinkle in Time  (brought  up to date)

Up to Date

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

"Plato's cave was brought up to date in 1978…."

— Keith Devlin in Mathematics: The Science of Patterns

Related material from yesterday: Touchy-Feely and Plan 9.

"Plan 9 deals with the resurrection of the dead.

IMAGE- Bill Murray explains Ed Wood's 'Plan 9 from Outer Space'

For a rather different approach to Plato, see three posts of August 16, 2012—

Hope and Pope

Filed under: General — Tags: , , — m759 @ 4:59 AM

IMAGE- 'Hope of Heaven,' by John O'Hara, 1947 Avon paperback

Hope of Heaven , by John O'Hara
Avon paperback edition, 1947

   Heaven from all creatures hides the book of Fate,
All but the page prescribed, their present state:
From brutes what men, from men what spirits know:
Or who could suffer being here below?
The lamb thy riot dooms to bleed to-day,
Had he thy reason, would he skip and play?
Pleased to the last, he crops the flowery food,
And licks the hand just raised to shed his blood.
Oh, blindness to the future! kindly given,
That each may fill the circle, marked by Heaven:
Who sees with equal eye, as God of all,
A hero perish, or a sparrow fall,
Atoms or systems into ruin hurled,
And now a bubble burst, and now a world.
   Hope humbly, then; with trembling pinions soar;
Wait the great teacher Death; and God adore.
What future bliss, He gives not thee to know,
But gives that hope to be thy blessing now.
Hope springs eternal in the human breast:
Man never is, but always to be blest:
The soul, uneasy and confined from home,
Rests and expatiates in a life to come.

— Alexander Pope in An Essay on Man

Monday, August 27, 2012

Plan 9

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


IMAGE- 'The Ninth Configuration,' based on a novel by William Peter Blatty

See also "Or Only Die" and Corpus Hypercubus .


Filed under: General — Tags: , — m759 @ 5:24 AM

A remark by the late William P. Thurston

Please note: I'm not advocating that
we turn mathematics into a touchy-feely subject.

Noted. But see this passage—

The Mathematical Experience , by Philip J. Davis and Reuben Hersh (1981), updated study edition, Springer, 2011—

From the section titled "Four-Dimensional Intuition," pages 445-446:

"At Brown University Thomas Banchoff, a mathematician, and Charles Strauss, a computer scientist, have made computer-generated motion pictures of a hypercube….

… at the Brown University Computing Center, Strauss gave me a demonstration of the interactive graphic system which made it possible to produce such a film….

… Strauss showed me how all these controls could be used to get various views of three-dimensional projections of a hypercube. I watched, and tried my best to grasp what I was looking at. Then he stood up, and offered me the chair at the control.

I tried turning the hypercube around, moving it away, bringing it up close, turning it around another way. Suddenly I could feel  it!. The hypercube had leaped into palpable reality, as I learned how to manipulate it, feeling in my fingertips the power to change what I saw and change it back again. The active control at the computer console created a union of kinesthetics and visual thinking which brought the hypercube up to the level of intuitive understanding."

Thanks to the Web, a version of this experience created by Harry J. Smith
has been available to non-academics for some time.

IMAGE- The Harry J. Smith Memorial Tesseract

IMAGE- From 'Touchy-Feely: The Musical!'

Saturday, August 25, 2012

One Small Step

Filed under: General — Tags: — m759 @ 8:19 PM

Click image for some related material.

Illogical Songs*

Filed under: General — m759 @ 1:00 PM

IMAGE- Ship Ahoy

     Image from the New York Times Book Review  of August 26.
     See also a related song for Marxists who like Brecht.
     For some lighter entertainment, see a 1942 movie trailer.

* A sequel to today's noon post Logical Song (itself suggested
   by a Chautauqua, NY, end-of season event)

Logical Song

Filed under: General — m759 @ 12:00 PM

" Und ein Schiff mit acht Segeln…"

Seeräuber Jenny

For the Feast of Saint Louis

" Oed' und leer das Meer "

— Eliot, The Waste Land , from
     Wagner, Tristan und Isolde

Für Seeräuber Jenny

Filed under: General — m759 @ 2:01 AM


  1. Tonight's New York Times  obituaries —
    with an ad for a Terracotta Warriors  exhibit
  2. "Turn the page" in this  journal
  3. "A Page is a Door," by Remy Charlip
  4. Wendy Derleth in "Wishmaster."

Des Todes*

Filed under: General — m759 @ 1:22 AM

For a racecar driver who reportedly died in
Orange, California, on August 12— 

"Never one to take it slow, Grant was also an avid boater,
motorcyclist and aerobatic pilot. He last rode his motorcycle,
a BMW R1200R, on July 12."

"I love those Bavarians… so meticulous."

"The 'Valley of Death' is the oldest
concentration camp memorial in Bavaria."

* German for "Of Death."
   For a different Todes, see an obituary of a poet.
   See also Rosetta Jacobs in this journal.

Friday, August 24, 2012

Down for the Count

Filed under: General — m759 @ 8:00 PM

IMAGE- Jerry Nelson, voice of Count von Count, is dead at 78.

"For every kind of vampire…"

IMAGE- Eight-pointed star formed by the four symmetry axes of the square

Midnight in Geneva

Filed under: General — m759 @ 6:00 PM

Six PM EDT is midnight CEST in Geneva.

For the late Marvin W. Meyer, professor at Chapman
University in Orange, California, and a graduate
of Calvin College in Grand Rapids, Michigan…

A ticket out of town .

(Some background: Marilynne Robinson.)

Formal Pattern

Filed under: General,Geometry — m759 @ 4:28 PM

(Continued from In Memoriam (Aug. 22), Chapman's Homer (Aug. 23),
and this morning's Colorful Tale)

An informative, but undated, critique of the late Marvin W. Meyer
by April D. DeConick at the website of the Society of Biblical Literature
appeared in more popular form in an earlier New York Times
op-ed piece, "Gospel Truth," dated Dec. 1, 2007.

A check, in accord with Jungian synchronicity, of this  journal
on that date yields a quotation from Plato's Phaedrus  —

"The soul or animate being has the care of the inanimate."

Related verses from T. S. Eliot's Four Quartets

"The detail of the pattern is movement."

"So we moved, and they, in a formal pattern."

Some background from pure mathematics (what the late
William P. Thurston called "the theory of formal patterns")—

The Animated Diamond Theorem.

A Colorful Tale

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

(Continued from July 19, 2008)

From the Diamond 16 Puzzle

IMAGE- The Diamond 16 Puzzle

The resemblance between the "quadrants" part of
the above picture and the new Microsoft symbol

IMAGE- New Microsoft symbol, August 2012

— is of course purely coincidental, as is the fact
that the new symbol illustrates four colors.

Thursday, August 23, 2012

Chapman’s Homer

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

Louis Sahagun in today's Los Angeles Times

The late Professor Marvin W. Meyer

 "was our Indiana Jones,"  said James L. Doti,
president of Chapman University in Orange,
where Meyer held the Griset Chair in Bible
and Christian Studies and was director of
the Albert Schweitzer Institute.

Meyer reportedly died on August 16.

IMAGE- The late Professor Marvin W. Meyer of Chapman University in Orange, CA, with the university's emblem, the eight-pointed star

Thursday, August 16, 2012


m759 @ 4:00 AM

IMAGE- Eight-pointed star formed by the four symmetry axes of the square

"Two clichés make us laugh, but
a hundred clichés move us
because we sense dimly that the clichés
are talking among themselves and
celebrating a reunion."

— Umberto Eco

"'Casablanca': Cult Movies and Intertextual Collage,"
by Umberto Eco in SubStance , Vol. 14, No. 2, Issue 47:
In Search of Eco's Roses  (1985), pp. 3-12.

(This paper was presented at a symposium,
"Semiotics of the Cinema: The State of the Art,"
in Toronto on June 18, 1984.)
Journal article published by U. of Wisconsin Press.
Stable URL: http://www.jstor.org/stable/3685047.

Click image for some related material.



Midnight Again

Filed under: General — m759 @ 12:00 AM

See tonight's leading obituaries 
from The New York Times .

Wednesday, August 22, 2012

In Memoriam

Filed under: General — m759 @ 9:48 PM

IMAGE- Cornell mathematics department on the death of William P. Thurston on Aug. 21, 2012

A quotation from William P. Thurston,
who died yesterday—

"It may sound almost circular to say that
what mathematicians are accomplishing
is to advance human understanding of mathematics.
I will not try to resolve this
by discussing what mathematics is,
because it would take us far afield.
Mathematicians generally feel that they know
what mathematics is, but find it difficult
to give a good direct definition.
It is interesting to try. For me,
'the theory of formal patterns'
has come  the closest, but to discuss this
would be a whole essay in itself."

Related material from a literate source

"So we moved, and they, in a formal pattern"

— and from a different source, cached shortly after midnight 
on the (GMT) date of Thurston's death —

(Click for Google Cache information and to enlarge.)

Detail from the above Math Overflow discussion— 

IMAGE- A four-diamond pattern

The Company

Filed under: General — m759 @ 2:48 PM

IMAGE- Thurston obit at ams.org

Relativity Blues

Filed under: General — m759 @ 12:21 PM

(Continued from the day of Hunter S. Thompson's suicide)

See "The First Church of Marilynne Robinson."

(The New Yorker , May 30, 2012)

About the People

Filed under: General — m759 @ 3:28 AM

(Continued from March 28, 2001)

"Hillbillies, Okies, Arkies—  they're all the same people."

— Hunter S. Thompson, Hell's Angels

Related cinematic art:

Hunger Games (2012)

Winter’s Bone (2010)—

For John Denver*

Filed under: General — m759 @ 1:01 AM

A followup

* Of "Country Roads"

Midnight Special

Filed under: General — m759 @ 12:00 AM

Coltrane, not coal train.

See also a children's version.

Tuesday, August 21, 2012


Filed under: General — Tags: — m759 @ 4:59 PM

From the July 28, 2012, post "Hey"—

"You know my methods."


Filed under: General — Tags: — m759 @ 6:25 AM

Last night's 2:01 AM post suggests …

Inaction Film

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

It could be worse.

Monday, August 20, 2012

Extended Metaphor

Filed under: General — Tags: — m759 @ 5:17 AM

The Washington Post  on yesterday's presidential Sunday—

"Accompanied by his wife, Michelle, and daughters
Sasha and Malia on the mild, overcast morning,
Obama walked through Lafayette Square
to St. John’s Episcopal Church.

The Rev. Michael Angell delivered a sermon
from John 6 about the extended metaphor
of eating Jesus’ flesh….

The Obamas, all wearing shades of blue,
participated in Holy Communion before
motorcading back to the White House."

In related news—

" We praised him and then we ate him,
all courtesy of a generous catering budget
from film director Tony Scott."

— "Death in the Center Ring:
      Timothy Leary's High Dive,"
      by Douglas Rushkoff, May 13, 2008

See also…

Sunday, August 19, 2012

O Marks the Spot

Filed under: General — m759 @ 9:00 PM

(Continued :  See Identity,  decomposition, and Sunshine Cleaning . )

"What, one might ask, does the suave, debonaire
Roger Thornhill have to do with the notion of
decomposition (emphasized by the unusual
coffin-shaped 'O') implied in the acronym
formed by his initials?" 

— Paul Gordon, Dial "M" for Mother ,
     Fairleigh Dickinson University Press, 2008, page 97

"To stay with the context of Cavell's brilliant reading 
of the film's relation to Hamlet, 'there is something rot -ten
in North by Northwest ' that also needs to be explained."

— Paul Gordon, op. cit., page 98

Related remarks— Sunday morning, May 20, 2007.


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

On the middle initial of the Cary Grant character
in yesterday's post Summer Reading

IMAGE- Matchbook with initials ROT in 'North by Northwest'

Click image for further details.

"The concept of nothingness follows Roger Thornhill throughout North by Northwest , first as another identity imposes itself upon him and later as circumstances force him to run from Vandamm as well as the police. When Eve asks him what the 'O' in 'ROT' stands for, Thornhill can only answer 'nothing.' His middle initial's lack of meaning connects well to the overall theme of the human self as possibly nothing." —Hitchcock and Identity, by Emily Pilgrim

Related material— Elementary Finite Geometry (Aug. 1).

See, too, a post for Holy Cross Day in 2002.

Saturday, August 18, 2012

Nightmare Alley

Filed under: General — m759 @ 11:00 PM

"History instructs. History also has
a very dark sense of humor.
Irish history, especially."

John Kelly in The Daily Beast  this morning

See also Joyce's Nightmare and
Nightmare Alley in this journal.

Summer Reading

Filed under: General — m759 @ 2:56 PM

On the author of a novel published August 14th,
 "Where'd You Go, Bernadette"—

"Semple moved to the Pacific Northwest several years ago
seeking refuge from Los Angeles, but that doesn't mean
that the Emerald City gets a free pass from Semple's
sharp, satirical eye." 

— Stewart Oksenhorn yesterday in The Aspen Times

Related art

IMAGE- 3x3 grid of movie stills with 'North by Northwest' at center

See also a detail from Thursday's 1.3 MB image
"Search for the Lost Tesseract"—

Update of 9 PM EDT (6 PM LA time) the same day, Saturday, Aug. 18—

IMAGE- Cover of 'This One Is Mine,' a novel by Maria Semple

Actually, that one is hers.


Filed under: General — m759 @ 4:01 AM

"Art indeed, so far from being
a playful diversion of the human race,
is the place of its most fundamental insight,
and the centre to which the more uncertain
steps of metaphysics must constantly return"

— Iris Murdoch, "On 'God' and 'Good,'" in
Existentialists and Mystics , Penguin Books,
1999, page 360

Related material —

Wendy Derleth

" 'In the West,' she observed, 'anything that must be hidden
is suspect; availability and honesty are interlinked. This clashes
irreconcilably with Islam… where the things that are
most precious, most perfect and most holy are always hidden….' "

— Pauls Toutonghi, review of a recent novel, Alif the Unseen

(page BR19, New York Times Sunday Book Review , August 12, 2012

Friday, August 17, 2012


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

Detail from last night's 1.3 MB image
"Search for the Lost Tesseract"—

The lost tesseract appears here on the cover of Wittgenstein's
Zettel  and, hidden in the form of a 4×4 array, as a subarray 
of the Miracle Octad Generator on the cover of Griess's
Twelve Sporadic Groups  and in a figure illustrating
the geometry of logic.

Another figure—

IMAGE- Serbian chess innovator Svetozar Gligoric dies at 89

Gligoric died in Belgrade, Serbia, on Tuesday, August 14.

From this journal on that date

"Visual forms, he thought, were solutions to 
specific problems that come from specific needs."

— Michael Kimmelman in The New York Times
    obituary of E. H. Gombrich (November 7th, 2001)

Thursday, August 16, 2012

Royal Wrap

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

For Elvis's Wrap Party 
  ( image, 1.3 MB )

Raiders of the Lost Tesseract

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

(Continued from August 13. See also Coxeter Graveyard.)

Coxeter exhuming Geometry

Here the tombstone says
"GEOMETRY… 600 BC — 1900 AD… R.I.P."

In the geometry of Plato illustrated below,
"the figure of eight [square] feet" is not , at this point
in the dialogue, the diamond in Jowett's picture.

An 1892 figure by Jowett illustrating Plato's Meno

Jowett's picture is nonetheless of interest for
its resemblance to a figure drawn some decades later
by the Toronto geometer H. S. M. Coxeter.

A similar 1950 figure by Coxeter illustrating a tesseract

For a less scholarly, but equally confusing, view of the number 8,
see The Eight , a novel by Katherine Neville.

The Ninth Year

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

A passage from the Benjamin Jowett translation of Plato's Meno

" 'For in the ninth year* Persephone sends the souls of those from whom she has received the penalty of ancient crime back again from beneath into the light of the sun above, and these are they who become noble kings and mighty men and great in wisdom and are called saintly heroes in after ages  .' The soul, then, as being immortal, and having been born again many times, and having seen all things that exist, whether in this world or in the world below, has knowledge of them all; and it is no wonder that she should be able to call to remembrance all that she ever knew about virtue, and about everything; for as all nature is akin, and the soul has learned all things; there is no difficulty in her eliciting or as men say learning, out of a single recollection all the rest, if a man is strenuous and does not faint; for all enquiry and all learning is but recollection."

* See this journal nine years ago, in August 2003.
 Jowett's note— "Pindar, Frag. 98 (Boeckh)"

Wikipedia authors like Protious, an alleged resident of Egypt and 
creator of The Socrates Swastika , may enjoy a less scholarly account:

From Babylon A. D.  (a 2008 film)— Toorop with Egyptian Sacred Scarab tattoo—           

— and Toorop with Aurora (who may be regarded as "the soul" in the Meno  passage above)—

Toorop's neck tattoo in the second image above is from a fictional book
described in the writings of H. P. Lovecraft.

As swastika-like sacred symbols go, I prefer St. Bridget's Cross.


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

"Two clichés make us laugh, but
a hundred clichés move us
because we sense dimly that the clichés
are talking among themselves and
celebrating a reunion."

Umberto Eco

"'Casablanca': Cult Movies and Intertextual Collage,"
by Umberto Eco in SubStance , Vol. 14, No. 2, Issue 47:
In Search of Eco's Roses  (1985), pp. 3-12.
(This paper was presented at a symposium,
"Semiotics of the Cinema: The State of the Art,"
in Toronto on June 18, 1984.)
Journal article published by U. of Wisconsin Press.
Stable URL: http://www.jstor.org/stable/3685047.

Click image for some related material.

Wednesday, August 15, 2012


Filed under: General — m759 @ 6:29 PM


"Here, Bochner plays with these elements with the philosophical levity that made Conceptual art (which art historians see Bochner as one of the kingpins) so refreshing, graceful, and funny, especially after a generation of painters made artmaking seem so serious, heavy, emotional." —ArtSlant.com

See also The Wikipedia Meno  and Bochner in this journal.

Tuesday, August 14, 2012

Hacking 1984

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

Ian Hacking in 1984

"… theories about mathematics have had a big place in Western philosophy. All kinds of outlandish doctrines have tried to explain the nature of mathematical knowledge. Socrates set the ball rolling by using a proof in geometry to argue for the transmigration of souls. As reported by Plato in Meno , the boy who invents a proof of a theorem did not experiment on the physical world, but used only his mind in response to Socratic questions. Hence he must have had inborn knowledge of the proof and he must have got this knowledge in a previous incarnation.

Mathematics has never since been a subject for such philosophical levity."

See also this afternoon's post.

Space Odyssey

Filed under: General — m759 @ 1:00 PM

(An episode of Art Wars )

"Visual forms, he thought, were solutions to
specific problems that come from specific needs."

— Michael Kimmelman in The New York Times
    obituary of E. H. Gombrich (November 7th, 2001)

"… deep cultural fears within the art world— 
fears that art is elitist,
or some kind of confidence game,
or not a serious endeavor (a fear that has
dogged art since at least the time of Plato)."

Philip Kennicott, quoted here on July 22, 2012

See also today's date in 2003.

Monday, August 13, 2012

Something Between

Filed under: General — m759 @ 6:07 PM

"I am a skeptic to whom the idea that a benign God 
created us and watches over us is something between
a fairy story and a bad joke." 

— The late art critic Robert Hughes in Things I Didn't Know*

A followup to this afternoon's previous Amy Adams post—

"Here was finality indeed, and cleavage!" 

             — Under the Volcano

     * Vintage paperback, December 2007, page 7

Raiders of the Lost Tesseract

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

(An episode of Mathematics and Narrative )

A report on the August 9th opening of Sondheim's Into the Woods

Amy Adams… explained why she decided to take on the role of the Baker’s Wife.

“It’s the ‘Be careful what you wish’ part,” she said. “Since having a child, I’m really aware that we’re all under a social responsibility to understand the consequences of our actions.” —Amanda Gordon at businessweek.com

Related material—

Amy Adams in Sunshine Cleaning  "quickly learns the rules and ropes of her unlikely new market. (For instance, there are products out there specially formulated for cleaning up a 'decomp.')" —David Savage at Cinema Retro

Compare and contrast…

1.  The following item from Walpurgisnacht 2012

IMAGE- Excerpt from 'Unified Approach to Functional Decompositions of Switching Functions,' by Marek A. Perkowski et al., 1995

2.  The six partitions of a tesseract's 16 vertices 
       into four parallel faces in Diamond Theory in 1937

Sunday, August 12, 2012

Doctor Who

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

On Robert A. Heinlein's novel Glory Road

"Glory Road  (1963) included the foldbox , a hyperdimensional packing case that was bigger inside than outside. It is unclear if Glory Road  was influenced by the debut of the science fiction television series Doctor Who  on the BBC that same year. In Doctor Who , the main character pilots a time machine called a TARDIS, which is built with technology which makes it 'dimensionally transcendental,' that is, bigger inside than out."

— Todd, Tesseract article at exampleproblems.com

From the same exampleproblems.com article—

"The connection pattern of the tesseract's vertices is the same as that of a 4×4 square array drawn on a torus; each cell (representing a vertex of the tesseract) is adjacent to exactly four other cells. See geometry of the 4×4 square."

For further details, see today's new page on vertex adjacency at finitegeometry.org.

Thursday, August 9, 2012

Just Once

Filed under: General — m759 @ 5:18 AM

IMAGE- Dr. James West, a recovering alcoholic who became Betty Ford Center director, died at 98 on July 24, 2012

In Dr. West's memory…

Wednesday, August 8, 2012

Quadruple Bypass

Filed under: General — m759 @ 9:29 PM

"The first human to walk on the moon, Neil Armstrong,
is 'doing great' after undergoing cardiac bypass surgery,
his wife reported…..

… Armstrong… went to the hospital on Monday
for a stress test. He flunked, and on Tuesday,
surgeons bypassed four blockages in his
coronary arteries. His wife reports that his spirits
are high, and the doctors expect no problems
with his recovery…." — Alan Boyle, NBCNews.com

Over the life of Man
We watch and wait,
The Four who manage
His fallen estate:

We who are four were
Once but one,
Before his act of

We were himself when
His will was free,
His error became our
Chance to be.

Powers of air and fire,
Water and earth,
Into our hands is given
Man from his birth….

Auden, not Goethe

See also Tuesday morning's post.

Tuesday was Charlize Theron's birthday.
See June 9, 2012.

Tuesday, August 7, 2012

The Space of Horizons

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

“In the space of horizons that neither love nor hate”
— Wallace Stevens, “Things of August”

Seven years ago yesterday—

IMAGE- 3x3 grid related to Borofsky's 'Four Gods'

For some context, see Rosetta Stone as a Metaphor.

Related material from the University of Western Australia

Projective plane of order 3

(The four points on the curve
at the right of the image are
the points on the line at infinity.)

Art critic Robert Hughes,  who nearly died in Western
Australia in a 1999 car crash, actually met his death
yesterday at Calvary Hospital in the Bronx.

See also Hughes on “slow art” in this journal.

Sunday, August 5, 2012

Cube Partitions

Filed under: General,Geometry — Tags: , , — m759 @ 7:59 AM

The second Logos  figure in the previous post
summarized affine group actions on partitions
that generate a group of about 1.3 trillion
permutations of a 4x4x4 cube (shown below)—

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

Click for further details.

Thursday, August 2, 2012


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

(Continued from December 26th, 2011)

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

Some material at math.stackexchange.com related to
yesterday evening's post on Elementary Finite Geometry

Questions on this topic have recently been
discussed at Affine plane of order 4? and at
Turning affine planes into projective planes.

(For a better discussion of the affine plane of order 4,
see Affine Planes and Mutually Orthogonal Latin Squares
at the website of William Cherowitzo, professor at UC Denver.)

Wednesday, August 1, 2012

Triple Feature

Filed under: General — m759 @ 11:11 PM

IMAGE- Triple Feature: 'Twelve Monkeys,' Reagan National Airport on July 31, 2012, and 'Die Hard 2'

For related material, see this morning's post Defining Form.

Elementary Finite Geometry

Filed under: General,Geometry — Tags: , — m759 @ 7:16 PM

I. General finite geometry (without coordinates):

A finite affine plane of order has n^2 points.

A finite projective plane of order n  has n^2 + n + 1 

points because it is formed from an order-n finite affine 

plane by adding a line at infinity  that contains n + 1 points.


Affine plane of order 3

Projective plane of order 3

II. Galois finite geometry (with coordinates over a Galois field):

A finite projective Galois plane of order n has n^2 + n + 1

points because it is formed from a finite affine Galois 3-space

of order n with n^3 points by discarding the point (0,0,0) and 

identifying the points whose coordinates are multiples of the

(n-1) nonzero scalars.

Note: The resulting Galois plane of order n has 

(n^3-1)/(n-1)= (n^2 + n + 1) points because 

(n^2 + n + 1)(n – 1) =

(n^3 + n^2 + n – n^2 – n – 1) = (n^3 – 1) .

III. Related art:

Another version of a 1994 picture that accompanied a New Yorker
article, "Atheists with Attitude," in the issue dated May 21, 2007:

IMAGE- 'Four Gods,' by Jonathan Borofsky

The Four Gods  of Borofsky correspond to the four axes of 
  of a square and to the four points on a line at infinity 
in an order-3 projective plane as described in Part I above.

Those who prefer literature to mathematics may, if they like,
view the Borofsky work as depicting

"Blake's Four Zoas, which represent four aspects
of the Almighty God" —Wikipedia

Defining Form

Filed under: General — m759 @ 11:01 AM

Continued from July 29 in memory of filmmaker Chris Marker,
who reportedly* died on that date at 91 at his home in Paris.

See Slides and Chantingand Where Madness Lies.

See also Sherrill Grace on Malcolm Lowry.

* Washington Post. Other sources say Marker died on July 30.

 These notably occur in Marker's masterpiece
     La Jetée (review with spoilers).

Gore Vidal

Filed under: General — m759 @ 1:09 AM

IMAGE- Gore Vidal has died.

IMAGE- Gore Vidal at Movie Nation

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