Thursday, May 31, 2012

Matrix Problem

Filed under: General,Geometry — Tags: — m759 @ 7:20 PM

IMAGE- Charlize Theron as Ravenna with raven in poster for 'Snow White and the Huntsman'

Poster from Walpurgisnacht 2012

Raven’s Progressive Matrices problem:

IMAGE- Raven's Progressive Matrices problem based on triangular quarter- and half-diamonds

Click the problem for a related story.

For some related geometry, see Elements Diamond.
See also a post (Dream Time, May 3, 2010)
about geometry and an earlier Walpurgisnacht.

Black Diamond

Filed under: General — Tags: — m759 @ 12:26 PM

IMAGE- Four-elements-diamond test problem in the style of Raven's Progressive Matrices (answer: the black diamond)

“To say more is to say less.”
― Harlan Ellison, as quoted at goodreads.com

Saying less—

Wednesday, May 30, 2012


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


The "New Books" link in today's Arts & Letters Daily leads to a review of Andrew Delbanco's College: What it Was, Is, and Should Be . From that review—

Some, like Delbanco, remind us what the word ‘professor’ once meant: ‘A person who professes a faith, as in the Puritan churches, where the profession was made before the congregation as a kind of public initiation.’

I am not now, nor have I ever been, a professor.

I did, however, once profess the following:

(Click to enlarge.)

IMAGE- Letter to the editor, Mathematical Intelligencer, Vol. 10 No. 1, 1988

This 1988 letter advocated viewing pure  mathematics as one of the liberal arts. Twenty-four years later, that position still seems worth defending.

Arithmetic (i.e., number theory) and geometry are, by the way, two of the seven traditional  liberal arts.

Tuesday, May 29, 2012

The Shining of May 29

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

(Continued from May 29, 2002)

May 29, 1832—


Évariste Galois, Lettre de Galois à M. Auguste Chevalier

Après cela, il se trouvera, j'espère, des gens qui trouveront leur profit à déchiffrer tout ce gâchis.

(Later there will be, I hope, some people who will find it to their advantage to decipher all this mess.)

Martin Gardner on the above letter—

"Galois had written several articles on group theory, and was merely annotating and correcting those earlier published papers."

The Last Recreations , by Martin Gardner, published by Springer in 2007, page 156.

Commentary from Dec. 2011 on Gardner's word "published" —

(Click to enlarge.)

IMAGE- Peter M. Neumann, 'Galois and His Groups,' EMS Newsletter, Dec. 2011

Graveyard Shift

Filed under: General — m759 @ 1:28 AM


IMAGE- Nicolas Cage in 'Bringing Out the Dead'


For TapiaLooking Back at "Mi Vida Loca"

For RichmondGoodnight, Irene

Monday, May 28, 2012

Fundamental Dichotomy

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

Jamie James in The Music of the Spheres
(Springer paperback, 1995),  page 28

Pythagoras constructed a table of opposites
from which he was able to derive every concept
needed for a philosophy of the phenomenal world.
As reconstructed by Aristotle in his Metaphysics,
the table contains ten dualities….



Of these dualities, the first is the most important;
all the others may be seen as different aspects
of this fundamental dichotomy.

For further information, search on peiron + apeiron  or
consult, say, Ancient Greek Philosophy , by Vijay Tankha.

The limited-unlimited contrast is not unrelated to the
contrasts between

Sunday, May 27, 2012

Finite Jest

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

IMAGE- History of Mathematics in a Nutshell

The books pictured above are From Discrete to Continuous ,
by Katherine Neal, and Geometrical Landscapes , by Amir Alexander.


“Harriot has given no indication of how to resolve
such problems, but he has pasted in in English,
at the bottom of his page, these three enigmatic

‘Much ado about nothing.
Great warres and no blowes.
Who is the foole now?’

Harriot’s sardonic vein of humour, and the subtlety of
his logical reasoning still have to receive their full due.”

— “Minimum and Maximum, Finite and Infinite:
Bruno and the Northumberland Circle,” by Hilary Gatti,
Journal of the Warburg and Courtauld Institutes ,
Vol. 48 (1985), pp. 144-163

And Not So Live…

Filed under: General — m759 @ 12:25 AM

A midrash on tonight's obituaries

Saturday, May 26, 2012

Live from New York, It’s…

Filed under: General,Geometry — Tags: — m759 @ 11:30 PM

Shift Happens!

Another shift — Geometry as Discrete .

Desert of the Real Numbers

Filed under: General — m759 @ 10:30 PM

New York Lottery today—

Without imagination, these digits are a meaningless jumble.

With  imagination…

608 might refer to June 8, the Saint's Day  of Gerard Manley Hopkins.
        (See the date July 29, 2002, that appeared in an earlier post today
         as the publication date of Geometrical Landscapes . In this
         journal, a post on that date, "At Random," referred to Hopkins.)

8516 might refer to 8/5/1916. A check of a hometown newspaper
         on that date yields…
         "St. Joseph's Garden Party and Bazaar 22, 23, 24.
          Pictures. Everybody Welcome. Admission to Garden Ten Cents"

And in the evening…

937 might refer to a post on the nihilistic philosophy of Joan Didion, and

7609 might refer to an occurrence of these digits in a link 
          to "7/11" in a post from the feast of St. Ignatius of Loyola last year.

For a more cynical view of lottery hermeneutics, see
"High on RAM (overload)," by Jo Lyxe.

Happy birthday to Stevie Nicks.

Talk Amongst Yourselves

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

Hard Science Fiction weekend at Dragon Press Bookstore

Saturday May 26:
11am-noon Playing with the net up:
Hard Science Fiction in the era of
short attention spans, crowd-sourcing,
and rapid obsolescence
( Greg Benford, James Cambias, Kathryn Cramer)
3pm-4:30 Technological optimism and pessimism;
utopia and dystopia; happy endings & sad endings:
what do these oppositions have to do with one another?
Are they all the same thing? How are they different
from one another? Group discussion.

My own interests in this area include…

(Click image for some context)

IMAGE- 'The Stars My Destination' (with cover slightly changed)

    The above was adapted from a 1996 cover

IMAGE- PyrE on the 1996 Vintage Books cover of 'The Stars My Destination'

 Vintage Books, July 1996. Cover: Evan Gaffney.

For the significance of the flames, 
see PyrE in the book. For the significance
of the cube in the altered cover, see
The 2×2×2 Cube and The Diamond Archetype.

Harriot’s Cubes

Filed under: General,Geometry — Tags: — m759 @ 1:28 PM

See also Finite Geometry and Physical Space.

Related material from MacTutor

Harriot and binary numbers

The paper by J. W. Shirley, Binary numeration before Leibniz, Amer. J. Physics 19 (8) (1951), 452-454, contains an interesting look at some mathematics which appears in the hand written papers of Thomas Harriot [1560-1621]. Using the photographs of the two original Harriot manuscript pages reproduced in Shirley’s paper, we explain how Harriot was doing arithmetic with binary numbers.

Leibniz [1646-1716] is credited with the invention [1679-1703] of binary arithmetic, that is arithmetic using base 2. Laplace wrote:-

Leibniz saw in his binary arithmetic the image of Creation. … He imagined the Unity represented God, and Zero the void; that the Supreme Being drew all beings from the void, just as unity and zero express all numbers in his system of numeration. This conception was so pleasing to Leibniz that he communicated it to the Jesuit, Grimaldi, president of the Chinese tribunal for mathematics, in the hope that this emblem of creation would convert the Emperor of China, who was very fond of the sciences …

However, Leibniz was certainly not the first person to think of doing arithmetic using numbers to base 2. Many years earlier Harriot had experimented with the idea of different number bases….

For a discussion of Harriot on the discrete-vs.-continuous question,
see Katherine Neal, From Discrete to Continuous: The Broadening
of Number Concepts in Early Modern England  (Springer, 2002),
pages 69-71.

Friday, May 25, 2012

Desert of the Real

Filed under: General — m759 @ 10:00 PM


See "How Deep the Darkness" + Koestler.


Filed under: General — m759 @ 2:01 PM

Today is commencement day at College of the Desert.

Without Graduation
(from a poem by Jorie Graham)

IMAGE- Description of crow from page 178 of 'Dream of the Unified Field,' a book by Jorie Graham

With  Graduation

IMAGE- From 'Ulysses,' 1922 first edition, page 178-- 'dagger definitions'

Click either passage above for some commentary.


Filed under: General — m759 @ 12:00 AM

Sisteen Chapel

See Log24 two years ago on this date—

Darkness Visible and Sisteen.

Thursday, May 24, 2012

Home Schooling…

Filed under: General — m759 @ 11:01 PM

For The Hunger Games

Spoiler Alert

For readers unfamilar either with the film "Point of No Return"
or with the "Raven's Progressive Matrices" intelligence test,
here is a spoiler alert. This post links to details of both.

Backstory— The above film and Raven in this journal

Part I:      Problem b in this intelligence test

Part II:    Take Your Pick in this journal (Dec. 16, 2011)

Part III:   Pick

Dark, Dark, Dark

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

Damnation Morning

From her left arm hung a black handbag that closed with a drawstring and from which protruded the tip of a silvery object about which I found myself apprehensively curious.

Her right arm was raised and bent, the elbow touching the door frame, the hand brushing back the very dark bangs from her forehead to show me the sigil, as if that had a bearing on her question.

The sigil was an eight-limbed asterisk made of fine dark lines and about as big as a silver dollar. An X superimposed on a plus sign. It looked permanent.

IMAGE- 'Eight-limbed asterisk' of Fritz Leiber (square version)

Except for the bangs she wore her hair pinned up. Her ears were flat, thin-edged, and nicely shaped, with the long lobes that in Chinese art mark the philosopher. Small square silver flats with rounded corners ornamented them.

Her face might have been painted by Toulouse-Lautrec or Degas. The skin was webbed with very fine lines; the eyes were darkly shadowed and there was a touch of green on the lids (Egyptian?—I asked myself); her mouth was wide, tolerant, but realistic. Yes, beyond all else, she seemed realistic.

Mary Karr

You’re not afraid to show yourself at your lowest ebb. In Lit, you stop breast-feeding because you’ve started drinking again. You describe yourself hiding in a closet with a bottle of whiskey, a bottle of Listerine, and a spit bowl.

It’s not a proud moment. The temptation in Lit was to either make myself seedy or show some glamour. But there wasn’t any. It was just dark, dark, dark for days. Ugly.

Were you surprised by how deeply people related to this dark stuff?

If I’m doing my job then I’m able to make the strange seem familiar. Bad memoirs try to make the strange stranger, to provide something for people to gawk at. I try to create an experience where no matter how bizarre something is, it seems normal. I don’t want readers to balk, I want them to be in the experience. My goal isn’t for people to go, “Oh, poor little Mary Karr,” but rather to have the reader go, “I can be an asshole too,” or just to have enthusiasm for the possibility for change.

What Then?

Filed under: General — m759 @ 11:30 AM

Last October, Harvard celebrated its 375th anniversary
with Pandemonium. For remarks of a different sort,
see Andrew Cusack on Walpurgisnacht.

Wednesday, May 23, 2012

Now What?

Filed under: General — m759 @ 10:30 PM

(Rhetorical question on the NY Times  online front page, 
10:01 PM May 23, 2012, in teaser for "The Stone" column
about Philip K. Dick, "Sci-Fi Philosopher")

Where Entertainment Is God

Perhaps The Last Airbender ?

The NY Times  philosophy column "The Stone" is currently about gnosticism
and science fiction.

The Last Airbender  is about an avatar who is master of the four elements
air, water, earth, and fire. For a more sophisticated approach to gnosticism
and the four elements, see Irenaeus: Against Heresies.

See, too, Elements Diamond in this journal.

ART WARS (continued)

Filed under: General — m759 @ 9:00 PM

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

"When you come to a fork in the road…"

Alyssa Milano as a child, with fork

* 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.

Ageometretos Medeis Eisito

Filed under: General — m759 @ 8:00 PM

See Bagombo Snuff Box and
"Will this be on the test?"

IMAGE- Dr. Hannibal Lecter


Filed under: General — m759 @ 12:00 PM

From this date in 2010—

IMAGE- 'Frame Tale,' from a Sunday, May 23, 2010, 2:02 AM EDT Log24 post titled 'Annals of Conceptual Art'

Tuesday, May 22, 2012


Filed under: General — m759 @ 10:31 PM

Gary Snyder poem, Google+, May 22, 2012

Included Middle

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


"In logic, the law of excluded middle (or the principle of excluded middle) is the third of the so-called three classic laws of thought. It states that for any proposition, either that proposition is true, or its negation is.

The law is also known as the law (or principleof the excluded third (or of the excluded middle), or, in Latinprincipium tertii exclusi. Yet another Latin designation for this law is tertium non datur: 'no third (possibility) is given.'"

"Clowns to the left of me, jokers to the right"

 — Songwriter who died on January 4, 2011.

Online NY Times  on the date of the songwriter's death—

"A version of this review appeared in print
on January 4, 2011, on page C6 of the New York edition." 


"The philosopher Hubert Dreyfus and his former student
Sean Dorrance Kelly have a story to tell, and it is not
a pretty tale for us moderns. Ours is an age of nihilism,
they say, meaning not so much that we have nothing
in which to believe, but that we don’t know how to choose
among the various things to which we might commit
ourselves. Looking down from their perches at Berkeley
and Harvard, they see the 'human indecision that
plagues us all.'"

For an application of the excluded-middle law, see
Non-Euclidean Blocks and Deep Play.

Violators of the law may have trouble* distinguishing
between "Euclidean" and "non-Euclidean" phenomena
because their definition of the latter is too narrow,
based only on examples that are historically well known.

See the Non-Euclidean Blocks  footnote.

* Followers  of the excluded-middle law will avoid such
trouble by noting that "non-Euclidean" should mean
simply "not  Euclidean in some  way "— not  necessarily
in a way contradicting Euclid's parallel postulate.

But see Wikipedia's defense of the standard, illogical,
usage of the phrase "non-Euclidean."


Tertium Datur

Froebel's Third Gift

"Here I am, stuck in the middle with you."

Monday, May 21, 2012

Child’s Play (continued*)

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

You and I …

we are just like a couple of tots…



Born 1973 in Bergen. Lives and works in Oslo.


2000 – 2004 National Academy of Fine Arts, Oslo
1998 – 2000 Strykejernet Art School, Oslo, NO
1995 – 1998 Philosophy, University of Bergen

University of Bergen—

 It might therefore seem that the idea of digital and analogical systems as rival fundaments to human experience is a new suggestion and, like digital technology, very modern. In fact, however, the idea is as old as philosophy itself (and may be much older). In his Sophist, Plato sets out the following ‘battle’ over the question of ‘true reality’:

What we shall see is something like a battle of gods and giants going on between them over their quarrel about reality [γιγαντομαχία περì της ουσίας] ….One party is trying to drag everything down to earth out of heaven and the unseen, literally grasping rocks and trees in their hands, for they lay hold upon every stock and stone and strenuously affirm that real existence belongs only to that which can be handled and offers resistance to the touch. They define reality as the same thing as body, and as soon as one of the opposite party asserts that anything without a body is real, they are utterly contemptuous and will not listen to another word. (…) Their adversaries are very wary in defending their position somewhere in the heights of the unseen, maintaining with all their force that true reality [την αληθινήν ουσίαν] consists in certain intelligible and bodiless forms. In the clash of argument they shatter and pulverize those bodies which their opponents wield, and what those others allege to be true reality they call, not real being, but a sort of moving process of becoming. On this issue an interminable battle is always going on between the two camps [εν μέσω δε περι ταυτα απλετος αμφοτέρων μάχη τις (…) αει συνέστηκεν]. (…) It seems that only one course is open to the philosopher who values knowledge and truth above all else. He must refuse to accept from the champions of the forms the doctrine that all reality is changeless [and exclusively immaterial], and he must turn a deaf ear to the other party who represent reality as everywhere changing [and as only material]. Like a child begging for 'both', he must declare that reality or the sum of things is both at once [το όν τε και το παν συναμφότερα] (Sophist 246a-249d).

The gods and the giants in Plato’s battle present two varieties of the analog position. Each believes that ‘true reality’ is singular, that "real existence belongs only to" one side or other of competing possibilities. For them, difference and complexity are secondary and, as secondary, deficient in respect to truth, reality and being (την αληθινήν ουσίαν, το όν τε και το παν). Difference and complexity are therefore matters of "interminable battle" whose intended end for each is, and must be (given their shared analogical logic), only to eradicate the other. The philosophical child, by contrast, holds to ‘both’ and therefore represents the digital position where the differentiated two yet belong originally together. Here difference, complexity and systematicity are primary and exemplary.

It is an unfailing mark of the greatest thinkers of the tradition, like Plato, that they recognize the digital possibility and therefore recognize the principal difference of it from analog possibilities.

— Cameron McEwen, "The Digital Wittgenstein,"
    The Wittgenstein Archives at the University of Bergen

* See that phrase in this journal.

Wittgenstein’s Kindergarten

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

A web search for the author Cameron McEwen  mentioned
in today's noon post was unsuccessful, but it did yield an
essay, quite possibly by a different  Cameron McEwen, on

The Digital Wittgenstein:

"The fundamental difference between analog
and digital systems may be understood as
underlying philosophical discourse since the Greeks."

The University of Bergen identifies the Wittgenstein 
McEwen as associated with InteLex  of Charlottesville.

The title of this post may serve to point out an analogy*
between the InteLex McEwen's analog-digital contrast
and the Euclidean-Galois contrast discussed previously
in this journal.

The latter contrast is exemplified in Pilate Goes to Kindergarten.

* An analogy, as it were, between  analogies.

Brightness at Noon

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

Occultation according to McLuhan

Marshall McLuhan writing to Ezra Pound  on Dec. 21, 1948—

"The American mind is not even close to being amenable to the ideogram principle as yet.  The reason is simply this. America is 100% 18th Century. The 18th century had chucked out the principle of metaphor and analogy— the basic fact that as A is to B so is C to D.  AB:CD.   It can see AB relations.  But relations in four terms are still verboten.  This amounts to deep occultation of nearly all human thought for the U.S.A.

I am trying to devise a way of stating this difficulty as it exists.  Until stated and publicly recognized for what it is, poetry and the arts can’t exist in America."

For context, see Cameron McEwen, "Marshall McLuhan, John Pick, and Gerard Manley Hopkins." (Renascence , Fall 2011, Vol. 64 Issue 1, 55-76)

Sunday, May 20, 2012


Filed under: General — m759 @ 11:00 PM

"An occultation is an event that occurs
when one object is hidden by another object
that passes between it and the observer.
The word is used in astronomy…"


AP story, 10:26 PM EDT May 20, 2012

IMAGE- Annular solar eclipse as seen in Yokohama on May 21, 2012

See also Darkness Visible in this journal.

(11 PM EDT, the time of this post, is noon
the next day in Tokyo. The above eclipse was
seen in Japan on May 21, 2012, in the morning.)

Rainbow Girl*

Filed under: General — m759 @ 5:01 PM

* See Wikipedia… and…

    Don't  forget The Yellow Book

David Carradine displays a yellow book-- the Princeton I Ching.

For Eliza Doolittle Day*

Filed under: General — m759 @ 3:33 PM

Film ad in today's New York Times  (see previous post)—


Applying this advice—

IMAGE- Beatrix Kiddo ('the Bride') watches Budd's trailer

* See today's Times Colonist .

There You Go Again…

Filed under: General — m759 @ 2:19 PM

Maureen Dowd misquoting Joyce today—

IMAGE- Maureen Dowd on the Church and 'Here comes everybody' in 'Finnegans Wake'

Dowd's confusion seems derived from that of Richard John Neuhaus

IMAGE- Richard John Neuhaus on confusion, the Church, and James Joyce

Click for further details.

Dueling Menus

Filed under: General — m759 @ 1:00 PM

From Sunday Dinner in this journal—

Guess Who's Coming to Dinner?

Judith Shulevitz at The New York Times
on Sunday, July 18, 2010 —

"What would an organic Christian Sabbath look like today?"

IMAGE- Obit for archaeologist, an expert on Sardis

Menu: Sardi's, not Sardis.

Saturday, May 19, 2012

But Seriously…

Filed under: General — m759 @ 11:01 PM

Here is a link to a copy of  the home page of a Turkish
author quoted here on May 4, 2012… in honor of
archaeologist Crawford Greenewalt Jr., who reportedly
died on that date. Greenewalt was an expert on the
ancient city of Sardis, in what is now western Turkey.

The May 4 quote was about 
"Heraclitus’s Aion and His Transformations."

Powers for Mick

Filed under: General — m759 @ 9:00 PM

(A post suggested by an ad in this evening's online New York Times )

"After being brought to the village's Patriarch… Mick learns
 the intent of the colony and how they operate."

— Summary of a story by Orson Scott Card, a Latter-Day Saint.

For some context, see Saints Have Powers in this journal.

Related material — 

The Saturday Evening Post  and tonight's Saturday Night Live .

IMAGE- Mick Jagger and Kristen Wiig, SNL promo


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

"The  group of 8" is a phrase from politics, not mathematics.
Of the five groups of order 8 (see today's noon post),

the one pictured* in the center, Z2 × Z2 × Z2 , is of particular
interest. See The Eightfold Cube. For a connection of this 
group of 8 to the last of the five pictured at noon, the
quaternion group, see Finite Geometry and Physical Space.

* The picture is of the group's cycle graph.


Filed under: General — m759 @ 7:59 PM

For those who prefer politics to mathematics—

IMAGE- Sailor pats pinup in 'Run Silent, Run Deep'

Language Game

Filed under: General — m759 @ 12:00 PM
IMAGE- The five groups of order 8

See also Bab-ilu.


Filed under: General — m759 @ 10:18 AM

38, 23, 7B

May 19, 2012 9:06 AM

Expert: Facebook targeting all 7B people on Earth

(CBS News) NEW YORK — After all the hype, Facebook's
stock fell flat on its first day of trading. Shares in the
social networking giant opened at 38 dollars, shot up briefly,
then fell— and finished just 23 cents higher.

Midrash— "Fullness… Multitude"

Friday, May 18, 2012

Capture the Flags

Filed under: General — m759 @ 12:00 PM

Continued from Banderas  (Aug. 18, 2011)—

Balakrishnan's Banners

See also The Colors of Halloween and Smiling Buddha.

Thursday, May 17, 2012

One Night in Bangkok

Filed under: General — m759 @ 7:59 PM

"… this campaign, relatively speaking, will not be
fierce or hotly contested. Instead it'll be disappointing,
embarrassing, and over very quickly, like a hand job
in a Bangkok bathhouse." — Matt Taibbi in Rolling Stone

Smash Finale

Filed under: General — m759 @ 7:00 PM


Filed under: General — m759 @ 12:48 PM

The Entertainment*

Filed under: General — m759 @ 11:19 AM

From a film released Friday, April 13th, 2012—

"Time for you to see the field." — Bagger Vance, as quoted here yesterday.

* Title courtesy of David Foster Wallace.

Wednesday, May 16, 2012

Curb Your Enthusiasm*

Filed under: General — m759 @ 8:00 PM

From "Crude Foyer," a Wallace Stevens poem

In which we read the critique of paradise
And say it is the work
Of a comedian, this critique….

Whatever Works

IMAGE- Actors from 'Curb Your Enthusiasm' representing Cleavage and Finality

Related comedy — Finality and Cleavage.

* TV series starring the above actors. See Wikipedia.

The Field

Filed under: General — m759 @ 7:00 PM

"Time for you to see the field." —Bagger Vance

IMAGE- Marie-Louise von Franz on the 'field' that represents 'the structural outlines of the collective unconscious'

See also The Matthew Field .

Midnight in Paris– The Morning After

Filed under: General — m759 @ 10:31 AM

(Continued from yesterday evening)

On Max Bialystock's Spider-Man Godspell Seminar

"… for surrealism to be entertaining
onstage, it must be shaped into
some kind of satisfying form."

— Charles Isherwood
    in today's New York Times

(RSS:  Wed, 16  May  2012  00:37:17 GMT)

From Fritz Leiber's 1959 story "Damnation Morning" —

She drew from her handbag a pale grey gleaming
implement that looked by quick turns to me
like a knife, a gun, a slim sceptre, and a delicate
branding iron— especially when its tip sprouted
an eight-limbed star of silver wire.

“The test?” I faltered, staring at the thing.

“Yes, to determine whether you can live
in the fourth dimension or only die in it.”

Xbox Games

Filed under: General — m759 @ 2:00 AM

(Continued from Sunday, April 22, 2012)

Xbox Background—

Design Sermon from Sunday, November 6, 2011, and
The X Box from Monday, November 7, 2011.


Ay que bonito es volar

Tuesday, May 15, 2012

Midnight in Paris

Filed under: General — m759 @ 6:00 PM

Six PM EDT is midnight in Paris.

Así Que Pasen Cinco Años

Theater review from The Guardian

" 'Impossible' was how the Spanish playwright
Lorca described his own 1931 'legend of time
in three acts and five scenes,' which draws
strongly on the surrealist influences and experiments
of his close friends Salvador Dali and Luis Buñuel."

Related material—

This afternoon's previous post Murió Fuentes  and,
from this date five years ago…

A Flag for Sunrise and Jerry Falwell Dies.

Murió Fuentes

Filed under: General — m759 @ 5:01 PM

Monday, May 14, 2012

Mathematics, Logic, and Faith

Filed under: General,Geometry — m759 @ 4:44 PM

From the NY Times  philosophy column "The Stone" 
yesterday at 5 PM—

Timothy Williamson, Wykeham Professor of Logic at Oxford,
claims that all the theorems of mathematics

"… are ultimately derived from a few simple axioms
by chains of logical reasoning, some of them
hundreds of pages long…."

Williamson gives as an example recent (1986-1995)
work on Fermat's conjecture.

He does not, however, cite any axioms or "chains of
logical reasoning" in support of his claim that 
a proof of Fermat's conjecture can be so derived.

Here is a chain of reasoning that forms a crucial part
of recent arguments for the truth of Fermat's conjecture—

K. A. Ribet, "On modular representations of Gal(Q̄/Q)
arising from modular forms
," Invent. Math. 100 (1990), 431-476.

Whether this chain of reasoning is in fact logical  is no easy question.
It is not the sort of argument easily reduced to a series of purely
logical symbol-strings that could be checked by a computer.

Few mathematicians, even now, can follow each step
in the longer chain of reasoning that led to a June 1993 claim
that Fermat's conjecture is true. 

Williamson is not a mathematician, and his view of
Fermat's conjecture as a proven fact is clearly based
not on logic, but on faith.

Sunday, May 13, 2012

Blue Hotel

Filed under: General — m759 @ 4:09 PM

Steve Cropper on the late Donald Dunn

"He's in the hotel right now."

Bill Murray and Scarlett Johansson in 'Lost in Translation'

Click image for a related post.

Children of Light*

Filed under: General — m759 @ 8:28 AM

IMAGE- Nassau Presbyterian scripture for May 13, 2012- 1 John 5:1-5.

An earlier verse in 1 John—

1 John 1:5 "This then is the message
which we have heard of him,
and declare unto you, that God is light,
and in him is no darkness at all."

Catechism from a different cult—

"Who are you, anyway?" 

— Question at 00:41 of 15:01,
Rainbow Bridge (Part 5 of 9) at YouTube

See also the video accompanying artist Josefine Lyche's version
of the 2×2 case of the diamond theorem.

* Title of a Robert Stone novel

Saturday, May 12, 2012


Filed under: General — m759 @ 8:28 PM

Mormon Mitt Romney at the Baptist school Liberty University today:

"The task set before you four years ago
  is now completed in full."

I do not know what that task was. In this journal four years ago,
the task was lottery hermeneutics… a subject I doubt is taught
at Liberty University.

The New York lottery numbers from Sunday, May 11, 2008,
in a May 12 post four years ago could be interpreted as
pointing to the date 3/13— 

Say, 3/13, 2006— a date on which this journal quoted some
remarks on the biblical phrase "the fullness of time."

Those remarks were neither Baptist nor
Mormon, but rather Presbyterian.

Friday, May 11, 2012

Fair Play for the Devil

Filed under: General — m759 @ 5:09 PM

IMAGE- Garrett McNamara surfs a 78-foot wave on All Hallows Day, 2011

Quoted here on that date (All Hallows Day)—

See as well A Dante for Our Times.

For Frigg’s Day

Filed under: General — m759 @ 10:30 AM

A Parting Glance

(See also Josefine Lyche, Lens Flare.)

Thursday, May 10, 2012

For Thor’s Day

Filed under: General — m759 @ 7:11 PM

Today's previous post was "Midnight in Oslo (continued)."

The link "a 4-element set" in "Midnight"
was to a more elaborate structure in a post titled "Tesseract."

In memory of an Oslo "hero of midnight"
(a phrase quoted here last September 1)—

A search for material that is more entertaining
Odin 's Tesseract.

See also a related Hollywood story in The Washington Post .

Midnight in Oslo (continued)

Filed under: General,Geometry — m759 @ 9:29 AM

Last evening's Geometry of the Dance discussed
a book on the Norwegian mathematician
Niels Henrik Abel. The post dealt with the group
S4 of 24 permutations of a 4-element set.

                                                    "In that open field
If you do not come too close, if you do not come too close,
On a summer midnight, you can hear the music…."

— The dance in Four Quartets

For a summer midnight related to the group S4,
see Midnight in Oslo from last August.

"At the still point…." — T. S. Eliot

"…a dance results." — Marie-Louise von Franz

Wednesday, May 9, 2012

Geometry of the Dance

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

Peter Pesic uses a dance metaphor to explain
finite group theory, with permutations of four elements
represented by symmetries of a tetrahedron—

IMAGE- 'The geometry of the dance' is that of a tetrahedron, according to Peter Pesic

For a different approach to the dance metaphor, see
the dance in Four Quartets and Poetry's Bones.

                                             In that open field
If you do not come too close, if you do not come too close,
On a summer midnight, you can hear the music
Of the weak pipe and the little drum
And see them dancing around the bonfire
The association of man and woman
In daunsinge, signifying matrimonie—
A dignified and commodiois sacrament.
Two and two, necessarye coniunction….

The English Wars

Filed under: General — m759 @ 2:20 PM

By Joan Acocella

Click image for article.


Tuesday, May 8, 2012

Exit, Pursued by Wild Thing

Filed under: General — m759 @ 1:00 PM

In memory of author Maurice Sendak,
who has died at 83—

"President Obama and his family read from
Where the Wild Things Are  at this year’s
White House Easter Egg Roll." —ABC News

See also Easter Act and Shaggy Dance.

Staging the Self

Filed under: General — m759 @ 9:29 AM

This post links to a column that
partially reveals the ending of
The Hunger Games  series of novels.

The title is from a column by Stanley Fish
on The Hunger Games  books in today's
online New York Times . The column
was posted at 9 PM EDT on May 7th, but I
did not see it until this morning.

Fish says—

"In the end… [spoiler details omitted]…
children… 'don’t know they play
on a graveyard'…."

For some literary background, see last night's post
on the May 7th, 2012, NY Times  obituaries as well
as the May 7th, 2006, Log24 post featuring 24 squares
arranged in a rectangular frame.

IMAGE- 4x6 grid

See also Frame Tales and, more generally,
The King and the Corpse.

"Et cetera, et cetera, et cetera." — Yul Brynner

Game Theory

Filed under: General — m759 @ 1:00 AM

Leading The New York Times  obituaries on the evening of
May 7th, 2012, was "Bob Stewart, Inventor of Game Shows"


From a publication linked to here on May 4th,
the reported date of Stewart's death—



For Eastern illusion involving a (presumably different)
"Bob Stewart," see this journal on May 7th six years ago.

Monday, May 7, 2012

More on Triality

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

John Baez wrote in 1996 ("Week 91") that

"I've never quite seen anyone come right out
and admit that triality arises from the
permutations of the unit vectors i, j, and k
in 3d Euclidean space."

Baez seems to come close to doing this with a
somewhat different i , j , and kHurwitz
— in his 2005 book review
quoted here yesterday.

See also the Log24 post of Jan. 4 on quaternions,
and the following figures. The actions on cubes
in the lower figure may be viewed as illustrating
(rather indirectly) the relationship of the quaternion
group's 24 automorphisms to the 24 rotational
symmetries of the cube.

IMAGE- Actions of the unit quaternions in finite geometry, on a ninefold square and on an eightfold cube

Sunday, May 6, 2012

Triality continued

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

This post continues the April 9 post
commemorating Élie Cartan's birthday.

That post mentioned triality .
Here is John Baez reviewing
On Quaternions and Octonions:
Their Geometry, Arithmetic, and Symmetry

by John H. Conway and Derek A. Smith
(A.K. Peters, Ltd., 2003)—

IMAGE- John Baez on quaternions and triality

"In this context, triality manifests itself
as the symmetry that cyclically permutes
the Hurwitz integers  i , j ,  and k ."

Related material— Quaternion Acts in this journal
as well as Finite Geometry and Physical Space.

Saturday, May 5, 2012

Collected Notes, 1978-1986

Filed under: General,Geometry — m759 @ 7:30 PM

Now online

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

PDF, 3.4 MB.

Friday, May 4, 2012

That Krell Lab (continued)

Filed under: General — m759 @ 12:00 PM

“… Which makes it a gilt-edged priority that one  of us
 gets into that Krell lab and takes that brain boost.”

— American adaptation of Shakespeare's Tempest , 1956

From "The Onto-theological Origin of Play:
Heraclitus and Plato," by Yücel Dursun, in
Lingua ac Communitas  Vol 17 (October 2007)—

"Heraclitus’s Aion and His Transformations

 The saying is as follows:

αἰὼν παῖς ἐστι παίζων, πεττεύων·
παιδὸς ἡ βασιληίη

(Aion is a child playing draughts;
the kingship is the child’s)

(Krell 1972: 64).*

 * KRELL, David Farrell.
   “Towards an Ontology of Play:
   Eugen Fink’s Notion of Spiel,”
   Research in Phenomemology ,
   2, 1972: 63-93.

This is the translation of the fragment in Greek by Krell.
There are many versions of the translation of the fragment….."

See also Child's Play and Froebel's Magic Box.

Update of May 5— For some background
from the date May 4 seven years ago, see
The Fano Plane Revisualized.

For some background on the word "aion,"
see that word in this journal.

Thursday, May 3, 2012

Child’s Play

Filed under: General — m759 @ 9:00 PM

Click to enlarge


"… a long seat, or a seat with a back,
     or a throne for the Queen;
     or again, a cross, a doorway, etc."

     — Joseph Payne

"… etc., etc." — Yul Brynner

Everybody Comes to Rick’s

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


Bogart and Lorre in 'Casablanca' with chessboard and cocktail

The key is the cocktail that begins the proceedings.”

– Brian Harley, Mate in Two Moves

See also yesterday's Endgame , as well as Play and Interplay
from April 28…  and, as a key, the following passage from
an earlier April 28 post

Euclidean geometry has long been applied
to physics; Galois geometry has not.
The cited webpage describes the interplay
of both  sorts of geometry— Euclidean
and Galois, continuous and discrete—
within physical space— if not within
the space of physics .

Wednesday, May 2, 2012


Filed under: General — m759 @ 9:48 PM

In memory of actress Patricia Medina


Medina, who died at 92 on April 28, starred in the 1954 Alan Ladd film The Black Knight .

April 28 is also the date the above photo appeared in this journal. See Play and Interplay.

Tuesday, May 1, 2012

What is Truth? (continued)

Filed under: General — m759 @ 11:01 PM

"There is a pleasantly discursive treatment of
 Pontius Pilate's unanswered question 'What is truth?'"
— H. S. M. Coxeter, 1987

Returning to the Walpurgisnacht posts
Decomposition (continued) and
Decomposition– Part III —

Some further background…


(Not  a Scholastic Aptitude Test)

"In computer sciencesatisfiability (often written
in all capitals or abbreviated 
SAT) is the problem
of determining if the variables of a given 
 formula can be assigned in such a way as to
make the formula evaluate to TRUE."

— Wikipedia article Boolean satisfiability problem

For the relationship of logic decomposition to SAT,
see (for instance) these topics in the introduction to—

Advanced Techniques in Logic Synthesis,
Optimizations and Applications* 

Click image for a synopsis.

* Edited by Sunil P. Khatri and Kanupriya Gulati

Off Broadway–

Filed under: General — m759 @ 2:01 PM

From this journal last Christmas—

Sunday, December 25, 2011


— m759 @ 3:59 PM 

"Woher dieser Sprung von Endlichen zum Unendlichen? "

— Wittgenstein, Zettel § 273

Antwort— Accomplished in Steps and For 34th Street.

See also Boundary Method.

The "Boundary Method" link above leads to a Christmas Day obituary
for Maurice Jaswon, co-author of a book on color symmetry.

Those who prefer entertainment may consult the previous Christmas.


Filed under: General — m759 @ 12:00 PM

Tony Award Nominations

"The losers? 'Spider-Man: Turn Off the Dark,'
the $75 million blockbuster that received just
two nominations. 'Seminar' and 'Godspell,'
which have some strong fans but were
shut out of the nominations." 

Patrick Healy in this morning's New York Times

A thought for Max Bialystock

The Spider-Man Godspell Seminar!

Jeff Goldblum in "Seminar"

Update of 12:25 PM —

The reviews are in!

IMAGE- May Day 2012 - Front page NY Times piece on religiously oriented theater

"A version of this article appeared in print on May 1, 2012, on page A1 of the New York edition…."

Powered by WordPress