Log24

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

Professing

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

http://www.log24.com/log/pix12A/120530-ALdaily-NewBooks.jpg

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—

http://www.log24.com/log/pix12A/120529-Galois-Signature-500w.jpg

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

(Happens)

IMAGE- Nicolas Cage in 'Bringing Out the Dead'

http://www.log24.com/log/pix12A/120528-May28-TopObits.jpg

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….

Limited
Odd
One
Right
Male
Rest
Straight
Light
Good
Square

Unlimited
Even
Many
Left
Female
Motion
Curved
Dark
Bad
Oblong

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.

Commentary—

“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
lines:

‘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

Welcome.

See "How Deep the Darkness" + Koestler.

Graduation

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.

Review–

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

Tale

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

Requiem

Filed under: General — m759 @ 10:31 pm

Gary Snyder poem, Google+, May 22, 2012

Included Middle

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

Wikipedia— 

"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." 

REVIEW

"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."

Postscript—

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…

Sinatra

JOSEFINE LYCHE

Born 1973 in Bergen. Lives and works in Oslo.

Education

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 — Tags: — 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

Occultation

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…"

Wikipedia

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 — Tags: — m759 @ 3:33 pm

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

IMAGE- 'WATCH THE TRAILER' film ad

Applying this advice—

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

* See today's Times Colonist .

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