Log24

Saturday, July 30, 2016

Darkness Visible

Filed under: General — m759 @ 9:00 AM

Andrew O'Hehir on July 22 —

— and on July 27 —

"Unless th' Almighty Maker them ordain
His dark materials to create more Worlds
Into this wilde Abyss the warie fiend
Stood on the brink of Hell and look'd a while,
Pondering his Voyage…."

— John Milton, Paradise Lost , Book II

For Benedict Cumberbatch as a "warie fiend,"
see posts now tagged Both Hands.

Friday, May 25, 2012

Review–

Filed under: General — m759 @ 12:00 AM

Sisteen Chapel

See Log24 two years ago on this date—

Darkness Visible and Sisteen.

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.)

Tuesday, November 9, 2010

Design

Filed under: General — m759 @ 5:01 PM

A Theory of Pure Design

by Denman Waldo Ross

Lecturer on the Theory of Design
in Harvard University

Boston and New York
Houghton, Mifflin and Company, 1907

PREFACE

"My purpose in this book is to elucidate, so far as I can, the
principles which underlie the practice of drawing and painting
as a Fine Art.  Art is generally regarded as the expression of
feelings and emotions which have no explanation except per-
haps in such a word as inspiration , which is expletive rather
than explanatory
.  Art is regarded as the one activity of man
which has no scientific basis, and the appreciation of Art is
said to be a matter of taste in which no two persons can be
expected to agree.  It is my purpose in this book to show how,
in the practice of Art, as in all other practices, we use certain
terms and follow certain principles.  Being defined and ex-
plained, these terms and principles may be known and under-
stood by everybody.  They are, so to speak, the form of the
language
.

While an understanding of the terms and principles of Art
will not, in itself, enable any one to produce important works,
such works are not produced without it.  It must be understood,
however, that the understanding of terms and principles
is not, necessarily, an understanding in words.  It may lie in
technical processes and in visual images and may never rise,
or shall I say fall, to any formulation in words, either spoken
or written."

_________________________________________________

One of Ross's protégés, Jack Levine, died yesterday at 95. He
is said to have remarked, "I want to paint with the dead ones."

Related material: This journal on the day of Levine's death
and on the day of Martin Gardner's death.

The latter post has an image illustrating Ross's remarks on
formulations in words—
 

Image-- The Case of the Lyche Gate Asterisk

For further details, see Finale, Darkness Visible, and Packed.

Saturday, May 29, 2010

Packed

Filed under: General — m759 @ 7:11 AM

Significant Passage:
On the Writing Style of Visual Thinkers

"The words are filled with unstated meaning.
They are (the term is Ricoeur's) 'packed'
and need unpacking." —Gerald Grow

From the date of Ricoeur's death,
May 20, 2005

“Plato’s most significant passage
    may be found in Phaedrus  265b…."

From Sept. 30, 2004

With a little effort,
anything can be shown
to connect with anything else:
existence is infinitely

cross-referenced."Image-- 8-rayed asterisk

— Opening sentence
of Martha Cooley's
The Archivist

Image-- 8-rayed asterisk Example:
Mozart's K 265,
the page number 265,
and a story by George MacDonald.

Mozart's K 265 is variations on the theme
now known as "Twinkle, Twinkle, Little Star."

For darker variations on the Twinkle theme,
see the film "Joshua" and Martin Gardner's
Annotated Alice  (Norton, 2000, pp. 73-75).

Image-- From the film 'Joshua,' Joshua with the Alice statue in Central Park

Joshua

For darker variations on the asterisk theme,
see Darkness Visible (May 25)
and Vonnegut's Asterisk.

Tuesday, May 25, 2010

ART WARS continued

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

Darkness Visible

The inevitable tribute to Martin Gardner
has now appeared at the AMS website—

Image-- American Mathematical Society (AMS) tribute to Martin Gardner, May 25, 2010

Related Imagery—

The following is an image from Saturday morning—

Image-- 'Darkness Visible,' a picture from Log24 on Saturday, May 22, 2010

See also Art Wars and
Mathematics and Narrative.

Sunday, November 16, 2008

Sunday November 16, 2008

Filed under: General — m759 @ 9:00 PM
Atwood on Art

From the previous entry:

“If it’s a seamless whole you want,
 pray to Apollo, who sets the limits
  within which such a work can exist.”

— Margaret Atwood,
author of Cat’s Eye

“The power of the dark is ascending.
 The light retreats to security, so that
 the dark cannot encroach upon it.”

Richard Wilhelm

 Related material:
Darkness Visible

Tuesday, April 3, 2007

Tuesday April 3, 2007

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

Mathematics Awareness Month

 
Related material:

"But what is it?"
Calvin demanded.
"We know that it's evil,
but what is it?"

"Yyouu hhave ssaidd itt!"
Mrs. Which's voice rang out.
"Itt iss Eevill. Itt iss thee
Ppowers of Ddarrkknesss!"

A Wrinkle in Time

AMS Notices cover, April 2007

"After A Wrinkle in Time was finally published, it was pointed out to me that the villain, a naked disembodied brain, was called 'It' because It stands for Intellectual truth as opposed to a truth which involves the whole of us, heart as well as mind.  That acronym had never occurred to me.  I chose the name It intuitively, because an IT does not have a heart or soul.  And I did not understand consciously at the time of writing that the intellect, when it is not informed by the heart, is evil."

See also
"Darkness Visible"
in ART WARS.
 
"When all is said and done,
science is about things and
theology is about words."
— Freeman Dyson,
New York Review of Books,
issue dated May 28, 1998

"Does the word 'tesseract'
mean anything to you?"
 

Friday, March 16, 2007

Friday March 16, 2007

Filed under: General,Geometry — Tags: — m759 @ 10:48 AM
"Geometry,
 Theology,
 and Politics:

 
Context and Consequences of 

the Hobbes-Wallis Dispute"
(pdf)

 

by Douglas M. Jesseph
Dept. of Philosophy and Religion
North Carolina State University

Excerpt:

"We are left to conclude that there was something significant in Hobbes's philosophy that motivated Wallis to engage in the lengthy and vitriolic denunciation of all things Hobbesian.

In point of fact, Wallis made no great secret of his motivations for attacking Hobbes's geometry, and the presence of theological and political motives is well attested in a 1659 letter to Huygens. He wrote:

But regarding the very harsh diatribe against Hobbes, the necessity of the case, and not my manners, led to it. For you see, as I believe, from other of my writings how peacefully I can differ with others and bear those with whom I differ. But this was provoked by our Leviathan (as can be easily gathered fro his other writings, principally those in English), when he attacks with all his might and destroys our universities (and not only ours, but all, both old and new), and especially the clergy and all institutions and all religion. As if the Christian world knew nothing sound or nothing that was not ridiculous in philosophy or religion; and as if it has not understood religion because it does not understand philosophy, nor philosophy because it does not understand mathematics. And so it seemed necessary that now some mathematician, proceeding in the opposite direction, should show how little he understand this mathematics (from which he takes his courage). Nor should we be deterred from this by his arrogance, which we know will vomit poison and filth against us. (Wallis to Huygens, 11 January, 1659; Huygens 1888-1950,* 2: 296-7)

The threats that Hobbes supposedly posed to the universities, the clergy, and all religion are a consequence of his political and theological doctrines. Hobbes's political theory requires that the power of the civil sovereign be absolute and undivided. As a consequence, such institutions as universities and the clergy must submit to the dictates of the sovereign in all matters. This extends, ironically enough, to geometry, since Hobbes notoriously claimed that the sovereign could ban the teaching of the subject and order 'the burning of all books of Geometry' if he should judge geometric principles 'a thing contrary to [his] right of dominion, or to the interest of men that have dominion' (Leviathan (1651) 1.11, 50; English Works** 3: 91). In the area of church government, Hobbes's doctrines are a decisive rejection of the claims of Presbyterianism, which holds that questions of theological doctrine is [sic] to be decided by the elders of the church– the presbytery– without reference to the claims of the sovereign. As a Presbyterian minister, a doctor of divinity, and professor of geometry at Oxford, Wallis found abundant reason to reject this political theory."

* Huygens, Christiaan. 1888-1950. Les oeuvres complètes de Chrisiaan Huygens. Ed. La Société Hollandaise des Sciences. 22 vols. The Hague: Martinus Nijhoff.

** Hobbes, Thomas. [1839-45] 1966. The English Works of Thomas Hobbes of Malmesbury, now First Collected and Edited by Sir William Molesworth. Edited by William Molesworth. 11 vols. Reprint. Aalen, Germany: Scientia Verlag.

 

Related material:

"But what is it?"
Calvin demanded.
"We know that it's evil,
but what is it?"

"Yyouu hhave ssaidd itt!"
Mrs. Which's voice rang out.
"Itt iss Eevill. Itt iss thee
Ppowers of Ddarrkknesss!"

A Wrinkle in Time

The image “http://www.log24.com/log/pix07/070316-AMScover.jpg” cannot be displayed, because it contains errors.

"After A Wrinkle in Time was finally published, it was pointed out to me that the villain, a naked disembodied brain, was called 'It' because It stands for Intellectual truth as opposed to a truth which involves the whole of us, heart as well as mind.  That acronym had never occurred to me.  I chose the name It intuitively, because an IT does not have a heart or soul.  And I did not understand consciously at the time of writing that the intellect, when it is not informed by the heart, is evil."

 

See also
"Darkness Visible"
in ART WARS.
 

Sunday, December 31, 2006

Sunday December 31, 2006

Filed under: General — m759 @ 7:15 PM
7/15, 2005:

From Darkness Visible:

“Ed Rinehart [sic] made a fortune painting canvases that were just one solid color.  He had his black period in which the canvas was totally black.  And then he had a blue period in which he was painting the canvas blue.”

— Martin Gardner interview in AMS Notices, June/July 2005

Sunday, October 22, 2006

Sunday October 22, 2006

Filed under: General — m759 @ 9:00 AM
Ad
 
The image “http://www.log24.com/log/pix05A/050619-AdReinhardt.gif” cannot be displayed, because it contains errors.
Ad Reinhardt

 

Ad for "The Prestige":

"Every great magic trick consists of three acts. The first act is called 'The Pledge.' The magician shows you something ordinary, but of course… it probably isn't. The second act is called 'The Turn.' The magician makes his ordinary 'some thing' do something extraordinary. Now if you're looking for the secret… you won't find it.   That's why there's a third act, called 'The Prestige.' This is the part with the twists and turns, where lives hang in the balance, and you see something shocking you've never seen before."
 

The Associated Press
Thought for Today,
Oct. 22, 2006:

"You can fool
too many of the people
too much of the time."

— James Thurber,
American humorist
(1894-1961)

 
The image “http://www.log24.com/log/pix06A/061020-Halmos.gif” cannot be displayed, because it contains errors.

For more detail,

click on the above
tombstone.

Friday, July 15, 2005

Friday July 15, 2005

Filed under: General — m759 @ 6:00 PM

Feast of St. Bonaventure

From Darkness Visible:

“Ed Rinehart [sic] made a fortune painting canvases that were just one solid color.  He had his black period in which the canvas was totally black.  And then he had a blue period in which he was painting the canvas blue.”

— Martin Gardner interview in AMS Notices, June/July 2005 

From Art History:

“Art history was very personal through the eyes of Ad Reinhardt.”

— Robert Morris,
    Smithsonian Archives of American Art

From The Edge of Eternity:

Christopher Fry’s obituary
in The New York Times

“His plays radiated an optimistic faith in God and humanity, evoking, in his words, ‘a world in which we are poised on the edge of eternity, a world which has deeps and shadows of mystery, and God is anything but a sleeping partner.’ He said he wrote his plays in poetry because that was ‘the language in which man expresses his own amazement’ at the complexity both of himself and of a reality which, beneath the surface, was ‘wildly, perilously, inexplicably fantastic.'”

From
Arrangement in
Black and Blue:

 

The image “http://www.log24.com/log/pix05A/050703-Cold.jpg” cannot be displayed, because it contains errors.

Adapted from cover of
German edition of Cold Mountain

Thursday, June 23, 2005

Thursday June 23, 2005

Filed under: General,Geometry — m759 @ 3:00 PM

Mathematics and Metaphor

The current (June/July) issue of the Notices of the American Mathematical Society has two feature articles.  The first, on the vulgarizer Martin Gardner, was dealt with here in a June 19 entry, Darkness Visible.  The second is related to a letter of André Weil (pdf) that is in turn related to mathematician Barry Mazur’s attempt to rewrite mathematical history  and to vulgarize other people’s research by using metaphors drawn, it would seem, from the Weil letter.
 
A Mathematical Lie conjectures that Mazur’s revising of history was motivated by a desire to dramatize some arcane mathematics, the Taniyama conjecture, that deals with elliptic curves and modular forms, two areas of mathematics that have been known since the nineteenth century to be closely related.

Mazur led author Simon Singh to believe that these two areas of mathematics were, before Taniyama’s conjecture of 1955, completely unrelated — 

“Modular forms and elliptic equations live in completely different regions of the mathematical cosmos, and nobody would ever have believed that there was the remotest link between the two subjects.” — Simon Singh, Fermat’s Enigma, 1998 paperback, p. 182

This is false.  See Robert P. Langlands, review of Elliptic Curves, by Anthony W. Knapp, Bulletin of the American Mathematical Society, January 1994.

It now appears that Mazur’s claim was in part motivated by a desire to emulate the great mathematician André Weil’s manner of speaking; Mazur parrots Weil’s “bridge” and “Rosetta stone” metaphors —

From Peter Woit’s weblog, Feb. 10, 2005:

“The focus of Weil’s letter is the analogy between number fields and the field of algebraic functions of a complex variable. He describes his ideas about studying this analogy using a third, intermediate subject, that of function fields over a finite field, which he thinks of as a ‘bridge‘ or ‘Rosetta stone.'” 

In “A 1940 Letter of André Weil on Analogy in Mathematics,” (pdf), translated by Martin H. Krieger, Notices of the A.M.S., March 2005, Weil writes that

“The purely algebraic theory of algebraic functions in any arbitrary field of constants is not rich enough so that one might draw useful lessons from it. The ‘classical’ theory (that is, Riemannian) of algebraic functions over the field of constants of the complex numbers is infinitely richer; but on the one hand it is too much so, and in the mass of facts some real analogies become lost; and above all, it is too far from the theory of numbers. One would be totally obstructed if there were not a bridge between the two.  And just as God defeats the devil: this bridge exists; it is the theory of the field of algebraic functions over a finite field of constants….

On the other hand, between the function fields and the ‘Riemannian’ fields, the distance is not so large that a patient study would not teach us the art of passing from one to the other, and to profit in the study of the first from knowledge acquired about the second, and of the extremely powerful means offered to us, in the study of the latter, from the integral calculus and the theory of analytic functions. That is not to say that at best all will be easy; but one ends up by learning to see something there, although it is still somewhat confused. Intuition makes much of it; I mean by this the faculty of seeing a connection between things that in appearance are completely different; it does not fail to lead us astray quite often. Be that as it may, my work consists in deciphering a trilingual text {[cf. the Rosetta Stone]}; of each of the three columns I have only disparate fragments; I have some ideas about each of the three languages: but I know as well there are great differences in meaning from one column to another, for which nothing has prepared me in advance. In the several years I have worked at it, I have found little pieces of the dictionary. Sometimes I worked on one column, sometimes under another.”

Here is another statement of the Rosetta-stone metaphor, from Weil’s translator, Martin H.  Krieger, in the A.M.S. Notices of November 2004,  “Some of What Mathematicians Do” (pdf):

“Weil refers to three columns, in analogy with the Rosetta Stone’s three languages and their arrangement, and the task is to ‘learn to read Riemannian.’  Given an ability to read one column, can you find its translation in the other columns?  In the first column are Riemann’s transcendental results and, more generally, work in analysis and geometry.  In the second column is algebra, say polynomials with coefficients in the complex numbers or in a finite field. And in the third column is arithmetic or number theory and combinatorial properties.”

For greater clarity, see  Armand Borel (pdf) on Weil’s Rosetta stone, where the three columns are referred to as Riemannian (transcendental), Italian (“algebraico-geometric,” over finite fields), and arithmetic (i.e., number-theoretic).
 
From Fermat’s Enigma, by Simon Singh, Anchor paperback, Sept. 1998, pp. 190-191:

Barry Mazur: “On the one hand you have the elliptic world, and on the other you have the modular world.  Both these branches of mathematics had been studied intensively but separately…. Than along comes the Taniyama-Shimura conjecture, which is the grand surmise that there’s a bridge between these two completely different worlds.  Mathematicians love to build bridges.”

Simon Singh: “The value of mathematical bridges is enormous.  They enable communities of mathematicians who have been living on separate islands to exchange ideas and explore each other’s  creations…. The great potential of the Taniyama-Shimura conjecture was that it would connect two islands and allow them to speak to each other for the first time.  Barry Mazur thinks of the Taniyama-Shimura conjecture as a translating device similar to the Rosetta stone…. ‘It’s as if you know one language and this Rosetta stone is going to give you an intense understanding of the other language,’ says Mazur.  ‘But the Taniyama-Shimura conjecture is a Rosetta stone with a certain magical power.'”

If Mazur, who is scheduled to speak at a conference on Mathematics and Narrative this July, wants more material on stones with magical powers, he might consult The Blue Matrix and The Diamond Archetype.

Sunday, June 19, 2005

Sunday June 19, 2005

Filed under: General,Geometry — Tags: — m759 @ 4:00 AM
ART WARS:
Darkness Visible
“No light, but rather darkness visible
 Serv’d only to discover sights of woe”
John Milton, Paradise Lost,
Book I,  lines 63-64

From the cover article (pdf) in the
June/July 2005 Notices of the
American Mathematical Society–

Martin Gardner


A famed vulgarizer, Martin Gardner,
summarizes the art of Ad Reinhardt
(Adolph Dietrich Friedrich Reinhardt,
  Dec. 24, 1913 – Aug. 30, 1967):

“Ed Rinehart [sic] made a fortune painting canvases that were just one solid color.  He had his black period in which the canvas was totally black.  And then he had a blue period in which he was painting the canvas blue.  He was exhibited in top shows in New York, and his pictures wound up in museums.  I did a column in Scientific American on minimal art, and I reproduced one of Ed Rinehart’s black paintings.  Of course, it was just a solid square of pure black.  The publisher insisted on getting permission from the gallery to reproduce it.”

Related material
from Log24.net,
Nov. 9-12, 2004:

Fade to Black

“…that ineffable constellation of talents that makes the player of rank: a gift for conceiving abstract schematic possibilities; a sense of mathematical poetry in the light of which the infinite chaos of probability and permutation is crystallized under the pressure of intense concentration into geometric blossoms; the ruthless focus of force on the subtlest weakness of an opponent.”

— Trevanian, Shibumi

“‘Haven’t there been splendidly elegant colors in Japan since ancient times?’

‘Even black has various subtle shades,’ Sosuke nodded.”

— Yasunari Kawabata, The Old Capital

An Ad Reinhardt painting
described in the entry of
noon, November 9, 2004
is illustrated below.

Ad Reinhardt,  Greek Cross

Ad Reinhardt,
Abstract Painting,
1960-66.
Oil on canvas, 60 x 60 inches.
Solomon R. Guggenheim Museum

The viewer may need to tilt
the screen to see that this
painting is not uniformly black,
but is instead a picture of a
Greek cross, as described below.

“The grid is a staircase to the Universal…. We could think about Ad Reinhardt, who, despite his repeated insistence that ‘Art is art,’ ended up by painting a series of… nine-square grids in which the motif that inescapably emerges is a Greek cross.

Greek Cross

There is no painter in the West who can be unaware of the symbolic power of the cruciform shape and the Pandora’s box of spiritual reference that is opened once one uses it.”

— Rosalind Krauss,
Meyer Schapiro Professor
of Modern Art and Theory
at Columbia University

(Ph.D., Harvard U., 1969),
in “Grids”

The image “http://www.log24.com/log/pix04B/041109-Krauss.jpg” cannot be displayed, because it contains errors.

Krauss

 
In memory of
St. William Golding
(Sept. 19, 1911 – June 19, 1993)

Friday, June 27, 2003

Friday June 27, 2003

Filed under: General,Geometry — Tags: — m759 @ 6:16 PM

For Fred Sandback:
Time's a Round

The following entry of Feb. 25, 2003, was written for painter Mark Rothko, and may serve as well for minimalist artist Fred Sandback, also connected to the de Menil family of art patrons, who, like Rothko, has killed himself.

Plagued in life by depression — what Styron, quoting Milton, called "darkness visible" — Rothko took his own life on this date [Feb. 25] in 1970.  As a sequel to the previous note, "Song of Not-Self," here are the more cheerful thoughts of the song "Time's a Round," the first of Shiva Dancing: The Rothko Chapel Songs, by C. K. Latham.  See also my comment on the previous entry (7:59 PM).

Time’s a round, time’s a round,
A circle, you see, a circle to be.

— C. K. Latham

 

10/23/02

The following is from the cover of
"Finnegans Wake: a Symposium,"

a reprint of

Our Exagmination Round His Factification
for Incamination of Work in Progress
,

 

Paris, Shakespeare and Company, 1929.

As well as being a memorial to Rothko and Sandback, the above picture may serve to mark the diamond anniversary of a dinner party at Shakespeare and Company on this date in 1928.  (See previous entry.)

A quotation from aaparis.org also seems relevant on this, the date usually given for the death of author Malcolm Lowry, in some of whose footsteps I have walked:

"We are not saints." 

— Chapter V, Alcoholics Anonymous

Tuesday, February 25, 2003

Tuesday February 25, 2003

Filed under: General,Geometry — Tags: — m759 @ 10:23 PM

For Mark Rothko

Plagued in life by depression — what Styron, quoting Milton, called "darkness visible" — Rothko took his own life on this date in 1970.  As a sequel to the previous note, "Song of Not-Self," here are the more cheerful thoughts of the song "Time's a Round," the first of Shiva Dancing: The Rothko Chapel Songs, by C. K. Latham.  See also my comment on the previous entry (7:59 PM).

Time’s a round, time’s a round,
A circle, you see, a circle to be.

— C. K. Latham

10/23/02

 

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