Log24

Friday, December 27, 2013

Space Epiphany

Filed under: General — m759 @ 12:00 pm

For posts related to the title, click here.

Jodie Foster in 'Contact'

Saturday, January 14, 2017

1984: A Space Odyssey

Filed under: General,Geometry — m759 @ 2:40 pm

See Eightfold 1984 in this journal.

Related material —

"… the object sets up a kind of
 frame or space or field
 within which there can be epiphany."

"… Instead of an epiphany of being,
we have something like
an epiphany of interspaces."

— Charles Taylor, "Epiphanies of Modernism,"
Chapter 24 of Sources of the Self ,
Cambridge University Press, 1989

"Perhaps every science must start with metaphor
and end with algebra; and perhaps without the metaphor
there would never have been any algebra."

— Max Black, Models and Metaphors ,
Cornell University Press, Ithaca, NY, 1962

Epiphany 2017 —

Click to enlarge:

Tuesday, January 10, 2017

Eightfold Epiphany

Filed under: General — m759 @ 1:00 pm

The reported death today at 105 of an admirable war correspondent,
"a perennial fixture at the Foreign Correspondents’ Club in Hong Kong," 
suggested a search in this journal for that city.

The search recalled to mind a notable quotation from
a Montreal philosopher —

“… the object sets up a kind of
 frame or space or field
 within which there can be epiphany.”

Charles Taylor, "Epiphanies of Modernism,"
Chapter 24 of Sources of the Self
(Cambridge U. Press, 1989, p. 477)

For some context, see St. Lucia's Day, 2012.
See also Epiphany 2017 —

Thursday, July 23, 2015

Space

Filed under: General — m759 @ 1:15 pm

   It's Space Week at Camp Google


“… the object sets up
 a kind of frame or space or field 
   within which there can be epiphany.”
— Charles Taylor       
Kylie Minogue does the Locomotion

“My little baby sister can do it with ease.
It’s easier to learn than those ABC’s.”

— Kylie Minogue           

Friday, February 14, 2014

Epiphany

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

“… the object sets up a kind of 
 frame or space or field 
 within which there can be epiphany.”

Charles Taylor

A frame or space or field —

IMAGE- The ninefold square

Related material —

Star Wars (January 11, 2014),

The Lyche Gate Asterisk , from 10:31 AM ET on May 22, 2010,
the date of Martin Gardner's death —

Image-- The Case of the Lyche Gate Asterisk

— and the March 2014 issue of the
Notices of the American Mathematical Society  —

See as well Epiphany 2014 (Jan. 6) in this journal and the
March Notices  on the Shaw prize —

"Established under the auspices of Run Run Shaw
in November 2002, the prize is managed and
administered by the Shaw Prize Foundation
based in Hong Kong." 

Thursday, December 13, 2012

Space

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

The sequel to Vibrations

Charles Taylor, "Epiphanies of Modernism,"
Chapter 24 of Sources of the Self
(Cambridge U. Press, 1989, p. 477) — 

“… the object sets up a kind of
 frame or space or field
 within which there can be epiphany.”

Or place.

See  A Prince of Darkness
and "A Clean, Well-Lighted Place."

Thursday, January 6, 2011

Epiphany Riddle

Filed under: General,Geometry — Tags: — m759 @ 11:32 am

"Spaces and geometries, those which we perceive,
which we can’t perceive, or which only some of us perceive,
are a recurring theme in Against  the Day ."

Michael White

"大哉大哉  宇宙之谜
 美哉美哉  真理之源"

"Great indeed is the riddle of the universe.
 Beautiful indeed is the source of truth."

— Shing-Tung Yau, Chairman,
Department of Mathematics, Harvard University

"Always keep a diamond in your mind."

King Solomon at the Paradiso

IMAGE-- Imaginary movie poster- 'The Galois Connection'- from stoneship.org

Image from stoneship.org

Friday, August 25, 2023

On the Night Road from Marfa

Filed under: General — Tags: , , — m759 @ 11:04 pm

"I’m really interested in exploring space."

New Yorker  cover artist for the Aug. 28, 2023, issue.

Related cinematic  art . . .

From a search in this journal for Nocturnal —

For some Bright Art Blocks Moments , see Cube Epiphany .

Sunday, October 11, 2020

Saniga on Einstein

Filed under: General — m759 @ 8:25 am

See Einstein on Acid” by Stephen Battersby
(New Scientist , Vol. 180, issue 2426 — 20 Dec. 2003, 40-43).

That 2003 article is about some speculations of Metod Saniga.

“Saniga is not a professional mystic or
a peddler of drugs, he is an astrophysicist
at the Slovak Academy of Sciences in Bratislava.
It seems unlikely that studying stars led him to
such a way-out view of space and time. Has he
undergone a drug-induced epiphany, or a period
of mental instability? ‘No, no, no,’ Saniga says,
‘I am a perfectly sane person.'”

Some more recent and much less speculative remarks by Saniga
are related to the Klein correspondence —

arXiv.org > math > arXiv:1409.5691:
Mathematics > Combinatorics
[Submitted on 17 Sep 2014]
The Complement of Binary Klein Quadric
as a Combinatorial Grassmannian

By Metod Saniga

“Given a hyperbolic quadric of PG(5,2), there are 28 points
off this quadric and 56 lines skew to it. It is shown that the
(286,563)-configuration formed by these points and lines
is isomorphic to the combinatorial Grassmannian of type
G2(8). It is also pointed out that a set of seven points of
G2(8) whose labels share a mark corresponds to a
Conwell heptad of PG(5,2). Gradual removal of Conwell
heptads from the (286,563)-configuration yields a nested
sequence of binomial configurations identical with part of
that found to be associated with Cayley-Dickson algebras
(arXiv:1405.6888).”

Related entertainment —

See Log24 on the date, 17 Sept. 2014, of Saniga’s Klein-quadric article:

Articulation Day.

Friday, May 15, 2020

Review

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

Charles Taylor,
“Epiphanies of Modernism,”
Chapter 24 of Sources of the Self
(Cambridge U. Press, 1989, p. 477) —

“… the object sets up
a kind of frame or space or field
within which there can be epiphany.”

See also Talking of Michelangelo.

Related material for comedians —

BOX: Binary Object Extension

Literature ad absurdum

Tuesday, July 9, 2019

Dreamtimes

Filed under: General — Tags: , , — m759 @ 4:27 am

“I am always the figure in someone else’s dream. I would really rather
sometimes make my own figures and make my own dreams.”

— John Malkovich at squarespace.com, January 10, 2017

Also on that date . . .

.

Wednesday, April 12, 2017

Knucklebone

Filed under: General — Tags: — m759 @ 7:22 pm

"The state of the universe, physicists say, is a cosmological
relic—a glass ark with hammered-gold seams, pip trapped inside, god’s
knucklebone, nanosecond high-energy outward burst—kaboom!

and space fills up with proto-stars . . . ."

— "A Natural History of Light," a poem by Marsha de la O,
     The New Yorker , issue of December 12, 2016


"Angel's Bone," by Du Yun, premiered on January 6, 2016 . . . ."

Saturday, August 30, 2014

Physics and Theology

Filed under: General,Geometry — m759 @ 7:00 pm

The titles of the previous three posts refer to
Hermann Weyl’s 1918 book Raum, Zeit, Materie
(Space, Time, Matter).

This suggests a look at a poetically parallel 1950 title —
The Lion, the Witch and the Wardrobe —
and at its underlying philosophy:

I am among “those who do not know that this great myth became Fact.”
I do, however, note that some other odd things have become fact.
Those who wish more on this topic may consult:

Thursday, February 13, 2014

Plan 9

Filed under: General — Tags: , — m759 @ 6:29 pm

(Continued)

The final link in today's previous post leads to
a post whose own final link leads to

Thursday, December 13, 2012

Space

Filed under: Uncategorized — m759 @ 12:00 PM                

 The sequel to Vibrations

Charles Taylor, "Epiphanies of Modernism,"
Chapter 24 of Sources of the Self
(Cambridge U. Press, 1989, p. 477) — 

“… the object sets up a kind of 
 frame or space or field 
 within which there can be epiphany.”

Or place.

See  A Prince of Darkness 
and "A Clean, Well-Lighted Place."

Wednesday, December 12, 2012

Chromatic Plenitude

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

(Continued from 2 PM ET Tuesday)

“… the object sets up a kind of frame or space or field 
within which there can be epiphany.”

— Charles Taylor, "Epiphanies of Modernism,"
Chapter 24 of Sources of the Self
(Cambridge U. Press, 1989, p. 477) 

"The absolute consonance is a state of chromatic plenitude."

Charles Rosen

"… the nearest precedent might be found in Becky Sharp .
The opening of the Duchess of Richmond's ball,
with its organization of strong contrasts and
display of chromatic plenitude, presents a schema…."

— Scott Higgins, Harnessing the Technicolor Rainbow:
Color Design in The 1930s 
, University of Texas Press,
2007, page 142

Schema I    (Click to enlarge.)

Note the pattern on the dance floor.

(Click for wider image.)


Schema II 

"At the still point…" — Four Quartets

Monday, June 29, 2009

Monday June 29, 2009

Filed under: General,Geometry — m759 @ 6:29 pm
Calvinist Epiphany
for St. Peter’s Day

Have your people
  call my people.
— George Carlin 


Diamond life, lover boy;
we move in space
with minimum waste
 and maximum joy.

— Sade, quoted here on
 Lincoln’s Birthday, 2003

This is perhaps suitable
for the soundtrack of
the film “Blockheads
  (currently in development)–

Kohs Block Design Test


Diamond Life

Related material from Wikipedia:

“Uta Frith, in her book Autism: Explaining the Enigma,[5] addresses the superior performance of autistic individuals on the block design [link not in Wikipedia] test. This was also addressed in [an] earlier paper.[6] A particularly interesting article demonstrates the differences in construction time in the performance of the block design task by Asperger syndrome individuals and non-Asperger’s individuals. An essential point here is that in an unsegmented version of the task, Asperger’s individuals performed dramatically faster than non-Asperger’s individuals: [7].”

5. Frith, Uta (2003). Autism: explaining the enigma (2nd ed. ). Cambridge, MA: Blackwell Pub. ISBN 0-631-22901-9.

6. Shah A, Frith U (Nov 1993). “Why do autistic individuals show superior performance on the block design task?”. J Child Psychol Psychiatry 34 (8): 1351–64. PMID 8294523. 

7. Caron MJ, Mottron L, Berthiaume C, Dawson M (Jul 2006). “Cognitive mechanisms, specificity and neural underpinnings of visuospatial peaks in autism”. Brain 129 (Pt 7): 1789–802. doi:10.1093/brain/awl072. PMID 16597652. “Fig 3”.

Lover Boy

Related material from a film (see Calvinist Epiphany, June 17):

Still from the film 'Adam'-- Adam looking at photo

Related material from another film:

Monty Python - Bright Side of Life

For the relevance of this maxim to autism, see Markoff Process (March 4, 2009).

Friday, May 22, 2009

Friday May 22, 2009

Filed under: General,Geometry — Tags: — m759 @ 9:29 am
Steiner System

New York Times
banner this morning:

NYT banner, 9:21 AM Friday, May 22, 2009-- Ears are ads for HSBC.

Click to enlarge.

Related material from
July 11, 2008:

HSBC logo with framed version

The HSBC Logo Designer —

Henry Steiner

Henry Steiner, designerHe is an internationally recognized corporate identity consultant. Based in Hong Kong, his work for clients such as HongkongBank, IBM and Unilever is a major influence in Pacific Rim design.

Born in Austria and raised in New York, Steiner was educated at Yale under Paul Rand and attended the Sorbonne as a Fulbright Fellow. He is a past President of Alliance Graphique Internationale. Other professional affiliations include the American Institute of Graphic Arts, Chartered Society of Designers, Design Austria, and the New York Art Directors' Club.

His Cross-Cultural Design: Communicating in the Global Marketplace was published by Thames and Hudson (1995).

Yaneff.com

 

Charles Taylor,
"Epiphanies of Modernism,"
Chapter 24 of Sources of the Self
  (Cambridge U. Press, 1989, p. 477):

 

"… the object sets up
 a kind of frame or space or field
   within which there can be epiphany."

 

Related material suggested by
an ad last night on
ABC's Ugly Betty season finale:

Poster for 'Diamonds' miniseries on ABC starting May 24, 2009

Credit for 'Diamonds' miniseries poster: Diane Robertson Design, London

Diamond from last night's
Log24 entry, with
four colored pencils from
Diane Robertson Design:

Diamond-shaped face of Durer's 'Melencolia I' solid, with  four colored pencils from Diane Robertson Design
 
See also
A Four-Color Theorem.

Saturday, April 25, 2009

Saturday April 25, 2009

Filed under: General,Geometry — Tags: — m759 @ 9:22 pm
State of Play

Russell Crowe in 'State of Play'

The Russell Crowe
Hotel Puzzle

by John Tierney

"Russell Crowe arrives at the Hotel Infinity looking tired and ornery. He demands a room. The clerk informs him that there are no vacancies…."

Footprints from California today
(all by a person or persons using Firefox browsers):

7:10 AM
http://m759.xanga.com/679142359/concepts-of-space/?
Concepts of Space: Euclid vs. Galois

8:51 AM
http://m759.xanga.com/689601851/art-wars-continued/?
Art Wars continued: Behind the Picture

1:33 PM
http://m759.xanga.com/678995132/a-riff-for-dave/?
A Riff for Dave: Me and My Shadow

2:11 PM
http://m759.xanga.com/638308002/a-death-of-kings/?
A Death of Kings: In Memory of Bobby Fischer

2:48 PM
http://m759.xanga.com/691644175/art-wars-in-review–/?
Art Wars in review– Through the Looking Glass: A Sort of Eternity

3:28 PM and
http://m759.xanga.com/684680406/annals-of-philosophy/?
Annals of Philosophy: The Dormouse of Perception

4:28 PM
http://m759.xanga.com/641536988/epiphany-for-roy-part-i/?
Epiphany for Roy, Part I

6:03 PM
http://m759.xanga.com/641949564/art-wars-continued/?
At the Still Point: All That Jazz

6:22 PM
http://m759.xanga.com/644330798/where-entertainment-is-not-god/?
Where Entertainment is Not God: The Just Word

7:14 PM
http://m759.xanga.com/643490468/happy-new-yorker-day/?
Happy New Yorker Day– Class Galore

7:16 PM
http://m759.xanga.com/643812753/the-politics-of-change/?
The Politics of Change: Jumpers
 

"Relax," said the night man.
"We are programmed to receive."
— Hotel California
 

Tuesday, January 6, 2009

Tuesday January 6, 2009

Filed under: General,Geometry — Tags: , , — m759 @ 12:00 am
Archetypes, Synchronicity,
and Dyson on Jung

The current (Feb. 2009) Notices of the American Mathematical Society has a written version of Freeman Dyson’s 2008 Einstein Lecture, which was to have been given in October but had to be canceled. Dyson paraphrases a mathematician on Carl Jung’s theory of archetypes:

“… we do not need to accept Jung’s theory as true in order to find it illuminating.”

The same is true of Jung’s remarks on synchronicity.

For example —

Yesterday’s entry, “A Wealth of Algebraic Structure,” lists two articles– each, as it happens, related to Jung’s four-diamond figure from Aion as well as to my own Notes on Finite Geometry. The articles were placed online recently by Cambridge University Press on the following dates:

R. T. Curtis’s 1974 article defining his Miracle Octad Generator (MOG) was published online on Oct. 24, 2008.

Curtis’s 1987 article on geometry and algebraic structure in the MOG was published online on Dec. 19, 2008.

On these dates, the entries in this journal discussed…

Oct. 24:
Cube Space, 1984-2003

Material related to that entry:

Dec. 19:
Art and Religion: Inside the White Cube

That entry discusses a book by Mark C. Taylor:

The Picture in Question: Mark Tansey and the Ends of Representation (U. of Chicago Press, 1999).

In Chapter 3, “Sutures of Structures,” Taylor asks —

“What, then, is a frame, and what is frame work?”

One possible answer —

Hermann Weyl on the relativity problem in the context of the 4×4 “frame of reference” found in the above Cambridge University Press articles.

“Examples are the stained-glass
windows of knowledge.”
— Vladimir Nabokov 

Friday, July 11, 2008

Friday July 11, 2008

Filed under: General — Tags: — m759 @ 1:00 pm
AND MORE LOGOS:

"Serious numbers will
always be heard."
Paul Simon  

http://www.log24.com/log/pix08/080711-DowLg.jpg

http://www.log24.com/log/pix08/080711-NYSE.jpg

http://www.log24.com/log/pix08/080711-HSBClogo.jpg

The HSBC Logo Designer —

Henry Steiner

He is an internationally recognized corporate identity consultant. Based in Hong Kong, his work for clients such as HongkongBank, IBM and Unilever is a major influence in Pacific Rim design.

Born in Austria and raised in New York, Steiner was educated at Yale under Paul Rand and attended the Sorbonne as a Fulbright Fellow. He is a past President of Alliance Graphique Internationale. Other professional affiliations include the American Institute of Graphic Arts, Chartered Society of Designers, Design Austria, and the New York Art Directors' Club.

His Cross-Cultural Design: Communicating in the Global Marketplace was published by Thames and Hudson (1995).

Yaneff.com

 

Related material
from the past

Wittgenstein and Fly from Fly-Bottle

Fly from Fly Bottle:

Graphic structures from Diamond Theory and from Kyocera logo

Charles Taylor,
"Epiphanies of Modernism,"
Chapter 24 of Sources of the Self
  (Cambridge U. Press, 1989, p. 477) —

"… the object sets up
 a kind of frame or space or field
   within which there can be epiphany."

Related material
from today —

Escape from a
  cartoon graveyard:

http://www.log24.com/log/pix08/080711-BabyBlues.jpg

Thursday, June 26, 2008

Thursday June 26, 2008

Filed under: General — m759 @ 10:04 am
Review
 
Yesterday, June 25, was the 100th anniversay of W.V. Quine's birth and also the day on the calendar opposite Christmas–  In the parlance of Quine's son Douglas, AntiChristmas.

Having survived that ominous date, I feel it is fitting to review what Wallace Stevens called "Credences of Summer"– religious principles for those who feel that faith and doubt are best reconciled by art.

 

"Credences of Summer," VII,

by Wallace Stevens, from
Transport to Summer (1947)

"Three times the concentred
     self takes hold, three times
The thrice concentred self,
     having possessed
The object, grips it
     in savage scrutiny,
Once to make captive,
     once to subjugate
Or yield to subjugation,
     once to proclaim
The meaning of the capture,
     this hard prize,
Fully made, fully apparent,
     fully found."

Definition of Epiphany

From James Joyce's Stephen Hero, first published posthumously in 1944. The excerpt below is from a version edited by John J. Slocum and Herbert Cahoon (New York: New Directions Press, 1959).

Three Times:

… By an epiphany he meant a sudden spiritual manifestation, whether in the vulgarity of speech or of gesture or in a memorable phase of the mind itself. He believed that it was for the man of letters to record these epiphanies with extreme care, seeing that they themselves are the most delicate and evanescent of moments. He told Cranly that the clock of the Ballast Office was capable of an epiphany. Cranly questioned the inscrutable dial of the Ballast Office with his no less inscrutable countenance:

— Yes, said Stephen. I will pass it time after time, allude to it, refer to it, catch a glimpse of it. It is only an item in the catalogue of Dublin's street furniture. Then all at once I see it and I know at once what it is: epiphany.

— What?

— Imagine my glimpses at that clock as the gropings of a spiritual eye which seeks to adjust its vision to an exact focus. The moment the focus is reached the object is epiphanised. It is just in this epiphany that I find the third, the supreme quality of beauty.

— Yes? said Cranly absently.

— No esthetic theory, pursued Stephen relentlessly, is of any value which investigates with the aid of the lantern of tradition. What we symbolise in black the Chinaman may symbolise in yellow: each has his own tradition. Greek beauty laughs at Coptic beauty and the American Indian derides them both. It is almost impossible to reconcile all tradition whereas it is by no means impossible to find the justification of every form of beauty which has ever been adored on the earth by an examination into the mechanism of esthetic apprehension whether it be dressed in red, white, yellow or black. We have no reason for thinking that the Chinaman has a different system of digestion from that which we have though our diets are quite dissimilar. The apprehensive faculty must be scrutinised in action.

— Yes …

— You know what Aquinas says: The three things requisite for beauty are, integrity, a wholeness, symmetry and radiance. Some day I will expand that sentence into a treatise. Consider the performance of your own mind when confronted with any object, hypothetically beautiful. Your mind to apprehend that object divides the entire universe into two parts, the object, and the void which is not the object. To apprehend it you must lift it away from everything else: and then you perceive that it is one integral thing, that is a thing. You recognise its integrity. Isn't that so?

— And then?

— That is the first quality of beauty: it is declared in a simple sudden synthesis of the faculty which apprehends. What then? Analysis then. The mind considers the object in whole and in part, in relation to itself and to other objects, examines the balance of its parts, contemplates the form of the object, traverses every cranny of the structure. So the mind receives the impression of the symmetry of the object. The mind recognises that the object is in the strict sense of the word, a thing, a definitely constituted entity. You see?

— Let us turn back, said Cranly.

They had reached the corner of Grafton St and as the footpath was overcrowded they turned back northwards. Cranly had an inclination to watch the antics of a drunkard who had been ejected from a bar in Suffolk St but Stephen took his arm summarily and led him away.

— Now for the third quality. For a long time I couldn't make out what Aquinas meant. He uses a figurative word (a very unusual thing for him) but I have solved it. Claritas is quidditas. After the analysis which discovers the second quality the mind makes the only logically possible synthesis and discovers the third quality. This is the moment which I call epiphany. First we recognise that the object is one integral thing, then we recognise that it is an organised composite structure, a thing in fact: finally, when the relation of the parts is exquisite, when the parts are adjusted to the special point, we recognise that it is that thing which it is. Its soul, its whatness, leaps to us from the vestment of its appearance. The soul of the commonest object, the structure of which is so adjusted, seems to us radiant. The object achieves its epiphany.

Having finished his argument Stephen walked on in silence. He felt Cranly's hostility and he accused himself of having cheapened the eternal images of beauty. For the first time, too, he felt slightly awkward in his friend's company and to restore a mood of flippant familiarity he glanced up at the clock of the Ballast Office and smiled:

— It has not epiphanised yet, he said.

Under the Volcano,

by Malcolm Lowry,
1947, Chapter VI:

"What have I got out of my life? Contacts with famous men… The occasion Einstein asked me the time, for instance. That summer evening…. smiles when I say I don't know. And yet asked me. Yes: the great Jew, who has upset the whole world's notions of time and space, once leaned down… to ask me… ragged freshman… at the first approach of the evening star, the time. And smiled again when I pointed out the clock neither of us had noticed."

An approach of
the evening star yesterday:

Four-elements figure from webpage 'The Rotation of the Elements'

This figure is from a webpage,
"The Rotation of the Elements,"
cited here yesterday evening.

As noted in yesterday's early-
morning entry on Quine
, the
figure is (without the labels)
a classic symbol of the
evening star.

"The appearance of the evening star brings with it long-standing notions of safety within and danger without. In a letter to Harriet Monroe, written December 23, 1926, Stevens refers to the Sapphic fragment that invokes the genius of evening: 'Evening star that bringest back all that lightsome Dawn hath scattered afar, thou bringest the sheep, thou bringest the goat, thou bringest the child home to the mother.' Christmas, writes Stevens, 'is like Sappho's evening: it brings us all home to the fold' (Letters of Wallace Stevens, 248)."

— Barbara Fisher,
"The Archangel of Evening,"
Chapter 5 of Wallace Stevens:
The Intensest Rendezvous
,
The University Press of Virginia, 1990

Wednesday, June 25, 2008

Wednesday June 25, 2008

Filed under: General — m759 @ 8:06 am
Prize Dance

“I would not know what the spirit
of a philosopher might wish more
 to be than a good dancer.
For the dance is his ideal,
also his art, and finally also his
only piety, his ‘service of God.'”

Nietzsche

Charles Taylor, winner
of this year’s Kyoto Prize
in arts and philosophy:

“… the object sets up
 a kind of frame or space or field
   within which there can be epiphany.”


Kylie Minogue does the Locomotion

“My little baby sister
can do it with ease.
It’s easier to learn
  than those ABC’s.”

Kylie Minogue 

Wednesday June 25, 2008

Filed under: General — m759 @ 2:02 am
Born 100 years ago today:

Willard Van Orman Quine, picture from cover of his autobiography

From A Logical Point of View,  Harvard U. Press, 1980, p. 72
From A Logical Point of View,  Harvard U. Press, 1980, p. 73
Other approaches to the
eight-ray star figure

Figure by Quine for an argument against univesals in 'From a Logical Point of View'

have been sketched in
various Log24 entries.

See, for instance, the
June 21 entries on
the Kyoto Prize for
arts and philosophy.
Quine won this prize
 in 1996.

Quine’s figure, cited in an
argument against universals,
is also a classic symbol for
the morning or evening star.

This year’s winner http://www.log24.com/images/asterisk8.gif
of the Kyoto Prize has
a more poetic approach
to philosophy:

“… the object sets up
 a kind of frame or space or field
   within which there can be epiphany.”

For one such frame or space,
a Mexican cantina, see
Shining Forth.

See also Damnation Morning and
The Devil and Wallace Stevens.

http://www.log24.com/images/asterisk8.gif Charles Taylor.  See
“Epiphanies of Modernism,”
Chapter 24 of Sources of the Self
  (Cambridge U. Press, 1989, p. 477)

Saturday, June 21, 2008

Saturday June 21, 2008

Filed under: General,Geometry — m759 @ 6:00 am

The Kyoto Prize

for lifetime achievement
in arts and philosophy
this year goes to
Charles Taylor,

Charles Margrave Taylor, professor emeritus of philosophy at McGill University

Montreal philosophy professor.

“The Kyoto Prize has been given in three domains since 1984:
advanced technology, basic sciences, and the arts and philosophy.
It is administered by the Inamori Foundation, whose president,
Kazuo Inamori, is founder and chairman emeritus of Kyocera and
KDDI Corporation, two Japanese telecommunications giants.”

 

Kyocera Logo

“The Kyocera brand symbol is composed of a corporate mark
and our corporate logotype. The mark represents the initial
‘K’ (for Kyocera) encircling a ‘C’ (for ceramics). It was
introduced in October 1982 when the company name was
changed from ‘Kyoto Ceramic’ to ‘Kyocera.'”

global.kyocera.com

Related material —

Wittgenstein and Fly from Fly-Bottle

Fly from Fly Bottle:

Graphic structures from Diamond Theory and from Kyocera logo

Charles Taylor,
“Epiphanies of Modernism,”
Chapter 24 of Sources of the Self
(Cambridge U. Press, 1989, p. 477) —

“… the object sets up
a kind of frame or space or field
within which there can be epiphany.”

See also Talking of Michelangelo.

Thursday, May 22, 2008

Thursday May 22, 2008

Filed under: General,Geometry — Tags: , — m759 @ 9:00 am
The Undertaking:
An Exercise in
Conceptual Art

I Ching hexagram 54: The Marrying Maiden

Hexagram 54:
THE JUDGMENT

Undertakings bring misfortune.
Nothing that would further.

The image “http://www.log24.com/log/pix08/080522-Irelandslide1.jpg” cannot be displayed, because it contains errors.

Brian O’Doherty, an Irish-born artist,
before the [Tuesday, May 20] wake
of his alter ego* ‘Patrick Ireland’
on the grounds of the
Irish Museum of Modern Art.”
New York Times, May 22, 2008    

THE IMAGE

Thus the superior man
understands the transitory
in the light of
the eternity of the end.

Another version of
the image:

Images of time and eternity in memory of Michelangelo
See 2/22/08
and  4/19/08.


Related material:

Michael Kimmelman in today’s New York Times

“An essay from the ’70s by Mr. O’Doherty, ‘Inside the White Cube,’ became famous in art circles for describing how modern art interacted with the gallery spaces in which it was shown.”

Brian O’Doherty, “Inside the White Cube,” 1976 Artforum essays on the gallery space and 20th-century art:

“The history of modernism is intimately framed by that space. Or rather the history of modern art can be correlated with changes in that space and in the way we see it. We have now reached a point where we see not the art but the space first…. An image comes to mind of a white, ideal space that, more than any single picture, may be the archetypal image of 20th-century art.”

An archetypal image

THE SPACE:

The Eightfold Cube: The Beauty of Klein's Simple Group

A non-archetypal image

THE ART:

Jack in the Box, by Natasha Wescoat

Natasha Wescoat, 2004
See also Epiphany 2008:

How the eightfold cube works

“Nothing that would further.”
— Hexagram 54

Lear’s fool:

 …. Now thou art an 0
without a figure. I am better
than thou art, now. I am a fool;
thou art nothing….

“…. in the last mystery of all the single figure of what is called the World goes joyously dancing in a state beyond moon and sun, and the number of the Trumps is done.  Save only for that which has no number and is called the Fool, because mankind finds it folly till it is known.  It is sovereign or it is nothing, and if it is nothing then man was born dead.”

The Greater Trumps,
by Charles Williams, Ch. 14

* For a different, Jungian, alter ego, see Irish Fourplay (Jan. 31, 2003) and “Outside the Box,” a New York Times review of O’Doherty’s art (featuring a St. Bridget’s Cross) by Bridget L. Goodbody dated April 25, 2007. See also Log24 on that date.

Monday, April 28, 2008

Monday April 28, 2008

Filed under: General,Geometry — Tags: , — m759 @ 7:00 am
Religious Art

The black monolith of
Kubrick's 2001 is, in
its way, an example
of religious art.

Black monolith, proportions 4x9

One artistic shortcoming
(or strength– it is, after
all, monolithic) of
that artifact is its
resistance to being
analyzed as a whole
consisting of parts, as
in a Joycean epiphany.

The following
figure does
allow such
  an epiphany.

A 2x4 array of squares

One approach to
 the epiphany:

"Transformations play
  a major role in
  modern mathematics."
– A biography of
Felix Christian Klein

The above 2×4 array
(2 columns, 4 rows)
 furnishes an example of
a transformation acting
on the parts of
an organized whole:

The 35 partitions of an 8-set into two 4-sets

For other transformations
acting on the eight parts,
hence on the 35 partitions, see
"Geometry of the 4×4 Square,"
as well as Peter J. Cameron's
"The Klein Quadric
and Triality" (pdf),
and (for added context)
"The Klein Correspondence,
Penrose Space-Time, and
a Finite Model
."

For a related structure–
  not rectangle but cube– 
see Epiphany 2008.

Saturday, April 28, 2007

Saturday April 28, 2007

Filed under: General,Geometry — m759 @ 11:07 pm
Cubism

PA Lottery April 28, 2007: Midday 510, Evening 223

See last year’s   
entries for 5/10

My Space

4x4x4 cube

and for 2/23

Cubist Epiphany

4x4x4 cube

“This is a crazy world and
the only way to enjoy it
is to treat it as a joke.”

— Robert A. Heinlein,
The Number of the Beast

Tuesday, January 9, 2007

Tuesday January 9, 2007

Filed under: General — Tags: — m759 @ 12:00 pm
For Balanchine's Birthday

(continued from
January 9, 2003)

George Balanchine

Encyclopædia Britannica Article

born January 22
[January 9, Old Style], 1904,
St. Petersburg, Russia
died April 30, 1983, New York,
New York, U.S.

Photograph:George Balanchine.
George Balanchine.
©1983 Martha Swope

original name 
Georgy Melitonovich Balanchivadze

most influential choreographer of classical ballet in the United States in the 20th century.  His works, characterized by a cool neoclassicism, include The Nutcracker (1954) and Don Quixote (1965), both pieces choreographed for the New York City Ballet, of which he was a founder (1948), the artistic director, and the…


Balanchine,  George… (75 of 1212 words)

"What on earth is
a concrete universal?"
— Robert M. Pirsig

Review:

From Wikipedia's
"Upper Ontology"
and
Epiphany 2007:

"There is no neutral ground
that can serve as
a means of translating between
specialized (lower) ontologies."

There is, however,
"the field of reason"–

the 3×3 grid:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

Click on grid
for details.

As Rosalind Krauss
has noted, some artists
regard the grid as

"a staircase to
  the Universal."

Other artists regard
Epiphany itself as an
approach to
the Universal:

"Epiphany signals the traversal
of the finite by the infinite,
of the particular by the universal,
of the mundane by the mystical,
of time by eternity.
"

Richard Kearney, 2005,
in The New Arcadia Review

The image “http://www.log24.com/log/pix07/070109-Kearney2.jpg” cannot be displayed, because it contains errors.

Kearney (right) with
Martin Scorsese (left)
and Gregory Peck
in 1997.

"… one of the things that worried me about traditional metaphysics, at least as I imbibed it in a very Scholastic manner at University College Dublin in the seventies, is that philosophy was realism and realism was truth. What disturbed me about that was that everything was already acquired; truth was always a systematic given and it was there to be learned from Creation onwards; it was spoken by Jesus Christ and then published by St. Thomas Aquinas: the system as perfect synthesis. Hence, my philosophy grew out of a hunger for the 'possible' and it was definitely a reaction to my own philosophical formation. Yet that wasn't my only reaction. I was also reacting to what I considered to be the deep pessimism, and even at times 'nihilism' of the postmodern turn."

— Richard Kearney, interview (pdf) in The Leuven Philosophy Newsletter, Vol. 14, 2005-2006

For more on "the possible," see Kearney's The God Who May Be, Diamonds Are Forever, and the conclusion of Mathematics and Narrative:

 

"We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

 

Keith Allen Korcz 

The image “http://www.log24.com/log/pix05B/050802-Stone.gif” cannot be displayed, because it contains errors.

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity,
Christ Church College, Oxford
(the home of Lewis Carroll)

Thursday, February 23, 2006

Thursday February 23, 2006

Filed under: General,Geometry — m759 @ 1:06 pm
Cubist Epiphany

4x4x4 cube

“In The Painted Word, a rumination on the state of American painting in the 1970s, Tom Wolfe described an epiphany….”

Peter Berkowitz, “Literature in Theory”

“I had an epiphany.”

— Apostolos Doxiadis, organizer of last summer’s conference on mathematics and narrative.  See the Log24 entry of 1:06 PM last August 23 and the four entries that preceded it.

“… das Durchleuchten des ewigen Glanzes des ‘Einen’ durch die materielle Erscheinung

A definition of beauty from Plotinus, via Werner Heisenberg

“By groping toward the light we are made to realize how deep the darkness is around us.”

— Arthur Koestler, The Call Girls: A Tragi-Comedy, Random House, 1973, page 118, quoted in The Shining of May 29

“Perhaps we are meant to see the story as a cubist retelling of the crucifixion….”

— Adam White Scoville, quoted in Cubist Crucifixion, on Iain Pears’s novel, An Instance of the Fingerpost

Related material:

Log24 entries of
Feb. 20, 21, and 22.

Tuesday, November 29, 2005

Tuesday November 29, 2005

Filed under: General — m759 @ 12:25 am
The Way of the Pilgrim,
Part III:
 
For the Birthday
of C. S. Lewis

The image “http://www.log24.com/log/pix05B/051129-Tao.jpg” cannot be displayed, because it contains errors.

The Tao, Chapter I

“The Chinese… speak of a great thing (the greatest thing) called the Tao. It is the reality beyond all predicates, the abyss that was before the Creator Himself. It is Nature, it is the Way, the Road. It is the Way in which the universe goes on, the Way in which things everlastingly emerge, stilly and tranquilly, into space and time. It is also the Way which every man should tread in imitation of that cosmic and supercosmic progression, conforming all activities to that great exemplar.”

— C. S. Lewis in The Abolition of Man

“In his preface to That Hideous Strength, Lewis says the novel has a serious point that he has tried to make in this little book, The Abolition of Man.  The novel is a work of fantasy or science fiction, while Abolition is a short philosophical work about moral education, but as we shall see the two go together; we will understand either book better by having read and thought about the other.”

— Dale Nelson, Notes on The Abolition of Man

“In Epiphany Term, 1942, C.S. Lewis delivered the Riddell Memorial Lectures… in….  the University of Durham….  He delivered three lectures entitled ‘Men without Chests,’ ‘The Way,’ and ‘The Abolition of Man.’  In them he set out to attack and confute what he saw as the errors of his age. He started by quoting some fashionable lunacy from an educationalists’ textbook, from which he developed a general attack on moral subjectivism.  In his second lecture he argued against various contemporary isms, which purported to replace traditional objective morality.  His final lecture, ‘The Abolition of Man,’ which also provided the title of the book published the following year, was a sustained attack on hard-line scientific anti-humanism. The intervening fifty years have largely vindicated Lewis.”

— J. R. Lucas, The Restoration of Man

Tuesday, May 31, 2005

Tuesday May 31, 2005

Filed under: General — m759 @ 1:06 pm

Subject and Predicates

“A Chu space is a set X of subjects and a set A of predicates on those subjects. These stand in a symbiotic relationship in which the nature of each is determined by the other. Each subject is characterized by the values the predicates take on it, while each predicate is characterized by its values on subjects.”

— Vaughan Pratt, Chu Spaces

Sambin's Basic Picture

Click here for Sambin’s paper (ps).

It would seem that Pratt and Sambin need to reconcile their similar predicates for the same subject.

For some background on Sambin’s approach to the subject, see

Mathematical Modal Logic:
A View of its Evolution (pdf),
by Robert Goldblatt at
Victoria University of Wellington’s
Centre for Logic, Language,
and Computation

For some background on Pratt’s approach to the subject, see

Information Transfer
Across Chu Spaces
(pdf),
by Johan van Benthem
at the University of Amsterdam’s
Institute for Logic, Language,
and Computation

For a gloss on Sambin’s words
The image “http://www.log24.com/theory/images/SambinBP1-Diamondx.jpg” cannot be displayed, because it contains errors.
see the Log24 entry of Epiphany, 2005.

Tuesday, January 6, 2004

Tuesday January 6, 2004

Filed under: General,Geometry — Tags: , , — m759 @ 10:10 pm

720 in the Book

Searching for an epiphany on this January 6 (the Feast of the Epiphany), I started with Harvard Magazine, the current issue of January-February 2004.

An article titled On Mathematical Imagination concludes by looking forward to

“a New Instauration that will bring mathematics, at last, into its rightful place in our lives: a source of elation….”

Seeking the source of the phrase “new instauration,” I found it was due to Francis Bacon, who “conceived his New Instauration as the fulfilment of a Biblical prophecy and a rediscovery of ‘the seal of God on things,’ ” according to a web page by Nieves Mathews.

Hmm.

The Mathews essay leads to Peter Pesic, who, it turns out, has written a book that brings us back to the subject of mathematics:

Abel’s Proof:  An Essay
on the Sources and Meaning
of Mathematical Unsolvability

by Peter Pesic,
MIT Press, 2003

From a review:

“… the book is about the idea that polynomial equations in general cannot be solved exactly in radicals….

Pesic concludes his account after Abel and Galois… and notes briefly (p. 146) that following Abel, Jacobi, Hermite, Kronecker, and Brioschi, in 1870 Jordan proved that elliptic modular functions suffice to solve all polynomial equations.  The reader is left with little clarity on this sequel to the story….”

— Roger B. Eggleton, corrected version of a review in Gazette Aust. Math. Soc., Vol. 30, No. 4, pp. 242-244

Here, it seems, is my epiphany:

“Elliptic modular functions suffice to solve all polynomial equations.”


Incidental Remarks
on Synchronicity,
Part I

Those who seek a star
on this Feast of the Epiphany
may click here.


Most mathematicians are (or should be) familiar with the work of Abel and Galois on the insolvability by radicals of quintic and higher-degree equations.

Just how such equations can be solved is a less familiar story.  I knew that elliptic functions were involved in the general solution of a quintic (fifth degree) equation, but I was not aware that similar functions suffice to solve all polynomial equations.

The topic is of interest to me because, as my recent web page The Proof and the Lie indicates, I was deeply irritated by the way recent attempts to popularize mathematics have sown confusion about modular functions, and I therefore became interested in learning more about such functions.  Modular functions are also distantly related, via the topic of “moonshine” and via the  “Happy Family” of the Monster group and the Miracle Octad Generator of R. T. Curtis, to my own work on symmetries of 4×4 matrices.


Incidental Remarks
on Synchronicity,
Part II

There is no Log24 entry for
December 30, 2003,
the day John Gregory Dunne died,
but see this web page for that date.


Here is what I was able to find on the Web about Pesic’s claim:

From Wolfram Research:

From Solving the Quintic —

“Some of the ideas described here can be generalized to equations of higher degree. The basic ideas for solving the sextic using Klein’s approach to the quintic were worked out around 1900. For algebraic equations beyond the sextic, the roots can be expressed in terms of hypergeometric functions in several variables or in terms of Siegel modular functions.”

From Siegel Theta Function —

“Umemura has expressed the roots of an arbitrary polynomial in terms of Siegel theta functions. (Mumford, D. Part C in Tata Lectures on Theta. II. Jacobian Theta Functions and Differential Equations. Boston, MA: Birkhäuser, 1984.)”

From Polynomial

“… the general quintic equation may be given in terms of the Jacobi theta functions, or hypergeometric functions in one variable.  Hermite and Kronecker proved that higher order polynomials are not soluble in the same manner. Klein showed that the work of Hermite was implicit in the group properties of the icosahedron.  Klein’s method of solving the quintic in terms of hypergeometric functions in one variable can be extended to the sextic, but for higher order polynomials, either hypergeometric functions in several variables or ‘Siegel functions’ must be used (Belardinelli 1960, King 1996, Chow 1999). In the 1880s, Poincaré created functions which give the solution to the nth order polynomial equation in finite form. These functions turned out to be ‘natural’ generalizations of the elliptic functions.”

Belardinelli, G. “Fonctions hypergéométriques de plusieurs variables er résolution analytique des équations algébrique générales.” Mémoral des Sci. Math. 145, 1960.

King, R. B. Beyond the Quartic Equation. Boston, MA: Birkhäuser, 1996.

Chow, T. Y. “What is a Closed-Form Number.” Amer. Math. Monthly 106, 440-448, 1999. 

From Angel Zhivkov,

Preprint series,
Institut für Mathematik,
Humboldt-Universität zu Berlin:

“… discoveries of Abel and Galois had been followed by the also remarkable theorems of Hermite and Kronecker:  in 1858 they independently proved that we can solve the algebraic equations of degree five by using an elliptic modular function….  Kronecker thought that the resolution of the equation of degree five would be a special case of a more general theorem which might exist.  This hypothesis was realized in [a] few cases by F. Klein… Jordan… showed that any algebraic equation is solvable by modular functions.  In 1984 Umemura realized the Kronecker idea in his appendix to Mumford’s book… deducing from a formula of Thomae… a root of [an] arbitrary algebraic equation by Siegel modular forms.”  

— “Resolution of Degree Less-than-or-equal-to Six Algebraic Equations by Genus Two Theta Constants


Incidental Remarks
on Synchronicity,
Part III

From Music for Dunne’s Wake:

Heaven was kind of a hat on the universe,
a lid that kept everything underneath it
where it belonged.”

— Carrie Fisher,
Postcards from the Edge

     

720 in  
the Book”

and
Paradise

“The group Sp4(F2) has order 720,”
as does S6. — Angel Zhivkov, op. cit.

Those seeking
“a rediscovery of
‘the seal of God on things,’ “
as quoted by Mathews above,
should see
The Unity of Mathematics
and the related note
Sacerdotal Jargon.

For more remarks on synchronicity
that may or may not be relevant
to Harvard Magazine and to
the annual Joint Mathematics Meetings
that start tomorrow in Phoenix, see

Log24, June 2003.

For the relevance of the time
of this entry, 10:10, see

  1. the reference to Paradise
    on the “postcard” above, and
  2. Storyline (10/10, 2003).

Related recreational reading:

Labyrinth



The Shining

Shining Forth

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