Log24

Friday, November 9, 2012

Norway High Chair

Filed under: General — m759 @ 11:00 am

This post was suggested by today's previous post,
"Bali High Chair," that links to an empty chair award for
evangelical supporters of Mitt Romney, by Bauhaus style,
and by the example of Norwegian  design shown below—

(Happy Frigg's Day to Josefine Lyche.)

Friday, October 19, 2012

Inconvenient Art

Filed under: General — m759 @ 6:00 pm

Barry Schwabsky in The Nation  on October 16, 2012:

"… sculpture is the most inconvenient of the fine arts.
Tedious physical labor is often involved in its making—
not necessarily the artist’s, but still, someone’s."

Happy Frigg's Day to Josefine Lyche.

Tuesday, September 25, 2012

High White in the Dark Fields

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

"High white noon"

— Phrase of Don DeLillo and Josefine Lyche

"Spellbinding visuals dwarf weak characters."

Fox News review of Snow White and the Huntsman

For some stronger characters, see Limitless , a 2011 film 
based on a 2001 novel by Alan Glynn, The Dark Fields .

See also St. Andrew's Day 2011 in this journal.

Sunday, September 23, 2012

Plan 9 (continued)–

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

In Like Flynn

From the Wall Street Journal  site Friday evening—

ESSAY September 21, 2012, 9:10 p.m. ET

Are We Really Getting Smarter?

Americans’ IQ scores have risen steadily over the past century.
James R. Flynn examines why.

IMAGE- Raven's Progressive Matrices problem with ninth configuration a four-diamonds grid

No, thank you. I prefer the ninth configuration as is—

IMAGE- Four-diamonds grid, the ninth configuration in a Raven's Progressive Matrices problem

Why? See Josefine Lyche’s art installation “Grids, you say?

Her reference there to “High White Noon” is perhaps
related to the use of that phrase in this journal.

The phrase is from a 2010 novel by Don DeLillo.
See “Point Omega,” as well as Lyche’s “Omega Point,”
in this journal.

The Wall Street Journal  author above, James R. Flynn (born in 1934),
“is famous for his discovery of the Flynn effect, the continued
year-after-year increase of IQ scores in all parts of the world.”
Wikipedia

His son Eugene Victor Flynn is a mathematician, co-author
of the following chapter on the Kummer surface— 

For use of the Kummer surface in Buddhist metaphysics, see last night’s
post “Occupy Space (continued)” and the letters of Nanavira Thera from the
late 1950s at nanavira.blogspot.com.

These letters, together with Lyche’s use of the phrase “high white noon,”
suggest a further quotation

You know that it would be untrue
You know that I would be a liar
If I was to say to you
Girl, we couldn’t get much higher

See also the Kummer surface at the web page Configurations and Squares.

Tuesday, September 18, 2012

4D Ambassador

Filed under: General — Tags: — m759 @ 1:00 pm

IMAGE- '4D Ambassador (Hypercube), 2012' by Josefine Lyche at The Boiler Room Gallery in Oslo

Friday, June 22, 2012

Bowling in Diagon Alley

Filed under: General,Geometry — Tags: , — m759 @ 8:28 am

IMAGE- Josefine Lyche bowling, from her Facebook page

Josefine Lyche bowling (Facebook, June 12, 2012)

"Where Does Math Come From?"

A professor of philosophy in 1984 on Socrates's geometric proof in Plato's Meno  dialogue—

"These recondite issues matter because theories about mathematics have had a big place in Western philosophy. All kinds of outlandish doctrines have tried to explain the nature of mathematical knowledge. Socrates set the ball rolling…."

— Ian Hacking in The New York Review of Books , Feb. 16, 1984

The same professor introducing a new edition of Kuhn's Structure of Scientific Revolutions

"Paradigms Regained" (Los Angeles Review of Books , April 18, 2012)—

"That is the structure of scientific revolutions: normal science with a paradigm and a dedication to solving puzzles; followed by serious anomalies, which lead to a crisis; and finally resolution of the crisis by a new paradigm. Another famous word does not occur in the section titles: incommensurability. This is the idea that, in the course of a revolution and paradigm shift, the new ideas and assertions cannot be strictly compared to the old ones."

The Meno  proof involves inscribing diagonals  in squares. It is therefore related, albeit indirectly, to the classic Greek discovery that the diagonals of a square are incommensurable  with its sides. Hence the following discussion of incommensurability seems relevant.

IMAGE- Von Fritz in 1945 on incommensurability and the tetractys (10 as a triangular number)

See also von Fritz and incommensurability in The New York Times  (March 8, 2011).

For mathematical remarks related to the 10-dot triangular array of von Fritz, diagonals, and bowling, see this  journal on Nov. 8, 2011— "Stoned."

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.

Sunday, May 13, 2012

Children of Light*

Filed under: General — m759 @ 8:28 am

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

An earlier verse in 1 John—

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

Catechism from a different cult—

"Who are you, anyway?" 

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

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

* Title of a Robert Stone novel

Friday, May 11, 2012

For Frigg’s Day

Filed under: General — m759 @ 10:30 am

A Parting Glance

(See also Josefine Lyche, Lens Flare.)

Friday, April 27, 2012

References

Filed under: General — m759 @ 12:00 pm

"These lowbrow, popular cultural references bring the possibilities
of interpretation down to an everyday level, forcing us to acknowledge
that not every painting that looks like a splatter is necessarily a
homage/anti-homage to Jackson Pollock."

— Stina Högqvist, review of the art of Josefine Lyche

Thursday, April 26, 2012

Rainbow Bridge for Thor’s Day

Filed under: General — m759 @ 9:00 pm

(Not  necessarily for Rainbow People )

About the artist—

Monday, March 26, 2012

Smackdown!

Filed under: General — m759 @ 2:00 pm

(The title is a nod to Peter Woit's recent post "Nothingness Smackdown.")

"To wrestle new mediums to the mat of specificity has been a preoccupation of mine since the inception of October , the magazine I founded in 1976 with Annette Michelson, the first issue of which carried my essay 'Video and Narcissism' which attempts to tie the essence of video to the spectacular nature of mirrors."

Rosalind Krauss, 2008, introduction to Perpetual Inventory  (MIT Press, 2010)

Related material— The video art and mirror art of Josefine Lyche.

See also Krauss's essay on video in Perpetual Inventory—  "Video: The Aesthetics of Narcissism" (first published as "Video and Narcissism," October , no. 1 (Spring 1976))—

"In The Language of the Self , Lacan begins by characterizing the space of the therapeutic transaction as an extraordinary void created by the silence of the analyst. Into this void the patient projects the monologue of his own recitation, which Lacan calls 'the monumental construct of his narcissism.'"

— and related remarks on October  and the void quoted here March 10 in "Boo Boo Boo."

Monday, March 5, 2012

For the Nine Muses

Filed under: General — m759 @ 1:00 pm

From "The Talented," a post of April 26, 2011—

http://www.log24.com/log/pix11A/110426-ApolloAndDionysus.jpg

And for Josefine Lyche

Unity in Multiplicity —

Pink  in Wikipedia

Sunday, March 4, 2012

The Haunted Galaxy

Filed under: General — m759 @ 1:00 pm

(Continued from Big Art 1 PM EST yesterday)

'IMAGE- The Galaxy has been haunted by ugly colours for centuries'- Josefine Lyche, 2001 video

In related news…

Ralph McQuarrie, who designed the Star Wars  trilogy, died yesterday.

See also Haunting Time.

Saturday, March 3, 2012

Big Art

Filed under: General — m759 @ 1:00 pm

For Women's History Month—

The Beam of Pink Light

Beam of pink light in Philip K. Dick's 'VALIS'

Video by Josefine Lyche ('Jo Lyxe')

From a post linked to on Lyxe's upload date, Feb. 6, 2012

“… with primitives the beginnings of art, science, and religion
coalesce in the undifferentiated chaos of the magical mentality….”

— Carl G. Jung, “On the Relation of Analytical Psychology to Poetry,”
     Collected Works, Vol. 15, The Spirit in Man, Art, and Literature,
     Princeton University Press, 1966, excerpted in
    Twentieth Century Theories of Art, edited by James M. Thompson.

See also the NY Lottery for St. Luke's Day, 2011, publication date
of the new edition of Philip K. Dick's VALIS  quoted above.

Saturday, February 11, 2012

Grids

Filed under: General — Tags: , — m759 @ 3:17 pm

See Notes for a Haiku.

Related material—

A novel published on Groundhog Day, 2010—

IMAGE- 'Point Omega' by DeLillo

— as well as Conceptual Art, Josefine Lyche's
"Grids, You Say?" and The Speed of Thought.

Saturday, January 7, 2012

Number and Form

Filed under: General — Tags: , — m759 @ 10:09 am

A link for Josefine Lyche in memory of Anne Tyng.

Thursday, December 22, 2011

The Speed of Thought

Filed under: General — Tags: — m759 @ 4:18 am

"As if an apparently meaningless frame of reference,
traveling at the speed of thought, suddenly became relevant…."

— Stephen Rachman, "Lost in Translation"

Unclean Frame

IMAGE- The perception of doors in the film 'Sunshine Cleaning'

Detail from the film "Sunshine Cleaning"

Clean Frame

IMAGE- Part of 'Grids, You Say?' installation by Josefine Lyche

See also Psychic Art and "The Speed of Thought."

For another form of psychic art, see Game of Shadows.

Monday, December 5, 2011

The Shining (Norwegian Version)

Filed under: General,Geometry — m759 @ 4:01 am

A check tonight of Norwegian artist Josefine Lyche's recent activities
shows she has added a video to her web page that has for some time
contained a wall piece based on the 2×2 case of the diamond theorem

http://www.log24.com/log/pix11C/111205-Lyche-DiamondTheoremPage.jpg

The video (top left in screenshot above) is a tasteless New-Age discourse
that sounds frighteningly like the teachings of the late Heaven's Gate cult.

Investigating the source of the video on vimeo.com, I found the account of one "Jo Lyxe,"
who joined vimeo in September 2011. This is apparently a variant of Josefine Lyche's name.

The account has three videos—

  1. "High on RAM (OverLoad)"– Fluid running through a computer's innards
  2. "Death 2 Everyone"– A mystic vision of the afterlife
  3. "Realization of the Ultimate Reality (Beyond Form)"– The Blue Star video above

Lyche has elsewhere discussed her New-Age interests, so the contents of the videos
were not too surprising… except for one thing. Vimeo.com states that all three videos
were uploaded "2 months ago"— apparently when "Lyxe" first set up an account.*

I do not know, or particularly care, where she got the Blue Star video, but the other
videos interested me considerably when I found them tonight… since they are
drawn from films I discussed in this journal much more recently than "2 months ago."

"High on RAM (OverLoad)" is taken from the 1984 film "Electric Dreams" that I came across
and discussed here yesterday afternoon, well before  re-encountering it again tonight.

http://www.log24.com/log/pix11C/111205-Lyxe-HighOnRam.jpg

http://www.log24.com/log/pix11C/111205-ElectricDreamsTrailer.jpg

And "Death 2 Everyone" (whose title** is perhaps a philosophical statement about inevitable mortality
rather than a mad terrorist curse) is taken from the 1983 Natalie Wood film "Brainstorm."

http://www.log24.com/log/pix11C/111205-Lyxe-Death2.jpg

http://www.log24.com/log/pix11C/111205-Brainstorm-FreakyPart.jpg

"Brainstorm" was also discussed here recently… on November 18th, in a post suggested by the
reopening of the investigation into Wood's death.

I had no inkling that these "Jo Lyxe" videos existed until tonight.

The overlapping content of Lyche's mental ramblings and my own seems rather surprising.
Perhaps it is a Norwegian mind-meld, perhaps just a coincidence of interests.

* Update: Google searches by the titles  on Dec. 5 show that all three "Lyxe" videos
                 were uploaded on September 20 and 21, 2011.

** Update: A search shows a track with this title on a Glasgow band's 1994 album.

Wednesday, November 30, 2011

Grids

Filed under: General — m759 @ 9:00 pm

For those who think "right-brain" means something—

Thursday, September 8, 2011

Endings

Filed under: General — m759 @ 8:00 pm

IMAGE- American Mathematical Society obituaries for Patrick C. Fischer and Frank Birtel published Sept. 8, 2011

For Fischer's fellow database enthusiast Codd, see Cross-Referenced (April 24, 2003).

For Birtel's fellow pseudoscience enthusiast Frank Tipler, see the artist's comment linked to in Romancing the Omega (April 19, 2011)—

"Omega Point" is a term used by mathematical physicist Frank Tipler for what he maintains is the ultimate fate of the universe required by the laws of physics."

Josefine Lyche, 2009

Saturday, August 6, 2011

Norway Summer

Filed under: General — m759 @ 4:00 pm

(Continued from June 21)

Footnote to a new web page from the European Culture Congress—

Photo credit: Josefine Lyche, “The 2×2 Case (Diamond Theorem)
after Steven H. Cullinane”, 450 x 650 cm,
Tromsø Kunstforening, 2010, image courtesy: the artist.

Thursday, August 4, 2011

Midnight in Oslo

Filed under: General,Geometry — Tags: — m759 @ 6:00 pm

For Norway's Niels Henrik Abel (1802-1829)
on his birthday, August Fifth

(6 PM Aug. 4, Eastern Time, is 12 AM Aug. 5 in Oslo.)

http://www.log24.com/log/pix11B/110804-Pesic-PlatosDiamond.jpg

Plato's Diamond

The above version by Peter Pesic is from Chapter I of his book Abel's Proof , titled "The Scandal of the Irrational." Plato's diamond also occurs in a much later mathematical story that might be called "The Scandal of the Noncontinuous." The story—

Paradigms

"These passages suggest that the Form is a character or set of characters common to a number of things, i.e. the feature in reality which corresponds to a general word. But Plato also uses language which suggests not only that the forms exist separately (χωριστά ) from all the particulars, but also that each form is a peculiarly accurate or good particular of its own kind, i.e. the standard particular of the kind in question or the model (παράδειγμα ) [i.e. paradigm ] to which other particulars approximate….

… Both in the Republic  and in the Sophist  there is a strong suggestion that correct thinking is following out the connexions between Forms. The model is mathematical thinking, e.g. the proof given in the Meno  that the square on the diagonal is double the original square in area."

– William and Martha Kneale, The Development of Logic , Oxford University Press paperback, 1985

Plato's paradigm in the Meno

http://www.log24.com/log/pix11/110217-MenoFigure16bmp.bmp

Changed paradigm in the diamond theorem (2×2 case) —

http://www.log24.com/log/pix11/110217-MenoFigureColored16bmp.bmp

Aspects of the paradigm change—

Monochrome figures to
   colored figures

Areas to
   transformations

Continuous transformations to
   non-continuous transformations

Euclidean geometry to
   finite geometry

Euclidean quantities to
   finite fields

The 24 patterns resulting from the paradigm change—

http://www.log24.com/log/pix11B/110805-The24.jpg

Each pattern has some ordinary or color-interchange symmetry.

This is the 2×2 case of a more general result. The patterns become more interesting in the 4×4 case. For their relationship to finite geometry and finite fields, see the diamond theorem.

Related material: Plato's Diamond by Oslo artist Josefine Lyche.

Plato’s Ghost  evokes Yeats’s lament that any claim to worldly perfection inevitably is proven wrong by the philosopher’s ghost….”

— Princeton University Press on Plato’s Ghost: The Modernist Transformation of Mathematics  (by Jeremy Gray, September 2008)

"Remember me to her."

— Closing words of the Algis Budrys novel Rogue Moon .

Background— Some posts in this journal related to Abel or to random thoughts from his birthday.

Friday, July 8, 2011

Baudelaire, Your Shiny Friend

Filed under: General — Tags: — m759 @ 8:48 pm

Google Translate version of a recent Norwegian art review

Josefine Lyche show is working on the basis of crop circles occur in Pewsey, Wiltshire in England for exactly one year ago on 21 June. Three circulars forms of aluminum quote forms from the field in England. With this as a starting point invites Lyche viewer to explore the sacred shapes and patterns through painting, floor work and sculpture. In the monumental painting "Wisdom Luxury Romance" draws Lyche lines to both Matisse and Baudelaire in his poem "L'invitation au voyage ."

From the artist's website, JosefineLyche.com

Click to enlarge

http://www.log24.com/log/pix11B/110708-WISDOM_LUXURY_ROMANCE-500W.jpg

WISDOM LUXURY ROMANCE

From elsewhere—

http://www.log24.com/log/pix11B/110708-Alcoa_Logo.jpg

Related material

From Antichristmas 2002— Aluminum, Your Shiny Friend.

From Sept. 22, 2004— Tribute… in the context of
today's previous entry  and of the conclusion of the story
that later became Childhood's End

http://www.log24.com/log/pix11B/110708-ClarkeSm.jpg

Wednesday, April 20, 2011

ART WARS continued

Filed under: General — m759 @ 9:00 pm

Part I— A Naples, Florida obituary for artist Robert Vickrey, who died Sunday.
            (See also this evening's earlier post Soul Art.)

Part II— "Stairway to Heaven," by Vickrey

Part III— Definition of "cornette"

Part IV— Recent photo of artist Josefine Lyche

Tuesday, April 19, 2011

Romancing the Omega

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

Today's news from Oslo suggests a review—

Image- Josefine Lyche work (with 1986 figures by Cullinane) in a 2009 exhibition in Oslo

Click for further details.

The circular sculpture in the foreground
is called by the artist "The Omega Point."
This has been described as
"a portal that leads in or out of time and space."

Some related philosophical remarks—

Oslo Connection and some notes on Galois connections.

Sunday, February 20, 2011

Sermon

Filed under: General,Geometry — Tags: — m759 @ 10:30 am

From Galleri MGM in Oslo —

IMAGE- 'PRESS RELEASE' headline

Josefine Lyche
Theme and Variations
26. February – 28. March 2009
Opening reception 26. February 19.00 – 21.00

"Why do we remember the past, but not the future?"
Stephen Hawking, A Brief History of Time, Ch. 9, "The Arrow of Time"

"If you want a vision of the future, imagine a boot stamping on a human face – forever."
George Orwell

Galleri MGM is pleased to present the second solo exhibition by Josefine Lyche (b.1973).

Lyche presents a body of work consisting of sculptures and a wall painting, as well as a series of new paperwork, all using geometrical abstractions and light as a medium. Her work dissolves boundaries between fiction and documentation, depicting how fantasies and dreams collide with and yet help determine the shape of reality.

Theme and variations is a term most commonly used in the music genre as a musical form in which the fundamental musical idea, or theme, is repeated in altered form or accompanied in a different manner.

The exhibition explores geometric shapes and solids and revisits work of artists like Robert Morris and Ellsworth Kelly, giving it a disco treatment of glitter, neon and gloss. The mathematical, science-fiction and new age references incorporated in the works comments on the ambivalent foretelling of utopian hope and dystopian vision of a near, yet unknown future.

The transmission between past and future is shown in the sculpture "The Omega Point" a portal that leads in or out of time and space. …

A connection to today's earlier post, Sunday SchoolThe Oslo Version, from Friday, May 21, 2010.

Lyche's "Omega Point" portal, together with her last name, suggested three posts from the following Saturday morning— which later proved to be the date of Martin Gardner's death—

Art Space, Through the Lyche Gate and The Lyche Gate Asterisk.

For some further religious remarks, see November 9th, 2010— A Theory of Pure Design.

Friday, February 11, 2011

Omega*

Filed under: General — m759 @ 1:00 pm

And I'd  like to thank the heroine of Finale

Image-- Josefine Lyche as Diamond Girl, representing the soul's triumph over evil

*  The title refers to a 2009 sculpture by Lyche

  http://www.log24.com/log/pix11/110212-OmegaPoint-Lyche-360w.jpg

   For a related shape, see today's noon post.

Wednesday, December 15, 2010

Punch

Filed under: General,Geometry — m759 @ 10:31 am

David Corfield discusses the philosophy of mathematics (Dec. 14) —

"It’s very tricky choosing a rich and interesting case study which is philosophically salient. To encourage the reader or listener to follow up the mathematics to understand what you’re saying, there must be a decent pay-off. An intricate twentieth century case study had better pack plenty of meta-mathematical punch."

Steve Martin discusses the philosophy of art (Dec. 5) —

http://www.log24.com/log/pix10B/101215-BraverMartin.jpg http://www.log24.com/log/pix10B/101215-WallPower.jpg

CBS News interviews Martin at the Whitney Museum —

"We paused to consider the impact of a George Bellows fight scene. Martin said it has 'wall power.'

What does that phrase mean? 'How it holds the wall. How it feels when you're ten or 20 feet away from it. It really takes hold of the room.'"

See also Halloween 2010

IMAGE- The 2x2 case of the diamond theorem as illustrated by Josefine Lyche, Oct. 2010

Tuesday, November 2, 2010

A Dozen Pairs of Opposites —

Filed under: General,Geometry — Tags: — m759 @ 5:24 am

24 graphic patterns arranged in space
as 12 pairs of opposites

IMAGE- 'Permutahedron of Opposites'-- 24 graphic patterns arranged in space as 12 pairs of opposites

Click image for an illustration of how the above labeling was derived.

For further background, see Cases of the Diamond Theorem
and recent art by Josefine Lyche of Norway.

Sunday, October 31, 2010

Diamond Theorem in Norway

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

IMAGE- The 2x2 case of the diamond theorem as illustrated by Josefine Lyche, Oct. 2010

Click on above image for artist's page.

Click here for exhibit page.

Click here for underlying geometry.

Thursday, July 15, 2010

Brightness at Noon, continued

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

"What exactly was Point Omega?"

This is Robert Wright in Nonzero: The Logic of Human Destiny.

Wright is discussing not the novel Point Omega  by Don DeLillo,
but rather a (related) concept of  the Jesuit philosopher Pierre Teilhard de Chardin.

My own idiosyncratic version of a personal "point omega"—

Image- Josefine Lyche work (with 1986 figures by Cullinane) in a 2009 exhibition in Oslo

Click for further details.

The circular sculpture in the foreground
is called by the artist "The Omega Point."
This has been described as
"a portal that leads in or out of time and space."

For some other sorts of points, see the drawings
on the wall and Geometry Simplified

Image-- The trivial two-point affine space and the trivial one-point projective space, visualized

The two points of the trivial affine space are represented by squares,
and the one point of the trivial projective space is represented by
a line segment separating the affine-space squares.

For related darkness  at noon, see Derrida on différance
as a version of Plato's khôra

(Click to enlarge.)

Image-- Fordham University Press on Derrida, differance, and khora

The above excerpts are from a work on and by Derrida
published in 1997 by Fordham University,
a Jesuit institutionDeconstruction in a Nutshell

Image-- A Catholic view of Derrida

For an alternative to the Villanova view of Derrida,
see Angels in the Architecture.

Thursday, July 1, 2010

Omega at Eight

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

The "compact key to universal wisdom" passage in the previous post seemed
too well written to be the work of an anonymous webforum author.

Here is a slightly expanded version—

Throughout history mystics and philosophers have sought
a compact key to universal wisdom, a finite formula or text
that would provide the answer to every question. The use of
the Bible, the Koran and the I Ching for divination and the
tradition of the secret books of Hermes Trismegistus and the
medieval Jewish Cabala exemplify this belief or hope.  Such
sources of universal wisdom are traditionally protected from
casual use by being difficult to find as well as difficult to un-
derstand and dangerous to use, tending to answer more quest-
ions and deeper ones than the searcher wishes to ask. The
esoteric book is, like God, simple yet undescribable. It is om-
niscient, and it transforms all who know it. The use of clas-
sical texts to foretell mundane events is considered supersti-
tious nowadays, yet in another sense science is in quest of its
own Cabala, a concise set of natural laws that would explain
all phenomena. In mathematics, where no set of axioms can
hope to prove all true statements, the goal might be a concise
axiomatization of all "interesting" true statements.
      Ω is in many senses a Cabalistic number. It can be known
of through human reason, but not known. To know it in detail
one must accept its uncomputable sequence of digits on faith,
like words of a sacred text.   

This is Martin Gardner's* and Charles H. Bennett's
revised version of a passage from Bennett's  paper
"On Random and Hard-to-Describe Numbers," 1979.

The original passage from Bennett's paper—

Throughout history mystics and philosophers have sought a compact key to
universal wisdom, a finite formula or text which, when known and understood,
would provide the answer to every question. The Bible, the Koran, the mythical
secret books of Hermes Trismegistus, and the medieval Jewish Cabala have
been so regarded. Sources of universal wisdom are traditionally protected from
casual use by being hard to find, hard to understand when found, and dangerous
to use, tending to answer more and deeper questions than the user wishes to
ask. Like God the esoteric book is simple yet undescribable, omniscient, and
transforms all who know It. The use of classical texts to fortell [sic] mundane events
is considered superstitious nowadays, yet, in another sense, science is in quest of
its own Cabala, a concise set of natural laws which would explain all phenomena.
In mathematics, where no set of axioms can hope to prove all true statements,
the goal might be a concise axiomatization of all "interesting" true statements.
      Ω is in many senses a Cabalistic number. It can be known of, but not known,
through human reason. To know it in detail, one would have to accept its un-
computable digit sequence on faith, like words of a sacred text.

The Bennett paper deals with Gregory Chaitin's concept of an "Omega Number."

I prefer the Omega of Josefine Lyche—

Image-- Uncertified copy of 1986 figures by Cullinane in a 2009 art exhibit in Oslo

Click for further details.

See also All Hallows' Eve, 2002.

* Martin Gardner's Mathematical Games  column
"The Random Number Omega Bids Fair to Hold the Mysteries of the Universe,"
Scientific American, November 1979, 241(5), pp. 20–34.
The column is reprinted as "Chaitin's Omega," Ch. 21, pp. 307-319 in the
collection of Gardner's columns titled Fractal Music, Hypercards and More,
W.H. Freeman & Co., 1991

Tuesday, June 15, 2010

Imago, Imago, Imago

Filed under: General,Geometry — Tags: , , , , — m759 @ 11:07 am

Recommended— an online book—

Flight from Eden: The Origins of Modern Literary Criticism and Theory,
by Steven Cassedy, U. of California Press, 1990.

See in particular

Valéry and the Discourse On His Method.

Pages 156-157—

Valéry saw the mind as essentially a relational system whose operation he attempted to describe in the language of group mathematics. “Every act of understanding is based on a group,” he says (C, 1:331). “My specialty—reducing everything to the study of a system closed on itself and finite” (C, 19: 645). The transformation model came into play, too. At each moment of mental life the mind is like a group, or relational system, but since mental life is continuous over time, one “group” undergoes a “transformation” and becomes a different group in the next moment. If the mind is constantly being transformed, how do we account for the continuity of the self? Simple; by invoking the notion of the invariant. And so we find passages like this one: “The S[elf] is invariant, origin, locus or field, it’s a functional property of consciousness” (C, 15:170 [2: 315]). Just as in transformational geometry, something remains fixed in all the projective transformations of the mind’s momentary systems, and that something is the Self (le Moi, or just M, as Valéry notates it so that it will look like an algebraic variable). Transformation theory is all over the place. “Mathematical science . . . reduced to algebra, that is, to the analysis of the transformations of a purely differential being made up of homogeneous elements, is the most faithful document of the properties of grouping, disjunction, and variation in the mind” (O, 1:36). “Psychology is a theory of transformations, we just need to isolate the invariants and the groups” (C, 1:915). “Man is a system that transforms itself” (C, 2:896).

Notes:

  Paul Valéry, Oeuvres (Paris: Pléiade, 1957-60)

C   Valéry, Cahiers, 29 vols. (Paris: Centre National de le Recherche Scientifique, 1957-61)

Compare Jung’s image in Aion  of the Self as a four-diamond figure:

http://www.log24.com/log/pix10A/100615-JungImago.gif

and Cullinane’s purely geometric four-diamond figure:

http://www.log24.com/log/pix10A/100615-FourD.gif

For a natural group of 322,560 transformations acting on the latter figure, see the diamond theorem.

What remains fixed (globally, not pointwise) under these transformations is the system  of points and hyperplanes from the diamond theorem. This system was depicted by artist Josefine Lyche in her installation “Theme and Variations” in Oslo in 2009.  Lyche titled this part of her installation “The Smallest Perfect Universe,” a phrase used earlier by Burkard Polster to describe the projective 3-space PG(3,2) that contains these points (at right below) and hyperplanes (at left below).

Image-- Josefine Lyche's combination of Polster's phrase with<br /> Cullinane's images in her gallery show, Oslo, 2009-- 'The Smallest<br /> Perfect Universe -- Points and Hyperplanes'

Although the system of points (at right above) and hyperplanes (at left above) exemplifies Valéry’s notion of invariant, it seems unlikely to be the sort of thing he had in mind as an image of the Self.

Tuesday, June 1, 2010

Annals of Art History

Filed under: General — m759 @ 11:00 am

On Misplaced Concreteness

An excerpt from China and Vietnam: The Politics of Asymmetry, by Brantly Womack (Cambridge U. Press, 2006)—

The book is intended to be a contribution to the general theory of international relations as well as to the understanding of China and Vietnam, but I give greater priority to “the case” rather than to the theory. This is a deliberate methodological decision. As John Gerring has argued, case studies are especially appropriate when exploring new causal mechanisms.2  I would argue more broadly that the “case” is the reality to which the theory is secondary. In international relations theory, “realism” is often contrasted to “idealism,” but surely a more basic and appropriate meaning of “realism” is to give priority to reality rather than to theory. The philosopher Alfred North Whitehead defined the Fallacy of Misplaced Concreteness as “neglecting the degree of abstraction involved when an actual entity is considered merely so far as it exemplifies certain categories of thought.”3 In effect, the concept is taken as the concrete reality, and actual reality is reduced to a mere appendage of data. Misplaced Concreteness may well be the cardinal sin of modern social science. It is certainly pandemic in international relations theory, where a serious consideration of the complexities of real political situations is often dismissed as mere “area studies.” Like the Greek god Anteus who was sustained by touching his Mother Earth, theory is challenged and rejuvenated by planting its feet in thick reality.

2 John Gerring, "What Is a Case Study and What Is It Good For?"
   American Political Science Review  98:2 (May 2004), pp. 341-54
3 Alfred North Whitehead, Process and Reality
   (New York: Harper, 1929), p. 11

Remarks—

"Whitehead defined the Fallacy of Misplaced Concreteness…."

The phrase "misplaced concreteness" occurs in the title of a part of an exhibition, "Theme and Variations," by artist Josefine Lyche (Oslo, 2009). I do not know what Lyche had in mind when she used the phrase. A search for possible meanings yielded the above passage.

"In international relations theory, “realism” is often contrasted to “idealism….”

For a more poetic look at "realism" and "idealism" and international relations theory, see Midsummer Eve's Dream.

Sunday, May 30, 2010

Trilateral

Filed under: General — m759 @ 5:01 am

Image-- 'Greater East Asia' characters

"Greater East Asia" (大東亜 Dai-tō-a)
was a Japanese term
(banned during the post-war Occupation)
referring to Far East Asia. —Wikipedia

Image-- East Asia trilateral trade talks

Related historical remarks from Wikipedia

"From the Japanese point of view, one common principal reason stood behind both forming the Greater East Asia Co-Prosperity Sphere and initiating war with the Allies: Chinese markets. Japan wanted their 'paramount relations' in regard to Chinese markets acknowledged by the U.S. government. The U.S., recognizing the abundance of potential wealth in these markets, refused to let the Japanese have an advantage in selling to China."

"Shine on, shine on,
there is work to be done
in the dark before the dawn."

Daisy May Erlewine

Image-- trilateral corner piece 'White Light (Grey)' by Josefine Lyche, 2009

"The exhibition title Theme and Variations
hints at the analytical-intellectual undertone
Josefine Lyche takes this time, but
not without humorous touches."

Tuesday, May 25, 2010

Sisteen

Filed under: General — Tags: , , — m759 @ 9:57 am

“Nuvoletta in her lightdress, spunn of sisteen shimmers,
was looking down on them, leaning over the bannistars….

Fuvver, that Skand, he was up in Norwood’s sokaparlour….”

Finnegans Wake

To counteract the darkness of today’s 2:01 AM entry—

Part I— Artist Josefine Lyche describes her methods

A “Internet and hard work”
B “Books, both fiction and theory”

Part II I, too, now rely mostly on the Internet for material. However, like Lyche, I have Plan B— books.

Where I happen to be now, there are piles of them. Here is the pile nearest to hand, from top to bottom.

(The books are in no particular order, and put in the same pile for no particular reason.)

  1. Philip Rieff— Sacred Order/Social Order, Vol. I: My Life Among the Deathworks
  2. Dennis L. Weeks— Steps Toward Salvation: An Examination of Coinherence and Substitution in the Seven Novels of Charles Williams
  3. Erwin Panofsky— Idea: A Concept in Art Theory
  4. Max Picard— The World of Silence
  5. Walter J. Ong, S. J.— Hopkins, the Self, and God
  6. Richard Robinson— Definition
  7. X. J. Kennedy and Dana Gioia, eds.— An Introduction to Poetry
  8. Richard J. Trudeau— The Non-Euclidean Revolution
  9. William T. Noon, S. J.— Joyce and Aquinas
  10. Munro Leaf— Four-and-Twenty Watchbirds
  11. Jane Scovell— Oona: Living in the Shadows
  12. Charles Williams— The Figure of Beatrice
  13. Francis L. Fennell, ed.— The Fine Delight: Centenary Essays on the Poetry of Gerard Manley Hopkins
  14. Hilary Putnam— Renewing Philosophy
  15. Paul Tillich— On the Boundary
  16. C. S. Lewis— George MacDonald

Lyche probably could easily make her own list of what Joyce might call “sisteen shimmers.”

Monday, May 24, 2010

Finale

Filed under: General — m759 @ 4:16 pm

The weekend's posts in this journal coincided,
more or less, with the finale of the TV series "Lost."
Recalling each story brings to mind
the subtitle of Heinrich Zimmer's classic
  The King and the Corpse

Tales of the Soul's Conquest of Evil.

Here, in the spirit of "The Fifth Element," is a
brief graphic summary of such a conquest—

The Soul

(Click for details)

Image-- Josefine Lyche as Diamond Girl, representing the soul's triumph over evil

Evil

(from Saturday morning)

Image-- The Asterisk of Evil

Sunday, May 23, 2010

Annals of Conceptual Art

Filed under: General — Tags: , , — m759 @ 2:02 am

Josefine Lyche's
  "Theme and Variations" (Oslo, 2009)

http://www.log24.com/log/pix10A/100523-LycheTandV.jpg

Some images in reply—

  Frame Tale

Confession in 'The Seventh Seal'

Image by R. T. Curtis from 'Further Elementary Techniques...'

Click on images for further details.

"In the name of the former
and of the latter
and of their holocaust.
  Allmen."

Finnegans Wake

Saturday, May 22, 2010

In the Details

Filed under: General — Tags: — m759 @ 10:31 am

Today's New York Times

Byzantine

"…there were fresh questions about whether the intelligence overhaul that created the post of national intelligence director was fatally flawed, and whether Mr. Obama would move gradually to further weaken the authorities granted to the director and give additional power to individual spy agencies like the Central Intelligence Agency. Mr. Blair and each of his predecessors have lamented openly that the intelligence director does not have enough power to deliver the intended shock therapy to America’s byzantine spying apparatus."

Catch-22 in Doonesbury today—

Image-- Chaplain and doctor in Doonesbury

From Log24 on Jan. 5, 2010—
   Artifice of Eternity

A Medal

In memory of Byzantine scholar Ihor Sevcenko,
who died at 87 on St. Stephen's Day, 2009–

Image-- Cross-in-circle design based on figure in Weyl's 'Symmetry'

Thie above image results from a Byzantine
meditation based on a detail in the previous post

Image-- 'Lyche Gate' with asterisk, from Google Books, digitized April 24, 2008

 

Image-- The Case of the Lyche Gate Asterisk

"This might be a good time to
call it a day." –Today's Doonesbury

"TOMORROW ALWAYS BELONGS TO US"
Title of an exhibition by young Nordic artists
in Sweden during the summer of 2008.

The exhibition included, notably, Josefine Lyche.

Art Space

Filed under: General,Geometry — Tags: , — m759 @ 2:02 am

From an interview with artist Josefine Lyche (see previous post) dated March 11, 2009—

Can you name a writer or book, fiction or theory that has inspired your works?
– Right now I am reading David Foster Wallace, which is great and inspiring. Others would be Aleister Crowley, Terence McKenna, James Joyce, J.L Borges, J.D Ballard, Stanislaw Lem, C. S. Lewis and Plato to mention some. Books, both fiction and theory are a great part of my life and work.

This journal on the date of the interview had a post about a NY Times  story, Paris | A Show About Nothing."

Related images—

 

Box symbol

Pictorial version
of Hexagram 20,
Contemplation (View)

http://www.log24.com/log/pix10A/100522-Clouseau.gif

Space: what you damn well have to see.
– James Joyce, Ulysses

Friday, May 21, 2010

The Oslo Version

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

From an art exhibition in Oslo last year–

Image-- Josefine Lyche's combination of Polster's phrase with Cullinane's images in her gallery show, Oslo, 2009-- 'The Smallest Perfect Universe -- Points and Hyperplanes'

The artist's description above is not in correct left-to-right order.
Actually the hyperplanes above are at left, the points at right.

Compare to "Picturing the Smallest Projective 3-Space,"
a note of mine from April 26, 1986—

Image-- Points and hyperplanes in the finite 3-space PG(3,2), April 1986, by Cullinane

Click for the original full version.

Compare also to Burkard Polster's original use of
the phrase "the smallest perfect universe."

Polster's tetrahedral model of points and hyperplanes
is quite different from my own square version above.

See also Cullinane on Polster.

Here are links to the gallery press release
and the artist's own photos.

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