Log24

Saturday, August 3, 2019

The Therefore Trinity

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

Friday, March 15, 2019

Trinity vs. Illuminati

Filed under: General — m759 @ 2:08 PM

Trinity Song —

"For ten years we've been on our own . . . ."

See as well a post of ten years ago:  Angels, Demons, "Symbology"

Illuminati Song —

"Far from the shallow now."

Wednesday, September 26, 2018

Trinity Tale

Filed under: General — m759 @ 11:34 AM

For Flowers and  Brown —

See also, in this  journal, A Fellow of Trinity . 

Tuesday, September 25, 2018

Trinity

Filed under: General — Tags: , — m759 @ 10:10 AM

See some posts related to three names
associated with Trinity College, Cambridge —

Atiyah + Shaw + Eddington .

Sunday, July 1, 2018

The Trinity Pretzel

Filed under: General — m759 @ 9:41 PM

The previous post suggests a review of a post from July 26, 2008
Jung's birthday — that mentions "The Trinity Pretzel."

For the pretzel itself, see the previous post and the posts of May 6, 2005.

Thursday, June 28, 2018

Trinity Meditation

Filed under: General — m759 @ 2:45 AM

See Interpenetration and Trinity Cube.

Monday, June 4, 2018

The Trinity Stone Defined

Filed under: General,Geometry — Tags: — m759 @ 8:56 PM

"Unsheathe your dagger definitions." — James Joyce, Ulysses

The "triple cross" link in the previous post referenced the eightfold cube
as a structure that might be called the trinity stone .

An Approach to Symmetric Generation of the Simple Group of Order 168

Some small Galois spaces (the Cullinane models)

Sunday, June 3, 2018

Trinity Stone

Filed under: General — m759 @ 9:18 PM

Or:  "What Dreams May Come"

(For the foxtail girl)

"Most religious beliefs are not true. But here’s the crux.
The emotional brain doesn’t care. It doesn’t operate on
the grounds of true and false. Emotions are not true or false.
Even a terrible fear inside a dream is still a terrible fear."

— Stephen T. Asma in the New York Times  philosophy
column "The Stone" today

See also Triple Cross

In greater depth:

Posts tagged on131004, a tag derived from a date in
a Google search today 

For enthusiasts of symbology, a webpage illustrated here this morning —

.

This morning's review of this Ajna webpage was suggested by posts from 
the Oct. 4, 2013, date  in the Google crux  search above.

Sunday, November 5, 2017

Trinity

Filed under: General,Geometry — m759 @ 11:00 AM

A model of the smallest projective  line:

Related drama:  See Wicker Man in this journal.

Wednesday, June 22, 2016

Bloomsday Trinity

Filed under: General — m759 @ 12:48 PM

NYT 'distinctive cultural tang' obituary

"He attended the Trinity School in Manhattan
before enrolling in the Lawrenceville School
in New Jersey, where he began writing poetry.
He graduated in 1957. Under his yearbook
photograph appeared the motto:

'Plato or comic books, I’m versatile.' "

He reportedly died on Bloomsday, June 16.
See also this journal on that date —

Tuesday, April 12, 2016

Black Trinity

Filed under: General — m759 @ 8:12 PM

In memory of a producerBlack Trinity.

See also a phrase from an image* in today's earlier post
For Non -Charlatans:

"Let us make a small example. . . ."

* Page 149 of "Groups and Symmetries," by F. Oggier
& A. M. Bruckstein. "These notes were designed to fit
the syllabus of the course 'Groups and Symmetries',
taught at Nanyang Technological University in autumn
2012, and 2013."

Saturday, January 3, 2015

Trinity for Jews

Filed under: General — Tags: — m759 @ 2:08 PM

See also Interpenet-  in this  journal.

"Interpenetration, that's what I  say!"
— Adapted from Humpty Dumpty

Sunday, October 6, 2013

Trinity

Filed under: General — m759 @ 12:00 PM

Father

Son

Holy Spirit

Ite, missa est.

Thursday, June 7, 2012

Trinity Riddle

Filed under: General — Tags: — m759 @ 3:00 PM

IMAGE- Raven's Progressive Matrices problem, Bertrand Russell, the Mad Hatter, and the Hatter's riddle

Click image for some background.

Thursday, January 20, 2011

Trinity

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

Reynolds Price died today. See Lore of the Manhattan Project in this journal.

In memoriam : Descartes's Twelfth Step and Symmetry and a Trinity.

Monday, July 22, 2019

The Four Diamonds Meet the Five Red Herrings

Filed under: General — Tags: — m759 @ 11:34 AM

Lord Peter Wimsey (Balliol 1912) on the Balliol-Trinity rivalry at Oxford:

See also Balliol College in the post subtitled Spidey Goes to Church.

Signed, Sealed, Delivered

Filed under: General — Tags: — m759 @ 5:58 AM

Visual Languages

Filed under: General — Tags: — m759 @ 4:48 AM

Good question. See also this  journal on the above date —

September 15, 2018.

Space, Time, Form

Filed under: General — Tags: — m759 @ 3:33 AM

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

Click the image for some remarks on a related novel.

Friday, July 5, 2019

“Darkly Enchanting”

Filed under: General — m759 @ 11:05 PM

For the Church of Synchronology

Sunday, December 2, 2018

Symmetry at Hiroshima

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 6:43 AM

A search this morning for articles mentioning the Miracle Octad Generator
of R. T. Curtis within the last year yielded an abstract for two talks given
at Hiroshima on March 8 and 9, 2018

http://www.math.sci.hiroshima-u.ac.jp/
branched/files/2018/abstract/Aitchison.txt

Iain AITCHISON

Title:

Construction of highly symmetric Riemann surfaces, related manifolds, and some exceptional objects, I, II

Abstract:

Since antiquity, some mathematical objects have played a special role, underpinning new mathematics as understanding deepened. Perhaps archetypal are the Platonic polyhedra, subsequently related to Platonic idealism, and the contentious notion of existence of mathematical reality independent of human consciousness.

Exceptional or unique objects are often associated with symmetry – manifest or hidden. In topology and geometry, we have natural base points for the moduli spaces of closed genus 2 and 3 surfaces (arising from the 2-fold branched cover of the sphere over the 6 vertices of the octahedron, and Klein's quartic curve, respectively), and Bring's genus 4 curve arises in Klein's description of the solution of polynomial equations of degree greater than 4, as well as in the construction of the Horrocks-Mumford bundle. Poincare's homology 3-sphere, and Kummer's surface in real dimension 4 also play special roles.

In other areas: we have the exceptional Lie algebras such as E8; the sporadic finite simple groups; the division algebras: Golay's binary and ternary codes; the Steiner triple systems S(5,6,12) and S(5,8,24); the Leech lattice; the outer automorphisms of the symmetric group S6; the triality map in dimension 8; and so on. We also note such as: the 27 lines on a cubic, the 28 bitangents of a quartic curve, the 120 tritangents of a sextic curve, and so on, related to Galois' exceptional finite groups PSL2(p) (for p= 5,7,11), and various other so-called `Arnol'd Trinities'.

Motivated originally by the `Eightfold Way' sculpture at MSRI in Berkeley, we discuss inter-relationships between a selection of these objects, illustrating connections arising via highly symmetric Riemann surface patterns. These are constructed starting with a labeled polygon and an involution on its label set.

Necessarily, in two lectures, we will neither delve deeply into, nor describe in full, contexts within which exceptional objects arise. We will, however, give sufficient definition and detail to illustrate essential inter-connectedness of those exceptional objects considered.

Our starting point will be simplistic, arising from ancient Greek ideas underlying atomism, and Plato's concepts of space. There will be some overlap with a previous talk on this material, but we will illustrate with some different examples, and from a different philosophical perspective.

Some new results arising from this work will also be given, such as an alternative graphic-illustrated MOG (Miracle Octad Generator) for the Steiner system S(5,8,24), and an alternative to Singerman – Jones' genus 70 Riemann surface previously proposed as a completion of an Arnol'd Trinity. Our alternative candidate also completes a Trinity whose two other elements are Thurston's highly symmetric 6- and 8-component links, the latter related by Thurston to Klein's quartic curve.

See also yesterday morning's post, "Character."

Update: For a followup, see the next  Log24 post.

Friday, November 23, 2018

Artfield Studio

Filed under: General,Geometry — m759 @ 12:10 PM

The title is that of an new Internet domain, artfield.studio,
that is used only to store branded links  such as . . .

artfield.studio/trinity-dice

artfield.studio/dirac-and-geometry

artfield.studio/eddington

artfield.studio/kummerhenge

artfield.studio/pinterest .

Some context —

artfield.studio/patrick-blackburn.

Wednesday, September 26, 2018

Analogies Between Analogies

Filed under: General — m759 @ 8:05 PM

On the new Netflix series "Maniac" —

(Spoiler alert)

"The treatment Owen and Annie sign up for promises to fix
its subjects’ brains with just three little pills—A, B, and C—
administered one after another over the span of three days.
The first forces you to relive your trauma;
the second exposes your blind spots; and
the third pill forces a confrontation."

— Kara Weisenstein at vice.com, Sept. 26, 2018, 12:19 PM

See also, from Log24 earlier 

A.  Monday — Mathematics as Art
B.  Tuesday — Trinity and Denkraum  Revisited
C.  Wednesday — Trinity Tale

'Out of nothing' opening of 'Maniac' at Netflix

Saturday, September 1, 2018

Ron Shaw — D. 21 June 2016

The date of Ron Shaw's 2016 death appears to be June 21:

http://www.log24.com/log/pix18/180901-Ron_Shaw-d_21_June_2016-LMS-500w.jpg

All other Internet sources I have seen omit the June 21 date.

This  journal on that date —

http://www.log24.com/log/pix18/180901-The_Central_Structure-21_June_2016.jpg

Saturday, August 11, 2018

Key-Awareness

Filed under: General — m759 @ 1:28 PM

In three generations of MacDonalds

http://www.log24.com/log/pix18/180811-George_MacDonald-The_Golden_Key-1867.gif

http://www.log24.com/log/pix18/180811-Ronald_MacDonald-A_Human_Trinity-1907-p224.gif

http://www.log24.com/log/pix18/180811-Philip_MacDonald-story-Private-Keep_Out-1949.gif

Sunday, July 22, 2018

Space

Filed under: General,Geometry — Tags: , — m759 @ 10:29 AM


See also interality in the eightfold cube.

IMAGE- The Trinity Cube (three interpenetrating planes that split the eightfold cube into its eight subcubes)

Tuesday, July 3, 2018

De Trinitate

Filed under: General — m759 @ 6:55 AM

This post on the Holy Trinity was suggested by the June 29
Boston Globe  obituary of reporter Kathy Shaw.

A related film review from December 29, 2016 —

"Trinity (2016): Surreal and Haunting Imagery" —

See also this  journal on December 29, 2016, featuring
a ghost spokesman for White Owl cigars:

Wednesday, June 27, 2018

Taken In

Filed under: General,Geometry — Tags: , — m759 @ 9:36 AM

A passage that may or may not have influenced Madeleine L'Engle's
writings about the tesseract :

From Mere Christianity , by C. S. Lewis (1952) —

"Book IV – Beyond Personality:
or First Steps in the Doctrine of the Trinity"
. . . .

I warned you that Theology is practical. The whole purpose for which we exist is to be thus taken into the life of God. Wrong ideas about what that life is, will make it harder. And now, for a few minutes, I must ask you to follow rather carefully.

You know that in space you can move in three ways—to left or right, backwards or forwards, up or down. Every direction is either one of these three or a compromise between them. They are called the three Dimensions. Now notice this. If you are using only one dimension, you could draw only a straight line. If you are using two, you could draw a figure: say, a square. And a square is made up of four straight lines. Now a step further. If you have three dimensions, you can then build what we call a solid body, say, a cube—a thing like a dice or a lump of sugar. And a cube is made up of six squares.

Do you see the point? A world of one dimension would be a straight line. In a two-dimensional world, you still get straight lines, but many lines make one figure. In a three-dimensional world, you still get figures but many figures make one solid body. In other words, as you advance to more real and more complicated levels, you do not leave behind you the things you found on the simpler levels: you still have them, but combined in new ways—in ways you could not imagine if you knew only the simpler levels.

Now the Christian account of God involves just the same principle. The human level is a simple and rather empty level. On the human level one person is one being, and any two persons are two separate beings—just as, in two dimensions (say on a flat sheet of paper) one square is one figure, and any two squares are two separate figures. On the Divine level you still find personalities; but up there you find them combined in new ways which we, who do not live on that level, cannot imagine.

In God's dimension, so to speak, you find a being who is three Persons while remaining one Being, just as a cube is six squares while remaining one cube. Of course we cannot fully conceive a Being like that: just as, if we were so made that we perceived only two dimensions in space we could never properly imagine a cube. But we can get a sort of faint notion of it. And when we do, we are then, for the first time in our lives, getting some positive idea, however faint, of something super-personal—something more than a person. It is something we could never have guessed, and yet, once we have been told, one almost feels one ought to have been able to guess it because it fits in so well with all the things we know already.

You may ask, "If we cannot imagine a three-personal Being, what is the good of talking about Him?" Well, there isn't any good talking about Him. The thing that matters is being actually drawn into that three-personal life, and that may begin any time —tonight, if you like.

. . . .

But beware of being drawn into the personal life of the Happy Family .

https://www.jstor.org/stable/24966339

"The colorful story of this undertaking begins with a bang."

And ends with

Martin Gardner on Galois

"Galois was a thoroughly obnoxious nerd,
 suffering from what today would be called
 a 'personality disorder.'  His anger was
 paranoid and unremitting."

Thursday, June 21, 2018

Dirac and Geometry (continued)

Filed under: General,Geometry — Tags: , — m759 @ 10:04 AM

"Just fancy a scale model of Being 
made out of string and cardboard."

Nanavira Thera, 1 October 1957,
on a model of Kummer's Quartic Surface
mentioned by Eddington

"… a treatise on Kummer's quartic surface."

The "super-mathematician" Eddington did not see fit to mention
the title or the author of the treatise he discussed.

See Hudson + Kummer in this  journal.

See also posts tagged Dirac and Geometry.

Thursday, June 7, 2018

For Dan Brown

Filed under: General,Geometry — Tags: — m759 @ 1:09 PM

See also Eightfold Trinity in this  journal.

Symbologist Robert Langdon views a corner of Solomon's Cube

Saturday, February 17, 2018

The Binary Revolution

Filed under: General,Geometry — Tags: , — m759 @ 5:00 PM

Michael Atiyah on the late Ron Shaw

Phrases by Atiyah related to the importance in mathematics
of the two-element Galois field GF(2) —

  • "The digital revolution based on the 2 symbols (0,1)"
  • "The algebra of George Boole"
  • "Binary codes"
  • "Dirac's spinors, with their up/down dichotomy"

These phrases are from the year-end review of Trinity College,
Cambridge, Trinity Annual Record 2017 .

I prefer other, purely geometric, reasons for the importance of GF(2) —

  • The 2×2 square
  • The 2x2x2 cube
  • The 4×4 square
  • The 4x4x4 cube

See Finite Geometry of the Square and Cube.

See also today's earlier post God's Dice and Atiyah on the theology of 
(Boolean) algebra vs. (Galois) geometry:

God’s Dice

Filed under: General,Geometry — Tags: , — m759 @ 10:45 AM

On a Trinity classmate of Ian Macdonald (see previous post)—

Atiyah's eulogy of Shaw in Trinity Annual Record 2017 
is on pages 137 through 146.  The conclusion —

 

Thursday, November 30, 2017

The Matrix for Quantum Mystics

Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 10:29 PM

Scholia on the title — See Quantum + Mystic in this journal.

The Matrix of Lévi-Strauss

"In Vol. I of Structural Anthropology , p. 209, I have shown that
this analysis alone can account for the double aspect of time
representation in all mythical systems: the narrative is both
'in time' (it consists of a succession of events) and 'beyond'
(its value is permanent)." — Claude Lévi-Strauss, 1976

I prefer the earlier, better-known, remarks on time by T. S. Eliot
in Four Quartets , and the following four quartets (from
The Matrix Meets the Grid) —

.

From a Log24 post of June 26-27, 2017:

A work of Eddington cited in 1974 by von Franz

See also Dirac and Geometry and Kummer in this journal.

Ron Shaw on Eddington's triads "associated in conjugate pairs" —

For more about hyperbolic  and isotropic  lines in PG(3,2),
see posts tagged Diamond Theorem Correlation.

For Shaw, in memoriam — See Contrapuntal Interweaving and The Fugue.

Sunday, August 6, 2017

Dark Tower Theology

Filed under: General — m759 @ 9:00 PM

In memory of a TV gunslinger who reportedly died Thursday, August 3, 2017 . . .

From this journal on that day (posts now tagged Dark Tower Theology) —

"The concept under review is that of the Holy Trinity.
  See also, in this  journal, Cube Trinity.
  For a simpler Trinity model, see the three-point line  "

"Would that it were so simple."

Thursday, August 3, 2017

Poetic Theology at the New York Times

Filed under: General — Tags: — m759 @ 12:19 PM

Or:  Trinity Test Site

From the New York Times Book Review  of
next Sunday, August 6, 2017 —

"In a more conventional narrative sequence,
even a sequence of poems,
this interpenetration would acquire
sequence and evolution." [Link added.]

The concept under review is that of the Holy Trinity.

See also, in this  journal, Cube Trinity.

For a simpler Trinity model, see the three-point line  

Monday, June 26, 2017

Upgrading to Six

This post was suggested by the previous post — Four Dots —
and by the phrase "smallest perfect" in this journal.

Related material (click to enlarge) —

Detail —

From the work of Eddington cited in 1974 by von Franz —

See also Dirac and Geometry and Kummer in this journal.

Updates from the morning of June 27 —

Ron Shaw on Eddington's triads "associated in conjugate pairs" —

For more about hyperbolic  and isotropic  lines in PG(3,2),
see posts tagged Diamond Theorem Correlation.

For Shaw, in memoriam — See Contrapuntal Interweaving and The Fugue.

Friday, April 28, 2017

A Problem for Houston…

Filed under: General — m759 @ 9:42 PM

And a memorable Houston lawyer who reportedly died today
at 90 at his home in Trinity, Texas

"Da hats ein Eck . "

See as well Sunday Review and Clooney Omega in this journal.

Sunday, November 13, 2016

Shell Game

Filed under: General — m759 @ 3:10 PM

See "No Space or Time" in this journal and
the new trailer, starring Scarlett Johansson,
for "Ghost in the Shell."

Related philosophy — Search Log24 for "Trinity."

Thursday, October 27, 2016

“Space Is the Place!”

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

Or:  Pentagram Meets Counting-Pattern, Continued

Arts & Letters Daily  today links to a Chronicle of Higher Education
piece on philosophy with an illustration by the late Paul Laffoley 

This suggests a review of Laffoley's work. In particular —

For a larger view of the above Laffoley pentagram, click here.
Contrast with Wittgenstein's "counting-pattern" above, which
is, in fact, a hyperspace.

Monday, May 2, 2016

Quality

Filed under: General,Geometry — Tags: — m759 @ 3:48 PM

The previous post, on subjective  and objective  quality,
suggests a review of Pirsig

     "And finally: Phaedrus, following a path
that to his knowledge had never been taken before
in the history of Western thought,
went straight between the horns of
the subjectivity-objectivity dilemma and said
Quality is neither a part of mind, nor is it a part of matter.
It is a third  entity which is independent of the two.
     He was heard along the corridors
and up and down the stairs of Montana Hall
singing softly to himself, almost under his breath,
'Holy, holy, holy…blessed Trinity.' "

See also Guitart in this journal, noting esp. Zen and the Art.

Monday, March 28, 2016

De Trinitate

Filed under: General — m759 @ 12:00 AM

Friday, March 11, 2016

Spacey

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

"You know that in space you can move in three ways…."

See also Cube Trinity and Many Dimensions.

Friday, March 4, 2016

Cube Bricks 1984

Filed under: General,Geometry — Tags: , — m759 @ 12:06 PM

An Approach to Symmetric Generation of the Simple Group of Order 168

Related aesthetics —

"Poincaré said that science is no more a collection of facts
than a house is a collection of bricks. The facts have to be
ordered or structured, they have to fit a theory, a construct
(often mathematical) in the human mind. . . . 

Mathematics may be art, but to the general public it is
a black art, more akin to magic and mystery. This presents
a constant challenge to the mathematical community: to
explain how art fits into our subject and what we mean by beauty.

In attempting to bridge this divide I have always found that
architecture is the best of the arts to compare with mathematics.
The analogy between the two subjects is not hard to describe
and enables abstract ideas to be exemplified by bricks and mortar,
in the spirit of the Poincaré quotation I used earlier."

— Sir Michael Atiyah, "The Art of Mathematics"
     in the AMS Notices , January 2010

Monday, November 23, 2015

Dirac and Line Geometry

Filed under: General,Geometry — Tags: , , — m759 @ 2:29 AM

Some background for my post of Nov. 20,
"Anticommuting Dirac Matrices as Skew Lines" —

First page of 'Configurations in Quantum Mechanics,' by E.M. Bruins, 1959

His earlier paper that Bruins refers to, "Line Geometry
and Quantum Mechanics," is available in a free PDF.

For a biography of Bruins translated by Google, click here.

For some additional historical background going back to
Eddington, see Gary W. Gibbons, "The Kummer
Configuration and the Geometry of Majorana Spinors,"
pages 39-52 in Oziewicz et al., eds., Spinors, Twistors,
Clifford Algebras, and Quantum Deformations:
Proceedings of the Second Max Born Symposium held
near Wrocław, Poland, September 1992
 . (Springer, 2012,
originally published by Kluwer in 1993.)

For more-recent remarks on quantum geometry, see a
paper by Saniga cited in today's update to my Nov. 20 post

Tuesday, October 20, 2015

Verhexung

Filed under: General — m759 @ 5:04 AM

"Die Philosophie ist ein Kampf gegen die Verhexung
unsres Verstandes durch die Mittel unserer Sprache."

— Philosophical Investigations  (1953),  Section 109

An example of Verhexung  from the René Guitart article in the previous post

See also Ein Kampf .

Tuesday, June 2, 2015

Nightmare

Filed under: General — m759 @ 4:21 PM

Continued from August 5, 2002

See also Venn's Trinity ("diamonds and rust") and a Monday death.

Wednesday, April 8, 2015

The Names

Filed under: General — m759 @ 2:04 PM

"Russell makes an extremely interesting and
important proposal about proper names."

— "Notes on Russell," by Curtis Brown

"The Names  (1982) is the seventh novel of
American novelist Don DeLillo. The work, set
mostly in Greece, is primarily a series of
character studies, interwoven with a plot about
a mysterious 'language cult' that is behind
a number of unexplained murders."

For other fiction about language cults,
see Dan  Brown.  

Tuesday, January 20, 2015

Purely Coincidental

Filed under: General — Tags: — m759 @ 2:00 PM

"The character and events depicted in this
motion picture are fictitious. Any similarity
to actual persons, living or dead, is purely
coincidental."

— Ending credits of the 2012 film
      "Travelling Salesman"

From that film's introduction to the
main character:

"He is presently the Rouse Ball Professor
of Mathematics in the Department of
Pure Mathematics and Mathematical Statistics
at Cambridge University and a fellow at
Trinity College. In 2008 he was awarded
the greatest honor in our profession
when he was presented with the Fields Medal
….
Ladies and gentlemen, it is with great honor
that I now present to you Dr. Timothy Horton."

See also

A line for a fellow of Trinity:

"What am I, the farmer's daughter?"

Thursday, January 8, 2015

ABC Verlag, Zurich

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

IMAGE- Dust jacket, 'Conceptions of International Exhibitions,' by Hans Neuburg, ABC Verlag, Zurich, 1969

"The motive for metaphor, shrinking from
The weight of primary noon,
The A B C of being…." — Wallace Stevens

See also Cube Trinity in this journal.

Sunday, January 4, 2015

Culture War

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

From a NY Times  obituary for an Arkansas poet,
Miller Williams, who reportedly died at 84
on New Year's Day —

The title of Lucinda Williams’s most recent album,
"Down Where the Spirit Meets the Bone,” is a
slightly altered line from one of her father’s poems,
which reads in its entirety:

Have compassion for everyone you meet,
even if they don’t want it. What seems conceit,
bad manners, or cynicism is always a sign
of things no ears have heard, no eyes have seen.
You do not know what wars are going on
down there where the spirit meets the bone.

Related material:

And from a sequel to
New Year's Greeting from Franz Kafka:

The above phrase "aimed at the heart of poetic language"
suggests an image from the poet's daughter's album —

Monday, November 24, 2014

Metaphysician in the Dark

Filed under: General — m759 @ 1:00 AM

Continued from Friday, November 21:

Friday, November 21, 2014

More

Filed under: General — Tags: — m759 @ 9:00 AM

"When Three Into One Equals MoreNew York Times  headline 

See also Trinity in this journal.  From that search:

                     … The actor is
A metaphysician in the dark….

— Wallace Stevens, 
   "Of Modern Poetry

Monday, September 1, 2014

Mathematics, Not Theology

Filed under: General — m759 @ 5:00 PM

(Continued)

“A set having three members is a single thing
wholly constituted by its members but distinct from them.
After this, the theological doctrine of the Trinity as
‘three in one’ should be child’s play.”

— Max Black, Caveats and Critiques: Philosophical Essays
in Language, Logic, and Art
 , Cornell U. Press, 1975

IMAGE- The Trinity of Max Black (a 3-set, with its eight subsets arranged in a Hasse diagram that is also a cube)

“There is  such a thing as a three-set.”
— Saying adapted from a novel by Madeleine L’Engle

Friday, August 29, 2014

Raum

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

A possible answer to the 1923 question of Walter Gropius, "Was ist Raum?"—

See also yesterday's Source of the Finite and the image search
on the Gropius question in last night's post.

Friday, January 31, 2014

Diamond Star

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

From The Diamond and the Star ,  by John Warden*
(London, Shepheard-Walwyn Ltd.,  June 1, 2009) —

(The quotation is from Kipling's "The Conundrum of the Workshops.")

IMAGE- The Devil's question - 'It's pretty, but is it Art?'

Answer — Some would say "Yes."

Part I: From a search for "Diamond Star" in this journal —

The Diamond Star

http://www.log24.com/log/pix11B/110905-StellaOctangulaView.jpg

Part II: From the Facebook photos of Oslo artist Josefine Lyche—

* Obituary link, added at 10:45 PM ET Jan. 31 after reading  a publisher's note 
  saying that "The author sadly died before the book was published."

  Perhaps sadly, perhaps not.

Wednesday, November 27, 2013

For St. Fergal O’Neill

Filed under: General — m759 @ 12:00 PM

Also known as Virgil the Geometer.

" Art, in other words, can speak to social conflicts,
and not always how you might think. Yvonne Scott,
a professor here at Trinity College, remarked
before the wake that in 1972 the invention of
Patrick Ireland was 'hard for people to grasp
because for a long while conceptual art wasn’t
understood here.' She added, 'Times have changed.' "

Michael Kimmelman in The New York Times ,
     May 22, 2008

Related art:

The "Square Round" link at the end of the previous post.

A story dated December 16, 2008, from the parish of Shannon.

A post dated December 16, 2008, from this journal.

Saturday, November 23, 2013

Frame Tale (continued)

Filed under: General — m759 @ 10:30 AM

See The X-Men Tree,  another tree,  and Trinity MOG.

Sunday, October 6, 2013

Sunday in the Park

Filed under: General — m759 @ 1:20 PM

(Continued from Frame Tale (Oct. 1) and 
this morning's Church with Josefine.)

See Trinity Knot in this journal.

Sermon

Filed under: General — Tags: — m759 @ 11:00 AM

A sequel to last night's "For Baron Samedi" —

Sigils

The music in the trailer for the new film "American Hustle"
is a 1969 tune by Led Zeppelin.  This, together with the
magick sigils posted at Facebook yesterday by artist
Josefine Lyche, suggests a review of Zeppelin sigils
from a 1971 album. These are, as shown above on a
record label,  the personal symbols of the four musicians
in the band. Two of the symbols may, of course, be
interpreted as representing the Holy Trinity.

Thursday, January 24, 2013

Cube Space

Filed under: General — Tags: — m759 @ 12:24 PM

For the late Cardinal Glemp of Poland,
who died yesterday, some links:

Sunday, January 20, 2013

On the Road

Filed under: General — m759 @ 9:00 PM

(For Your Consideration  continued)

Today's New York Times  story on Jacobin  magazine
suggests the following sequel to a Jan. 10 post on
Spielberg's Lincoln .

The magazine has, the Times  says,

"earned [its creator] Mr. Sunkara, now a ripe 23,
extravagant praise from members of a (slightly) older
guard who see his success as heartening sign that
the socialist 'brand'— to use a word he throws around
with un-self-conscious ease— hasn’t been totally
killed off by Tea Party invective." —Jennifer Schuessler

Jacobin  magazine, summer 2012 double issue—

A related trinity of the Left:

Playwright Tom Stoppard, his son actor Ed Stoppard
(shown below in the 2012 film Branded ), and the late
activist Aaron Swartz

Tuesday, October 9, 2012

Too Much Meaning

Filed under: General — m759 @ 12:00 PM

Last night's post discussed ways of draining the world of meaning.

For some tastes, poets like Dante do the opposite, supplying too much  meaning.

See a New Republic  review, dated Oct. 5, in which Harvard atheist Helen Vendler discusses Dante's

"… assertion that Beatrice herself  'was this number [nine],' since nine is the square of three, the number belonging to the Trinity. Dante’s fantastic reasoning requires pages of annotation, which Frisardi, drawing on a number of commentators, furnishes to the bewildered reader. The theological elaboration of the number nine— merely one instance of how far from our own* are Dante’s habits of thought— will convince any doubting reader that the Vita Nuova  requires annotation far beyond what its pages might seem to demand."

Related material— Ninefold in this journal, and remarks by Joseph Campbell in a post, Plan 9, from Sept. 5.

* Speak for yourself, Helen.

Tuesday, June 26, 2012

Looking Deeply

Filed under: General,Geometry — Tags: , — m759 @ 3:48 PM

Last night's post on The Trinity of Max Black  and the use of
the term "eightfold" by the Mathematical Sciences Research Institute
at Berkeley suggest a review of an image from Sept. 22, 2011

IMAGE- Eightfold cube with detail of triskelion structure

The triskele  detail above echoes a Buddhist symbol found,
for instance, on the Internet in an ad for meditation supplies—

Related remarks

http://www.spencerart.ku.edu/about/dialogue/fdpt.shtml

Mary Dusenbury (Radcliffe '64)—

"… I think a textile, like any work of art, holds a tremendous amount of information— technical, material, historical, social, philosophical— but beyond that, many works of art are very beautiful and they speak to us on many layers— our intellect, our heart, our emotions. I've been going to museums since I was a very small child, thinking about what I saw, and going back to discover new things, to see pieces that spoke very deeply to me, to look at them again, and to find more and more meaning relevant to me in different ways and at different times of my life. …

… I think I would suggest to people that first of all they just look. Linger by pieces they find intriguing and beautiful, and look deeply. Then, if something interests them, we have tried to put a little information around the galleries to give a bit of history, a bit of context, for each piece. But the most important is just to look very deeply."

http://en.wikipedia.org/wiki/Nikaya_Buddhism

According to Robert Thurman, the term "Nikāya Buddhism" was coined by Professor Masatoshi Nagatomi of Harvard University, as a way to avoid the usage of the term Hinayana.[12] "Nikaya Buddhism" is thus an attempt to find a more neutral way of referring to Buddhists who follow one of the early Buddhist schools, and their practice.

12. The Emptiness That is Compassion:
An Essay on Buddhist Ethics, Robert A. F. Thurman, 1980
[Religious Traditions , Vol. 4 No. 2, Oct.-Nov. 1981, pp. 11-34]

http://dsal.uchicago.edu/cgi-bin/philologic/getobject.pl?c.2:1:6.pali

Nikāya [Sk. nikāya, ni+kāya]
collection ("body") assemblage, class, group

http://en.wiktionary.org/wiki/नि

Sanskrit etymology for नि (ni)

From Proto-Indo-European *ni …

Prefix

नि (ni)

  • down
  • back
  • in, into

http://www.rigpawiki.org/index.php?title=Kaya

Kaya (Skt. kāya སྐུ་, Tib. ku Wyl. sku ) —
the Sanskrit word kaya literally means ‘body’
but can also signify dimension, field or basis.

སྐུ། (Wyl. sku ) n. Pron.: ku

structure, existentiality, founding stratum ▷HVG KBEU

gestalt ▷HVG LD

Note that The Trinity of Max Black  is a picture of  a set
i.e., of an "assemblage, class, group."

Note also the reference above to the word "gestalt."

"Was ist Raum, wie können wir ihn
erfassen und gestalten?"

Walter Gropius

Bright Black

Filed under: General,Geometry — Tags: — m759 @ 12:12 AM

“‘In the dictionary next to [the] word “bright,” you should see Paula’s picture,’ he said. ‘She was super smart, with a sparkling wit. … She had a beautiful sense of style and color.'”

— Elinor J. Brecher in The Miami Herald  on June 8, quoting Palm Beach Post writer John Lantigua on the late art historian Paula Hays Harper

This  journal on the date of her death—

IMAGE- The Trinity of Max Black (a 3-set, with its eight subsets arranged in a Hasse diagram that is also a cube)

For some simpleminded commentary, see László Lovász on the cube space.

Some less simpleminded commentary—

Was ist Raum, wie können wir ihn
erfassen und gestalten?”

Walter Gropius,

The Theory and
Organization of the
Bauhaus
  (1923)

Tuesday, June 12, 2012

Dance Theology

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

Background: Geometry of the Dance (May 9)
and Midnight in Oslo (May 10).

Peter Pesic has described the action of the
symmetric group S4 on a tetrahedron as a dance

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

Compare and contrast:

The following figure may be seen as a tetrahedron,
viewed from above

IMAGE- The 'Shield of the Trinity' may be viewed as a tetrahedron, as in Peter Pesic's 'Geometry of the Dance.'

  See also Masterman and Child's Play.

Sunday, June 3, 2012

Child’s Play

Filed under: General,Geometry — Tags: — m759 @ 2:56 PM

(Continued)

“A set having three members is a single thing
wholly constituted by its members but distinct from them.
After this, the theological doctrine of the Trinity as
‘three in one’ should be child’s play.”

– Max Black, Caveats and Critiques: Philosophical Essays
in Language, Logic, and Art
, Cornell U. Press, 1975

IMAGE- The Trinity of Max Black (a 3-set, with its eight subsets arranged in a Hasse diagram that is also a cube)

Related material—

The Trinity Cube

IMAGE- The Trinity Cube (three interpenetrating planes that split the eightfold cube into its eight subcubes)

Saturday, June 2, 2012

High Society

Filed under: General — m759 @ 12:00 PM

In memory of Sir Andrew Huxley, OM, who died on May 30, 2012

C. P. Snow on G. H. Hardy at Trinity College, Cambridge

He played his games and indulged his eccentricities.
He was living in some of the best intellectual company
in the world— G. E. Moore, Whitehead, Bertrand Russell,
Trevelyan, the high Trinity society  which was shortly to
find its artistic complement in Bloomsbury. (Hardy himself
had links with Bloomsbury, both of personal friendship
and of sympathy.)

See also "Max Black" + Trinity  in this journal.

Saturday, February 25, 2012

The Rock

Filed under: General — m759 @ 9:26 PM

(Continued. See previous post and Red and Gray in this journal.)

"Give faith a fighting chance." —Country song

From a post of June 3, 2007—

Related illustration relevant to theology—

http://www.log24.com/log/pix11A/110625-CubeHypostases.gif

For some background, see Cube Trinity in this journal.

For greater depth, see Levering's Scripture and Metaphysics:
Aquinas and the Renewal of Trinitarian Theology 
,
Blackwell, 2004, page 150.

Tuesday, January 10, 2012

Defining Form

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

(Continued from Epiphany and from yesterday.)

Detail from the current American Mathematical Society homepage

http://www.log24.com/log/pix12/120110-AMS_page-Detail.jpg

Further detail, with a comparison to Dürer's magic square—

http://www.log24.com/log/pix12/120110-Donmoyer-Still-Life-Detail.jpg http://www.log24.com/log/pix12/120110-DurerSquare.jpg

The three interpenetrating planes in the foreground of Donmoyer's picture
provide a clue to the structure of the the magic square array behind them.

Group the 16 elements of Donmoyer's array into four 4-sets corresponding to the
four rows of Dürer's square, and apply the 4-color decomposition theorem.
Note the symmetry of the set of 3 line diagrams that result.

Now consider the 4-sets 1-4, 5-8, 9-12, and 13-16, and note that these
occupy the same positions in the Donmoyer square that 4-sets of
like elements occupy in the diamond-puzzle figure below—

http://www.log24.com/log/pix12/120110-DiamondPuzzleFigure.jpg

Thus the Donmoyer array also enjoys the structural  symmetry,
invariant under 322,560 transformations, of the diamond-puzzle figure.

Just as the decomposition theorem's interpenetrating lines  explain the structure
of a 4×4 square , the foreground's interpenetrating planes  explain the structure
of a 2x2x2 cube .

For an application to theology, recall that interpenetration  is a technical term
in that field, and see the following post from last year—

Saturday, June 25, 2011

 

Theology for Antichristmas

— m759 @ 12:00 PM

Hypostasis (philosophy)

"… the formula 'Three Hypostases  in one Ousia '
came to be everywhere accepted as an epitome
of the orthodox doctrine of the Holy Trinity.
This consensus, however, was not achieved
without some confusion…." —Wikipedia

http://www.log24.com/log/pix11A/110625-CubeHypostases.gif

Ousia

Click for further details:

http://www.log24.com/log/pix11A/110625-ProjectiveTrinitySm.jpg

 

Monday, January 9, 2012

M Theory

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

Yesterday's All About Eve post featured Pope John Paul II
with his close friend and confidant Jerzy Kluger.
Their counterparts Xavier and Magneto in the recent film
"X-Men: First Class," together with Catholic doctrine on telepathy,
suggest  the following meditations.

Douglas Hofstadter on interpenetration

IMAGE- 'Interpenetration' in Douglas Hofstadter's 'I Am a Strange Loop'

— as well as Trinity in this journal.

First the punchline—

Script M (interpreted by some scanners as '771.')

Then the joke.

Tuesday, August 30, 2011

Boundary

Filed under: General — Tags: — m759 @ 11:07 AM

A comment yesterday on the New York Times  philosophy column “The Stone” quoted Karl Barth—

Man is the creature of the boundary between heaven and earth.”

See also Plato’s theory of ideas (or “forms”) and the I Ching

The eight trigrams are images not so much of objects as of states of change. This view is associated with the concept expressed in the teachings of Lao-tse, as also in those of Confucius, that every event in the visible world is the effect of an “image,” that is, of an idea in the unseen world. Accordingly, everything that happens on earth is only a reproduction, as it were, of an event in a world beyond our sense perception; as regards its occurrence in time, it is later than the suprasensible event. The holy men and sages, who are in contact with those higher spheres, have access to these ideas through direct intuition and are therefore able to intervene decisively in events in the world. Thus man is linked with heaven, the suprasensible world of ideas, and with earth, the material world of visible things, to form with these a trinity of the primal powers.

— Richard Wilhelm, Introduction to the I Ching

Sunday, August 28, 2011

The Cosmic Part

Filed under: General,Geometry — Tags: — m759 @ 6:29 PM

Yesterday's midday post, borrowing a phrase from the theology of Marvel Comics,
offered Rubik's mechanical contrivance as a rather absurd "Cosmic Cube."

A simpler candidate for the "Cube" part of that phrase:

http://www.log24.com/log/pix10/100214-Cube2x2x2.gif

The Eightfold Cube

As noted elsewhere, a simple reflection group* of order 168 acts naturally on this structure.

"Because of their truly fundamental role in mathematics,
even the simplest diagrams concerning finite reflection groups
(or finite mirror systems, or root systems—
the languages are equivalent) have interpretations
of cosmological proportions."

Alexandre V. Borovik in "Coxeter Theory: The Cognitive Aspects"

Borovik has a such a diagram—

http://www.log24.com/log/pix11B/110828-BorovikM.jpg

The planes in Borovik's figure are those separating the parts of the eightfold cube above.

In Coxeter theory, these are Euclidean hyperplanes. In the eightfold cube, they represent three of seven projective points that are permuted by the above group of order 168.

In light of Borovik's remarks, the eightfold cube might serve to illustrate the "Cosmic" part of the Marvel Comics phrase.

For some related theological remarks, see Cube Trinity in this journal.

Happy St. Augustine's Day.

* I.e., one generated by reflections : group actions that fix a hyperplane pointwise. In the eightfold cube, viewed as a vector space of 3 dimensions over the 2-element Galois field, these hyperplanes are certain sets of four subcubes.

Monday, July 11, 2011

Accentuate the Positive

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

An image that may be viewed as
a cube with a "+" on each face—

http://www.log24.com/log/pix11B/110711-EightfoldCube.gif

The eightfold cube

http://www.log24.com/log/pix11B/110711-CubeHypostases.gif

Underlying structure

For the Pope and others on St. Benedict's Day
who prefer narrative to mathematics—

Saturday, June 25, 2011

Theology for Antichristmas

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

Hypostasis (philosophy)

"… the formula 'Three Hypostases  in one Ousia '
came to be everywhere accepted as an epitome
of the orthodox doctrine of the Holy Trinity.
This consensus, however, was not achieved
without some confusion…." —Wikipedia

http://www.log24.com/log/pix11A/110625-CubeHypostases.gif

Ousia

Click for further details:

http://www.log24.com/log/pix11A/110625-ProjectiveTrinitySm.jpg

Friday, June 10, 2011

Hierophant

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

Some background for yesterday's posts:

Midrash for Gnostics and related notes,
as well as yesterday's New York Lottery

                                      ….    "We seek
The poem of pure reality, untouched
By trope or deviation, straight to the word,
Straight to the transfixing object, to the object
At the exactest point at which it is itself,
Transfixing by being purely what it is…."
— Wallace Stevens (1879-1955),
“An Ordinary Evening in New Haven” IX

"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals."
— Wallace Stevens,
“An Ordinary Evening in New Haven” VI

Wikipedia

"A hierophant is a person who brings religious congregants into the presence of that which is deemed holy . The word comes from Ancient Greece, where it was constructed from the combination of ta hiera , 'the holy,' and phainein , 'to show.' In Attica it was the title of the chief priest at the Eleusinian Mysteries. A hierophant is an interpreter of sacred mysteries and arcane principles."

Weyl as Alpha, Chern as Omega—

(Click to enlarge.)

http://www.log24.com/log/pix11A/110610-WeylChernSm.jpg

Postscript for Ellen Page, star of "Smart People"
and of "X-Men: The Last Stand"— a different  page 679.

Your assignment, should you choose to accept it—

Interpret today's  NY lottery numbers— Midday 815, Evening 888.

My own bias is toward 815 as 8/15 and 888 as a trinity,
but there may be less obvious and more interesting approaches.

Wednesday, September 15, 2010

Wittgenstein, 1935

Filed under: General — m759 @ 1:20 AM

http://www.wittgen-cam.ac.uk/biogre9.html

1935

With the expiry of his five-year Research Fellowship at Trinity College Wittgenstein was faced once more with the problem of loss of career. Accordingly he planned a journey to the Soviet Union, to find out whether he could find a suitable post there. Wittgenstein’s constant quest for the right career was not, as it is often misunderstood, a flight from himself. Rather, it was a search for the right place, a being at one with himself: Return him [Man] to his rightful element and everything will unfold and appear as healthy. (MS 125)

Since 1933/34 he had been taking lessons in Russian from the philosopher Fanja Pascal, initially with Francis Skinner. In June he asked Keynes for an introduction to the Soviet ambassador in London, Ivan M. Maiski. He sought contacts in two places above all, at the Northern Institute in Leningrad and the Institute for National Minorities in Moscow, writing to Keynes on 6 July: These Institutes, as I am told, deal with people who want to go to the ‘colonies’ the newly colonized parts at the periphery of the U. S. S. R. (Letters to Russell, Keynes and Moore)

On 12 September Wittgenstein arrived in Leningrad. There he met the author and educator Guryevich at the Northern Institute, then an autonomous faculty of Leningrad University. On the evening of the following day he travelled on to Moscow, arriving there on the morning of the 14th. Here he had contacts with various western Europeans and Americans, including the correspondent of the Daily Worker, Pat Sloane. Most of his discussions, however, were with scientists, for example the young mathematician Yanovskaya and the philosopher Yushevich from Moscow University, who were both close to so-called Mach Marxism and the Vienna Circle. He was invited by the philosopher Tatiana Nikolayeva Gornstein, a member of the Soviet Academy of Sciences, to teach philosophy at Leningrad University. He traveled to Kazakhstan, where he was offered a chair at the famous university where Tolstoy once studied. On 1 October he was back in Cambridge. The trip was shorter than planned, and it appears that he had given up the idea of settling in Russia.

His friend Gilbert Pattison, who picked him up from the ship on his return, recalled that Wittgenstein’s view was that he could not live there himself: One could live there, but only if one kept in mind the whole time that one could never speak one’s mind. … It is as though one were to spend the rest of one’s life in an army, any army, and that is a rather difficult thing for people who are educated. (Interview with Pattison)

Saturday, July 10, 2010

Child’s Play

Filed under: General — m759 @ 6:00 PM

Image-- 'Aion pais esti paizon....'

… twó flocks, twó folds—black, white; ' right, wrong; reckon but, reck but, mind
But thése two; wáre of a wórld where bút these ' twó tell, each off the óther….

— "Spelt from Sibyl's Leaves," by Gerard Manley Hopkins

http://www.log24.com/log/pix10A/100710-Nabokov-Black.GIF

Related material:

Max Black — "Beginners are taught that a set having three members is a single thing, wholly constituted by its members but distinct from them. After this, the theological doctrine of the Trinity as 'three in one' should be child's play." ("The Elusiveness of Sets," Review of Metaphysics, June 1971, p. 615– as quoted by Bill Vallicella)


 Edward Gibbon, Decline and Fall of the Roman Empire, Chapter XXI

Gibbon, discussing the theology of the Trinity, defines perichoresis as

“… the internal connection and spiritual penetration which indissolubly unites the divine persons59 ….

59 … The perichoresis  or ‘circumincessio,’ is perhaps the deepest and darkest corner of the whole theological abyss.”


 ”Whoever fights monsters should see to it that in the process he does not become a monster.  And when you look long into an abyss, the abyss also looks into you.”

– Friedrich Nietzsche, Beyond Good and Evil, section 146, translated by Walter Kaufmann


Tuesday, March 30, 2010

Eightfold Symmetries

Filed under: General,Geometry — Tags: , — m759 @ 9:48 PM

Harvard Crimson headline today–
"Deconstructing Design"

Reconstructing Design

The phrase "eightfold way" in today's
previous entry has a certain
  graphic resonance…

For instance, an illustration from the
Wikipedia article "Noble Eightfold Path" —

Dharma Wheel from Wikipedia

Adapted detail–

Adapted Dharma Wheel detail

See also, from
St. Joseph's Day

Weyl's 'Symmetry,' the triquetrum, and the eightfold cube

Harvard students who view Christian symbols
with fear and loathing may meditate
on the above as a representation of
the Gankyil rather than of the Trinity.

Thursday, February 4, 2010

Phenomenology of 256

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

From Peter J. Cameron's weblog today

According to the Buddha,

Scholars speak in sixteen ways of the state of the soul after death. They say that it has form or is formless; has and has not form, or neither has nor has not form; it is finite or infinite; or both or neither; it has one mode of consciousness or several; has limited consciousness or infinite; is happy or miserable; or both or neither.

He does go on to say that such speculation is unprofitable; but bear with me for a moment.

With logical constructs such as “has and has not form, or neither has nor has not form”, it is perhaps a little difficult to see what is going on. But, while I hesitate to disagree with the Compassionate One, I think there are more than sixteen possibilities described here: how many?

Cameron's own answer (from problem solutions for his book Combinatorics)–

One could argue here that the numbers of choices should be multiplied, not added; there are 4 choices for form, 4 for finiteness, 2 for modes of consciousness, 2 for finiteness of consciousness, and 4 for happiness, total 28 = 256. (You may wish to consider whether all 256 are really possible.)

Related material– "What is 256 about?"

Some partial answers–

April 2, 2003 — The Question (lottery number)

May 2, 2003 — Zen and Language Games (page number)

August 4, 2003 — Venn's Trinity (power of two)

September 28, 2005 — Mathematical Narrative (page number)

October 26, 2005 — Human Conflict Number Five (chronomancy)

June 23, 2006 — Binary Geometry (power of two)

July 23, 2006 — Partitions (power of two)

October 3, 2006 — Hard Lessons (number of pages,
                                 as counted in one review)

October 10, 2006 — Mate (lottery number)

October 8, 2008 — Serious Numbers (page number)

Quoted here Nov. 10, 2009

Epigraphs at
Peter Cameron’s home page:

Quotes from Brautigan's 'The Hawkline Monster' and Hoban's 'Riddley Walker'

Happy birthday, Russell Hoban.

Sunday, May 3, 2009

Sunday May 3, 2009

Filed under: General,Geometry — m759 @ 7:59 AM
Annals of
Sacred Geometry

(The phrase “sacred geometry”
is of course anathema to most
mathematicians, to whom
nothing is sacred.)

From “The Geometric
Art of John Michell
“:
John Michell rendition of  'Remember now thy Creator...'
From this morning’s
 New York Times:

John Michell, Counterculture Author Who Cherished Idiosyncrasy, Dies at 76

By DOUGLAS MARTIN 

Mr. Michell, a self-styled Merlin of the 1960s English counterculture, inspired disciples like the Rolling Stones with a deluge of writings….

Michell, who wrote on Glastonbury
(a site associated with King Arthur)
and on sacred geometry, seems to
have had a better education than
most sacred-geometry enthusiasts.
He is said to have studied at
Eton and at Trinity College,
Cambridge.

He is not to be
confused with an earlier
Trinity figure, mathematician
John Henry Michell,
who died at 76 on the third
day of February in 1940
.

Related material:

See the Log24 entry
from the date of death
 of the later Michell —

  April 24

and, in light of the later
Michell’s interest in
geometry and King Arthur,
 the Log24 remarks for
Easter Sunday this year
(April 12).

These remarks include the
following figure by
Sebastian Egner related,
if only through myth,
to Arthur’s round table —

Conway's mystic circle of 13

— and the classic Delmore Schwartz
poem “Starlight Like Intuition
Pierced the Twelve
.”

Which of the two John Michells
(each a Merlin figure of sorts)
would be more welcome in
Camelot is open to debate.

Monday, March 2, 2009

Monday March 2, 2009

Filed under: General — m759 @ 7:00 PM
Straight

From this journal’s Sunday sermon:

“Flowers’s thoughts stray to Brown,
 with affectionate pity, as he
drinks port and eats walnuts
for the first time in
Senior Combination Room.”

— G. H. Hardy recounting the plot
of A Fellow of Trinity

A Glossary of Cambridge:

Combination Room
Attached to the High Table end of the largely unheated medieval college halls, this was a warm place for Fellows to gather before and after meals. Now known as the Senior Combination Room to distinguish it from the Junior and Middle combination rooms.

From Stanley Fish’s weblog
 in The New York Times
 (Sunday, March 1, 2009, 10 PM):

George Herbert’s “Redemption” —

“‘I resolved to be bold,/And make a suit unto him, to afford/A new small-rented lease and cancel th’old.’

But first he has to find him…. Either he’s just left or he hasn’t been seen, but then, unexpectedly and in the most unlikely circumstances, he turns up:

‘At length I heard a ragged noise and mirth/Of thieves and murderers: there I him espied.’

Before he or his reader can ask ‘what on earth are you doing here?,’ the final line provides an answer with a compact swiftness that is literally breathtaking:

 ‘Who straight, “Your suit is granted,” said, and died.'”

For Senior Combination Room as
a den of thieves and murderers,
see That Hideous Strength.

Related material:

The Painted Word

G. H. Hardy died at 70
 on December 1, 1947.
That date is now observed as
“Day Without Art.”

Day Without Art logo: X'd-out frame

Click on image
for further details.

Sunday, March 1, 2009

Sunday March 1, 2009

Filed under: General,Geometry — Tags: , — m759 @ 11:00 AM

Solomon's Cube
continued

"There is a book… called A Fellow of Trinity, one of series dealing with what is supposed to be Cambridge college life…. There are two heroes, a primary hero called Flowers, who is almost wholly good, and a secondary hero, a much weaker vessel, called Brown. Flowers and Brown find many dangers in university life, but the worst is a gambling saloon in Chesterton run by the Misses Bellenden, two fascinating but extremely wicked young ladies. Flowers survives all these troubles, is Second Wrangler and Senior Classic, and succeeds automatically to a Fellowship (as I suppose he would have done then). Brown succumbs, ruins his parents, takes to drink, is saved from delirium tremens during a thunderstorm only by the prayers of the Junior Dean, has much difficulty in obtaining even an Ordinary Degree, and ultimately becomes a missionary. The friendship is not shattered by these unhappy events, and Flowers's thoughts stray to Brown, with affectionate pity, as he drinks port and eats walnuts for the first time in Senior Combination Room."

— G. H. Hardy, A Mathematician's Apology

"The Solomon Key is the working title of an unreleased novel in progress by American author Dan Brown. The Solomon Key will be the third book involving the character of the Harvard professor Robert Langdon, of which the first two were Angels & Demons (2000) and The Da Vinci Code (2003)." —Wikipedia

"One has O+(6) ≅ S8, the symmetric group of order 8! …."

 — "Siegel Modular Forms and Finite Symplectic Groups," by Francesco Dalla Piazza and Bert van Geemen, May 5, 2008, preprint.

"The complete projective group of collineations and dualities of the [projective] 3-space is shown to be of order [in modern notation] 8! …. To every transformation of the 3-space there corresponds a transformation of the [projective] 5-space. In the 5-space, there are determined 8 sets of 7 points each, 'heptads' …."

— George M. Conwell, "The 3-space PG(3, 2) and Its Group," The Annals of Mathematics, Second Series, Vol. 11, No. 2 (Jan., 1910), pp. 60-76

"It must be remarked that these 8 heptads are the key to an elegant proof…."

— Philippe Cara, "RWPRI Geometries for the Alternating Group A8," in Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference (July 16-21, 2000), Kluwer Academic Publishers, 2001, ed. Aart Blokhuis, James W. P. Hirschfeld, Dieter Jungnickel, and Joseph A. Thas, pp. 61-97
 

Saturday, December 6, 2008

Saturday December 6, 2008

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

“While feasts of Saint Nicholas are not observed nationally, cities with strong German influences like Milwaukee, Cincinnati, and St. Louis celebrate St. Nick’s Day on a scale similar to the German custom.” —Wikipedia

A footprint from Germany:

Germany
Python-urllib
/504856559/item.html 12/6/2008
1:21 PM

The link in the above footprint leads
to an entry of July 5, 2006.

The access method:

The urllib Module

“The Python urllib module implements a fairly high-level abstraction for making any web object with a URL act like a Python file: i.e., you open it, and get back an object….”

For more pictures and discussion
of the object fetched by Python,
see Anti-Christmas 2007.

For a larger and more sophisticated
relative of that object,
 see Solomon’s Cube and
the related three presents
from the German link’s target:

Spellbound: A trinity of Christmas presents

1. Many Dimensions
2. Boggle
3. My Space

Monday, December 1, 2008

Monday December 1, 2008

Filed under: General — m759 @ 8:48 PM
A Version of
Heaven’s Gate

in memory of
G. H. Hardy,
who died on
this date in 1947

C. P. Snow on Hardy:

“He was living in some of the best intellectual company in the world– G.E. Moore, Whitehead, Bertrand Russell, Trevelyan, the high Trinity society which was shortly to find its artistic complement in Bloomsbury.”

For a rather different artistic complement, see the previous entry.

Monday, November 24, 2008

Monday November 24, 2008

Filed under: General,Geometry — m759 @ 12:00 PM
Frame Tale

'Brick' octads in the Miracle Octad Generator (MOG) of R. T. Curtis

Click on image for details.

Wednesday, November 12, 2008

Wednesday November 12, 2008

Filed under: General — m759 @ 8:35 AM

Quantum of Solace

Lottery Numbers
for November 11, 2008:

PA midday 007, evening 628
NY midday 153, evening 069

Experienced
readers of this journal will have little difficulty interpreting these results, except for 153. For that enigmatic number, see Object Lesson.

See also the entries of
this date two years ago:
Grace and Casino Royale.

Sunday, August 3, 2008

Sunday August 3, 2008

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

Preview of a Tom Stoppard play presented at Town Hall in Manhattan on March 14, 2008 (Pi Day and Einstein's birthday):

The play's title, "Every Good Boy Deserves Favour," is a mnemonic for the notes of the treble clef EGBDF.

The place, Town Hall, West 43rd Street. The time, 8 p.m., Friday, March 14. One single performance only, to the tinkle– or the clang?– of a triangle. Echoing perhaps the clang-clack of Warsaw Pact tanks muscling into Prague in August 1968.

The “u” in favour is the British way, the Stoppard way, "EGBDF" being "a Play for Actors and Orchestra" by Tom Stoppard (words) and André Previn (music).

And what a play!– as luminescent as always where Stoppard is concerned. The music component of the one-nighter at Town Hall– a showcase for the Boston University College of Fine Arts– is by a 47-piece live orchestra, the significant instrument being, well, a triangle.

When, in 1974, André Previn, then principal conductor of the London Symphony, invited Stoppard "to write something which had the need of a live full-time orchestra onstage," the 36-year-old playwright jumped at the chance.

One hitch: Stoppard at the time knew "very little about 'serious' music… My qualifications for writing about an orchestra," he says in his introduction to the 1978 Grove Press edition of "EGBDF," "amounted to a spell as a triangle player in a kindergarten percussion band."

Jerry Tallmer in The Villager, March 12-18, 2008

Review of the same play as presented at Chautauqua Institution on July 24, 2008:

"Stoppard's modus operandi– to teasingly introduce numerous clever tidbits designed to challenge the audience."

Jane Vranish, Pittsburgh Post-Gazette, Saturday, August 2, 2008

"The leader of the band is tired
And his eyes are growing old
But his blood runs through
My instrument
And his song is in my soul."

— Dan Fogelberg

"He's watching us all the time."

Lucia Joyce

 

Finnegans Wake,
Book II, Episode 2, pp. 296-297:

I'll make you to see figuratleavely the whome of your eternal geomater. And if you flung her headdress on her from under her highlows you'd wheeze whyse Salmonson set his seel on a hexengown.1 Hissss!, Arrah, go on! Fin for fun!

1 The chape of Doña Speranza of the Nacion.

 

Log 24, Sept. 3, 2003:
 
Reciprocity

From my entry of Sept. 1, 2003:

"…the principle of taking and giving, of learning and teaching, of listening and storytelling, in a word: of reciprocity….

… E. M. Forster famously advised his readers, 'Only connect.' 'Reciprocity' would be Michael Kruger's succinct philosophy, with all that the word implies."

— William Boyd, review of Himmelfarb, a novel by Michael Kruger, in The New York Times Book Review, October 30, 1994

Last year's entry on this date: 

 

Today's birthday:
James Joseph Sylvester

"Mathematics is the music of reason."
— J. J. Sylvester

Sylvester, a nineteenth-century mathematician, coined the phrase "synthematic totals" to describe some structures based on 6-element sets that R. T. Curtis has called "rather unwieldy objects." See Curtis's abstract, Symmetric Generation of Finite Groups, John Baez's essay, Some Thoughts on the Number 6, and my website, Diamond Theory.

 

The picture above is of the complete graph K6  Six points with an edge connecting every pair of points… Fifteen edges in all.

Diamond theory describes how the 15 two-element subsets of a six-element set (represented by edges in the picture above) may be arranged as 15 of the 16 parts of a 4×4 array, and how such an array relates to group-theoretic concepts, including Sylvester's synthematic totals as they relate to constructions of the Mathieu group M24.

If diamond theory illustrates any general philosophical principle, it is probably the interplay of opposites….  "Reciprocity" in the sense of Lao Tzu.  See

Reciprocity and Reversal in Lao Tzu.

For a sense of "reciprocity" more closely related to Michael Kruger's alleged philosophy, see the Confucian concept of Shu (Analects 15:23 or 24) described in

Shu: Reciprocity.

Kruger's novel is in part about a Jew: the quintessential Jewish symbol, the star of David, embedded in the K6 graph above, expresses the reciprocity of male and female, as my May 2003 archives illustrate.  The star of David also appears as part of a graphic design for cubes that illustrate the concepts of diamond theory:

Click on the design for details.

Those who prefer a Jewish approach to physics can find the star of David, in the form of K6, applied to the sixteen 4×4 Dirac matrices, in

A Graphical Representation
of the Dirac Algebra
.

The star of David also appears, if only as a heuristic arrangement, in a note that shows generating partitions of the affine group on 64 points arranged in two opposing triplets.

Having thus, as the New York Times advises, paid tribute to a Jewish symbol, we may note, in closing, a much more sophisticated and subtle concept of reciprocity due to Euler, Legendre, and Gauss.  See

The Jewel of Arithmetic and


FinnegansWiki:

Salmonson set his seel:

"Finn MacCool ate the Salmon of Knowledge."

Wikipedia:

"George Salmon spent his boyhood in Cork City, Ireland. His father was a linen merchant. He graduated from Trinity College Dublin at the age of 19 with exceptionally high honours in mathematics. In 1841 at age 21 he was appointed to a position in the mathematics department at Trinity College Dublin. In 1845 he was appointed concurrently to a position in the theology department at Trinity College Dublin, having been confirmed in that year as an Anglican priest."

Related material:

Kindergarten Theology,

Kindergarten Relativity,

Arrangements for
56 Triangles
.

For more on the
arrangement of
triangles discussed
in Finnegans Wake,
see Log24 on Pi Day,
March 14, 2008.

Happy birthday,
Martin Sheen.
 

Saturday, July 26, 2008

Saturday July 26, 2008

Filed under: General — m759 @ 10:22 PM
For Jung’s Birthday:

The Revelation Game
Revisited

Lotteries
on Jung’s
birthday,
July 26,
2008
Pennsylvania
(No revelation)
New York
(Revelation)
Mid-day
(No belief)
No belief,
no revelation

625


6/25 —
Quine’s
birthday

Revelation
without belief

003

The
Trinity
Pretzel

Evening
(Belief)
Belief without
revelation

087

1987 —
Quine
publishes
Quiddities
Belief and
revelation

829

8/29 —
Hurricane
Katrina,
McCain’s
birthday

From Josephine Klein, Jacob’s Ladder: Essays on Experiences of the Ineffable in the Context of Contemporary Psychotherapy, London, Karnac Books, 2003–

Page 14 —
Gerard Manley Hopkins

Quiddity and haeccity were contentious topics in medieval discussions about the nature of reality, and the poet Gerard Manley Hopkins would have encountered these concepts during his Jesuit training. W. H. Gardner, who edited much of Hopkins’s work, writes that

in 1872, while studying medieval philosophy… Hopkins came across the writing of Duns Scotus, and in that subtle thinker’s Principles of Individuation and Theory of Knowledge he discovered what seemed to be a philosophical corroboration of his own private theory of inscape and instress. [Gardner, Gerard Manley Hopkins: Poems and Prose, Penguin, 1953, p. xxiii]

In this useful introduction to his selection of Hopkins’s work, Gardner writes that Hopkins was always looking for the law or principle that gave an object ‘its delicate and surprising uniqueness.’ This was for Hopkins ‘a fundamental beauty which is the active principle of all true being, the source of all true knowledge and delight.’ Clive Bell called it ‘significant form’; Hopkins called it ‘inscape’– ‘the rich and revealing oneness of the natural object’ (pp. xx-xxiv). In this chapter, I call it quiddity.”

Tuesday, June 24, 2008

Tuesday June 24, 2008

Filed under: General,Geometry — m759 @ 5:01 AM
Plato’s Cave, continued:

                     … we know that we use
Only the eye as faculty, that the mind
Is the eye, and that this landscape of the mind


Is a landscape only of the eye; and that
We are ignorant men incapable
Of the least, minor, vital metaphor….

— Wallace Stevens, “Crude Foyer”

                                               … So, so,
O son of man, the ignorant night, the travail
Of early morning, the mystery of the beginning
Again and again,
                         while history is unforgiven.

— Delmore Schwartz,
  “In the Naked Bed, in Plato’s Cave


The Echo in Plato’s Cave:

Somewhere between
a flagrant triviality and
a resplendent Trinity we
have what might be called
“a resplendent triviality.”

For further details, see
A Four-Color Theorem.”

Friday, June 20, 2008

Friday June 20, 2008

Filed under: General — m759 @ 9:00 AM
Drunkard’s Walk

In memory of Episcopal priest
and Jungian analyst
Brewster Yale Beach,
who died on Tuesday,
June 17, 2008

“A man walks down the street…”

Paul Simon, Graceland album 

NY Times obituaries, Tuesday, June 17, 2008-- Tony Schwartz, Walter Netsch, Tim Russert

Related material:

In the above screenshot of New York Times obituaries on the date of Brewster Beach’s death, Tim Russert seems to be looking at the obituary of Air Force Academy chapel architect Walter Netsch.

This suggests another chapel, more closely related to my own experience, in Cuernavaca, Mexico. Some background…

Walter Netsch in Oral History (pdf, 467 pp.):

“I also had a book that inspired me– this is 1947– called Communitas by Percival and Paul Goodman. Percival Goodman was the architect, and Paul Goodman was the writer and leftist. And this came out of the University of Chicago– part of the leftist bit of the University of Chicago….

I had sort of in the back of my mind, Communitas appeared from my subconscious of the new town out of town, and there were other people who knew of it….”

Center of Town, Cuernavaca, from Paul Goodman's Communitas
Log24, Feb. 24, 2008:

Candela's 'Capilla Abierta' chapel, Cuernavaca, Mexico

Chapel, Cuernavaca, Mexico

“God As Trauma”
by Brewster Yale Beach:
“The problem of crucifixion is
  the beginning of individuation.”

Si me de veras quieres,
deja me en paz
.”

Lucero Hernandez,
Cuernavaca, 1962

A more impersonal approach
to my own drunkard’s walk
(Cuernavaca, 1962, after
reading the above words):

Cognitive Blending
and the Two Cultures

An approach from the culture
(more precisely, the alternate
religion) of Scientism–
The Drunkard’s Walk:
How Randomness
Rules Our Lives

is sketched in
Today’s Sermon:
The Holy Trinity vs.
The New York Times

(Sunday, June 8, 2008).

The Times illustrated its review
of The Drunkard’s Walk
with facetious drawings
by Jessica Hagy, who uses
Venn diagrams to make
cynical jokes.

A less cynical use of
a Venn diagram:

No se puede vivir sin amar.”

— Malcolm Lowry,
Under the Volcano

Photo by Gerry Gantt

(March 3, 2004)

Friday, June 13, 2008

Friday June 13, 2008

Filed under: General — m759 @ 6:11 AM
In Lieu of
Stained Glass

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

Vladimir Nabokov,
quoted here last Monday
in “Interpret This”

Illustration by Jessica Hagy
from “Today’s Sermon
last Sunday:
Jessica Hagy, card 675: The Holy Trinity

Application Form for
the Worst Camping Trip Ever:

(Click here for original pdf.)


PAHUK PRIDE – 2008

YOUTH LEADERSHIP
TRAINING CONFERENCE
MID-AMERICA COUNCIL –
 LITTLE SIOUX SCOUT RANCH
PARTICIPANT REGISTRATION
————————————–
THANK YOU FOR PRINTING
ALL INFORMATION LEGIBLY!!

* Former husband of Susan Sontag
and author of
My Life Among the Deathworks

Thursday, June 12, 2008

Thursday June 12, 2008

Filed under: General — m759 @ 1:06 AM
Feel lucky?

Dirty Harry asks the classic question

“The scientific mind does not so much
provide the right answers as
ask the right questions.”

Claude Lévi-Strauss

(The Raw and the Cooked,
1964, English translation 1969 —
paperback, U. of Chicago Press,
1983, “Overture,” p. 7
)

The Police, Synchronicity album

Context of the question:

A Venn diagram —
shown here last Sunday —
Jessica Hagy, card 675: The Holy Trinity

 by the illustrator of last Sunday’s
New York Times review of

The Drunkard’s Walk:

How Randomness
Rules Our Lives

Well, do you?

NY Lottery June 11, 2008: mid-day 610, evening 928

Related material:

6/10

(San Francisco’s new
Contemporary Jewish Museum
as a vision of Hell)
 
9/28

(A less theological,
more personal, discussion
of Venn diagrams)

Wednesday, June 11, 2008

Wednesday June 11, 2008

Filed under: General — m759 @ 8:00 PM
Indiana Jones and the
Worst Camping Trip Ever

Part I:

“Today’s Sermon”  
  from last Sunday —

The Holy Trinity vs.
   The New York Times

http://indexed.blogspot.com/

Thursday, February 15, 2007

Scary stories.
Jessica Hagy, card 675: The Holy Trinity

Posted by Jessica Hagy at 10:31 PM
39 comments Labels: ,

Part II:

Today’s previous entries

Wonder Woman delivers a diamond

Part III:

Harrison Ford and Shia LaBoeuf as Father and Son

Susan Sontag,
Notes on “Camp”

Sunday, June 8, 2008

Sunday June 8, 2008

Filed under: General — m759 @ 10:00 AM
The Holy Trinity vs.
The New York Times

From the illustrator of
today’s NY Times review of
The Drunkard’s Walk

http://indexed.blogspot.com/

Thursday, February 15, 2007

Scary stories.
Jessica Hagy, card 675: The Holy Trinity

Posted by Jessica Hagy at 10:31 PM
39 comments Labels: ,

The book under review–
The Drunkard’s Walk:
How Randomness Rules Our Lives
,
by the author of Euclid’s Window
is, appropriately, published by
Random House:

Random House logo (color-reversed image)

Click image for
related material.

Sunday, May 25, 2008

Sunday May 25, 2008

Filed under: General,Geometry — Tags: — m759 @ 9:00 AM
Wechsler Cubes

 "Confusion is nothing new."
— Song lyric, Cyndi Lauper  

Part I:
Magister Ludi

Hermann Hesse's 1943 The Glass Bead Game (Picador paperback, Dec. 6, 2002, pp. 139-140)–

"For the present, the Master showed him a bulky memorandum, a proposal he had received from an organist– one of the innumerable proposals which the directorate of the Game regularly had to examine. Usually these were suggestions for the admission of new material to the Archives. One man, for example, had made a meticulous study of the history of the madrigal and discovered in the development of the style a curved that he had expressed both musically and mathematically, so that it could be included in the vocabulary of the Game. Another had examined the rhythmic structure of Julius Caesar's Latin and discovered the most striking congruences with the results of well-known studies of the intervals in Byzantine hymns. Or again some fanatic had once more unearthed some new cabala hidden in the musical notation of the fifteenth century. Then there were the tempestuous letters from abstruse experimenters who could arrive at the most astounding conclusions from, say, a comparison of the horoscopes of Goethe and Spinoza; such letters often included pretty and seemingly enlightening geometric drawings in several colors."

Part II:
A Bulky Memorandum

From Siri Hustvedt, author of Mysteries of the Rectangle: Essays on Painting (Princeton Architectural Press, 2005)– What I Loved: A Novel (Picador paperback, March 1, 2004, page 168)–

A description of the work of Bill Wechsler, a fictional artist:

"Bill worked long hours on a series of autonomous pieces about numbers. Like O's Journey, the works took place inside glass cubes, but these were twice as large– about two feet square. He drew his inspiration from sources as varied as the Cabbala, physics, baseball box scores, and stock market reports. He painted, cut, sculpted, distorted, and broke the numerical signs in each work until they became unrecognizable. He included figures, objects, books, windows, and always the written word for the number. It was rambunctious art, thick with allusion– to voids, blanks, holes, to monotheism and the individual, the the dialectic and yin-yang, to the Trinity, the three fates, and three wishes, to the golden rectangle, to seven heavens, the seven lower orders of the sephiroth, the nine Muses, the nine circles of Hell, the nine worlds of Norse mythology, but also to popular references like A Better Marriage in Five Easy Lessons and Thinner Thighs in Seven Days. Twelve-step programs were referred to in both cube one and cube two. A miniature copy of a book called The Six Mistakes Parents Make Most Often lay at the bottom of cube six. Puns appeared, usually well disguised– one, won; two, too, and Tuesday; four, for, forth; ate, eight. Bill was partial to rhymes as well, both in images and words. In cube nine, the geometric figure for a line had been painted on one glass wall. In cube three, a tiny man wearing the black-and-white prison garb of cartoons and dragging a leg iron has

— End of page 168 —

opened the door to his cell. The hidden rhyme is "free." Looking closely through the walls of the cube, one can see the parallel rhyme in another language: the German word drei is scratched into one glass wall. Lying at the bottom of the same box is a tiny black-and-white photograph cut from a book that shows the entrance to Auschwitz: ARBEIT MACHT FREI. With every number, the arbitrary dance of associations worked togethere to create a tiny mental landscape that ranged in tone from wish-fulfillment dream to nightmare. Although dense, the effect of the cubes wasn't visually disorienting. Each object, painting, drawing, bit of text, or sculpted figure found its rightful place under the glass according to the necessary, if mad, logic of numerical, pictorial, and verbal connection– and the colors of each were startling. Every number had been given a thematic hue. Bill had been interested in Goethe's color wheel and in Alfred Jensen's use of it in his thick, hallucinatory paintings of numbers. He had assigned each number a color. Like Goethe, he included black and white, although he didn't bother with the poet's meanings. Zero and one were white. Two was blue. Three was red, four was yellow, and he mixed colors: pale blue for five, purples in six, oranges in seven, greens in eight, and blacks and grays in nine. Although other colors and omnipresent newsprint always intruded on the basic scheme, the myriad shades of a single color dominated each cube.

The number pieces were the work of a man at the top of his form. An organic extension of everything Bill had done before, these knots of symbols had an explosive effect. The longer I looked at them, the more the miniature constructions seemed on the brink of bursting from internal pressure. They were tightly orchestrated semantic bombs through which Bill laid bare the arbitrary roots of meaning itself– that peculiar social contract generated by little squiggles, dashes, lines, and loops on a page."

Part III:
Wechsler Cubes

(named not for
Bill Wechsler, the
fictional artist above,
but for the non-fictional
   David Wechsler) —

From 2002:

Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale "block design" subtest.


Part IV:
A Magic Gallery
 
Log24, March 4, 2004
 

ZZ
WW

Figures from the
Kaleidoscope Puzzle
of Steven H. Cullinane:


Poem by Eugen Jost:
Zahlen und Zeichen,
Wörter und Worte

Mit Zeichen und Zahlen
vermessen wir Himmel und Erde
schwarz
auf weiss
schaffen wir neue Welten
oder gar Universen


 Numbers and Names,
Wording and Words


With numbers and names
we measure heaven and earth
black
on white
we create new worlds
and universes


English translation
by Catherine Schelbert



A related poem:

Alphabets
by Hermann Hesse

From time to time
we take our pen in hand
and scribble symbols
on a blank white sheet
Their meaning is
at everyone's command;
it is a game whose rules
are nice and neat.

But if a savage
or a moon-man came
and found a page,
a furrowed runic field,
and curiously studied
lines and frame:
How strange would be
the world that they revealed.
a magic gallery of oddities.
He would see A and B
as man and beast,
as moving tongues or
arms or legs or eyes,
now slow, now rushing,
all constraint released,
like prints of ravens'
feet upon the snow.
He'd hop about with them,
fly to and fro,
and see a thousand worlds
of might-have-been
hidden within the black
and frozen symbols,
beneath the ornate strokes,
the thick and thin.
He'd see the way love burns
and anguish trembles,
He'd wonder, laugh,
shake with fear and weep
because beyond this cipher's
cross-barred keep
he'd see the world
in all its aimless passion,
diminished, dwarfed, and
spellbound in the symbols,
and rigorously marching
prisoner-fashion.
He'd think: each sign
all others so resembles
that love of life and death,
or lust and anguish,
are simply twins whom
no one can distinguish…
until at last the savage
with a sound
of mortal terror
lights and stirs a fire,
chants and beats his brow
against the ground
and consecrates the writing
to his pyre.
Perhaps before his
consciousness is drowned
in slumber there will come
to him some sense
of how this world
of magic fraudulence,
this horror utterly
behind endurance,
has vanished as if
it had never been.
He'll sigh, and smile,
and feel all right again.

— Hermann Hesse (1943),
"Buchstaben," from
Das Glasperlenspiel,
translated by
Richard and Clara Winston

Thursday, May 8, 2008

Thursday May 8, 2008

Filed under: General — m759 @ 4:48 PM
Synchronicity,
Part Deux

Footprints at Log24 on the afternoon of May 8, 2008, including two from France

From
“On the Holy Trinity,”
the entry in the 3:20 PM
French footprint:

“…while the scientist sees
everything that happens
in one point of space,
the poet feels
everything that happens
in one point of time…
all forming an
instantaneous and transparent
organism of events….”

Vladimir Nabokov

From
“Angel in the Details,”
 the entry in the 3:59 PM
French footprint:

“I dwell in Possibility –
A fairer House than Prose”

Emily Dickinson

These, along with this afternoon’s
earlier entry, suggest a review
of a third Log24 item, Windmills,
with an actress from France as…

Changing Woman:

“Kaleidoscope turning…

Juliette Binoche in 'Blue'  The 24 2x2 Cullinane Kaleidoscope animated images

Shifting pattern
within unalterable structure…”
— Roger Zelazny, Eye of Cat  

“When life itself seems lunatic,
who knows where madness lies?”

— For the source, see 
Joyce’s Nightmare Continues.

Sunday, April 13, 2008

Sunday April 13, 2008

Filed under: General,Geometry — m759 @ 7:59 AM
The Echo
in Plato’s Cave

“It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy.”

— Simon Blackburn, Think (Oxford, 1999)

Michael Harris, mathematician at the University of Paris:

“… three ‘parts’ of tragedy identified by Aristotle that transpose to fiction of all types– plot (mythos), character (ethos), and ‘thought’ (dianoia)….”

— paper (pdf) to appear in Mathematics and Narrative, A. Doxiadis and B. Mazur, eds.

Mythos —

A visitor from France this morning viewed the entry of Jan. 23, 2006: “In Defense of Hilbert (On His Birthday).” That entry concerns a remark of Michael Harris.

A check of Harris’s website reveals a new article:

“Do Androids Prove Theorems in Their Sleep?” (slighly longer version of article to appear in Mathematics and Narrative, A. Doxiadis and B. Mazur, eds.) (pdf).

From that article:

“The word ‘key’ functions here to structure the reading of the article, to draw the reader’s attention initially to the element of the proof the author considers most important. Compare E.M. Forster in Aspects of the Novel:

[plot is] something which is measured not be minutes or hours, but by intensity, so that when we look at our past it does not stretch back evenly but piles up into a few notable pinnacles.”

Ethos —

“Forster took pains to widen and deepen the enigmatic character of his novel, to make it a puzzle insoluble within its own terms, or without. Early drafts of A Passage to India reveal a number of false starts. Forster repeatedly revised drafts of chapters thirteen through sixteen, which comprise the crux of the novel, the visit to the Marabar Caves. When he began writing the novel, his intention was to make the cave scene central and significant, but he did not yet know how:

When I began a A Passage to India, I knew something important happened in the Malabar (sic) Caves, and that it would have a central place in the novel– but I didn’t know what it would be… The Malabar Caves represented an area in which concentration can take place. They were to engender an event like an egg.”

E. M. Forster: A Passage to India, by Betty Jay

Dianoia —

Flagrant Triviality
or Resplendent Trinity?

“Despite the flagrant triviality of the proof… this result is the key point in the paper.”

— Michael Harris, op. cit., quoting a mathematical paper

Online Etymology Dictionary
:

flagrant
c.1500, “resplendent,” from L. flagrantem (nom. flagrans) “burning,” prp. of flagrare “to burn,” from L. root *flag-, corresponding to PIE *bhleg (cf. Gk. phlegein “to burn, scorch,” O.E. blæc “black”). Sense of “glaringly offensive” first recorded 1706, probably from common legalese phrase in flagrante delicto “red-handed,” lit. “with the crime still blazing.”

A related use of “resplendent”– applied to a Trinity, not a triviality– appears in the Liturgy of Malabar:

http://www.log24.com/log/pix08/080413-LiturgyOfMalabar.jpg

The Liturgies of SS. Mark, James, Clement, Chrysostom, and Basil, and the Church of Malabar, by the Rev. J.M. Neale and the Rev. R.F. Littledale, reprinted by Gorgias Press, 2002

On Universals and
A Passage to India:

“”The universe, then, is less intimation than cipher: a mask rather than a revelation in the romantic sense. Does love meet with love? Do we receive but what we give? The answer is surely a paradox, the paradox that there are Platonic universals beyond, but that the glass is too dark to see them. Is there a light beyond the glass, or is it a mirror only to the self? The Platonic cave is even darker than Plato made it, for it introduces the echo, and so leaves us back in the world of men, which does not carry total meaning, is just a story of events.”

— Betty Jay,  op. cit.

http://www.log24.com/log/pix08/080413-Marabar.jpg

Judy Davis in the Marabar Caves

In mathematics
(as opposed to narrative),
somewhere between
 a flagrant triviality and
a resplendent Trinity we
have what might be called
“a resplendent triviality.”

For further details, see
A Four-Color Theorem.”

Monday, February 4, 2008

Monday February 4, 2008

Filed under: General — m759 @ 7:59 AM
New York Lottery,
 
Super Bowl Sunday, 2008:

NY Lottery Feb. 3, 2008: Mid-day 408, Evening 888

Susan Sontag,
 
Against Interpretation

“Of course, I don’t mean interpretation in the broadest sense, the sense in which Nietzsche (rightly) says, ‘There are no facts, only interpretations.’ By interpretation, I mean here a conscious act of the mind which illustrates a certain code, certain ‘rules’ of interpretation.”

A Certain Code

Edward Gibbon on the Trinity:

“perhaps the deepest and darkest corner of the whole theological abyss”

Friedrich Nietzsche on the abyss:

“Whoever fights monsters should see to it that in the process he does not become a monster.  And when you look long into an abyss, the abyss also looks into you.”

Frank Sinatra on narrative:

“You gotta be true to your code.”

The Lottery Code:

Log24, Feb. 27, 2007

Tuesday, November 6, 2007

Tuesday November 6, 2007

Filed under: General — m759 @ 12:25 PM
The Third Person

Of Modern Art


The New York Times
November 6, 2007

More on the Career of
the Genius Who Boldly
Compared Himself to God

By MICHIKO KAKUTANI

“Picasso… once said…

‘… No wonder his [Picasso’s] style is so ambiguous. It’s like God’s. God is really only another artist. He invented the giraffe, the elephant and the cat. He has no real style. He just keeps on trying other things. The same with this sculptor….’

The comparison to God, like the use of the third person, was deliberate, of course.”

Of Modern Poetry

The poem of the mind
    in the act of finding
What will suffice ….
                            … It has
To construct a new stage.
    It has to be on that stage,
And, like an insatiable actor,
    slowly and
With meditation, speak words
    that in the ear,
In the delicatest ear
    of the mind, repeat,
Exactly, that which it
    wants to hear, at the sound
Of which, an invisible
    audience listens,
Not to the play, but to
    itself, expressed
In an emotion as of
    two people, as of two
Emotions becoming one.
   The actor is
A metaphysician in the dark….

— Wallace Stevens in
    Parts of a World, 1942


Of Modern Metaphysics

“For every work [or act] of creation is threefold, an earthly trinity to match the heavenly.

First, [not in time, but merely in order of enumeration] there is the Creative Idea, passionless, timeless, beholding the whole work complete at once, the end in the beginning: and this is the image of the Father.

Second, there is the Creative Energy [or Activity] begotten of that idea, working in time from the beginning to the end, with sweat and passion, being incarnate in the bonds of matter: and this is the image of the Word.

Third, there is the Creative Power, the meaning of the work and its response in the lively soul: and this is the image of the indwelling Spirit.

And these three are one, each equally in itself the whole work, whereof none can exist without other: and this is the image of the Trinity.”

— Concluding speech of St. Michael the Archangel in a 1937 play, “The Zeal of Thy House,” by Dorothy Sayers, as quoted in her 1941 book The Mind of the Maker. That entire book was, she wrote, an expansion of St. Michael’s speech.

Related material:

Wednesday, October 24, 2007

Wednesday October 24, 2007

Filed under: General,Geometry — Tags: , — m759 @ 11:11 PM
 
Descartes's Twelfth Step

An earlier entry today ("Hollywood Midrash continued") on a father and son suggests we might look for an appropriate holy ghost. In that context…

Descartes

A search for further background on Emmanuel Levinas, a favorite philosopher of the late R. B. Kitaj (previous two entries), led (somewhat indirectly) to the following figures of Descartes:

The color-analogy figures of Descartes
This trinity of figures is taken from Descartes' Rule Twelve in Rules for the Direction of the Mind. It seems to be meant to suggest an analogy between superposition of colors and superposition of shapes.Note that the first figure is made up of vertical lines, the second of vertical and horizontal lines, and the third of vertical, horizontal, and diagonal lines. Leon R. Kass recently suggested that the Descartes figures might be replaced by a more modern concept– colors as wavelengths. (Commentary, April 2007). This in turn suggests an analogy to Fourier series decomposition of a waveform in harmonic analysis. See the Kass essay for a discussion of the Descartes figures in the context of (pdf) Science, Religion, and the Human Future (not to be confused with Life, the Universe, and Everything).

Compare and contrast:

The harmonic-analysis analogy suggests a review of an earlier entry's
link today to 4/30–  Structure and Logic— as well as
re-examination of Symmetry and a Trinity


(Dec. 4, 2002).

See also —

A Four-Color Theorem,
The Diamond Theorem, and
The Most Violent Poem,

Emma Thompson in 'Wit'

from Mike Nichols's birthday, 2003.

Saturday, October 13, 2007

Saturday October 13, 2007

Filed under: General — m759 @ 9:22 AM
Simon’s Shema

“When times are mysterious
Serious numbers will always be heard
And after all is said and done
And the numbers all come home
The four rolls into three
The three turns into two
And the two becomes a
One”

Paul Simon, 1983


Related material:

Simon’s theology here, though radically reductive, is at least consistent with traditional Jewish thought. It may help counteract the thoughtless drift to the left of academic writing in recent decades. Another weapon against leftist nonsense appears, surprisingly, on the op-ed page of today’s New York Times:

“There is a Communist jargon recognizable after a single sentence. Few people in Europe have not joked in their time about ‘concrete steps,’ ‘contradictions,’ ‘the interpenetration of opposites,’ and the rest.”

— Doris Lessing, winner of this year’s Nobel Prize in Literature

The Times offers Lessing’s essay to counter Harold Bloom’s remark that this year’s award of a Nobel Prize to Lessing is “pure political correctness.” The following may serve as a further antidote to Bloom.

The Communist use of “interpenetration,” a term long used to describe the Holy Trinity, suggests– along with Simon’s hymn to the Unity, and the rhetorical advice of Norman Mailer quoted here yesterday—  a search for the full phrase “interpenetration of opposites” in the context* of theology.  Such a search yields a rhetorical gem from New Zealand:

“Dipolarity and God”
by Mark D. Brimblecombe,
Ph.D. thesis,
University of Auckland, 1999
.

* See the final footnote on the final page (249) of Brimblecombe’s thesis:

3 The Latin word contexo means to interweave, join, or braid together.

A check of the Online Eymology Dictionary supports this assertion:

context 1432, from L. contextus “a joining together,” orig. pp. of contexere “to weave together,” from com “together” + textere “to weave” (see texture).

See also Wittgenstein on “theology as grammar” and “context-sensitive” grammars as (unlike Simon’s reductive process) “noncontracting”– Log24, April 16, 2007: Happy Birthday, Benedict XVI.

Thursday, October 11, 2007

Thursday October 11, 2007

Filed under: General — m759 @ 12:00 PM
The Nobel Prize
in Literature

this year goes to the author
of The Golden Notebook
and The Cleft.

Related material:
The Golden Obituary
and Cleavage —
Log24, Oct. 9, 2007

Art History, 1955: Scenes from Bad Day at Black Rock

Background from 1947:

The image “http://www.log24.com/log/pix07A/071011-Cleavage.jpg” cannot be displayed, because it contains errors.

Further details:

WheelThe image “http://www.log24.com/log/images/asterisk8.gif” cannot be displayed, because it contains errors.

Quoted by physics writer
Heinz Pagels at the end of
The Cosmic Code
:

“For the essence and the end
Of his labor is beauty… one beauty,
the rhythm of that Wheel….”

— Robinson Jeffers

From Holy Saturday, 2004:

The Ferris wheel came into view again, just the top, silently burning high on the hill, almost directly in front of him, then the trees rose up over it.  The road, which was terrible and full of potholes, went steeply downhill here; he was approaching the little bridge over the barranca, the deep ravine.  Halfway across the bridge he stopped; he lit a new cigarette from the one he’d been smoking, and leaned over the parapet, looking down.  It was too dark to see the bottom, but: here was finality indeed, and cleavage!  Quauhnahuac was like the times in this respect, wherever you turned the abyss was waiting for you round the corner. Dormitory for vultures and city of Moloch! When Christ was being crucified, so ran the sea-borne, hieratic legend, the earth had opened all through this country…”

— Malcolm Lowry, Under the Volcano, 1947. (Harper & Row reissue, 1984, p. 15)

Comment by Stephen Spender:

“There is a suggestion of Christ descending into the abyss for the harrowing of Hell.  But it is the Consul whom we think of here, rather than of Christ.  The Consul is hurled into this abyss at the end of the novel.”

— Introduction to Under the Volcano


 Edward Gibbon, Decline and Fall of the Roman Empire, Chapter XXI

Gibbon, discussing the theology of the Trinity, defines perichoresis as

“… the internal connection and spiritual penetration which indissolubly unites the divine persons59 ….

59 … The perichoresis  or ‘circumincessio,’ is perhaps the deepest and darkest corner of the whole theological abyss.”


 “Whoever fights monsters should see to it that in the process he does not become a monster.  And when you look long into an abyss, the abyss also looks into you.”

— Friedrich Nietzsche, Beyond Good and Evil, section 146, translated by Walter Kaufmann


William Golding:

 “Simon’s head was tilted slightly up.  His eyes could not break away and the Lord of the Flies hung in space before him. 

‘What are you doing out here all alone?  Aren’t you afraid of me?’

Simon shook.

‘There isn’t anyone to help you.  Only me.  And I’m the Beast.’

Simon’s mouth labored, brought forth audible words.

‘Pig’s head on a stick.’

‘Fancy thinking the Beast was something you could hunt and kill!’ said the head.  For a moment or two the forest and all the other dimly appreciated places echoed with the parody of laughter.  ‘You knew, didn’t you?  I’m part of you?  Close, close, close!’ “


“Thought of the day:
You can catch more flies with honey than vinegar… if you’re into catchin’ flies.”

Alice Woodrome, Good Friday, 2004

Anne Francis,
also known as
Honey West:

“Here was finality indeed,
and cleavage!”

Under the Volcano

The image “http://www.log24.com/log/images/asterisk8.gif” cannot be displayed, because it contains errors. For further details of
the wheel metaphor, see

Rock of Ages

(St. Cecilia’s Day, 2006).

Wednesday, October 3, 2007

Wednesday October 3, 2007

Filed under: General,Geometry — m759 @ 3:09 PM
Janitor Monitor

The image “http://www.log24.com/log/pix07A/070803-Trees.jpg” cannot be displayed, because it contains errors.

Will Hunting may be
interested in the following
vacant editorships at
The Open Directory:

Graph Theory
and
Combinatorics.

Related material:

The Long Hello and
On the Holy Trinity

Hey, Carrie-Anne, what’s
your game now….?

The image “http://www.log24.com/log/pix07A/071003-Magdalene.GIF” cannot be displayed, because it contains errors.

Picture sources:
azstarnet.com,
vibrationdata.com.

Personally, I prefer
Carol Ann:

From Criticism,  Fall, 2001,
by Carol Ann Johnston

“Drawing upon Platonic thought, Augustine argues that ideas are actually God’s objective pattern and as such exist in God’s mind. These ideas appear in the mirror of the soul. (35).”

(35.) In Augustine, De Trinitate, trans., Stephen McKenna (Washington, D.C.: Catholic University Press, 1970). See A. B. Acton, “Idealism,” in The Encyclopedia of Philosophy, ed., Paul Edwards. Vol. 4 (New York: Macmillan, 1967): 110-118; Robert McRae, “`Idea’ as a Philosophical Term in the Seventeenth Century,” JHI 26 (1965): 175-190, and Erwin Panofsky, Idea: A Concept in Art History, trans., Joseph J. S. Peake (Columbia, S.C.: University of South Carolina Press, 1968) for explications of this term.

See also
Art Wars: Geometry as Conceptual Art
and Ideas and Art: Notes on Iconology.

For more on Augustine and geometry,
see Today’s Sinner (Aug. 28, 2006).

Sunday, September 30, 2007

Sunday September 30, 2007

Filed under: General — m759 @ 8:28 AM
Trinity Church

The image “http://www.log24.com/log/pix07A/070930-Trinity_Church_today.jpg” cannot be displayed, because it contains errors.

“Funeral services will be held
at Trinity Church, Upperville,
at 2 p.m. Sunday, Sept. 30.”

The source:

William D. Rogers, Diplomat and Attorney

Today’s previous entry had
 a different image of Rogers
with a quotation from
  Wallace Stevens’s “The Rock.”
Stevens, though raised as
a Presbyterian, was a
secular poet.

Since Rogers’s funeral
is to take place in
a Christian church,
it seems fitting to
grant equal time to
a Christian poet of
at least equal stature:

“Though you forget the way
    to the Temple,
There is one who remembers
    the way to your door:
Life you may evade,
    but Death you shall not.
You shall not deny the Stranger.”

— Thomas Stearns Eliot,
  “Choruses from ‘The Rock’

Sunday, May 27, 2007

Sunday May 27, 2007

Filed under: General — m759 @ 8:00 AM
Random Number
The previous entry links back to May 18’s “Devil in the Details,” an entry quoting Peter Woit.  Yesterday afternoon Woit, who sometimes writes on pure mathematics as well as physics, posted an entry on a talk said to be related to something called “the ABC-conjecture,” which has been called “the most important unsolved problem in diophantine analysis.” (Dorian Goldfeld,  “Beyond the Last Theorem,” The Sciences, March/April 1996, 34-40)

On the ABC-conjecture in number theory:

“We hope to elucidate the beautiful connections between elliptic curves, modular forms and the ABC–conjecture.” —Dorian Goldfeld (pdf)

An Edinburgh postgraduate student on the conjecture:

“… abc brings us full circle to Fermat’s Last Theorem….” —Graeme Taylor at Everything2.com

I regret I can add nothing to Taylor’s admirable exposition and to Goldfeld’s “beautiful connections” except the following observation of a rather ugly connection.

The previous Log24 entry, from yesterday afternoon, related the May 18 “details” entry to Friday’s PA evening lottery number, 005.  A  followup seems (if only to honor the madcap tradition of John Nash) to be called for.  The PA evening number yesterday evening, Saturday, was 443.  Nash, in his younger days, might have been pleased to note that this number is associated (if only by coincidence) with a topic Woit mentioned earlier yesterday– Fermat’s famed conjecture:

The image “http://www.log24.com/log/pix07/070527-Fermat.jpg” cannot be displayed, because it contains errors.
Page 443

in The Annals of Mathematics,
2nd Ser., Vol. 141, No. 3 (May, 1995)
This is the first page of a rather
 famous paper by Andrew Wiles.

Such coincidences are, of course, anathema to believers in the religion of Scientism.  But one such believer, Natalie Angier (yesterday morning’s entry), at least acknowledges the charm of “the atheist’s favorite Christmas movie, ‘Coincidence on 34th Street.'” (pdf)

Thursday, May 17, 2007

Thursday May 17, 2007

Filed under: General — m759 @ 7:31 AM
Logos
 
for
Yolanda King,
who died May 15,
the birthday of
L. Frank Baum:

Tin Man, Lion, Scarecrow

The image “http://www.log24.com/log/pix07/070517-Trinity.jpg” cannot be displayed, because it contains errors.

Symbols of, left to right,
Philip K. Dick (see 3/2/06),
Robert Anton Wilson (see 6/11/03),
and Kurt Vonnegut (see Palm Sunday,
an Autobiographical Collage
).
See also An Unholy Trinity (5/6/07).
The “sunrise” logo at top,
  along with the three-part motto
“Educate, Empower, Entertain,”
is Yolanda King’s own.

Tuesday, February 27, 2007

Tuesday February 27, 2007

Filed under: General,Geometry — m759 @ 9:25 PM
Suggested by today’s 
New York Times story
on a Harvard student’s
research on pattern in
Islamic art —

and in memory of
George Sadek

From Log24 in July 2005:

Intersections

A Trinity Sunday sermon
quotes T. S. Eliot:

“… to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint.”

See also The Diamond Project.

Related material:

                                  ” … an alphabet
By which to spell out holy doom and end,
A bee for the remembering of happiness.”

— Wallace Stevens,
“The Owl in the Sarcophagus”

The image “http://www.log24.com/theory/images/HeathI47A-Illustrations.jpg” cannot be displayed, because it contains errors.

Some context for these figures:
The Diamond Theory of Truth

Tuesday February 27, 2007

Filed under: General,Geometry — m759 @ 7:59 AM
Continued from 2/06:

The Poetics of Space

Log24 yesterday:

“Imprimatur.
+John Cardinal Farley,
Archbishop of New York”

Tom Hanks as Robert Langdon in The Da Vinci Code

Tom Hanks as Robert Langdon
in “The Da Vinci Code”

“… and by ‘+’ I mean
artistic vision.”

New York State Lottery
yesterday, Feb. 26, 2007:

Mid-day 206
Evening 888


For more on the artistic
significance of 206,
see 2/06.

For more on the artistic
significance of 888, see
St. Bonaventure on the
Trinity at math16.com.

A trinity:

Click on picture for further details.

Saturday, January 27, 2007

Saturday January 27, 2007

Filed under: General — Tags: — m759 @ 9:00 AM
Art and the
Holy Spirit

Madeleine L'Engle in The Irrational Season (1977), beginning of Chapter 9 (on Pentecost):

"The Holy Spirit, the third person of the Trinity, is the easiest of this not-at-all-easy concept for me to understand.  Any artist, great or small, knows moments when something more than he takes over, and he moves into a kind of 'overdrive,' where he works as ordinarily he cannot work.  When he is through, there is a sense of exhilaration, exhaustion, and joy.  All our best work comes in this fashion, and it is humbling and exciting.

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."
 

Saturday, December 23, 2006

Saturday December 23, 2006

Filed under: General,Geometry — m759 @ 9:00 AM
Black Mark

Bernard Holland in The New York Times on Monday, May 20, 1996:

“Philosophers ponder the idea of identity: what it is to give something a name on Monday and have it respond to that name on Friday….”

Log24 on Monday,
Dec. 18, 2006:

“I did a column in
Scientific American
on minimal art, and
I reproduced one of
Ed Rinehart’s [sic]
black paintings.”

Martin Gardner (pdf)

“… the entire profession
has received a very public
and very bad black mark.”

Joan S. Birman (pdf)

Lottery on Friday,
Dec. 22, 2006:

The image “http://www.log24.com/log/pix06B/061222-PAlottery.jpg” cannot be displayed, because it contains errors.

5/04
, 2005:

Analysis of the structure
of a 2x2x2 cube

The Eightfold Cube

via trinities of
projective points
in a Fano plane.

7/15, 2005:

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

  — Robert Morris,
Smithsonian Archives
of American Art

Also on 7/15, 2005,
a quotation on Usenet:

“A set having three members is a
single thing wholly constituted by
its members but distinct from them.
After this, the theological doctrine
of the Trinity as ‘three in one’
should be child’s play.”

— Max Black,
Caveats and Critiques:
Philosophical Essays in
Language, Logic, and Art

Wednesday, October 25, 2006

Wednesday October 25, 2006

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

Conceit
at Harvard

conceit (See definition.)
“c.1374, from conceiven (see conceive). An Eng. formation based on deceit and receipt. Sense evolved from ‘something formed in the mind,’ to ‘fanciful or witty notion’ (1513), to ‘vanity’ (1605)….”

Online Eytmology Dictionary

“… there is some virtue in tracking cultural trends in terms of their relation to the classic Trinitarian framework of Christian thought.”

Description of lectures to be given Monday, Tuesday, and Wednesday of this week (on Father, Son, and Holy Spirit, respectively, and their relationship to “cultural trends”) at Harvard’s Memorial Church

I prefer more-classic trinitarian frameworks– for example,

the classic Pythagorean
trinity of 4, 3, and 5


The image “http://www.log24.com/log/pix06A/061025-Pyth2.gif” cannot be displayed, because it contains errors.

and the structural trinity
underlying
classic quilt patterns:

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

Click on pictures for further details.

These mathematical trinities are
conceits in the sense of concepts
or notions; examples of the third
kind of conceit are easily
found, especially at Harvard.

For a possible corrective to
examples of the third kind,
see
To Measure the Changes.

Thursday, September 28, 2006

Thursday September 28, 2006

Filed under: General,Geometry — m759 @ 9:15 AM
A Table

From the diary
of John Baez:

September 22, 2006

… Meanwhile, the mystics beckon:

Out beyond ideas of wrongdoing and rightdoing, there is a field. I’ll meet you there. – Rumi

September 23, 2006

I’m going up to San Rafael (near the Bay in Northern California) to visit my college pal Bruce Smith and his family. I’ll be back on Wednesday the 27th, just in time to start teaching the next day.

A check on the Rumi quote yields
this, on a culinary organization:

“Out beyond rightdoing and wrongdoing there is a field.  I’ll meet you there.”

This is the starting place of good spirit for relationship healing and building prescribed centuries ago in the Middle East by Muslim Sufi teacher and mystic, Jelaluddin Rumi (1207-1273).

Even earlier, the Psalmists knew such a meeting place of adversaries was needed, sacred and blessed:

“Thou preparest a table before me in the presence of mine enemies….” (23rd Psalm)

A Field and a Table:

The image “http://www.log24.com/theory/GF8-Table.gif” cannot be displayed, because it contains errors.

From “Communications Toolbox”
at MathWorks.com

For more on this field
in a different context, see
Generating the Octad Generator
and
“Putting Descartes Before Dehors”
in my own diary for December 2003.

The image “http://www.log24.com/log/pix06A/060928-Descartes.jpg” cannot be displayed, because it contains errors.
Descartes



Après l’Office à l’Église
de la Sainte-Trinité, Noël 1890

(After the Service at Holy Trinity Church,
Christmas 1890), Jean Béraud

Let us pray to the Holy Trinity that
San Rafael guides the teaching of John Baez
this year.  For related material on theology
and the presence of enemies, see Log24 on
  the (former) Feast of San Rafael, 2003.

Monday, August 14, 2006

Monday August 14, 2006

Filed under: General — m759 @ 3:17 AM
Cleavage Term

“… a point of common understanding between the classic and romantic worlds. Quality, the cleavage term between hip and square, seemed to be it. Both worlds used the term. Both knew what it was. It was just that the romantic left it alone and appreciated it for what it was and the classic tried to turn it into a set of intellectual building blocks for other purposes.”

For such building blocks, see

A Trinity for Rebecca

(4/25/06)

and yesterday’s lottery
in Pennsylvania:
mid-day 713, evening 526.
These numbers prompt the
following meditation
on the square and the hip:

In memory of
Kermit Hall,
college president,
who died Sunday,
August 13, 2006:

Square
7/13:
Carpe Diem

The image “http://www.log24.com/log/pix06A/060814-WenzhouHall.jpg” cannot be displayed, because it contains errors.
President Hall
(SUNY Albany)
meets with
Wenzhou University*
delegation, 4/25/06.

In memory of
Duke Jordan,
jazz pianist,
who died Tuesday,
August 8, 2006:

Hip
5/26:
A Living Church

The image “http://www.log24.com/log/pix06A/060814-52ndSt.jpg” cannot be displayed, because it contains errors.
Jazz clubs
on 52nd Street
on a summer night
in 1948, pictured in
Log24 on 4/25/06.

  Square and hip may each have a place
in heaven; for a less pleasant destination,
see the previous entry.
__________________________________

* Update of 3 PM 8/14/06:

See Forrest Gump on God
in an Aug. 11 entry and
the related paper

Renegotiating Chinese Identity:
Between Local Group
and National Ideology,

by Kristen Parris:

Center and Locality in China

The Roots of Group Identity in Wenzhou

Wenzhou as a Negative Identity

The Wenzhou Model as a Positive Identity

The New Wenzhou Narrative

Wenzhou Identity and Emergent Class Interests

Conclusion: Local Group Identity and National Transformation.

The paper is found in
The Power of Identity:
Politics in a New Key
,
by Kenneth Hoover et al.,
Chatham House, 1997.

Related material
may be found
by a search on
“the Wenzhou model.”

Wednesday, July 26, 2006

Wednesday July 26, 2006

Filed under: General — m759 @ 4:00 AM

Jung’s Birthday, 4 AM:

Jung on the Trinity
and Quaternity

Wednesday July 26, 2006

Filed under: General — m759 @ 3:00 AM

Jung’s Birthday, 3 AM:

The Shape of God:
Deepening the Mystery
of the Trinity

Thursday, July 6, 2006

Thursday July 6, 2006

Filed under: General — m759 @ 12:25 PM

State and Church

Today’s birthdays:

George W. Bush and
Sylvester Stallone, born on
the same day 60 years ago.

Two birthday quotations from Kathleen Parker:

“Verily, I say unto you – Whatever.”

“No, wait, how about this: ‘Yo, Christ Buddy!‘”

Orlando Sentinel
   column written for release July 1, 2006

Parker’s column, on recent Presbyterian interpretations of the Holy Trinity, is titled

“I believe in Larry, Moe, and Curly Joe.”


What about Shemp?

Wednesday, May 24, 2006

Wednesday May 24, 2006

Filed under: General — m759 @ 3:00 PM
May 24
 

Related material:

Canonization,

Trinity and Counterpoint

Tuesday, April 25, 2006

Tuesday April 25, 2006

Filed under: General — m759 @ 7:35 AM
A Trinity
for Rebecca

(For Rebecca Goldstein of Trinity College)

The image “http://www.log24.com/log/pix06/060425-Trinity.gif” cannot be displayed, because it contains errors.

Sources: today's New York Times
and the five Log24 entries ending
on the morning of April 7, 2006:

ART WARS
in Poetry Month

Of what use the above trinity
might be to Rebecca, I am unsure.

I find it helpful in traveling back to
a summer night on 52nd St. in 1948

Jazz clubs on 52nd St. in 1948

Wednesday, April 5, 2006

Wednesday April 5, 2006

Filed under: General — m759 @ 3:00 PM
April is Poetry Month
and
Mathematics Awareness Month.

Three

Joni Mitchell
on the Trinity:

He is three
One’s in the middle unmoved
Waiting
To show what he sees
To the other two

Related material:

Perichoresis, or Coinherence,

Is Nothing Sacred?, and

A Contrapuntal Theme.

Wednesday, August 24, 2005

Wednesday August 24, 2005

Filed under: General — m759 @ 12:00 AM

High Concept, continued:

“In the beginning there was nothing.
 And God said, ‘Let there be light!’
 And there was still nothing,
 but now you could see it.

— Jim Holt, Big-Bang Theology,
    Slate‘s “High Concept” department

Related material:

  1. On the phrase “verbum mentis”
  2. From Satan’s Rhetoric, by Armando Maggi
    (University of Chicago Press, 2001):
Page 110:

“In chapter I I explained that devils first and foremost exist as semioticians of the world’s signs.  Devils solely live in their interpretations, in their destructive syllogisms.  As Visconti puts it, devils speak the idiom of the mind.37  …. The exorcist’s healing voice states that Satan has always been absent from the world, that his disturbing and unclear manifestations in the possessed person’s physicality are really nonexistent occurrences, nothing but disturbances of the mind, since evil itself is a lack of being.”   

Footnote 37, page 110:

“It is necessary to distinguish the devils’ ‘language of the mind’ and Augustine’s verbum mentis (word of the mind), as he theorizes it first of all in On the Trinity (book 15).  The devils’ language of the mind disturbs the subject’s internal and preverbal discourse.”

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