Journal Archives of
Steven H. Cullinane
Music for Pegasus  


This is the old site for journal archives of Steven H. Cullinane. The new site, which may not be as complete for a while, is at m759.net/wordpress/. The most recent entries in this archive (which ended on Oct. 18, 2009) may be found at right or here or here.


2009 Aug 01-15

2009 Jul 16-31

2009 Jul 01-15

2009 Jun 16-30

2009 Jun 01-15

2009 May 16-31

2009 May 01-15

2009 Apr 16-30

2009 Apr 01-15

2009 Mar 16-31

2009 Mar 01-15

2009 Feb 16-28

2009 Feb 01-15

2009 Jan 16-31

2009 Jan 01-15


2008 Dec 16-31

2008 Dec 01-15

2008 Nov 01-30

2008 Oct 01-31

2008 Sep 01-30

2008 Aug 16-31

2008 Aug 01-15

2008 Jul 16-31

2008 Jul 01-15

2008 Jun 16-30

2008 Jun 01-15

2008 May 16-31

2008 May 01-15

2008 Apr 16-30

2008 Apr 01-15

2008 Mar 01-31

2008 Feb 16-29

2008 Feb 01-15

2008 Jan 01-31


2007 Dec 01-31

2007 Nov 01-30

2007 Oct 16-31

2007 Oct 01-15

2007 Sep 16-30

2007 Sep 01-15

2007 Aug 16-31

2007 Aug 01-15

2007 Jul 16-31

2007 Jul 01-15

2007 Jun 16-30

2007 Jun 01-15

2007 May 16-31

2007 May 01-15

2007 Apr 16-30

2007 Apr 01-15

2007 Mar 16-31

2007 Mar 01-15

2007 Feb 16-28

2007 Feb 01-15

2007 Jan 16-31

2007 Jan 01-15


2006 Dec 16-31

2006 Dec 01-15

2006 Nov 16-30

2006 Nov 01-15

2006 Oct 16-31

2006 Oct 01-15

2006 Sep 16-30

2006 Sep 01-15

2006 Aug 16-31

2006 Aug 01-15

2006 Jul 16-31

2006 Jul 01-15

2006 Jun 16-30

2006 Jun 01-15

2006 May 01-31

2006 Apr 16-30

2006 Apr 01-15

2006 Mar 16-31

2006 Mar 01-15

2006 Feb 16-28

2006 Feb 01-15

2006 Jan 16-31

2006 Jan 01-15


2005 Dec 16-31

2005 Dec 01-15

2005 Nov 16-30

2005 Nov 01-15

2005 Oct 01-31

2005 Sep 01-30

2005 Aug 16-31

2005 Aug 1-15

2005 Jul 16-31

2005 Jul 1-15

2005 Jun 16-30

2005 Jun 10-15

2005 Jun 1-9

2005 May 16-31

2005 May 1-15

2005 Apr 16-30

2005 Apr 1-15

2005 Mar 1-31

2005 Feb 1-28

2005 Jan 1-31


2004 Dec 1-31

2004 Nov 1-30

2004 Oct 16-31

2004 Oct 1-15

2004 Sep 16-30

2004 Sep 1-15

2004 Aug 16-31

2004 Aug 1-15

2004 Jul 16-31

2004 Jul 1-15

2004 Jun 17-30

2004 Jun 01-16

2004 May 16-31

2004 May 01-15

2004 Apr 16-30

2004 Apr 01-15

2004 Mar 16-31

2004 Mar 01-15

2004 Feb 16-28

2004 Feb 01-15

2004 Jan 16-31

2004 Jan 01-15


2003 Dec 16-31

2003 Dec 01-15

2003 Nov 16-30

2003 Nov 01-15

2003 Oct 16-31

2003 Oct 01-15

2003 Sep 16-30

2003 Sep 01-15

2003 Aug 16-31

2003 Aug 08-15

2003 Aug 01-07

2003 Jul 24-31

2003 Jul 16-23

2003 Jul 01-15

2003 Jun 16-30

2003 Jun 01-15

2003 May 16-31

2003 May 01-15

2003 Apr 16-30

2003 Apr 01-15

2003 Mar 16-31

2003 Mar 01-15

2003 Feb 16-28

2003 Feb 01-15

2003 Jan 16-31

2003 Jan 08-15

2003 Jan 01-07


2002 Dec 16-31

2002 Dec 01-15

2002 Nov 16-30

2002 Nov 01-15

2002 Oct 16-31

2002 Oct 01-15

2002 Sep 16-30

2002 Sep 01-15

2002 Aug 16-31

2002 Aug 01-15

2002 Jul 16-31

June-July 2002

June 2002

Related Sites

Three Days
of the
Saint, 2002

Santa vs.
the Volcano

Satori at
Pearl Harbor

of Eternity

Some may feel that the Saint in question is Philip Berrigan, who joined Saburo Ienaga and Ivan Illich on Dec. 6, 2002.

Others may feel that the Saint is Don Ameche, who died on Dec. 6, 1993.

"Things change."

-- SHC 12/9/02


Stan Rice died on Dec. 9, 2002. A poem of his tells what happened next.

Eight is a Gate

Hollywood producer dies Dec. 14, meets Bach at Heaven's Gate. Realistic comedy.

The Diamond Project

Notes on dance, mortality, and "the still point" on the date of Irene Diamond's death.

Immortal Diamond,
NASA Meets Jesus

Thoughts on John O'Hara and G. M. Hopkins for James Joyce's birthday.

Blackbird Singing

The Fred Rogers memorial koan.

Art Wars

LeWitt vs. Witt

Stone, not Wood

best describes St. Peter

The Word

in the Desert

O'Hara's Crucifixion

Art Wars:

Fahne Hoch


Thorny Crown

Unity and Reciprocity

in mathematics

The Quality of Diamond

Da Vinci Code ,

Crimson Passion,

Cubist Crucifixion.

Truth and Style

The Line

Bush Mutiny

Symmetry and Change

A Shot at Redemption

Mathematics and Narrative

The Judas Seat

My other sites



The Diamond 16 Puzzle

Notes on Finite Geometry

The Diamond Theorem

The Geometry of Qubits

Diamond Theory

Diamond Theory
in 1937

Galois Geometry

A Four-Color Theorem

Latin-Square Geometry

Walsh Functions

The Fano Plane Revisualized



The Diamond Theory of Truth

Logos and Logic

Puzzle Notes

A Mathematician's Aesthetics

Reflection Groups in Finite Geometry

A Reflection Group of Order 168

Reflection Groups: The Missing Link

Geometry of
the I Ching

The Diamond Archetype

Modal Theology

The Eightfold Way and Solomon's Seal

Crystal and Dragon in Diamond Theory

Poetry's Bones

Time Fold

War of Ideas

The Proof
and the Lie

to Langlands

Symmetry Groups

Block Designs

Finite Relativity

Cognitive Blending

Geometry of the 4x4 Square

Visualizing GL(2,p)

Pattern Groups

Ideas and Art

Jung's Imago

Theme and Variations

The Geometry of Logic

Space-Time and a Finite Model

Quilt Geometry

Duality and Symmetry

Polster on Pictures


The Dharwadker Files

Certified Crank

Favorite Books

The Practical Cogitator


The Reader Over Your Shoulder

The Oxford Book of English Prose

Fancies and Goodnights

Other Online Commonplace Books

David Lavery

Peter J. Cameron

A. M. Kuchling

Constant Reader

Identity Theory

J. Jacobs

M. Magnus


Sites I Read:

Bloglines list

Some Recent Entries

(These may not be the most recent entries. If there are more recent entries, they may be found here or here.)

Monday, August 31, 2009  5:24 PM

Annals of Religion:

Ask a Stupid Question

continued from   
last Wednesday...

 Log24 on August 26--

"Did you see more glass?"


Wednesday, August 26,
was the date of death
for Hyman Bloom.

Bloom, described in
today's New York Times
as "a painter of the
 mystical," died at 96.

Bloom often painted portraits of imaginary rabbis; an article titled "American Mystic" describes
"... the mesmerizing paradox at the heart of the rabbi portraits-- they remember keepers of a tradition in a method that tradition expressly forbids. As Bloom explains, age and illness endowing his voice with a hoarse, prophetic quality, 'Jewish culture has nothing to do with painting. That’s a rule, "Thou shalt not make an image of anything in the air or on the earth."'"

-- Stephen Vider, Tablet Magazine, February 28. 2007

Related material:

An entry in this journal linked to twice on the date of Bloom's death--

Art and Man at Yale--

and an illustrated entry from this journal on the date of the "Mystic" article--

Elements of Geometry

"So, there is one place
where modernism triumphs.
As in the cases of the pyramids
and the Taj Mahal, the Siegfried line
 and the Atlantic wall, death always
 calls on the very best architects."

-- J. G. Ballard,
"A Handful of Dust"

Monday, August 31, 2009  10:00 AM

Black Rock song:

A Crown for Varnedoe

Oh, and while the King
    was looking down
The Jester stole
   his thorny crown....

-- Don McLean

Sunday, August 30, 2009  6:29 PM

Annals of Aesthetics:

by Doctorow

"And crown thy good
  with brotherhood...."

Farewell Aug. 29, 2009, to Sen. Edward Kennedy on Capitol steps

Click image to enlarge.

according to Doctorow:

The Collyer Brothers
Meet Flower Power

 Related material --

Blame It On Toby:

Toby Ziegler of 'West Wing'

Sunday, August 30, 2009  9:00 AM

Today's Theology:

Sunday, August 30, 2009  8:07 AM

In the Details:

"'Soul' of a Party
   Is Memorialized"

-- NY Times online
front page, 7:37 AM

Personally, I prefer
 the life of the party:

"Oh, children,
 catch me if you can!"

-- Aslan in
 The Chronicles of Narnia

"We haven't had
    that spirit here since..."

-- Hotel California 

   Click to enlarge --

NY Times online 8/30/09: 'Catch Me If You Can'

Sunday, August 30, 2009  7:00 AM

Today's Sermon:

Working Backward

Continued from
December 10, 2005:

"Death itself would start
  working backward."

-- Aslan in  
 The Chronicles of Narnia

Saturday, August 29, 2009  8:00 PM

For the Senator:

Continued from
Father's Day
  last year--

Shoe cartoon, detail, Sunday, June 15, 2008

I Ching hexagram 48, The Well

"For further details,
 click on the well."

From the above link:

James Hillman --

"The kind of movement Olson urges is
 an inward deepening of the image,
an in-sighting of the superimposed
 levels of significance within it.
This is the very mode that Jung
suggested for grasping dreams--
 not as a sequence in time,
but as revolving around
 a nodal complex."

And from Feb. 29, 2008:


and the following day:

Heraclitus: '...so deep is its logos'

-- Heraclitus

Saturday, August 29, 2009  9:29 AM


Ba Gua = 8 Sections.
Gua Ba = Section 8.

Friday, August 28, 2009  3:09 AM

Annals of Religion:

Rites of Passage

"Things fall apart;
   the centre cannot hold...."

Part I:

"Inside the church, the grief was real. Sen. Edward Kennedy's voice caught as he read his lovely eulogy, and when he was done, Caroline Kennedy Schlossberg stood up and hugged him. She bravely read from Shakespeare's 'The Tempest' ('Our revels now are ended. We are such stuff as dreams are made on'). Many of the 315 mourners, family and friends of the Kennedys and Bessettes, swallowed hard through a gospel choir's rendition of 'Amazing Grace,' and afterward, they sang lustily as Uncle Teddy led the old Irish songs at the wake."

-- Newsweek magazine, issue dated August 2, 1999

Part II:

The Ba gua (Chinese....) are eight diagrams used in Taoist cosmology to represent a range of interrelated concepts. Each consists of three lines, each either 'broken' or 'unbroken,' representing a yin line or a yang line, respectively. Due to their tripartite structure, they are often referred to as 'trigrams' in English. --Wikipedia

Part III:

3x3 array of symbols, cover of 'Dorm Room Feng Shui'

Above: detail from the cover of...
Bagua in Brief, from 'Dorm Room Feng Shui'
Figures explaining 'Dorm Room Feng Shui'

Thursday, August 27, 2009  3:09 PM

Annals of Philosophy:

The Shining
of Lucero

For John Cramer's
daughter Kathryn

(continued from
September 24, 2002)

"Mathematical relationships were
enough to satisfy him, mere formal
relationships which existed at
all times, everywhere, at once."

-- Broken Symmetries, 1983




See also Art Wars at
The New Criterion

(Jan. 19, 2007) and the
 four entries preceding it.

Wednesday, August 26, 2009  5:01 PM

Ask a Stupid Question, continued:

Wednesday, August 26, 2009  9:00 AM

New England Requiem:

A Puritan Settlement
in memory of
Sen. Edward Kennedy

"When New Haven was founded, the city was laid out into a grid of nine squares surrounded by a great wilderness.
    Last year [2000] History of Art Professor Emeritus Vincent Scully said the original town plan reflected a feeling that the new city should be sacred.
    Scully said the colony's founders thought of their new Puritan settlement as a 'nine-square paradise on Earth, heaven on earth, New Haven, New Jerusalem.'"

Yale Daily News, Jan. 11, 2001

"Real and unreal are two in one:
    New Haven
 Before and after one arrives...."

 -- Wallace Stevens,
    "An Ordinary Evening
     in New Haven," XXVIII

See also Art and Man at Yale.

Tuesday, August 25, 2009  12:00 PM

Geometry Lesson:

(continued from
  January 10th)

Equilateral triangle, each side's length equal to the square root of two

"Boo, boo, boo,
  square root of two.

Sunday, August 23, 2009  11:00 AM


Inside NY Times 8/23/09-- images of Brooklyn Bridge, poets Frost and Stevens

Click on image for further details.

Saturday, August 22, 2009  9:48 AM

Philosophy and Religion:

Thursday, August 20, 2009  4:00 PM

Annals of Philosophy:


From David Lavery's weblog today--

Kierkegaard on Sophists:
"If the natural sciences had been developed in Socrates' day as they are now, all the sophists would have been scientists. One would have hung a microscope outside his shop in order to attract customers, and then would have had a sign painted saying: Learn and see through a giant microscope how a man thinks (and on reading the advertisement Socrates would have said: that is how men who do not think behave)."

-- Søren Kierkegaard, Journals, edited and translated by Alexander Dru
To anyone familiar with Pirsig's classic Zen and the Art of Motorcycle Maintenance, the above remarks of Kierkegaard ring false. Actually, the sophists as described by Pirsig are not at all like scientists, but rather like relativist purveyors of postmodern literary "theory." According to Pirsig, the scientists are like Plato (and hence Socrates)-- defenders of objective truth.

Pirsig on Sophists:

"The pre-Socratic philosophers mentioned so far all sought to establish a universal Immortal Principle in the external world they found around them. Their common effort united them into a group that may be called Cosmologists. They all agreed that such a principle existed but their disagreements as to what it was seemed irresolvable. The followers of Heraclitus insisted the Immortal Principle was change and motion. But Parmenides’ disciple, Zeno, proved through a series of paradoxes that any perception of motion and change is illusory. Reality had to be motionless.

The resolution of the arguments of the Cosmologists came from a new direction entirely, from a group Phædrus seemed to feel were early humanists. They were teachers, but what they sought to teach was not principles, but beliefs of men. Their object was not any single absolute truth, but the improvement of men. All principles, all truths, are relative, they said. 'Man is the measure of all things.' These were the famous teachers of 'wisdom,' the Sophists of ancient Greece.

To Phaedrus, this backlight from the conflict between the Sophists and the Cosmologists adds an entirely new dimension to the Dialogues of Plato. Socrates is not just expounding noble ideas in a vacuum. He is in the middle of a war between those who think truth is absolute and those who think truth is relative. He is fighting that war with everything he has. The Sophists are the enemy.

Now Plato's hatred of the Sophists makes sense. He and Socrates are defending the Immortal Principle of the Cosmologists against what they consider to be the decadence of the Sophists. Truth. Knowledge. That which is independent of what anyone thinks about it. The ideal that Socrates died for. The ideal that Greece alone possesses for the first time in the history of the world. It is still a very fragile thing. It can disappear completely. Plato abhors and damns the Sophists without restraint, not because they are low and immoral people... there are obviously much lower and more immoral people in Greece he completely ignores. He damns them because they threaten mankind's first beginning grasp of the idea of truth. That's what it is all about.

The results of Socrates' martyrdom and Plato's unexcelled prose that followed are nothing less than the whole world of Western man as we know it. If the idea of truth had been allowed to perish unrediscovered by the Renaissance it's unlikely that we would be much beyond the level of prehistoric man today. The ideas of science and technology and other systematically organized efforts of man are dead-centered on it. It is the nucleus of it all.

And yet, Phaedrus understands, what he is saying about Quality is somehow opposed to all this. It seems to agree much more closely with the Sophists."

I agree with Plato's (and Rebecca Goldstein's) contempt for relativists. Yet Pirsig makes a very important point. It is not the scientists but rather the storytellers (not, mind you, the literary theorists) who sometimes seem to embody Quality.

As for hanging a sign outside the shop, I suggest (particularly to New Zealand's Cullinane College) that either or both of the following pictures would be more suggestive of Quality than a microscope:

Alfred Bester covers showing 'primordial protomatter' (altered here) from 'Stars' and Rogue Winter from 'Deceivers'

For the "primordial protomatter"
in the picture at left, see
The Diamond Archetype.

Wednesday, August 19, 2009  7:00 PM

Annals of Mathematics continued:

From Visualizing GL(2,p)
to Visualizing GL(2,Z)

A note from 1985 leads,
via today's earlier entry,
to an article from 1993:

Visualizing Toral Automorphisms-- The opening paragraphs
See also
 Arnold's Cat Map.

Wednesday, August 19, 2009  10:30 AM

Annals of Mathematics:

Group Actions, 1984-2009

From a 1984 book review:

"After three decades of intensive research by hundreds of group theorists, the century old problem of the classification of the finite simple groups has been solved and the whole field has been drastically changed. A few years ago the one focus of attention was the program for the classification; now there are many active areas including the study of the connections between groups and geometries, sporadic groups and, especially, the representation theory. A spate of books on finite groups, of different breadths and on a variety of topics, has appeared, and it is a good time for this to happen. Moreover, the classification means that the view of the subject is quite different; even the most elementary treatment of groups should be modified, as we now know that all finite groups are made up of groups which, for the most part, are imitations of Lie groups using finite fields instead of the reals and complexes. The typical example of a finite group is GL(n, q), the general linear group of n dimensions over the field with q elements. The student who is introduced to the subject with other examples is being completely misled."

-- Jonathan L. Alperin,
   review of books on group theory,
   Bulletin (New Series) of the American
   Mathematical Society
10 (1984) 121, doi:

Actions of GL(2,3) on a 3x3 coordinate-array

The same example
at Wolfram.com:

Ed Pegg Jr.'s program at Wolfram.com to display a large number of actions of small linear groups over finite fields

Caption from Wolfram.com:

"The two-dimensional space Z3×Z3 contains nine points: (0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,1), and (2,2). The 48 invertible 2×2 matrices over Z3 form the general linear group known as GL(2, 3). They act on Z3×Z3 by matrix multiplication modulo 3, permuting the nine points. More generally, GL(n, p) is the set of invertible n×n matrices over the field Zp, where p is prime. With (0, 0) shifted to the center, the matrix actions on the nine points make symmetrical patterns."

Citation data from Wolfram.com:

"GL(2,p) and GL(3,3) Acting on Points"
 from The Wolfram Demonstrations Project,
 Contributed by: Ed Pegg Jr"

As well as displaying Cullinane's 48 pictures of group actions from 1985, the Pegg program displays many, many more actions of small finite general linear groups over finite fields. It illustrates Cullinane's 1985 statement:
"Actions of GL(2,p) on a p×p coordinate-array have the same sorts of symmetries, where p is any odd prime."
Pegg's program also illustrates actions on a cubical array-- a 3×3×3 array acted on by GL(3,3). For some other actions on cubical arrays, see Cullinane's Finite Geometry of the Square and Cube.

Tuesday, August 18, 2009  12:00 PM

Angels and Demons Revisited:

Prima Materia

(Background: Art Humor: Sein Feld (March 11, 2009) and Ides of March Sermon, 2009)

From Cardinal Manning's review of Kirkman's Philosophy Without Assumptions--
"And here I must confess... that between something and nothing I can find no intermediate except potentia, which does not mean force but possibility."

-- Contemporary Review, Vol. 28 (June-November, 1876), page 1017

Cardinal Manning, Contemporary Review, Vol. 28, pages 1026-1027:
The following will be, I believe, a correct statement of the Scholastic teaching:--

1. By strict process of reason we demonstrate a First Existence, a First Cause, a First Mover; and that this Existence, Cause, and Mover is Intelligence and Power.

2. This Power is eternal, and from all eternity has been in its fullest amplitude; nothing in it is latent, dormant, or in germ: but its whole existence is in actu, that is, in actual perfection, and in complete expansion or actuality. In other words God is Actus Purus, in whose being nothing is potential, in potentia, but in Him all things potentially exist.

3. In the power of God, therefore, exists the original matter (prima materia) of all things; but that prima materia is pura potentia, a nihilo distincta, a mere potentiality or possibility; nevertheless, it is not a nothing, but a possible existence. When it is said that the prima materia of all things exists in the power of God, it does not mean that it is of the existence of God, which would involve Pantheism, but that its actual existence is possible.

4. Of things possible by the power of God, some come into actual existence, and their existence is determined by the impression of a form upon this materia prima. The form is the first act which determines the existence and the species of each, and this act is wrought by the will and power of God. By this union of form with the materia prima, the materia secunda or the materia signata is constituted.

5. This form is called forma substantialis because it determines the being of each existence, and is the root of all its properties and the cause of all its operations.

6. And yet the materia prima has no actual existence before the form is impressed. They come into existence simultaneously;

[p. 1027 begins]

as the voice and articulation, to use St. Augustine's illustration, are simultaneous in speech.

7. In all existing things there are, therefore, two principles; the one active, which is the form-- the other passive, which is the matter; but when united, they have a unity which determines the existence of the species. The form is that by which each is what it is.

8. It is the form that gives to each its unity of cohesion, its law, and its specific nature.*

When, therefore, we are asked whether matter exists or no, we answer, It is as certain that matter exists as that form exists; but all the phenomena which fall under sense prove the existence of the unity, cohesion, species, that is, of the form of each, and this is a proof that what was once in mere possibility is now in actual existence. It is, and that is both form and matter.

When we are further asked what is matter, we answer readily, It is not God, nor the substance of God; nor the presence of God arrayed in phenomena; nor the uncreated will of God veiled in a world of illusions, deluding us with shadows into the belief of substance: much less is it catter [pejorative term in the book under review], and still less is it nothing. It is a reality, the physical kind or nature of which is as unknown in its quiddity or quality as its existence is certainly known to the reason of man.

* "... its specific nature"
        (Click to enlarge) --
Footnote by Cardinal Manning on Aquinas
The Catholic physics expounded by Cardinal Manning above is the physics of Aristotle.

For a more modern treatment of these topics, see Werner Heisenberg's Physics and Philosophy. For instance:
"The probability wave of Bohr, Kramers, Slater, however, meant... a tendency for something. It was a quantitative version of the old concept of 'potentia' in Aristotelian philosophy. It introduced something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality."
Compare to Cardinal Manning's statement above:
"... between something and nothing I can find no intermediate except potentia..."
To the mathematician, the cardinal's statement suggests the set of real numbers between 1 and 0, inclusive, by which probabilities are measured. Mappings of purely physical events to this set of numbers are perhaps better described by applied mathematicians and physicists than by philosophers, theologians, or storytellers. (Cf. Voltaire's mockery of possible-worlds philosophy and, more recently, The Onion's mockery of the fictional storyteller Fournier's quantum flux. See also Mathematics and Narrative.)

Regarding events that are not purely physical-- those that have meaning for mankind, and perhaps for God-- events affecting conception, birth, life, and death-- the remarks of applied mathematicians and physicists are often ignorant and obnoxious, and very often do more harm than good. For such meaningful events, the philosophers, theologians, and storytellers are better guides. See, for instance, the works of Jung and those of his school. Meaningful events sometimes (perhaps, to God, always) exhibit striking correspondences. For the study of such correspondences, the compact topological space [0, 1] discussed above is perhaps less helpful than the finite Galois field GF(64)-- in its guise as the I Ching. Those who insist on dragging God into the picture may consult St. Augustine's Day, 2006, and Hitler's Still Point.

Monday, August 17, 2009  9:48 PM

Annals of Mathematics:

Design Theory,

"... Kirkman has established an incontestable claim to be regarded as the founding father of the theory of designs."

-- "T.P. Kirkman, Mathematician," by N.L. Biggs, Bulletin of the London Mathematical Society, Volume 13, Number 2 (March 1981), 97-120.

This paper is now available online for $12.

For more about this subject, see Design Theory, by Beth, Jungnickel, and Lenz, Cambridge U. Press, Volume I (2nd ed., 1999, 1120 pages) and Volume II (2nd ed., 2000, 513 pages).

For an apparently unrelated subject with the same name, see Graphic Design Theory: Readings from the Field, by Helen Armstrong (Princeton Architectural Press, 2009).

For what the two subjects have in common, see Block Designs in Art and Mathematics.

Monday, August 17, 2009  11:30 AM

Song for the Teasers:

Garden Prize

Teasers from today's
online New York Times:

NY Times teasers, morning of Monday, Aug. 17, 2009

High Line specialty:

"In spite of ourselves
 We'll end up a'sittin' on a rainbow
 Against all odds
 Honey, we're the big door prize"

Sunday, August 16, 2009  12:00 PM

Annals of Religion, continued:

Return to Paradise

(Title of a New Yorker
essay dated June 2, 2008)

Kenneth Bacon, an advocate for refugees, died yesterday at 64 on the Feast of the Assumption.

In his honor, we may perhaps be justified in temporarily ignoring the wise saying "never assume."

From a defense of the dogma of the Assumption:
"On another level, the Assumption epitomizes the reconciliation of the material and spiritual world, as the human Mary enters 'body and soul to heavenly glory.' Carl Jung, the transpersonal psychologist, concluded that the doctrine of the Assumption reflected an acceptance of the physical world."
For other such reconciliations, see
  • The New Yorker on Milton meeting Galileo: "Though Milton was the much younger man, in some ways his world system seems curiously older than the astronomer’s empirical universe."

  • This journal on Milton's world system: the four qualities "hot, cold, moist, and dry" and the four elements "Sea, Shore, Air, and Fire."

    But all these in thir pregnant causes mixt
    Confus'dly, and which thus must ever fight,
    Unless th' Almighty Maker them ordain
    His dark materials to create more Worlds....

  • This journal's "For Galois on Bastille Day" reconciles, if only in a literary way, physical and non-physical worlds. The work of Evariste Galois allows us to depict an analogue of Milton's (and Philip Pullman's) physical world of dark materials within the purely mathematical world of finite groups. (For a less literary connection between physical and mathematical worlds, see this journal on Bastille Eve.)

Sunday, August 16, 2009  11:29 AM

Annals of Philosophy, continued:


In memory of
Kenneth H. Bacon, dead at 64
on August 15th, 2009.

Bacon was an advocate for refugees.
"Even blue-blooded WASPs were refugees at one time; mine came over from England in 1630, fleeing debts for all I know," he said.

-- Today's New York Times
The Expulsion from Eden

Click cover to enlarge

Milton by Sorel

Click for details.

Bacon turned 64
last year on November 21.

Log24 on that date:

From a story in the November 21
 Chronicle of Higher Education
on a recent St. Olaf College
reading of Paradise Lost:

"Of man's first disobedience,
     and the fruit
Of that forbidden tree,
     whose mortal taste
Brought death into the World,
     and all our woe....

A red apple made the rounds,
each reader tempting the next."

"Do you like apples?"
-- Good Will Hunting    

Saturday, August 15, 2009  1:00 PM

Annals of Philosophy--

For St. Willard
Van Orman Quine

 " ... to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint"
-- Four Quartets

Quine receives
Kyoto Prize

The Timeless:


(64 years,
  and more):

Today in History

Today is Saturday, Aug. 15, the 227th day of 2009. There are 138 days left in the year.

Today's Highlight in History:

On Aug. 15, 1945, Japanese Emperor Hirohito announced to his subjects in a prerecorded radio address that Japan had accepted terms of surrender for ending World War II.

On this date:

In 1057, Macbeth, King of Scots, was killed in battle by Malcolm, the eldest son of King Duncan, whom Macbeth had slain.

"Life's but a walking shadow, a poor player
That struts and frets his hour upon the stage
And then is heard no more: it is a tale
Told by an idiot, full of sound and fury,
Signifying nothing."
"I really have nothing to add."
-- Quine, quoted
on this date in 1998.

Saturday, August 15, 2009  11:09 AM

Annals of Religion--

An Honest Question:

"Did the Catholic Church just jump the shark by electing Cardinal Joseph Ratzinger? This is an honest question... not a slam."

-- Anonymous user at an online forum on April 19, 2005

A Munificent Answer:

No. That leap of faith was taken long before, on November 1, 1950. See the note below.

Catholic Encyclopedia:
"The Feast of the Assumption of the Blessed Virgin Mary, 15 August....

...has a double object: (1) the happy departure of Mary from this life; (2) the assumption of her body into heaven. It is the principal feast of the Blessed Virgin....

Note: By promulgating the Bull Munificentissimus Deus, 1 November, 1950, Pope Pius XII declared infallibly that the Assumption of the Blessed Virgin Mary was a dogma of the Catholic Faith."
Also on today's date (AP, Today in History)--
"In 1998, 29 people were killed by a car bomb that tore apart the center of Omagh, Northern Ireland; a splinter group calling itself the Real IRA claimed responsibility."
On the same day in 1998, The New York Times published Sarah Boxer's century-end summary:

Page created Aug. 11, 2003.