Wednesday, May 28, 2003

Wednesday May 28, 2003

Filed under: General,Geometry — Tags: — m759 @ 5:55 AM

Mental Health Month, Day 28:

The Eightfold Way and
Solomon's Seal

For a continuation of the mathematical and religious themes in yesterday's entry, click on the figure below.


Tuesday, May 27, 2003

Tuesday May 27, 2003

Filed under: General,Geometry — Tags: — m759 @ 5:01 AM

Mental Health Month, Day 27:

Conspiracy Theory and
Solomon's Seal

In our journey through Mental Health Month, we have now arrived at day 27. This number, the number of lines on a non-singular cubic surface in complex projective 3-space, suggests it may be time to recall the following note (a sort of syllabus for an imaginary course) from August 1997, the month that the Mel Gibson film "Conspiracy Theory" was released.

Conspiracy Theory 101
August 13, 1997


(A) Masks of the Illuminati, by Robert Anton Wilson, Pocket Books, New York, 1981.  Freemasonry meets The Force (starring James Joyce and Albert Einstein).
(B) The Number of the Beast, by Robert A. Heinlein, Ballantine Books, New York, 1980.  "Pantheistic multiple solipsism" and transformation groups in n-dimensional space combine to yield "the ultimate total philosophy." (p. 438). 
(C) The Essential Blake, edited by Stanley Kunitz, MJF Books, New York, 1987.  "Fearful symmetry" in context.


(1) The Cosmic Trigger, by Robert Anton Wilson, Falcon Press, Phoenix, 1986 (first published 1977).  Page 245 reveals that "the most comprehensive conspiracy theory," that of the physicist Sir Arthur Eddington, is remarkably similar to Heinlein's theory in (B) above.
(2) The Development of Mathematics, by E. T. Bell, 2nd. ed., McGraw-Hill, New York, 1945.  See the discussion of "Solomon's seal," a geometric configuration in complex projective 3-space.  This is as good a candidate as any for Wilson's "Holy Guardian Angel" in (A) above.
(3) Finite Projective Spaces of Three Dimensions, by J. W. P. Hirschfeld, Clarendon Press, Oxford, 1985.  Chapter 20 shows how to represent Solomon's seal in the 63-point 5-dimensional projective space over the 2-element field.  (The corresponding 6-dimensional affine space, with 64 points, is reminiscent of Heinlein's 6-dimensional space.)

See also China's 3,000-year-old "Book of Transformations," the I Ching, for more philosophy and lore of the affine 6-dimensional space over the binary field.

© 1997 S. H. Cullinane 

For a more up-to-date and detailed look at the mathematics mentioned above, see

Abstract Configurations
in Algebraic Geometry

by Igor Dolgachev.

"Art isn't easy." — Stephen Sondheim

Monday, May 26, 2003

Monday May 26, 2003

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

Mental Health Month, Day 26:

Many Dimensions,

Part III — Why 26?

At first blush, it seems unlikely that the number 26=2×13, as a product of only two small primes (and those distinct) has any purely mathematical properties of interest. (On the other hand, consider the number 6.)  Parts I and II of “Many Dimensions,” notes written earlier today, deal with the struggles of string theorists to justify their contention that a space of 26 dimensions may have some significance in physics.  Let them struggle.  My question is whether there are any interesting purely mathematical properties of 26, and it turns out, surprisingly, that there are some such properties. All this is a longwinded way of introducing a link to the web page titled “Info on M13,” which gives details of a 1997 paper by J. H. Conway*.

Info on M13

“Conway describes the beautiful construction of a discrete mathematical structure which he calls ‘M13.’  This structure is a set of 1,235,520 permutations of 13 letters. It is not a group. However, this structure represents the answer to the following group theoretic question:

Why do the simple groups M12 and L3(3) share some subgroup structure?

In fact, both the Mathieu group M12 and the automorphism group L3(3) of the projective plane PG(2,3) over GF(3) can be found as subsets of M13.  In addition, M13 is 6-fold transitive, in the sense that it contains enough permutations to map any two 6-tuples made from the thirteen letters into each other.  In this sense, M13 could pass as a parent for both M12 and L3(3).  As it is known from the classification of primitive groups that there is no finite group which qualifies as a parent in this sense.  Yet, M13 comes close to being a group.

To understand the definition of M13 let us have a look at the projective geometry PG(2,3)….

The points and the lines and the “is-contained-in” relation form an incidence structure over PG(2,3)….

…the 26 objects of the incidence structure [are] 13 points and 13 lines.”

Conway’s construction involves the arrangement, in a circular Levi graph, of 26 marks representing these points and lines, and chords representing the “contains/is contained in” relation.  The resulting diagram has a pleasingly symmetric appearance.

For further information on the geometry of the number 26, one can look up all primitive permutation groups of degree 26.  Conway’s work suggests we look at sets (not just groups) of permutations on n elements.  He has shown that this is a fruitful approach for n=13.  Whether it may also be fruitful for n=26, I do not know.

There is no obvious connection to physics, although the physics writer John Baez quoted in my previous two entries shares Conway’s interest in the Mathieu groups. 

 * J. H. Conway, “M13,” in Surveys in Combinatorics, 1997, edited by R. A. Bailey, London Mathematical Society Lecture Note Series, 241, Cambridge University Press, Cambridge, 1997. 338 pp. ISBN 0 521 59840 0.

Monday May 26, 2003

Filed under: General,Geometry — m759 @ 4:25 AM

Mental Health Month, Day 26:

Many Dimensions,
Part II
— The Blue Matrix 

But seriously…

John Baez in July 1999:

"…it's really the fact that the Leech lattice is 24-dimensional that lets us compactify 26-dimensional spacetime in such a way as to get a bosonic string theory with the Monster group as symmetries."

Well, maybe.  I certainly hope so.  If the Leech lattice and the Monster group turn out to have some significance in theoretical physics, then my own work, which deals with symmetries of substructures of the Leech lattice and the Monster, might be viewed in a different light.  Meanwhile, I take (cold) comfort from some writers who pursue the "story" theory of truth, as opposed to the "diamond" theory.  See the following from my journal:

Evariste Galois and the Rock that Changed Things, and

A Time to Gather Stones Together: Readings for Yom Kippur.

See, too, this web page on Marion Zimmer Bradley's fictional

Matrices, or Blue Star-Stones, and

the purely mathematical site Diamond Theory, which deals with properties of the above "blue matrix" and its larger relatives.

Monday May 26, 2003

Filed under: General — m759 @ 3:14 AM

Mental Health Month, Day 26:

Many Dimensions

John Baez on why bosonic string theory is said to require 26 dimensions —

“By now, if you’re a rigorous sort of pure mathematician, you must be suffering from grave doubts about the sanity of this whole procedure.”

Doubts?  Let us just say I prefer

G-string theory:

“The G-string is unique in that it combines the properties of all known string theories. It has 26-dimensional modes propagating to the left, 10-dimensional modes propagating to the right, and 2-dimensional modes just sitting around wondering what the hell is going on.”

Sunday, May 25, 2003

Sunday May 25, 2003

Filed under: General,Geometry — m759 @ 9:26 PM

opened on this date in 1977.

From the web page Amande:

Le Christ et la Vierge apparurent souvent entourés d’une auréole en forme d’amande: la mandorle.

Étymologiquement, le mot amande est une altération de amandala, qui dérive lui-même du latin classique amygdala….

L’amande a… une connotation symbolique, celle du sexe féminin. Elle figure souvent la vulve. Elle est alors en analogie avec la yoni du vocabulaire de l’hindouisme, la vulve ou la matrice, représentée par une amande ou une noix coupée en deux.

Screenshot of the online
New York Times, May 25, 2003:

Ariel the Hutt and Princess Amygdala

Introduction to Yantra

by Horia Cristescu and
Dan Bozaru 

The Triangle (TRIKONA)
The triangle (TRIKONA) is the symbol of
SHAKTI , the feminine energy or aspect of Creation. The triangle pointing down represents the YONI , the feminine sexual organ and the symbol of the supreme source of the Universe, and when the triangle is pointing upwards it signifies intense spiritual aspiration, the sublimation of one’s nature into the most subtle planes and the element of fire (AGNI TATTVA). The fire is always oriented upwards, thus the correlation with the upward triangle – SHIVA KONA. On the other hand, the downward pointing triangle signifies the element of water which always tends to flown and occupy the lowest possible position. This triangle is known as SHAKTI KONA.

The intersection of two geometric forms (lines, triangles, circles, etc.) represents forces that are even more intense than those generated by the simple forms. Such an interpenetration indicates a high level in the dynamic interaction of the correspondent energies. The empty spaces generated by such combinations are described as very efficient operational fields of the forces emanating from the central point of the YANTRA. That is why we can very often encounter representations of MANTRAS in such spaces. YANTRA and MANTRA are complementary aspects of SHIVA and their use together is much more efficient than the use of one alone.

The Six Points Star (SHATKONA)
A typical combination often found in the graphical structure of a YANTRA is the superposition of two triangles, one pointing upwards and the other downwards, forming a star with six points (SHATKONA), also known as David’s Star. This form symbolically represents the union of
PURUSHA and PRAKRITI or SHIVA-SHAKTI, without which there could be no Creation.


Sunday May 25, 2003

Filed under: General,Geometry — Tags: — m759 @ 7:11 PM


Mental Health Month, Day 25:

Matrix of the Death God

Having dealt yesterday with the Death Goddess Sarah, we turn today to the Death God Abraham.  (See Jacques Derrida, The Gift of Death, University of Chicago Press, 1996.)  For a lengthy list of pictures of this damned homicidal lunatic about to murder his son, see The Text This Week.


See, too, The Matrix of Abraham, illustrated below.  This is taken from a book by R. M. Abraham, Diversions and Pastimes, published by Constable and Company, London, in 1933.

The Matrix of Abraham

A summary of the religious import of the above from Princeton University Press:

“Moslems of the Middle Ages were fascinated by pandiagonal squares with 1 in the center…. The Moslems thought of the central 1 as being symbolic of the unity of Allah.  Indeed, they were so awed by that symbol that they often left blank the central cell on which the 1 should be positioned.”

— Clifford A. Pickover, The Zen of Magic Squares, Circles, and Stars, Princeton U. Press, 2002, pp. 71-72

Other appearances of this religious icon on the Web:

On Linguistic Creation

Picasso’s Birthday

A less religious approach to the icon may be found on page 393 of R. D. Carmichael’s Introduction to the Theory of Groups of Finite Order (Ginn, Boston, 1937, reprinted by Dover, 1956).

This matrix did not originate with Abraham but, unlike Neo, I have not yet found its Architect.

Saturday, May 24, 2003

Saturday May 24, 2003

Filed under: General — m759 @ 1:06 AM

Mental Health Month, Day 24:

The Sacred Day of
Kali, the Dark Lady

On this day, Gypsies from all over Europe gather in Provence for the sacred day of St. Sarah, also known as Kali.

Various representations of Kali exist; there is a novel about the ways men have pictured her:

From the prologue to
The Dark Lady,

 by Mike Resnick.

She was old when the earth was young.

She stood atop Cemetery Ridge when Pickett made his charge, and she was there when the six hundred rode into the Valley of Death.  She was at Pompeii when Mount Vesuvius blew, and she was in the forests of Siberia when the comet hit.  She hunted elephant with Selous and buffalo with Cody, and she was there the night the high wire broke beneath the Flying Wallendas.  She was at the fall of Troy and the Little Bighorn, and she watched Manolete and Dominguez face the brave bulls in the bloodstained arenas of Madrid….

She has no name, no past, no present, no future.  She wears only black, and though she has been seen by many men, she is known to only a handful of them.  You’ll see her — if you see her at all — just after you’ve taken your last breath.  Then, before you exhale for the final time, she’ll appear, silent and sad-eyed, and beckon to you.

She is the Dark Lady, and this is her story.

The above is one of the best descriptions of Kali I know of in literature; another is in a short story by Fritz Leiber, “Damnation Morning.”   It is not coincidental that one collection of Leiber’s writings is called “Dark Ladies.”

My journal note “Biblical Proportions” was in part inspired by Leiber.

Frank Sinatra may have pictured her as Ava Gardner.  I think I saw her the night Sinatra died… hence my entries of March 31 and April 2, 2003. 

It is perhaps not irrelevant that Kali is, among other things, a mother goddess, and that my entry “Raiders of the Lost Matrix” of May 20 deals with this concept and with the number 24.

The above religious symbol (see “Damnation Morning“) pictures both the axes of symmetry of the square¹ and a pattern with intriguing combinatorial properties².  It also is the basis of a puzzle³ I purchased on August 29, 1997 — Judgment Day in Terminator 2.  Linda Hamilton as Sarah Connor in that film is an excellent representation of the Dark Lady, both as mother figure and as Death Goddess.

Sarah Connor

Background music: “Bit by bit…” — Stephen Sondheim… See Sondheim and the Judgment Day puzzle in my entry of May 20. The Lottery Covenant.

¹ A. W. Joshi, Elements of Group Theory for Physicists, Third Edition, Wiley, 1982, p. 5

² V. K. Balakrishnan, Combinatorics, McGraw-Hill, 1995, p. 180

³ The Izzi Puzzle

Friday, May 23, 2003

Friday May 23, 2003

Filed under: General — m759 @ 7:23 PM

Mental Health Month, Day 23:

The Prime Cut Gospel

On Christmas Day, 1949,
Mary Elizabeth Spacek was born in Texas.

Lee Marvin, Sissy Spacek in “Prime Cut”

Exercises for Mental Health Month:

Read this discussion of the phrase, suggested by Spacek’s date of birth, “God’s gift to men.”

Read this discussion of the phrase “the same yesterday, today, and forever,” suggested by the previous reading.

Read the more interesting of these discussions of the phrase “the eternal in the temporal.”

Read this discussion of eternal, or “necessary,” truths versus other sorts of alleged “truths.”

Read this discussion of unimportant mathematical properties of the prime number 23.

Read these discussions of important properties of 23:

  • R. D. Carmichael’s 1937 discussion of the linear fractional group modulo 23 in 

Introduction to the Theory of Groups of Finite Order, Ginn, Boston, 1937 (reprinted by Dover in 1956), final chapter, “Tactical Configurations,” and

  • Conway’s 1969 discussion of the same group in    

J. H. Conway, “Three Lectures on Exceptional Groups,” pp. 215-247 in Finite Simple Groups (Oxford, 1969), edited by M. B. Powell and G. Higman, Academic Press, London, 1971….. Reprinted as Ch. 10 in Sphere Packings, Lattices, and Groups 

Read this discussion of what might be called “contingent,” or “literary,” properties of the number 23. 

Read also the more interesting of  these discussions of the phrase “the 23 enigma.”

Having thus acquired some familiarity with both contingent and necessary properties of 23…

Read this discussion of Aquinas’s third proof of the existence of God.

Note that the classic Spacek film “Prime Cut” was released in 1972, the year that Spacek turned 23:

+ 23

Essay question:  
If Jesus was God’s gift to man, and (as many men would agree) so was the young Sissy Spacek (also born on Christmas Day), was young Sissy’s existence in her 23rd year contingent or necessary?  If the latter, should she be recognized as a Person of the Trinity? Quaternity? N-ity?
Talk amongst yourselves.

Friday May 23, 2003

Filed under: General — m759 @ 6:01 AM


As our celebration of Wagner’s May 22 birthday draws to a close, let us recall that on this date in 1966 the Beatles released “Paperback Writer” in the US.   Perhaps our most notable paperback writer is now Stephen King; in honor of a recurring theme in his Hearts in Atlantis, our site music today is “Twilight Time.”

Thursday, May 22, 2003

Thursday May 22, 2003

Filed under: General — m759 @ 7:29 PM

Seek and Ye Shall Find:

On the Mystical Properties
of the Number 162

On this date in history:

May 22, 1942:  Unabomber Theodore John Kaczynski is born in the Chicago suburb of Evergreen Park, Ill., to Wanda Kaczynski and her husband Theodore R. Kaczynski, a sausage maker. His mother brings him up reading Scientific American.

From the June 2003 Scientific American:

“Seek and ye shall find.” – Michael Shermer

From my note Mark of April 25, 2003:

“Tell me of runes to grave
 That hold the bursting wave,
 Or bastions to design
 For longer date than mine.”

— A. E. Housman, quoted by G. H. Hardy in A Mathematician’s Apology

“Here, as examples, are one rune and one bastion…. (illustrations: the Dagaz rune and the Nike bastion of the Acropolis)…. Neither the rune nor the bastion discussed has any apparent connection with the number 162… But seek and ye shall find.”

Here is a connection to runes:

Mayer, R.M., “Runenstudien,” Beiträge zur Geschichte der deutschen Sprache und Literatur 21 (1896): pp. 162 – 184.

Here is a connection to Athenian bastions from a UN article on Communist educational theorist Dimitri Glinos:

“Educational problems cannot be scientifically solved by theory and reason alone….” (D. Glinos (1882-1943), Dead but not Buried, Athens, Athina, 1925, p. 162)

“Schools are…. not the first but the last bastion to be taken by… reform….”

“…the University of Athens, a bastion of conservatism and counter-reform….”

I offer the above with tongue in cheek as a demonstration that mystical numerology may have a certain heuristic value overlooked by fanatics of the religion of Scientism such as Shermer.

For a more serious discussion of runes at the Acropolis, see the photo on page 16 of the May 15, 2003, New York Review of Books, illustrating the article “Athens in Wartime,” by Brady Kiesling.

Thursday May 22, 2003

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

Mental Health Month:
Springtime for Wagner

“And now what you’ve all been waiting for…


Colin Hay as Zac in the film “Cosi

“When I sought those who would sympathize with my plans, I had only you, the friends of my particular art, my most personal work and creation, to turn to.”

Wagner’s address at the ceremony for the laying of the foundation stone of the Festival Theater in Bayreuth, May 22 (Wagner’s birthday), 1872

“The new computer package DISCRETA which was created in Bayreuth is in the process of permanent development.”

— “A Computer Approach to the Enumeration of Block Designs Which Are Invariant With Respect to a Prescribed Permutation Group”

The above is a preprint from Dresden.

See, too, the work of Bierbrauer, who received his doctorate at Mainz in 1977 and taught at Heidelberg from 1977 to 1994.  Bierbrauer’s lecture notes give a particularly good background for the concepts involved in my Diamond Theory, in the tradition of Witt and Artin.  See

Introduction to Group Theory
and Applications

by Jürgen Bierbrauer, 138 pp., PostScript

Wednesday, May 21, 2003

Wednesday May 21, 2003

Filed under: General — m759 @ 3:57 PM

The 401 Club: Commentary on
yesterday’s “The Lottery Covenant”
and Monday’s “A Mighty Wind”

 “There are dark comedies. There are screwball comedies. But there aren’t many dark screwball comedies. And if Nora Ephron’s Lucky Numbers is any indication, there’s a good reason for that.”
Todd Anthony, South Florida Sun-Sentinel

See also the dark screwball comedy starring Pat Robertson and Michael Eisner,

Bizarre Marriage.

Tuesday, May 20, 2003

Tuesday May 20, 2003

Filed under: General — m759 @ 8:23 PM

Mental Health Month:
The Lottery Covenant

Here are the evening lottery numbers for Pennsylvania, the Keystone state, drawn on Monday, May 19, 2003:

401 and 1993.

This, by the sort of logic beloved of theologians, suggests we find out the significance of the divine date 4/01/1993.

It turns out that April 1, 1993, was the date of the New York opening of the Stephen Sondheim retrospective “Putting It Together.”

For material related to puzzles, games, Sondheim, and Mental Health Month, see

Notes on
Literary and Philosophical Puzzles

The figures below illustrate some recurrent themes in these notes.

WAIS blocks

IZZI puzzle

Michael Douglas
in “The Game”

Putting It

“Not games. Puzzles. Big difference. That’s a whole other matter. All art — symphonies, architecture, novels — it’s all puzzles. The fitting together of notes, the fitting together of words have by their very nature a puzzle aspect. It’s the creation of form out of chaos. And I believe in form.”

— Stephen Sondheim, in Stephen Schiff,
    “Deconstructing Sondheim,” 
    The New Yorker, March 8, 1993, p. 76

Tuesday May 20, 2003

Filed under: General — m759 @ 3:06 AM

Raiders of the Lost Matrix

“In general, a matrix is something that provides support or structure, especially in the sense of surrounding and/or shaping. It comes from the Latin word for ‘womb,’ itself derived from the Latin word for ‘mother,’ which is mater [as in alma mater].” — Wikipedia

For a mystical interpretation of the above matrix as it relates to the Hebrew words at the center of the official Yale seal, see Talmud


Monday, May 19, 2003

Monday May 19, 2003

Filed under: General — m759 @ 11:45 PM

Part II: A Mighty Wind

I just saw the John Travolta film “Phenomenon” for the first time.  (It was on the ABC Family Channel from 8 to 11.)

Why is it that tellers of uplifting stories (like Zenna Henderson, in “Day of the Mother Ship, Part I,” or the authors of “Phenomenon” or the Bible) always feel they have to throw in some cockamamie and obviously false miracles to hold people’s attention?

On May 11 (Mother’s Day), Mother Nature got my attention with a mighty wind waving the branches of nearby trees, just before a tornado watch was issued for the area I was in.  This made me recall a Biblical reference I had come across in researching references to “Our Lady of the Woods” for my Beltane (May 1) entry

Isaiah 7:2

…And his heart was moved, and the heart of his people, as the trees of the wood are moved with the wind.

This is what I thought of on May 11 watching branches swaying in the wind on Mother’s Day — which some might regard as a festival of Our Lady of the Woods.  John Travolta in “Phenomenon” sees a very similar scene partway through the picture; then, at the end, explains to his girlfriend how the swaying branches made him feel — without mentioning the branches — by asking her to describe how she would cradle and rock a child in her arms.  At the very end of the film, she herself is reminded of his question by the swaying branches of another tree.

Events like these are miracle enough for me.

Sunday, May 18, 2003

Sunday May 18, 2003

Filed under: General — m759 @ 2:00 PM

Phaedrus Lives!

Fans of Zen and the Art of Motorcycle Maintenance may recall that it is a sort of elegy for an earlier self named Phaedrus who vanished with the recovery of mental health.  Since this is Mental Health Month, the following observations seem relevant.

Reading another weblog’s comments today, I found the following remark:

“…the mind is an amazing thing and it can create patterns and interconnections among things all day it you let it, regardless of whether they are real connections.”
 – sejanus

This, of course, prompted me to look for patterns and interconnections.   The first thing I thought of was the fictional mathematician in “A Beautiful Mind” establishing an amazing — and, within the fiction, real — connection between the pattern on a colleague’s tie and the reflections from a glass.  A web search led to a really real connection…. i.e., to a lengthy listserver letter from an author named Christopher Locke, whose work is new to me but also strangely familiar…. I recognize in his writing both some of my own less-than-mentally-healthy preoccupations and also what might be called the spirit of Phaedrus, from Zen and the Art.

Here is a link to a cache I made of the Locke letter and a follow-up he wrote detailing his sources:

Christopher Locke as Phaedrus

One part of Locke’s letter seems particularly relevant in light of yesterday’s entries related to the death of June Carter Cash:

“Will the circle be unbroken?
  As if some southern congregation
  is praying we will come to understand.”


Concluding Unscientific Postscript

from Sir Arthur Quiller-Couch (“Q”), quoting Socrates’s remarks to the original Phaedrus:

‘By Hera,’ says Socrates, ‘a fair resting-place, full of summer sounds and scents! This clearing, with the agnus castus in high bloom and fragrant, and the stream beneath the tree so gratefully cool to our feet! Judging from the ornaments and statues, I think this spot must be sacred to Acheloüs and the Nymphs. 

This quotation illustrates a connection between Jesus (College) — from my entry of 3:33 PM Thursday — and a Nymph — from my entry of 11:44 PM Friday.  See, too, Q’s quoting of Socrates’s prayer to Pan, as well as the cover of the May 19, 2003, New Yorker:


For a discussion of the music
that Pan is playing (today’s site music),
see my entry of Sept. 10, 2002,
The Sound of Hanging Rock.”

Friday, May 16, 2003

Friday May 16, 2003

Filed under: General — m759 @ 11:44 PM


“If you can bounce high,
bounce for her too….”
 – F. Scott Fitzgerald, epigraph to
The Great Gatsby

Magazine purchased at
newsstand May 14, 2003:

A Whiff of Camelot
as ‘West Wing’
Ends an Era

– New York Times,
 May 14, 2003

Song title from the
June Carter Cash album “Press On“:

“Gatsby’s Restaurant”

From The Great Gatsby, Chapter Four:

“Highballs?” asked the head waiter.
“This is a nice restaurant here,”
said Mr. Wolfsheim, looking at the
Presbyterian nymphs on the ceiling.

Presbyterian Nymph:

Mimi Beardsley, JFK playmate,
in the news on May 15, 2003 

On JFK’s plane trips:
“Whenever the President traveled,
members of the press staff traveled as well.
You always have a press secretary
and a couple of girls traveling….
 Mimi, who obviously couldn’t perform
 any function at all, made all the trips!”

Apparently there was some function….

“Don’t forget the coffee!”
– Punchline from the film
  “Good Will Hunting.”

Friday May 16, 2003

Filed under: General — m759 @ 3:03 AM


Commentary on the May 15 death of
June Carter Cash, which I learned of
at the New York Times site
at about 2:10 AM today:

Jesus College

In light of yesterday's Jesus College entry
("The Only Pretty Ring Time," May 15),
the following song lyrics seem relevant.

While walking out one evening
                 not knowing where to go
Just to pass the time away      
                 before we held our show
 I heard a little mission band     
             playing with all their might
I gave my soul to Jesus           
             and left the show that night.

The day will soon be over         
                  and evening will begun;
No more gems to be gathered  
                     so let us all press on.
When Jesus comes to claim us  
                    and says it is enough
 The diamonds will be shining,    
                   no longer in the rough.

Diamonds in the Rough

June Carter Cash sings this song
on her album
 Press On.

an "old shape-note gospel song that A.P. Carter found
and rearranged. The song itself had been written and
copyrighted back in 1897, with composer credits
to C.W. Bryan."

Thursday, May 15, 2003

Thursday May 15, 2003

Filed under: General,Geometry — Tags: — m759 @ 3:33 PM

The Only Pretty Ring Time

On May 14 five years ago, the night Sinatra died, the Pennsylvania (State of Grace) lottery evening number was 256:  see my note, Symmetries, of April 2, 2003.

On May 14 this year, the Pennsylvania lottery evening number was 147.  Having, through meditation, perhaps established some sort of minor covenant with whatever supernatural lottery powers may exist, this afternoon I sought the significance of this number in Q's 1939 edition of the Oxford Book of English Verse.  It is the number of "It was a Lover and his Lass," a song lyric by William Shakespeare.  The song includes the following lines:

In the spring time,
    the only pretty ring time,
When birds do sing,
    Hey ding a ding, ding;
Sweet lovers love the spring.

For the Sinatra connection, see
Metaphysics for Tina.

The selection of Q's book for consultation was suggested by the home page of Simon Nickerson at Jesus College, Cambridge University, and by the dedication page of Q's 1925 Oxford Book of English Prose, which names Nickerson's school.

Ian Lee on the communion of saints and the association of ideas:

"The association is the idea."

For translation of the Greek phrase in Q's 1925 dedication, see

Greek and Roman Grammarians
on Motion Verbs and Place Adverbials

Malcolm D. Hyman
Harvard University
January 4, 2003

Thursday May 15, 2003

Filed under: General — m759 @ 1:23 PM

Birthday Present

Today is the birthday of Emile Mathieu.
Here is a present.

Thursday May 15, 2003

Filed under: General — m759 @ 12:00 PM

Well Done

“So tell me about the matrix reloaded… and what it’s like to finish a job well done.”

— Weblog entry by Harvard student, May 15, 2003

The matrix reloaded: 

See chapter VII, “Composition,” in Chinese Calligraphy: An Introduction to Its Aesthetic and Technique, by Chiang Yee, Harvard University Press, first published April 21st, 1938.

A job well done:

“The Best is Yet to Come”
— Epitaph of Francis Albert Sinatra

Wednesday, May 14, 2003

Wednesday May 14, 2003

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

Common Sense

On the mathematician Kolmogorov:

“It turns out that he DID prove one basic theorem that I take for granted, that a compact hausdorff space is determined by its ring of continuous functions (this ring being considered without any topology) — basic discoveries like this are the ones most likely to have their origins obscured, for they eventually come to be seen as mere common sense, and not even a theorem.”

Richard Cudney, Harvard ’03, writing at Xanga.com as rcudney on May 14, 2003

That this theorem is Kolmogorov’s is news to me.


The above references establish that Gelfand is usually cited as the source of the theorem Cudney discusses.  Gelfand was a student of Kolmogorov’s in the 1930’s, so who discovered what when may be a touchy question in this case.  A reference that seems relevant: I. M. Gelfand and A. Kolmogoroff, “On rings of continuous functions on topological spaces,” Doklady Akad. Nauk SSSR 22 (1939), 11-15.  This is cited by Gillman and Jerison in the classic Rings of Continuous Functions.

There ARE some references that indicate Kolmogorov may have done some work of his own in this area.  See here (“quite a few duality theorems… including those of Banaschewski, Morita, Gel’fand-Kolmogorov and Gel’fand-Naimark”) and here  (“the classical theorems of M. H. Stone, Gelfand & Kolmogorov”).

Any other references to Kolmogorov’s work in this area would be of interest.

Naturally, any discussion of this area should include a reference to the pioneering work of M. H. Stone.  I recommend the autobiographical article on Stone in McGraw-Hill Modern Men of Science, Volume II, 1968.

Tuesday, May 13, 2003

Tuesday May 13, 2003

Filed under: General — m759 @ 12:06 PM

Cubist Catechism

For the birthday of Georges Braque

From A Wrinkle in Time, by Madeleine L’Engle:

“Now we will tesser, we will wrinkle again. Do you understand?”

“No,” Meg said flatly….

“Oh, dear,” Meg sighed. “I guess I am a moron. I just don’t get it.”

“That is because you think of space only in three dimensions,” Mrs. Whatsit told her….

Meg sighed. “Just explain it to me.”

“Okay,” Charles said. “What is the first dimension?”

“Well — a line.”

“Okay. And the second dimension?”

“Well, you’d square the line. A flat square would be in the second dimension.”

“And the third?”

“Well, you’d square the second dimension. Then the square wouldn’t be flat any more. It would have a bottom, and sides, and a top.”

“And the fourth?”

“Well, I guess if you want to put it into mathematical terms you’d square the square. But you can’t take a pencil and draw it the way you can the first three.”


Tuesday May 13, 2003

Filed under: General — m759 @ 11:01 AM

Operation Playmate:

11:01 AM

On this date in 1938, Louis Armstrong and his orchestra recorded “When the Saints Go Marching In.”

On this date in 1961, Saint Gary Cooper died.

From my Jan. 2, 2003, entry:

Faces of the Twentieth Century:
The Harvest Continues

“I walk, I lift up, I lift up heart, eyes,
Down all that glory in the heavens
    to glean our Saviour;
And, éyes, héart, what looks, what lips
    yet gave you a
Rapturous love’s greeting of realer,
    of rounder replies?”

— Gerard Manley Hopkins,
   “Hurrahing in Harvest”

Mary Brian

Joe Foss

“Cowboy, take me away.
Fly this girl as high as you can
into the wild blue.”

The Dixie Chicks

From my March 31, 2003, entry:

“During the Gulf War, Playboy magazine’s celebrated Centerfolds reached out to U.S. military men and women… with their ‘Operation Playmate’ project….

Now, in light of the war in Iraq, ‘Operation Playmate’ has returned.”

Entertainment Weekly, May 2, 2003:

Perhaps, in heaven, Dixie Chick Natalie “Mattress Dancing” Maines will provide terpsichorean instruction. 

Etymology: Latin Terpsichor,
from Greek Terpsikhor,
from feminine of terpsikhoros,
dance-loving : terpein, to delight
+ khoros, dance.

See, too, my entry for Beltane (May 1), the day that death claimed the 13th Episcopal bishop of New York City.

All of these events are not without interest, but it is not easy to fit them into one coherent story, as Robert Penn Warren once requested:

“The name of the story will be Time,
But you must not pronounce its name.
Tell me a story of deep delight.”

It is perhaps relevant that, as T. S. Eliot well knew, there can be no dance except in time, and that the time of my May 1 entry is 5:13, today’s date in another guise.  To paraphrase an Eliot line, 

“Hurry up please, it’s 5/13.”

Monday, May 12, 2003

Monday May 12, 2003

Filed under: General — m759 @ 6:10 PM

The Tony Nominations

Dannie Abse quoting Robert Penn Warren:

“The name of the story will be Time,
But you must not pronounce its name.
Tell me a story of deep delight.”

 Dannie Abse

Abse deserves a Tony Smith award¹ for his play Pythagoras.

Frank Rich on Bush’s Top Gun speech:

“Only hours before President Bush’s prime-time speech came news of what Variety headlined on Page 1 as ‘Regime Change’ in Hollywood — the departure of the [West Wing] creator, the writer Aaron Sorkin.”

 George W. Bush

President Bush deserves a Tony Smith award² for his performance aboard the aircraft carrier Abraham Lincoln.

 Madeleine L’Engle on the religion of Cubism:

“There is such a thing as a tesseract.”

 Madeleine L’Engle

L’Engle, former librarian at the Cathedral of St. John the Divine in New York City, deserves a Tony Smith award³ for insisting on the existence of the tesseract, or 4-dimensional cube, as an object of conceptual art.

L’Engle is perhaps the best defender of the religious, or “story,” theory of truth, as opposed to the “diamond” theory of truth. (See my earlier May 12 entry, “Death and Truth,” which deals with the bishop of L’Engle’s cathedral.)

¹ See Tony Smith on mathematics.

² See Tony Smith on foreign policy.

³ See Tony Smith on conceptual art.

Monday May 12, 2003

Filed under: General — m759 @ 2:40 PM

Epiphany 1941:
Why We Fought

Jan. 6, 1941

Hepburn’s father was disgusted and heartsick over her decision to become an actor. He thought it was a silly profession, closely allied to street walking.
Heather Wilgar

Not the way she did it.
— S. H. Cullinane

Hepburn is 96 today.

Monday May 12, 2003

Filed under: General — m759 @ 3:33 AM

Death and Truth

Material related to my May 9, 2003, notes:

  1. Pilate, Truth, and Friday the Thirteenth
  2. The Diamond Theory of Truth
  3. Understanding

Sunday, May 11, 2003

Sunday May 11, 2003

Filed under: General — m759 @ 4:15 PM

Day of the Mother Ship:

A Close Encounter of the Third Level

Today is also the feast day of Saint Zenna Henderson, who was born on All Saints’ Day, 1917.   The Adherents.com website says she was a Mormon, but the printed reference work Contemporary Authors (written when she was still alive and could defend herself against any accusation of Mormonism) says she was a Methodist.  Maybe she was just one of The People — i.e., a Person.

“The concept of a person, which we find so familiar in its application to human beings, cannot be clearly and sharply expressed by any word in the vocabulary of Plato and Aristotle; it was wrought with the hammer and anvil* of theological disputes about the Trinity and the Person of Christ.”

Peter Geach, The Virtues, Cambridge U. Press, 1977, p. 75

See also Terpsichore and the Trinity.

* For a use of this phrase suited to Mental Health Month, see The Prisoner, Episode Ten.  See, too, Inaugural Address.

Friday, May 9, 2003

Friday May 9, 2003

Filed under: General,Geometry — Tags: — m759 @ 7:20 PM

The Religion of Cubism

In the dome of the Capitol at Washington, DC, a painting depicts The Apotheosis of Washington .  Personally, I prefer the following pair of pictures, which might be titled Apotheosis of the Cube.





A New York Times article says Tony Smith's instructions for fabricating Die  were as follows:

"a six-foot cube of quarter-inch hot-rolled steel with diagonal internal bracing."

The transparent cube in the upper picture above shows the internal diagonals.  The fact that there are four of these may be used to demonstrate the isomorphism of the group of rotations of the cube with the group of permutations on an arbitrary set of four elements.  For deeper results, see Diamond Theory.

For an explanation of why our current president might feel that the cube deserves an apotheosis, see the previous entry, "The Rhetoric of Power."

See, too, Nabokov's Transparent Things :

"Its ultimate vision was the incandescence of a book or a box grown completely transparent and hollow.  This is, I believe, it: not the crude anguish of physical death but the incomparable pangs of the mysterious mental maneuver needed to pass from one state of being to another.  Easy, you know, does it, son."

Friday May 9, 2003

Filed under: General,Geometry — m759 @ 6:30 PM


The Rhetoric of Power:
A meditation for Mental Health Month

From “Secondary Structures,” by Tom Moody, Sculpture Magazine, June 2000:

“By the early ’90s, the perception of Minimalism as a ‘pure’ art untouched by history lay in tatters. The coup de grâce against the movement came not from an artwork, however, but from a text. Shortly after the removal of Richard Serra’s Tilted Arc from New York City’s Federal Plaza, Harvard art historian Anna Chave published ‘Minimalism and the Rhetoric of Power’ (Arts Magazine, January 1990), a rousing attack on the boys’ club that stops just short of a full-blown ad hominem rant. Analyzing artworks (Walter de Maria’s aluminum swastika, Morris’s ‘carceral images,’ Flavin’s phallic ‘hot rods’), critical vocabulary (Morris’s use of ‘intimacy’ as a negative, Judd’s incantatory use of the word ‘powerful’), even titles (Frank Stella’s National Socialist-tinged Arbeit Macht Frei and Reichstag), Chave highlights the disturbing undercurrents of hypermasculinity and social control beneath Minimalism’s bland exterior.  Seeing it through the eyes of the ordinary viewer, she concludes that ‘what [most] disturbs [the public at large] about Minimalist art may be what disturbs them about their own lives and times, as the face it projects is society’s blankest, steeliest face; the impersonal face of technology, industry and commerce; the unyielding face of the father: a face that is usually far more attractively masked.’ ”

From Maureen Dowd’s New York Times column of June 9, 2002: 

“The shape of the government is not as important as the policy of the government. If he makes the policy aggressive and pre-emptive, the president can conduct the war on terror from the National Gallery of Art.”

From the New York Times
Friday, May 2, 2003:

The National Gallery of Art in Washington has just acquired Tony Smith’s first steel sculpture: “Die,” created in 1962 and fabricated in 1968.

“It’s a seminal icon of postwar American art,” said Earl A. Powell III, director of the National Gallery.

Die (Tony Smith)

Bishop Moore

From a New York Times obituary,
Friday, May 2, 2003:

Bishop Dies

by Ari L. Goldman

Paul Moore Jr., the retired Episcopal bishop of New York who for more than a decade was the most formidable liberal Christian voice in the city, died yesterday at home in Greenwich Village. He was 83….

Bishop Moore argued for his agenda in the most Christian of terms, refusing to cede Biblical language to the Christian right. Although he retired as bishop in 1989, he continued to speak out, taking to the pulpit of his former church as recently as March 24, even as illness overtook him, to protest the war in Iraq.

“It appears we have two types of religion here,” the bishop said, aiming his sharpest barbs at President Bush. “One is a solitary Texas politician who says, `I talk to Jesus, and I am right.’ The other involves millions of people of all faiths who disagree.”

He added: “I think it is terrifying. I believe it will lead to a terrible crack in the whole culture as we have come to know it.”….

[In reference to another question] Bishop Moore later acknowledged that his rhetoric was strong, but added, “In this city you have to speak strongly to be heard.”

Paul Moore’s early life does not immediately suggest an affinity for the kinds of social issues that he would later champion…. His grandfather was one of the founders of Bankers Trust. His father was a good friend of Senator Prescott Bush, whose son, George H. W. Bush, and grandson, George W. Bush, would become United States presidents.

Related material (update of May 12, 2003):

  1. Pilate, Truth, and Friday the Thirteenth
  2. The Diamond Theory of Truth
  3. Understanding


Which of the two theories of truth in reading (2) above is exemplified by Moore’s March 24 remarks?

Friday May 9, 2003

Filed under: General — m759 @ 4:44 PM

Invitation to the Dance

While checking the claim of art historian Anna Chave that “the veil is an age-old metaphor used from Plato through Hegel and Heidegger for the concept of truth as aletheia or unveiling,”  I came across the following essay:

“Taking the Veil,” by Jessica Kardon.

Kardon writes very well.  A related essay I particularly like is

“Invitation to the Dance.”

Today’s entry on Kardon is part of my “ART WARS” series of journal notes.  This title began partly as a joke, but it seems rather appropriate in light of Anna Chave’s claim that minimalism in the 1960’s was part of the “rhetoric of power.”  See my later entry today on Tony Smith at the National Gallery.

If we are in a war of art,

the essays of Jessica Kardon

are a powerful weapon.

Friday, May 2, 2003

Friday May 2, 2003

Filed under: General — m759 @ 4:15 PM


The following flashback to March 2002 seems a suitable entry for May, which is Mental Health Month.

Zen and Language Games

by Steven H. Cullinane
on March First, 2002

Two Experts Speak —

A Jew on Language Games

From On Certainty, by Ludwig Wittgenstein (Oxford, Basil Blackwell, 1969):

#508: What can I rely on?
#509: I really want to say that a language game is only possible if one trusts something. (I did not say “can trust something”).
— Quoted by Hilary Putnam in Renewing Philosophy, Chapter 8 (Harvard University Press, 1992)

An Arab on Deconstruction

From “Deconstructing Postmodernism,” by Ziauddin Sardar, at the website “The Free Arab Voice”:

Doubt, the perpetual and perennial condition of postmodernism, is best described by the motto of the cult television series The X-files: ‘Trust no One’….

Deconstruction – the methodology of discursive analysis – is the norm of postmodernism. Everything has to be deconstructed. But once deconstruction has reached its natural conclusion, we are left with a grand void: there is nothing, but nothing, that can remotely provide us with meaning, with a sense of direction, with a scale to distinguish good from evil.

Those who, having reviewed a thousand years of lies by Jews, Arabs, and Christians, are sick of language games, and who are also offended by the recent skillful deconstruction of the World Trade Center, may find some religious solace in the philosophy of Zen.

Though truth may be very hard to find in the pages of most books, the page numbers are generally reliable. This leads to the following Zen meditations.

From a review of the film “The Terminator”:

Some like to see Sarah as a sort of Mother of God, and her son as the saviour in a holy context. John Connor, J.C. , but these initials are also those of the director, so make up your own mind.
— http://www.geocities.com/

From a journal note on religion, science, and the meaning of life written in 1998 on the day after Sinatra died and the Pennsylvania lottery number came up “256”:

“What is 256 about?”
— S. H. Cullinane

From Michael Crichton’s Rising Sun (Ballantine paperback, 1993) —
John Connor (aka J. C.) offers the following metaphysical comment on the page number that appears above his words (256):

“It seems to be.”
“Is your investigation finished?”
“For all practical purposes, yes,” Connor said.

Connor is correct. The number 256 does indeed seem to be, and indeed it seemed to be again only yesterday evening, when the Pennsylvania lottery again made a metaphysical statement.

Our Zen meditation on the trustworthiness of page numbers concludes with another passage from Rising Sun, this time on page 373:

Connor sighed.
“The clock isn’t moving.”

Here J. C. offers another trenchant comment on his current page number.

The metaphysical significance of 373, “the eternal in the temporal,” is also discussed in the Buddhist classic A Flag for Sunrise, by Robert Stone (Knopf hardcover, 1981)… on, of course, page 373.

Thursday, May 1, 2003

Thursday May 1, 2003

Filed under: General — m759 @ 5:13 PM

Rhymes with Puck

Readings for May Day, also known as Beltane.

  I. The Playboy of the Western World

 II.  Beltane

III.  A is for Art


In 1993, The Mathematical Association of America published Constance Reid’s

also known as John Taine.

This is a biography of Eric Temple Bell, a mathematician and writer on mathematics, who also wrote fiction under the name John Taine.

On page 194, Reid records a question Bell’s son asked as a child.  Passing a church and seeing a cross on the steeple, he inquired, “Why is the plus up there?”

For an answer that makes some sort of sense

  • in the context of Part II above, and
  • in the context of last month’s “Math Awareness Month” theme, mathematics and art,

consider the phrase “A is for Art,” so aptly illustrated by Olivia Newton-John in “Wrestling Pablo Picasso,”  then examine the photograph of ballerina Margaret “Puck” Petit on page 195 of Reid’s book.  Puck, as the mother of Leslie Caron (see Terpsichore’s Birthday), clearly deserves an A+.

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