Satori at Pearl Harbor

Great Simplicity

Today

is the day that Daisetsu Suzuki attained satori,
according to the Zen Calendar.  “Daisetsu” is
said to mean “Great Simplicity.”

For those who prefer Harry Potter and
Diagon Alley, here is another calendar:

To Have and Have Not

Those who prefer traditional Western religions may like a site on the Trinity that contains this:

“Zen metaphysics is perhaps most succinctly set forth in the words ‘not-two.”  But even when he uses this expression, Suzuki is quick to assert that it implies no monism.  Not-two, it is claimed, is not the same as one.*  But when Suzuki discusses the relationship of Zen with Western mysticism, it is more difficult to escape the obvious monistic implications of his thinking.  Consider the following:

We are possessed of the habit of looking at Reality by dividing it into two… It is all due to the human habit of splitting one solid Reality into two, and the result is that my ‘have’ is no ‘have’ and my ‘have not’ is no ‘have not.’  While we are actually passing, we insist that the gap is impassable.**”

*See: Daisetz T. Suzuki, ‘Basic Thoughts Underlying  Eastern Ethical and Social Practice’ in Philosophy and Culture — East and West: East-West Philosophy in Practical Perspective, ed. Charles A. Moore (Honolulu: University of Hawaii Press, 1968), p. 429

** Daisetsu Teitaro Suzuki, Mysticism Christian and Buddhist (London: George Allen & Unwin, 1957, Unwin paperback, 1979), p. 57.

Personally, I am reminded by Suzuki’s satori on this date that today is the eve of the anniversary of Pearl Harbor.  I am also reminded by the rather intolerant tract on the Trinity quoted above that the first atomic bomb was exploded in the New Mexico desert at a test site named Trinity.  Of course, sometimes intolerance is justified.

Concluding unscientific postscript:

On the same day in 1896 that D. T. Suzuki attained satori,
lyricist Ira Gershwin was born.

Dies irae, dies illa.

St. Nicholas versus Mt. Doom

Today is the feast day of St. Nicholas, who is thought to have died on December 6.

For some meditations on time, click here. 

For a perhaps more pleasant meditation — on eternity — listen to this site’s background music, which has been changed in honor of the birth, on December 6, 1896, of lyricist Ira Gershwin.

For Otto Preminger’s birthday:

Lichtung!

Today’s symbol-mongering (see my Sept. 7, 2002, note The Boys from Uruguay) involves two illustrations from the website of the Deutsche Schule Montevideo, in Uruguay.  The first, a follow-up to Wallace Stevens’s remarks on poetry and painting in my note “Sacerdotal Jargon” of earlier today, is a poem, “Lichtung,” by Ernst Jandl, with an illustration by Lucia Spangenberg.

The second, from the same school, illustrates the meaning of “Lichtung” explained in my note The Shining of May 29:  

“We acknowledge a theorem’s beauty when we see how the theorem ‘fits’ in its place, how it sheds light around itself, like a Lichtung, a clearing in the woods.”
– Gian-Carlo Rota, page 132 of Indiscrete Thoughts, Birkhauser Boston, 1997

From the Deutsche Schule Montevideo mathematics page, an illustration of the Pythagorean theorem:

Key

Today is Joan Didion’s birthday.  It is also the date that the first Phi Beta Kappa chapter was formed, at the College of William and Mary.

A reading for today, from a web page called Respect:

“In her book Slouching Toward Bethlehem Didion writes about being a student in college. She says she expected to be voted into Phi Beta Kappa but discovered she didn’t have the grades for it. She says: ‘I had somehow thought myself [as being] exempt from the cause-effect relationships which hampered others.’ But, Didion continues:

Although even the humorless nineteen-year-old that I was must have recognized that the situation lacked tragic stature, the day that I did not make Phi Beta Kappa nonetheless marked the end of something, and innocence may well be the word for it. I lost the conviction that lights would always turn green for me, the pleasant certainty that those rather passive virtues which had won me approval as a child automatically guaranteed me not only Phi Beta Kappa keys but happiness, honor, and the love of a good man. I lost a certain touching faith in the totem power of good manners, clean hair, and proven competence on the Stanford-Binet scale. To such doubtful amulets had my self-respect been pinned, and I faced myself that day with the nonplused apprehension of someone who has come across a vampire and has no crucifix in hand.

What Joan Didion discovered in the wake of this incident was that self-respect, although it was of importance, had to come from something inside her, rather than from the approval of others. She says she learned that self-respect has to do with ‘a separate peace, a private reconciliation,’ and at the heart of it is a willingness to accept responsibility for one’s own life, whatever its rewards or lack of them. Didion says:

… people with self-respect have the courage of their mistakes. They know the price of things…. People with self-respect exhibit a certain toughness, a kind of moral nerve; they display what was once called character, a quality which, although approved in the abstract, sometimes loses ground to other, more instantly negotiable virtues.

— Comments by David Sammons

For more of Didion’s essay, click here.

Sacerdotal Jargon

From the website

Abstracts and Preprints in Clifford Algebra [1996, Oct 8]:

Paper:  clf-alg/good9601
From:  David M. Goodmanson
Address:  2725 68th Avenue S.E., Mercer Island, Washington 98040

Title:  A graphical representation of the Dirac Algebra

Abstract:  The elements of the Dirac algebra are represented by sixteen 4×4 gamma matrices, each pair of which either commute or anticommute. This paper demonstrates a correspondence between the gamma matrices and the complete graph on six points, a correspondence that provides a visual picture of the structure of the Dirac algebra.  The graph shows all commutation and anticommutation relations, and can be used to illustrate the structure of subalgebras and equivalence classes and the effect of similarity transformations….

Published:  Am. J. Phys. 64, 870-880 (1996)

The following is a picture of K₆, the complete graph on six points.  It may be used to illustrate various concepts in finite geometry as well as the properties of Dirac matrices described above.

From
“The Relations between Poetry and Painting,”
by Wallace Stevens:

“The theory of poetry, that is to say, the total of the theories of poetry, often seems to become in time a mystical theology or, more simply, a mystique. The reason for this must by now be clear. The reason is the same reason why the pictures in a museum of modern art often seem to become in time a mystical aesthetic, a prodigious search of appearance, as if to find a way of saying and of establishing that all things, whether below or above appearance, are one and that it is only through reality, in which they are reflected or, it may be, joined together, that we can reach them. Under such stress, reality changes from substance to subtlety, a subtlety in which it was natural for Cézanne to say: ‘I see planes bestriding each other and sometimes straight lines seem to me to fall’ or ‘Planes in color. . . . The colored area where shimmer the souls of the planes, in the blaze of the kindled prism, the meeting of planes in the sunlight.’ The conversion of our Lumpenwelt went far beyond this. It was from the point of view of another subtlety that Klee could write: ‘But he is one chosen that today comes near to the secret places where original law fosters all evolution. And what artist would not establish himself there where the organic center of all movement in time and space—which he calls the mind or heart of creation— determines every function.’ Conceding that this sounds a bit like sacerdotal jargon, that is not too much to allow to those that have helped to create a new reality, a modern reality, since what has been created is nothing less.”

Symmetry and a Trinity

From a web page titled Spectra: 

“What we learn from our whole discussion and what has indeed become a guiding principle in modern mathematics is this lesson:

Whenever you have to do with a structure-endowed entity S try to determine its group of automorphisms, the group of those element-wise transformations which leave all structural relations undisturbed. You can expect to gain a deep insight into the constitution of S in this way. After that you may start to investigate symmetric configurations of elements, i.e., configurations which are invariant under a certain subgroup of the group of all automorphisms . . .”

— Hermann Weyl in Symmetry, Princeton University Press, 1952, page 144

“… any color at all can be made from three different colors, in our case, red, green, and blue lights. By suitably mixing the three together we can make anything at all, as we demonstrated . . .

Further, these laws are very interesting mathematically. For those who are interested in the mathematics of the thing, it turns out as follows. Suppose that we take our three colors, which were red, green, and blue, but label them A, B, and C, and call them our primary colors. Then any color could be made by certain amounts of these three: say an amount a of color A, an amount b of color B, and an amount c of color C makes X:

From the Erlangen Program
to Category Theory

See the following, apparently all by Jean-Pierre Marquis, Département de Philosophie, Université de Montréal:

• Introduction
• Chapter 1: Klein’s Erlangen program
• Chapter 2: Eilenberg & Mac Lane’s methodological extension
• Chapter 3: Basic principles of category theory

See also the following by Marquis:

• Category Theory (article in the Stanford Encyclopedia of Philosophy), and
•  Categories, Sets, and the Nature of Mathematical Entities (abstract) 

Symmetry, Invariance, and Objectivity

The book Invariances: The Structure of the Objective World, by Harvard philosopher Robert Nozick, was reviewed in the New York Review of Books issue dated June 27, 2002.

On page 76 of this book, published by Harvard University Press in 2001, Nozick writes:

“An objective fact is invariant under various transformations. It is this invariance that constitutes something as an objective truth….”

Compare this with Hermann Weyl’s definition in his classic Symmetry (Princeton University Press, 1952, page 132):

“Objectivity means invariance with respect to the group of automorphisms.”

It has finally been pointed out in the Review, by a professor at Göttingen, that Nozick’s book should have included Weyl’s definition.

I pointed this out on June 10, 2002.

For a survey of material on this topic, see this Google search on “nozick invariances weyl” (without the quotes).

Nozick’s omitting Weyl’s definition amounts to blatant plagiarism of an idea.

Of course, including Weyl’s definition would have required Nozick to discuss seriously the concept of groups of automorphisms. Such a discussion would not have been compatible with the current level of philosophical discussion at Harvard, which apparently seldom rises above the level of cocktail-party chatter.

A similarly low level of discourse is found in the essay “Geometrical Creatures,” by Jim Holt, also in the issue of the New York Review of Books dated December 19, 2002. Holt at least writes well, and includes (if only in parentheses) a remark that is highly relevant to the Nozick-vs.-Weyl discussion of invariance elsewhere in the Review:

“All the geometries ever imagined turn out to be variations on a single theme: how certain properties of a space remain unchanged when its points get rearranged.”  (p. 69)

This is perhaps suitable for intelligent but ignorant adolescents; even they, however, should be given some historical background. Holt is talking here about the Erlangen program of Felix Christian Klein, and should say so. For a more sophisticated and nuanced discussion, see this web page on Klein’s Erlangen Program, apparently by Jean-Pierre Marquis, Département de Philosophie, Université de Montréal. For more by Marquis, see my later entry for today, “From the Erlangen Program to Category Theory.”

Art isn’t Easy

In honor of Georges Seurat, whose birthday is today, this site’s music is now “Putting It Together,” by Stephen Sondheim.

For a relevant quote by Sondheim and some related material, see

• The Diamond 16 Puzzle and
  
• Notes on Literary and Philosophical Puzzles,
  as well as
  
• Logos and Logic.