In memory of
Hunter S. Thompson

Big Time
Parts I, II, III

Part I:
April 17, 2003: Holiday Affair

Big Time, Part II:

April 16, 2003: Keeping Time

Big Time, Part III:

April 15, 2003: Green and Burning

"Man stands in his own shadow and wonders why it is dark."

-- "Ancient Zen saying," according to "Today in History," June 24, by the Associated Press

"A man may be free to travel where he likes, but there is no place on
earth where he can escape from his own Karma, and whether he lives on a
mountain or in a city he may still be the victim of an uncontrolled
mind. For man's Karma travels with him, like his shadow.
Indeed, it is his shadow, for it has been said, 'Man stands in his own
shadow and wonders why it is dark.'"

-- Alan W. Watts, The Spirit of Zen, third edition, Grove Press, 1958, page 97

Robert Pirsig, Zen and the Art of Motorcycle Maintenance, 1974:

"But what's happening is that each year our old flat earth of
conventional reason becomes less and less adequate to handle the
experiences we have and this is creating widespread feelings of
topsy-turviness. As a result we're getting more and more people in
irrational areas of thought... occultism, mysticism, drug changes and
the like... because they feel the inadequacy of classical reason to
handle what they know are real experiences."

"I'm not sure what you mean by classical reason."

"Analytic reason, dialectic reason. Reason which at
the University is sometimes considered to be the whole of
understanding. You've never had to understand it really. It's always
been completely bankrupt with regard to abstract art. Nonrepresentative
art is one of the root experiences I'm talking about. Some people still
condemn it because it doesn’t make 'sense.' But what's really wrong is
not the art but the 'sense,' the classical reason, which can't grasp
it. People keep looking for branch extensions of reason that will cover
art's more recent occurrences, but the answers aren't in the branches,
they're at the roots."

Related material:

D-Day Morning,
Figures of Speech,
Ursprache Revisited.

See also
the previous entry.

Binary Geometry

There is currently no area of mathematics named "binary
geometry." This is, therefore, a possible name for the geometry
of sets with 2ⁿ elements (i.e., a sub-topic of Galois geometry and of algebraic geometry over finite fields-- part of Weil's "Rosetta stone" (pdf)).

Examples:

• Charles Sanders Peirce, "The Simplest Mathematics."
• Donald E. Knuth's discussion of binary hypercubes in "Boolean Basics," a draft of section 7.1.1 in The Art of Computer Programming, Volume 4: Combinatorial Algorithms
• My own discussion of a binary hypercube in Geometry of the 4x4x4 Cube
• A more sophisticated example: the geometry of elliptic curves
  over a binary Galois field. For an excellent introduction,
  see the Certicom online elliptic curve tutorial. This has an applet
  illustrating elliptic curves in a space of 256 points (256=16x16, with
  the x and y variables of a curve each having 16 possible values).

• In summary, apart from the fact that the native language of computers has
  characteristic 2, "binary" mathematics, i.e. mathematics in
  characteristic 2, is of special interest both in the study of finite geometry (Finite Geometry of the Square and Cube) and in algebraic geometry (see, for instance, the work of Brian Conrad).

Go with the Flow

The previous entry links to a document that discusses the mathematical concept of "Ricci flow (pdf)."

Though the concept was not named for him, this seems as good a time as any to recall the virtues of St. Matteo Ricci,
a Jesuit who died in Beijing on May 11, 1610. (The Church does
not yet recognize him as a saint; so much the worse for the Church.)

There was no Log24 entry on Ricci's saint's day, May 11, this year, but
an entry for 4:29 PM May 10, 2006, seems relevant, since Beijing
is 12 hours ahead of my local (Eastern US) time.

The relevance of this structure
to memory and to Chinese culture
is given in Dragon School and in
Geometry of the 4x4x4 Cube.

For some related remarks on
the colloquial, rather than the
mathematical, concept of flow,
see
Philosophy, Religion, and Science
as well as Crystal and Dragon.

Yesterday's entry on the 1865
remarks on aesthetics of
Gerard Manley Hopkins,
who later became a Jesuit,
may also have some relevance.

Beijing String continued...

A comment left at Peter Woit's weblog:

Xinhua has a story
from June 20 on Yau showing a video in Beijing of a talk by Hamilton on
the Poincare conjecture. This Xinhua story is rather Sinocentric, but it is balanced nicely by a document from China's Morningside Center of Mathematics that gives a more complete record of Hamilton's talk.

Hopkins on Parallelism

"The structure of poetry is that of continuous parallelism,
ranging from the technical so-called Parallelism of Hebrew Poetry and the
antiphons of Church music up to the intricacy of Greek or Italian or English
verse. But parallelism is of two kinds necessarily – where the opposition
is clearly marked, and where it is transitional rather or chromatic. Only the
first kind, that of marked parallelism is concerned with the structure of verse
-- in rhythm, the recurrence of a certain sequence of rhythm, in alliteration,
in assonance and in rhyme. Now the force of this recurrence is to beget a
recurrence or parallelism answering to it in the words or thought and, speaking
roughly and rather for the tendency than the invariable result, the more marked
parallelism in structure whether of elaboration or of emphasis begets more
marked parallelism in the words and sense. And moreover parallelism in
expression tends to beget or passes into parallelism in thought. This point
reached we shall be able to see and account for the peculiarities of poetic
diction. To the marked or abrupt kind of parallelism belong metaphor, simile,
parable, and so on, where the effect is sought in likeness of things, and
antithesis, contrast, and so on, where it is sought in unlikeness. To the
chromatic parallelism belong gradation, intensity, climax, tone, expression (as
the word is used in music), chiaroscuro, perhaps emphasis: while the
faculties of Fancy and Imagination might range widely over both kinds, Fancy
belonging more especially to the abrupt than to the transitional
class."

-- From Gerard Manley Hopkins, "Poetic Diction," 1865

For an application to Hopkins's poetry, see an excerpt from Stephen Prickett, Words and the Word: Language,
Poetics and Biblical Interpretation (Cambridge: Cambridge University Press,
1986).

See also the publisher's description of Maria R. Lichtmann's
The Contemplative Poetry of Gerard Manley Hopkins, Princeton University Press, 1989.