Finite Relativity

Today is the 18th birthday of my note

"The Relativity Problem in Finite Geometry."

That note begins with a quotation from Weyl:

"This is the relativity problem: to fix objectively a class of equivalent coordinatizations and to ascertain the group of transformations S mediating between them."

-- Hermann Weyl, The Classical Groups, Princeton University Press, 1946, p. 16

Here is another quotation from Weyl, on the profound branch of mathematics known as Galois theory, which he says

"... is nothing else but the relativity theory for the set Sigma, a set which, by its discrete and finite character, is conceptually so much simpler than the infinite set of points in space or space-time dealt with by ordinary relativity theory."

-- Weyl, Symmetry, Princeton University Press, 1952, p. 138

This second quotation applies equally well to the much less profound, but more accessible, part of mathematics described in Diamond Theory and in my note of Feb. 20, 1986.

The Da Vinci Code
and Symbology at Harvard

The protagonist of the recent bestseller The Da Vinci Code is Robert Langdon, "a professor of Religious Symbology at Harvard University."  A prominent part in the novel is played by the well-known Catholic organization Opus Dei.  Less well known (indeed, like Langdon, nonexistent) is the academic discipline of "symbology."  (For related disciplines that do exist, click here.) What might a course in this subject at Harvard be like?

Harvard Crimson, April 10, 2003: While Opus Dei members said that they do not refer to their practices of recruitment as "fishing," the Work’s founder does describe the process of what he calls "winning new apostles" with an aquatic metaphor. Point #978 of The Way invokes a passage in the New Testament in which Jesus tells Peter that he will make him a "fisher of men." The point reads: " ‘Follow me, and I will make you into fishers of men.’ Not without reason does our Lord use these words: men—like fish—have to be caught by the head. What evangelical depth there is in the ‘intellectual apostolate!’ ”

Exercise for Symbology 101:

Describe the symmetry
in each of the pictures above.
Show that the second picture
retains its underlying structural
symmetry under a group of
322,560 transformations.

Having reviewed yesterday's notes
on Gombrich, Gadamer, and Panofsky,
discuss the astrological meaning of
the above symbols in light of
today's date, February 20.

Extra credit:

Relate the above astrological
symbolism to the four-diamond
symbol in Jung's Aion.

Happy metaphors!

Robert Langdon

What is Poetry, Part II --

Gombrich vs. Gadamer

Excerpts from
Tetsuhiro Kato on

Gombrich and the
Hermeneutics of Art

Kato on Gombrich

"... according to Gombrich, an image is susceptible to become a target for 'symbol detectives'.... But the hidden authorial intention... ([for example]... astrology, recalling the famous warning of Panofsky [1955: 32]), almost always tends to become a reproduction of the interpreter's own ideological prejudice. Not to give into the irrationalism such psychological overinterpretation might invite.... we have to look for the origin of meaning... in...  the social context.... The event of image making is not the faithful transcription of the outside world by an innocent eye, but it is the result of the artist's act of selecting the 'nearest equivalence'... based on social convention...."

Kato on Gadamer 

"For [Gadamer], picture reading is a process where a beholder encounters a picture as addressing him or her with a kind of personal question, and the understanding develops in the form of its answer (Gadamer 1981: 23-24; Gadamer 1985: 97,102-103).  But, it must be noted that by this Gadamer does not mean to identify the understanding of an image with some sort of 'subsumption' of the image into its meaning (Gadamer 1985: 100). He insists rather that we can understand an image only by actualizing what is implied in the work, and engage in a dialogue with it. This process is ideally repeated again and again, and implies different relations than the original conditions that gave birth to the work in the beginning (Gadamer 1985: 100).

What matters here for Gadamer is to let the aesthetic aspect of image take its own 'Zeitgestalt' (Gadamer 1985: 101)."

Example (?) -- the Zeitgestalt
of today's previous entry:

See, too,
 The Quality of Diamond.

Kato's References:

Gadamer, Hans-Georg. 1981. "Philosophie und Literatur: Was ist die Literatur?," Phänomenologische Forschungen 11 (1981): 18-45.

Gadamer, Hans-Georg. 1985. "Über das Lesen von Bauten und Bildern." Modernität und Tradition: Festschrift für Max Imdahl zum 60. Geburtstag. Ed. Gottfried Boehm, Karlheinz Stierle, Gundorf Winter. Munchen: Wilhelm Fink. 97-103.

Panofsky, Erwin. 1955. Meaning in the Visual Arts: Papers in and on Art History. New York: Anchor.

Five Easy Pieces
for Lee Marvin's Birthday

1.	"EVERYTHING'S a story. You are a story-- I am a story." -- Frances Hodgson Burnett, A Little Princess
2.	"You see that sign, sir?" [Pointing to a notice demanding courtesy from customers]
3.
4.	"You see this sign?"
5.	"Aquarians are extremely independent."

Diamonds and Whirls

New applets have rotating 3D versions of the diamond and whirl cubes in Block Designs.

Story

"Oh, Sara!" she whispered joyfully. "It is like a story!"

"It IS a story," said Sara. "EVERYTHING'S a story. You are a story-- I am a story."

-- Frances Hodgson Burnett,
    A Little Princess

For further details, see Why Narrative?

Hard Core, Part II:
Star of Africa

In memory of St. Katharine Hepburn,
who died on St. Peter's Day, 2003:
"Although the greater saints
are more acceptable to God
than the lesser,
it is sometimes profitable
to pray to the lesser."
-- St. Thomas Aquinas  

From The Times, UK, Feb. 18, 2004:

Straw denies
a big-three takeover
at EU summit 

Britain's Foreign Secretary "said that there were no plans to set up a small body within the EU to take control of its affairs.

However, he told a news conference at the Foreign Office that it made sense for the three biggest economies to work 'collaboratively' on matters of common interest....

At tonight’s summit Mr Blair, Gerhard Schröder, the German Chancellor, and President Chirac of France will discuss initiatives to co-ordinate and strengthen the EU’s industrial policy....

German commentators regard the summit as a sea-change in British policy towards Europe — a signal that London’s main aim is no longer to split Paris and Berlin."

Hard Core

From USATODAY.com,
Posted 2/16/2004 11:16 PM

Diamond at heart of star
outweighs any on Earth

Astronomers announced Friday that a white dwarf star they've been studying is a chunk of crystallized carbon that weighs 5 million trillion trillion pounds. That's the same as a diamond that is approximately 10 billion trillion trillion carats, or a one followed by 34 zeros.

Twinkle-twinkle indeed: An artist's conception of the diamond core of a dead white-dwarf star. Harvard-Smithsonian Center for Astrophysics.

"It's the mother of all diamonds," said astronomer Travis Metcalfe, Harvard-Smithsonian Center for Astrophysics....

The biggest diamond on Earth is the 530-carat Star of Africa, part of the Crown Jewels of England. It was cut from a 3,100-carat gem*, the biggest ever found.

* The Cullinan diamond

Black History Month

Gestalt Update

Updated Block Designs page with material on Gestalt aesthetics and the work of James J. Gibson.