Log24

Tuesday, May 7, 2019

Symbols and Mysteries

Filed under: General — Tags: , — m759 @ 11:21 AM

IMAGE- Like motions of a pattern's parts can induce motions of the whole. Escher-'Fishes and Scales,' Cullinane-'Invariance'

Monday, May 6, 2019

In Memoriam Goro Shimura (d. May 3, 2019)

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

From Richard Taylor, "Modular arithmetic:  driven by inherent beauty
and human curiosity
," The Letter of the Institute for Advanced Study  [IAS],
Summer 2012, pp. 6– 8 (links added) :

"Stunningly, in 1954, Martin Eichler (former IAS Member)
found a totally new reciprocity law . . . .

Within less than three years, Yutaka Taniyama and Goro Shimura
(former IAS Member) proposed a daring generalization of Eichler’s
reciprocity law to all cubic equations in two variables. A decade later,
André Weil (former IAS Professor) added precision to this conjecture,
and found strong heuristic evidence supporting the Shimura-Taniyama
reciprocity law. This conjecture completely changed the development of
number theory."

Sunday, March 25, 2012

Compare and Contrast

Filed under: General,Geometry — Tags: — m759 @ 9:00 AM
 

IMAGE- Escher, 'Fishes and Scales'

IMAGE- Cullinane, 'Invariance'

Background:

The Origin and Development of Erwin Panofsky's Theories of Art ,
Michael Ann Holly, doctoral thesis, Cornell University, 1981 (pdf, 10 MB)

Panofsky, Cassirer, and Perspective as Symbolic Form ,
Allister Neher, doctoral thesis, Concordia University, 2000

Friday, July 1, 2011

Symmetry Review

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

Popular novelist Dan Brown is to speak at Chautauqua Institution on August 1.

This suggests a review of some figures discussed here in a note on Brown from February 20, 2004

IMAGE- Like motions of a pattern's parts can induce motions of the whole. Escher-'Fishes and Scales,' Cullinane-'Invariance'

Related material: Notes from Nov. 5, 1981, and from Dec. 24, 1981.

For the lower figure in context, see the diamond theorem.

Friday, February 20, 2004

Friday February 20, 2004

Filed under: General,Geometry — Tags: — m759 @ 12:00 AM

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!’ ”

IMAGE- Escher, 'Fishes and Scales'

IMAGE- Cullinane, 'Invariance'

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

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