Log24

Monday, January 7, 2019

Resonant Clarity

Filed under: General — Tags: , , , — m759 @ 11:00 AM
 

Abstract for a talk at the City University of New York:

The Experience of Meaning 
Jan Zwicky, University of Victoria 
09:00-09:40 Friday, April 5, 2013

Once the question of truth is settled, and often prior to it, what we value in a mathematical proof or conjecture is what we value in a work of lyric art: potency of meaning. An absence of clutter is a feature of such artifacts: they possess a resonant clarity that allows their meaning to break on our inner eye like light. But this absence of clutter is not tantamount to 'being simple': consider Eliot's Four Quartets  or Mozart's late symphonies. Some truths are complex, and they are simplified  at the cost of distortion, at the cost of ceasing to be  truths. Nonetheless, it's often possible to express a complex truth in a way that precipitates a powerful experience of meaning. It is that experience we seek — not simplicity per se , but the flash of insight, the sense we've seen into the heart of things. I'll first try to say something about what is involved in such recognitions; and then something about why an absence of clutter matters to them.

For some context, see posts tagged Artifacts.

Monday, August 27, 2018

Geometry and Simplicity

Filed under: General,Geometry — Tags: — m759 @ 9:27 PM

From

Thinking in Four Dimensions
By Dusa McDuff

"I’ve got the rather foolhardy idea of trying to explain
to you the kind of mathematics I do, and the kind of
ideas that seem simple to me. For me, the search
for simplicity is almost synonymous with the search
for structure.

I’m a geometer and topologist, which means that
I study the structure of space
. . . .

In each dimension there is a simplest space
called Euclidean space … "

— In Roman Kossak, ed.,
Simplicity:  Ideals of Practice in Mathematics and the Arts
(Kindle Locations 705-710, 735). Kindle Edition.

For some much simpler spaces of various
dimensions, see Galois Space in this journal.

Some small Galois spaces (the Cullinane models)

http://www.log24.com/log/pix18/180827-Simplicity-Springer-April_2013_conference.jpg

Monday, July 2, 2018

Another Letterman Intro

Filed under: General — Tags: — m759 @ 12:06 PM

Recognitions, Corrections;  Corrections, Recognitions.

"It is the dawning of the second gestalt 
in relation to the first 
that is the experience of meaning."

— Jan Zwicky in "The Experience of Meaning"
(at 27:36 of 44:36 in the video of her talk) 

Related remarks by the author of The Corrections

" Even friends of The Recognitions  have found it a daunting
text.  Jonathan Franzen, the best known of the book's current
day champions, has offered both praise and words of warning
to potential readers. 'I loved it,' he proclaimed in the pages
of
The New Yorker  back in 2002, where he held up Gaddis's
novel as the preeminent example of what Franzen calls 'the
Status model' of literature.  Authors who subscribe to the
'Status model' embrace fiction as the springboard for
'a discourse of genius and art-historical importance' freed
from the demands of the marketplace or the requirements of
mass consumption.  Yet even Franzen acknowledges the toll
exacted by this particular masterpiece.  He declares that 
The
Recognitions
  is 'the most difficult book I ever voluntarily read
in its entirety,' adding that he completed the task 'as a kind
of penance.' "

Now try Euclid.

Sunday, July 1, 2018

Deutsche Ordnung

The title is from a phrase spoken, notably, by Yul Brynner
to Christopher Plummer in the 1966 film “Triple Cross.”

Related structures —

Greg Egan’s animated image of the Klein quartic —

For a smaller tetrahedral arrangement, within the Steiner quadruple
system of order 8 modeled by the eightfold cube, see a book chapter
by Michael Huber of Tübingen

Steiner quadruple system in eightfold cube

For further details, see the June 29 post Triangles in the Eightfold Cube.

See also, from an April 2013 philosophical conference:

Abstract for a talk at the City University of New York:

The Experience of Meaning
Jan Zwicky, University of Victoria
09:00-09:40 Friday, April 5, 2013

Once the question of truth is settled, and often prior to it, what we value in a mathematical proof or conjecture is what we value in a work of lyric art: potency of meaning. An absence of clutter is a feature of such artifacts: they possess a resonant clarity that allows their meaning to break on our inner eye like light. But this absence of clutter is not tantamount to ‘being simple’: consider Eliot’s Four Quartets  or Mozart’s late symphonies. Some truths are complex, and they are simplified  at the cost of distortion, at the cost of ceasing to be  truths. Nonetheless, it’s often possible to express a complex truth in a way that precipitates a powerful experience of meaning. It is that experience we seek — not simplicity per se , but the flash of insight, the sense we’ve seen into the heart of things. I’ll first try to say something about what is involved in such recognitions; and then something about why an absence of clutter matters to them.

For the talk itself, see a YouTube video.

The conference talks also appear in a book.

The book begins with an epigraph by Hilbert

Sunday, July 28, 2013

Sermon

Filed under: General,Geometry — Tags: — m759 @ 11:00 AM

(Simplicity continued)

"Understanding a metaphor is like understanding a geometrical
truth. Features of various geometrical figures or of various contexts
are pulled into revealing alignment with one another by  the
demonstration or the metaphor.

What is 'revealed' is not that the alignment is possible; rather,
that the alignment is possible reveals the presence of already-
existing shapes or correspondences that lay unnoticed. To 'see' a
proof or 'get' a metaphor is to experience the significance of the
correspondence for what the thing, concept, or figure is ."

— Jan Zwicky, Wisdom & Metaphor , page 36 (left)

Zwicky illustrates this with Plato's diamond figure
​from the Meno  on the facing page— her page 36 (right).

A more sophisticated geometrical figure—

Galois-geometry key to
Desargues' theorem:

   D   E   F
 S'  P Q R
 S  P' Q' R'
 O  P1 Q1 R1

For an explanation, see 
Classical Geometry in Light of Galois Geometry.

Saturday, July 27, 2013

Simplicity

Filed under: General — Tags: — m759 @ 10:00 AM

(Continued from July 16)

From the schedule of an April 2013 philosophical conference:

Why should anyone care what Zwicky thinks?

1.  Her writings. In particular, Plato as Artist .

2.  Her husband. See Robert Bringhurst in this journal.

3.  A reading by Zwicky and Bringhurst on March 20, 2013.

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