Monday, April 29, 2019

Like Decorations in a Cartoon Graveyard

Filed under: General — Tags: — m759 @ 2:24 PM


I need a photo opportunity, I want a shot at redemption.
 Don’t want to end up a cartoon in a cartoon graveyard.”
 — Paul Simon

A death on the date of the above New Yorker piece — Oct. 15, 2018 —

See as well the Pac-Man-like figures in today's previous post
as well as the Monday, Oct. 15, 2018, post "History at Bellevue."

The Hustvedt Array

Filed under: General — Tags: — m759 @ 12:58 PM

For Harlan Kane

"This time-defying preservation of selves,
this dream of plenitude without loss,
is like a snow globe from heaven,
a vision of Eden before the expulsion."

— Judith Shulevitz on Siri Hustvedt in
The New York Times  Sunday Book Review
of March 31, 2019, under the headline
"The Time of Her Life."

Edenic-plenitude-related material —

"Self-Blazon… of Edenic Plenitude"

(The Issuu text is taken from Speaking about Godard , by Kaja Silverman
and Harun Farocki, New York University Press, 1998, page 34.)

Preservation-of-selves-related material —

Other Latin squares (from October 2018) —

Thursday, October 25, 2018

Aesthetic Requiem

Filed under: General — Tags: , — m759 @ 12:01 AM

See also Aesthetics (Oct. 17, 2018).

Thursday, October 18, 2018

The Quick and the Dirty

Filed under: General — Tags: — m759 @ 2:32 PM

Two stars of the 2016 film "Urge"

See also other posts tagged QDOS (Quick and Dirty Operating System).

“Break on through” — The Doors

Filed under: General — Tags: — m759 @ 1:38 PM

Wednesday, October 17, 2018

Breakthrough Prize

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

181017-Breakthrough_Prize-news.jpg (500×212)

"…  what once seemed pure abstractions have turned out to
      underlie real physical processes."

— https://breakthroughprize.org/Prize/3

Related material from the current New Yorker


Filed under: General,Geometry — Tags: — m759 @ 11:22 AM

From "The Phenomenology of Mathematical Beauty,"
by Gian-Carlo Rota —

The Lightbulb Mistake

. . . . Despite the fact that most proofs are long, and despite our need for extensive background, we think back to instances of appreciating mathematical beauty as if they had been perceived in a moment of bliss, in a sudden flash like a lightbulb suddenly being lit. The effort put into understanding the proof, the background material, the difficulties encountered in unraveling an intricate sequence of inferences fade and magically disappear the moment we become aware of the beauty of a theorem. The painful process of learning fades from memory, and only the flash of insight remains.

We would like  mathematical beauty to consist of this flash; mathematical beauty should  be appreciated with the instantaneousness of a lightbulb being lit. However, it would be an error to pretend that the appreciation of mathematical beauty is what we vaingloriously feel it should be, namely, an instantaneous flash. Yet this very denial of the truth occurs much too frequently.

The lightbulb mistake is often taken as a paradigm in teaching mathematics. Forgetful of our learning pains, we demand that our students display a flash of understanding with every argument we present. Worse yet, we mislead our students by trying to convince them that such flashes of understanding are the core of mathematical appreciation.

Attempts have been made to string together beautiful mathematical results and to present them in books bearing such attractive titles as The One Hundred Most Beautiful Theorems of Mathematics . Such anthologies are seldom found on a mathematician’s bookshelf. The beauty of a theorem is best observed when the theorem is presented as the crown jewel within the context of a theory. But when mathematical theorems from disparate areas are strung together and presented as “pearls,” they are likely to be appreciated only by those who are already familiar with them.

The Concept of Mathematical Beauty

The lightbulb mistake is our clue to understanding the hidden sense of mathematical beauty. The stark contrast between the effort required for the appreciation of mathematical beauty and the imaginary view mathematicians cherish of a flashlike perception of beauty is the Leitfaden  that leads us to discover what mathematical beauty is.

Mathematicians are concerned with the truth. In mathematics, however, there is an ambiguity in the use of the word “truth.” This ambiguity can be observed whenever mathematicians claim that beauty is the raison d’être of mathematics, or that mathematical beauty is what gives mathematics a unique standing among the sciences. These claims are as old as mathematics and lead us to suspect that mathematical truth and mathematical beauty may be related.

Mathematical beauty and mathematical truth share one important property. Neither of them admits degrees. Mathematicians are annoyed by the graded truth they observe in other sciences.

Mathematicians ask “What is this good for?” when they are puzzled by some mathematical assertion, not because they are unable to follow the proof or the applications. Quite the contrary. Mathematicians have been able to verify its truth in the logical sense of the term, but something is still missing. The mathematician who is baffled and asks “What is this good for?” is missing the sense  of the statement that has been verified to be true. Verification alone does not give us a clue as to the role of a statement within the theory; it does not explain the relevance  of the statement. In short, the logical truth of a statement does not enlighten us as to the sense of the statement. Enlightenment , not truth, is what the mathematician seeks when asking, “What is this good for?” Enlightenment is a feature of mathematics about which very little has been written.

The property of being enlightening is objectively attributed to certain mathematical statements and denied to others. Whether a mathematical statement is enlightening or not may be the subject of discussion among mathematicians. Every teacher of mathematics knows that students will not learn by merely grasping the formal truth of a statement. Students must be given some enlightenment as to the sense  of the statement or they will quit. Enlightenment is a quality of mathematical statements that one sometimes gets and sometimes misses, like truth. A mathematical theorem may be enlightening or not, just as it may be true or false.

If the statements of mathematics were formally true but in no way enlightening, mathematics would be a curious game played by weird people. Enlightenment is what keeps the mathematical enterprise alive and what gives mathematics a high standing among scientific disciplines.

Mathematics seldom explicitly acknowledges the phenomenon of enlightenment for at least two reasons. First, unlike truth, enlightenment is not easily formalized. Second, enlightenment admits degrees: some statements are more enlightening than others. Mathematicians dislike concepts admitting degrees and will go to any length to deny the logical role of any such concept. Mathematical beauty is the expression mathematicians have invented in order to admit obliquely the phenomenon of enlightenment while avoiding acknowledgment of the fuzziness of this phenomenon. They say that a theorem is beautiful when they mean to say that the theorem is enlightening. We acknowledge a theorem’s beauty when we see how the theorem “fits” in its place, how it sheds light around itself, like Lichtung — a clearing in the woods. We say that a proof is beautiful when it gives away the secret of the theorem, when it leads us to perceive the inevitability of the statement being proved. The term “mathematical beauty,” together with the lightbulb mistake, is a trick mathematicians have devised to avoid facing up to the messy phenomenon of enlightenment. The comfortable one-shot idea of mathematical beauty saves us from having to deal with a concept that comes in degrees. Talk of mathematical beauty is a cop-out to avoid confronting enlightenment, a cop-out intended to keep our description of mathematics as close as possible to the description of a mechanism. This cop-out is one step in a cherished activity of mathematicians, that of building a perfect world immune to the messiness of the ordinary world, a world where what we think should be true turns out to be true, a world that is free from the disappointments, ambiguities, and failures of that other world in which we live.

How many mathematicians does  it take to screw in a lightbulb?

Tuesday, October 16, 2018


Filed under: General — Tags: — m759 @ 9:11 PM

For the title, see the Wikipedia article on the late Paul Allen.

See also . . .

Related material — the late Patrick Swayze in Ghost and King Solomon's Mines.

"Please wait as your operating system is initiated."


Monday, October 15, 2018

History at Bellevue

Filed under: General,Geometry — Tags: , — m759 @ 9:38 PM

The previous post, "Tesserae for a Tesseract," contains the following
passage from a 1987 review of a book about Finnegans Wake

"Basically, Mr. Bishop sees the text from above
and as a whole — less as a sequential story than
as a box of pied type or tesserae for a mosaic,
materials for a pattern to be made."

A set of 16 of the Wechsler cubes below are tesserae that 
may be used to make patterns in the Galois tesseract.

Another Bellevue story —

“History, Stephen said, is a nightmare
from which I am trying to awake.”

— James Joyce, Ulysses

Tesserae for a Tesseract

Filed under: General — Tags: , — m759 @ 8:22 PM

The source —

The Other Side

Filed under: General — Tags: , — m759 @ 1:00 PM

"As far as I know, there is no escape for mortal beings from time.
But experimental ideas of practical access to eternity
exerted tremendous sway on educated, intelligent, and forward-
looking people in the late nineteenth and early twentieth centuries,
with a cutoff that was roughly coincident with the First World War.
William James died in 1910 without having ceased to urge
an open-minded respect for occult convictions."

New Yorker  art critic Peter Schjeldahl in the Oct. 22, 2018, issue.

Also in that issue —

For Zingari Shoolerim*

Filed under: General,Geometry — Tags: , — m759 @ 12:19 PM

IMAGE- Site with keywords 'Galois space, Galois geometry, finite geometry' at DiamondSpace.net

The structure at top right is that of the
in the previous post.

* "Zingari shoolerim" is from
    Finnegans Wake .

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