Glow with the Flow
The above flashback was inspired by @marcelanow's IG today —
Some context (click to enlarge) . . .
Saturday, January 6, 2024
Monday, November 27, 2023
Problems with the Process
Condensed from Peter J. Cameron's weblog today —
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“Words that tear and strange rhymes” "In his youth, Paul Simon thought of himself as a poet . . . . And surprisingly often he describes problems with the process:
For me, things were somewhat similar. Like many people, I wrote poetry in my youth. Julian Jaynes says something like 'Poems are rafts grasped at by men drowning in inadequate minds', but I think I knew from early on that one of the main reasons was to practise my writing, so that when I had something to say I could say it clearly. When Bob Dylan renounced the over-elaborate imagery of Blonde on Blonde for the clean simplicity of John Wesley Harding, I took that as a role model. Could Simon’s experience happen in mathematics? It is possible to imagine that an important mathematical truth is expressed in 'words that tear and strange rhymes'. More worryingly, an argument written in the most elegant style could be wrong, and we may be less likely to see the mistake because the writing is so good." |
The problem with the process in this case is Cameron's misheard lyrics.
From https://www.paulsimon.com/track/kathys-song-2/ —
And a song I was writing is left undone
I don’t know why I spend my time
Writing songs I can’t believe
With words that tear and strain to rhyme
A rather different artist titled a more recent song
"Strange Rhymes Can Change Minds."
See also . . .
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Tuesday, April 25, 2023
Bedknobs and Broomsticks
"Bedknobs and Broomsticks is a 1971 American musical fantasy film
directed by Robert Stevenson and produced by Bill Walsh for
Walt Disney Productions. It is loosely based upon the books
The Magic Bedknob; or, How to Become a Witch in Ten Easy Lessons
(1944) and Bonfires and Broomsticks (1947) by English children's author
Mary Norton."
Glow with the Flow
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Saturday, August 23, 2014
Explicatio
(The title is from a post of July 8, 2010.)
“What is important is the ability to tell stories through character.”
— Diana Gabaldon, author of the Outlander series of novels
An image from the bottom line of images in the previous post:
In memory of Scottish folk singer Jean Redpath,
who reportedly died on Thursday, August 21:
See also this journal on August 21.
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Saturday, May 24, 2014
Lyric Stupidity
From a song discussed in yesterday’s online NY Times :
“Blue, blue, my love is blue.”*
Trigger warning from SNL’s Weekend Update on April 12, 2014:
“It was announced this week that in an upcoming issue of
Life With Archie , the main character Archie Andrews
will die, following a lifelong struggle with blue balls.”
* Misheard version of Bryan Blackburn‘s “blue, blue, my world is blue”
translation of the Pierre Cour lyric “bleu, bleu, l’amour est bleu “
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Sunday, January 26, 2014
Blazing Bride’s Chair
A sequel to last night's link Shear —
Some dead poet's words —
The "bride's chair" is the figure illustrating Euclid's proof
of the Pythagorean theorem (click image to enlarge) —
See also…
Not since Madeline Kahn in Blazing Saddles …
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Sunday, March 18, 2012
Square-Triangle Diamond
The diamond shape of yesterday's noon post
is not wholly without mathematical interest …
"Every triangle is an n -replica" is true
if and only if n is a square.
The 16 subdiamonds of the above figure clearly
may be mapped by an affine transformation
to 16 subsquares of a square array.
(See the diamond lattice in Weyl's Symmetry .)
Similarly for any square n , not just 16.
There is a group of 322,560 natural transformations
that permute the centers of the 16 subsquares
in a 16-part square array. The same group may be
viewed as permuting the centers of the 16 subtriangles
in a 16-part triangular array.
(Updated March 29, 2012, to correct wording and add Weyl link.)
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Wednesday, February 8, 2012
Lichtung!
(Continued from Dec. 5, 2002)
From Bad…
|
Braucht´s noch Text? |
To Verse—
|
manche meinen |
|
by Ernst Jandl |
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Tuesday, February 15, 2011
Road House
Again, this couldn't happen again.
This is that "once in a lifetime,"
this is the thrill divine.
The great 1949 days (according to Jack Kerouac)—
On the Road—
Shearing began to play his chords; they rolled out of the piano in great rich showers, you'd think the man wouldn't have time to line them up. They rolled and rolled like the sea. Folks yelled for him to "Go!" Dean was sweating; the sweat poured down his collar. "There he is! That's him! Old God! Old God Shearing! Yes! Yes! Yes!" And Shearing was conscious of the madman behind him, he could hear every one of Dean's gasps and imprecations, he could sense it though he couldn't see. "That's right!" Dean said. "Yes!" Shearing smiled; he rocked. Shearing rose from the piano, dripping with sweat; these were his great 1949 days before he became cool and commercial. When he was gone Dean pointed to the empty piano seat. "God's empty chair," he said.
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Sunday, February 21, 2010
Reflections
From the Wikipedia article "Reflection Group" that I created on Aug. 10, 2005— as revised on Nov. 25, 2009—
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Historically, (Coxeter 1934) proved that every reflection group [Euclidean, by the current Wikipedia definition] is a Coxeter group (i.e., has a presentation where all relations are of the form ri2 or (rirj)k), and indeed this paper introduced the notion of a Coxeter group, while (Coxeter 1935) proved that every finite Coxeter group had a representation as a reflection group [again, Euclidean], and classified finite Coxeter groups. Finite fields
When working over finite fields, one defines a "reflection" as a map that fixes a hyperplane (otherwise for example there would be no reflections in characteristic 2, as −1=1 so reflections are the identity). Geometrically, this amounts to including shears in a hyperplane. Reflection groups over finite fields of characteristic not 2 were classified in (Zalesskiĭ & Serežkin 1981). |
Related material:
"A Simple Reflection Group of Order 168," by Steven H. Cullinane, and
by Ascher Wagner, U. of Birmingham, received 27 July 1977
| Journal | Geometriae Dedicata |
| Publisher | Springer Netherlands |
| Issue | Volume 9, Number 2 / June, 1980 |
[A primitive permuation group preserves
no nontrivial partition of the set it acts upon.]
Clearly the eightfold cube is a counterexample.
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Friday, October 6, 2006
Friday October 6, 2006
A Visual Proof
The great mathematician
Robert P. Langlands
is 70 today.
In honor of his expository work–
notably, lectures at
The Institute for Advanced Study
on “The Practice of Mathematics“
and a very acerbic review (pdf) of
a book called Euclid’s Window—
here is a “Behold!” proof of
the Pythagorean theorem:
The picture above is adapted from
a sketch by Eves of a “dynamical”
proof suitable for animation.
The proof has been
described by Alexander Bogomolny
as “a variation on” Euclid I.47.
Bogomolny says it is a proof
by “shearing and translation.”
It has, in fact, been animated.
The following version is
by Robert Foote:
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