— Niall Ferguson, Kissinger, 1923-1968: The Idealist
From this journal on Guy Fawkes Day, 2011—
Shadows
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— Niall Ferguson, Kissinger, 1923-1968: The Idealist
From this journal on Guy Fawkes Day, 2011—
Shadows
|
"Some obviously very irrelevant and wildly nonsensical
interpretations that are not worth serious comment
are being put forward all the time."
— Fritz Senn, "
Indeed they are.
See David G. Poole, "The Stochastic Group,"
American Mathematical Monthly, volume 102, number 9
(November, 1995), pages 798–801.
* This post was suggested by the phrase "The Diamond Theorem,
also known as the von Neumann-Birkhoff conjecture" in a
ChatGPT-3.5 hallucination today.
That phrase suggests a look at the Birkhoff-von Neumann theorem:
The B.-von N. theorem suggests a search for analogous results
over finite fields. That search yields the Poole paper above,
which is related to my own "diamond theorem" via affine groups.
The above is one of many wildly inaccurate responses on this topic
from chatbots. A chatbot combined with search, however —
such as Bing Chat with GPT-4 — can be both accurate and helpful.
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 . . .
"Play Stella by Starlight for Lady Macbeth" — Bob Dylan
|
For enthusiasts of arithmetic rather than geometry —
"4 + 12 = 16."
And for fans of Christoper Nolan — Window Panes :
For Sam Levinson, a narrow window —
And away he gone day
And away he gone night
And away he gone dark
And away he gone light
— Song lyric, Edward Sharpe & the Magnetic Zeros
Related material from Wikipedia —
" 'Brother' was named after Ebert's good friend and famed actor
Heath Ledger, who died in 2008.* Ebert said in an interview with
the BuildSeriesNYC in early 2020 that he and Ledger, the night
before Ledger's death, were talking about a movie script concept
where they are brothers, and one of them dies, and the spirit is
with the other. Ebert talked about being stunned the next morning
to find out Ledger had died."
* Specifically, on January 22, 2008.
Related material from this journal —
A post of 11:30 PM ET January 21, 2008: Serious Numbers.
"The hard sand breaks,
And the grains of it
Are clear as wine."
— By "H. D."… “Hermes of the Ways,”
Pp. 21-23, Vol. 1, No. 5 of The Glebe —
Des Imagistes , February, 1914.
https://www.etymonline.com/word/dia- —
"… before vowels, di-, word-forming element meaning
'through, in different directions, between,' also often
merely intensive, 'thoroughly, entirely,' from Greek
dia 'through; throughout,' probably cognate with bi-
and related to duo 'two' (from PIE root *dwo- 'two')
with a base sense of 'twice.' "
A midrash for Heidegger —
Here "PIE" does not refer to food. It is an acronym
for "Proto-Indo-European."
See as well "Language Animal" in this journal.
The above two reported death dates:
Accuracy check for a post from midnight, October 10-11, 2023 —
"Blackboard Jungle," 1955 —
"Through the unknown, remembered gate . . . ."
A differently remembered gate —
509 Fourth Avenue, Warren, Pennsylvania —
Related material —

Friday, July 11, 2014
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* Author of Jewel Box: Stories ( Erewhon Books, Oct. 24, 2023).
The phrase "the mathematical concept of invariance of symmetry"
in the previous post suggests a Google search . . .
For those who prefer narrative to mathematics, the search result
"The Time Invariance of Snow" is not without interest.
See also "Snow Queen" in this journal.
"Sharpie, we have condensed six dimensions into four,
then we either work by analogy into six, or we have to use math
that apparently nobody but Jake and my cousin Ed understands.
Unless you can think of some way to project six dimensions into three–
you seem to be smart at such projections."
I closed my eyes and thought hard. "Zebbie, I don't think it can be done.
Maybe Escher could have done it."
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