Monday, July 3, 2023
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Also on July 3, 2023 —
* See Parul Sehgal, "What We Learn from the Lives of Critics."
Wednesday, December 6, 2023
Monday, December 4, 2023
Latin and Latin Squares
"… it is not just its beauty that has made Mathematics so attractive.
Thirty or so years ago, a philosopher friend of mine remarked
rather dolefully, 'I am afraid that Latin, the knowledge of which
used to be the mark of a civilised person, will be replaced by
Mathematics as the universally accepted mark of learning.'
This was probably the most prescient statement he ever made,
as the importance of Mathematics is now recognised in fields
as diverse as medicine, linguistics, and even literature."
— Address by mathematician Dominic Welsh on June 16, 2006
Some Latin-square images from pure mathematics —
Some related Latin from this journal on June 16, 2006 —
AD PULCHRITUDINEM TRIA REQUIRUNTUR:
INTEGRITAS, CONSONANTIA, CLARITAS.
INTEGRITAS, CONSONANTIA, CLARITAS.
For some remarks on Latin-square structure,
see other posts tagged Affine Squares.
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Wednesday, May 3, 2023
Art Lesson for Doktor Faustus
Exercise: Show that Dürer's 1514 "magic" square is an affine automorphism.
For a solution, see other posts now tagged Affine Squares.
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Sunday, April 30, 2023
For Harlan Kane: The Walpurgisnacht Hallucination
Note that if the "compact Riemann surface" is a torus formed by
joining opposite edges of a 4×4 square array, and the phrase
"vector bundle" is replaced by "projective line," and so forth,
the above ChatGPT hallucination is not completely unrelated to
the following illustration from the webpage "galois.space" —
See as well the Cullinane diamond theorem.
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Saturday, January 21, 2023
Dead-Poet Witcraft
"Death is the mother of beauty." — Wallace Stevens
From the 2020 Feast of St. Wallace Stevens,
who reportedly died in 1955 on August 2 —
Related material —
Exercise: Can each order-4 magic square be obtained by some
transformation like the one above (i.e., preserving affine hyperplanes)?
If not, why not?
Update of 31 Jan. 2023 — Spoiler: Remarks by Tilman Piesk.
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Thursday, September 22, 2022
Affine Dürer
The previous post's image illustrating the
ancient Lo Shu square as an affine transformation
suggests a similar view of Dürer's square.
That view illustrates the structural principle
underlying the diamond theorem —
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De Colores
See as well . . .
Three-color patterns from 1964,
rendered as shades of grey —
A rather different approach —
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