By Stephen King
The geometric object of the title appears in a post mentioning Bourgain
in this journal. Bourgain appears also in today's online New York Times —
https://www.nytimes.com/2019/01/16/
obituaries/jean-bourgain-dead.html .
Bourgain reportedly died on December 22.
An image from this journal on that date —
Related poetic meditations —
See also Holy Field in this journal.
Some related mathematics —
Analysis of the Lo Shu structure —
Structure of the 3×3 magic square:
4 9 2
3 5 7 decreased by 1 is …
8 1 6
3 8 1
2 4 6
7 0 5
In base 3 —
10 22 01
02 11 20
21 00 12
As orthogonal Latin squares
(a well-known construction) —
1 2 0 0 2 1
0 1 2 2 1 0
2 0 1 1 0 2 .
— Steven H. Cullinane,
October 17, 2017
A book by this title, Richard A. Brualdi’s Combinatorial Matrix Classes ,
was published by Cambridge University Press in 2006:
For some related remarks, see The Counter (March 13, 2011).
My own work deals with combinatorial properties of matrices
of 0’s and 1’s, but in the context of Galois (i.e., finite) fields,
not the real or complex fields. Despite the generality of
their titles, Combinatorial Matrix Theory and Combinatorial
Matrix Classes do not deal with Galois matrices.
In memory of Charles Rosen:
Related material:
The Magic Square in Doctor Faustus (October 10th, 2012)
Elementary Finite Geometry (August 1st, 2012)
The Space of Horizons (August 7th, 2012)
Chromatic Plenitude (Rosen on Schoenberg)
"…as we saw, there are two different Latin squares of order 4…."
— Peter J. Cameron, "The Shrikhande Graph," August 26, 2010
Cameron counts Latin squares as the same if they are isotopic .
Some further context for Cameron's remark—
Cover Illustration Number 1 (1976):
Cover Illustration Number 2 (1991):
The Shrikhande Graph
______________________________________________________________________________
This post was prompted by two remarks…
1. In a different weblog, also on August 26, 2010—
The Accidental Mathematician— "The Girl Who Played with Fermat's Theorem."
"The worst thing about the series is the mathematical interludes in The Girl Who Played With Fire….
Salander is fascinated by a theorem on perfect numbers—
one can verify it for as many numbers as one wishes, and it never fails!—
and then advances through 'Archimedes, Newton, Martin Gardner,*
and a dozen other classical mathematicians,' all the way to Fermat’s last theorem."
2. "The fact that the pattern retains its symmetry when you permute the rows and columns
is very well known to combinatorial theorists who work with matrices."
[My italics; note resemblance to the Brualdi-Ryser title above.]
–Martin Gardner in 1976 on the diamond theorem
* Compare Eric Temple Bell (as quoted at the MacTutor history of mathematics site)—
"Archimedes, Newton, and Gauss, these three, are in a class by themselves
among the great mathematicians, and it is not for ordinary mortals
to attempt to range them in order of merit."
This is from the chapter on Gauss in Men of Mathematics .
Lotteries on August 17, 2008 |
Pennsylvania (No revelation) |
New York (Revelation) |
Mid-day (No belief) |
No belief, no revelation 492 Chinese 4 9 2 (See below.) |
Revelation without belief 423 4/23: |
Evening (Belief) |
Belief without revelation 272 (See below.) |
Belief and revelation 406 4/06: |
“What is combinatorial mathematics? Combinatorial mathematics, also referred to as combinatorial analysis or combinatorics, is a mathematical discipline that began in ancient times. According to legend the Chinese Emperor Yu (c. 2200 B.C.) observed the magic square 4 9 2
3 5 7 8 1 6 on the shell of a divine turtle….” — H.J. Ryser, Combinatorial Mathematics, Mathematical Association of America, Carus Mathematical Monographs 14 (1963) |
From Christian Tradition Today, by Jeffrey C. K. Goh (Peeters Publishers, 2004), p. 438: “Insisting that theological statements are not simply deduced from human experience, Rahner nevertheless stresses the experience of grace as the ‘real, fundamental reality of Christianity 272 ‘Grace’ is a key category in Rahner’s theology. He has expended a great deal of energy on this topic, earning himself the title, amongst others, of a ‘theologian of the graced search for meaning.’ See G. B. Kelly (ed.), Karl Rahner, in The Making of Modern Theology series (Edinburgh: T&T Clark, 1992).” |
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