(A sequel to Social Geometry)
Number mysticism I prefer, from a post of Nov. 15 last year —
Tuesday, January 10, 2023
Social Number Mysticism
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Tuesday, December 7, 2021
Tortoise Variations
Fanciful version —
Less fanciful versions . . .
|
Unmagic Squares Consecutive positive integers:
1 2 3 Consecutive nonnegative integers:
0 1 2
Consecutive nonnegative integers
00 01 02
This last square may be viewed as
Note that the ninefold square so viewed
As does, similarly, the ancient Chinese
These squares are therefore equivalent under This method generalizes. — Steven H. Cullinane, Nov. 20, 2021 |
.jpg)
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Tuesday, August 10, 2021
Ex Fano Apollinis
|
Margaret Atwood on Lewis Hyde's "Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159) What is "the next world"? It might be the Underworld…. The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation and art all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254) If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist. Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart. |
"As a Chinese jar . . . ."
— Four Quartets
|
Rosalind Krauss "If we open any tract– Plastic Art and Pure Plastic Art or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter. They are talking about Being or Mind or Spirit. From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete. Or, to take a more up-to-date example…."
"He was looking at the nine engravings and at the circle,
"And it's whispered that soon if we all call the tune
The nine engravings of The Club Dumas
An example of the universal— or, according to Krauss,
"This is the garden of Apollo, |
The "Katz" of the August 7 post Art Angles
is a product of Princeton's
Department of Art and Archaeology.
ART —
ARCHAEOLOGY —
"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."
– The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71
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Saturday, July 3, 2021
Here, There, and Chicago
The above phrase "the intersection of storytelling and visual arts"
suggests a review . . .
Storytelling —
Visual arts —
"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."
– The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71
A Midrash for Michener —
For a connection of the above "Holy Field"
with pure mathematics, see Coxeter's Aleph.
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Monday, June 17, 2019
Wednesday, January 16, 2019
Permutahedron Dream
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 —
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Sunday, December 23, 2018
Sunday, December 9, 2018
Tuesday, October 17, 2017
Plan 9 Continues
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
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Friday, May 30, 2014
Combinatorial Matrix Classes
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.
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Tuesday, December 11, 2012
Plenitude
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)
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Sunday, March 13, 2011
The Counter
"…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 .
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Monday, August 18, 2008
Monday August 18, 2008
| 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: |
No belief, no revelation:
An encounter with “492”–
An encounter with “492”–
| “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) |
Belief without revelation:
Theology and human experience,
and the experience of “272”–
Theology and human experience,
and the experience of “272”–
| 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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