Monday, June 17, 2019

The Callahan Turtle

Filed under: General — Tags: , — m759 @ 10:54 PM

By Stephen King

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

Wednesday, January 16, 2019

Permutahedron Dream

Filed under: General — Tags: , , , — m759 @ 3:21 PM

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 —


Bourgain reportedly died on December 22.

An image from this journal on that date

Related poetic meditations —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

Sunday, December 23, 2018


Filed under: General — Tags: — m759 @ 8:40 PM

An exercise in bulk apperception.

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

Sunday, December 9, 2018

A Small Space

Filed under: General — Tags: — m759 @ 1:00 PM

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

Tuesday, October 17, 2017

Plan 9 Continues

Filed under: General,Geometry — Tags: , — m759 @ 9:00 PM

See also Holy Field in this journal.

Some related mathematics —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

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

Friday, May 30, 2014

Combinatorial Matrix Classes

Filed under: General,Geometry — Tags: — m759 @ 7:59 PM

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.

Tuesday, December 11, 2012


Filed under: General,Geometry — Tags: — m759 @ 2:00 PM

In memory of Charles Rosen:

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

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)

IMAGE- Charles Rosen on 'a final demarcation of form'

Sunday, March 13, 2011

The Counter

Filed under: General,Geometry — m759 @ 11:00 AM

"…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 .

Monday, August 18, 2008

Monday August 18, 2008

Filed under: General,Geometry — m759 @ 9:00 AM
The Revelation Game

(See also Jung’s birthday.)

Google logo, Aug. 18, 2008: Dragon playing Olympic ping pong

Lotteries on
August 17,
(No revelation)
New York
(No belief)
No belief,
no revelation



4 9 2
3 5 7
8 1 6

(See below.)

without belief



in Toronto

Belief without


on Grace

(See below.)

Belief and



and Art

No belief, no revelation:
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”–

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 itself.’ 272

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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