Choreography and Markov Process

Video Link from Spring 2021 MAA Meeting

video link



Here is one not banned by suchlike.  Suppose, that man is born into freedom and his potential is by way of symbol the one knot-band.  You are free to read as I am free to write, just as one knot-band with another would conceal nothing more together. So, we are not bound to each other. A grander design would have instead one knot-bound to the other by insinuation (and the symbol is the Klein Bottle, which is composed of the two by way of making ends meet).  Suppose, therefore, that for freedom there is no escape from being one-sided. 

One knot like the Other

One man and a woman apart from one another.

Man and woman who are knot-bound in matrimony.  Two become one as confluence, and the one is knot-split.

One Knot Split Over Rules

Page of Cups

Extract from Plato's Republic as Ruled Space

The Golden Section

Projective Geometry Construction


wrath. noun. retributory punishment for an offense or a crime : divine chastisement.  (Merriam-Webster)
Wrath isn't necessarily mere anger, but a qualified operation, with moral obligation.   Wrath belongs psychologically to a temperament  known as coleric.  One way or another, people would assert that  a mean tone (of voice) is a property of this temperament, but if for good purpose, then suppose that it is golden.  Hence, the golden meantone is a temperament involving the divine proportion, also known as the golden mean.
"algebraic temperament"


Luke 2:19 in harmonic perspective. The red word is the longer and the blue word is the shorter, in the divine section, meaning that the proportion of the short to the long is the same as the long to the whole of the two together. In reality, the two words are in the same-sized boxes, but the nature of perspective reduces the appearance of things at length.

The formula for proportion, supposing the longer is a unit length of one pica, is given also as a quadratic:

X * X + X - 1 = 0,

where X is the shorter length.

The page in the photo is from Biblia Sacra:  Iuxta Vulgatam Versionem, Deutsche Bibelgesellschaft. 

The camera for the photo is a digital model with macro by Samsung.

Geometric calculations are performed using "Cinderella Version 2.9" software (http://cinderella.de) and are based on mathematical theory given in Projective Geometry, by T. Ewan Faulkner, Dover Publications.

 (*)  Lama Lodo Rimpoche.  Quintessence of the Animate and Inanimate:  Discourse on the Holy Dharma.  page 114-115.  KDK Publications:  San Francisco.


Submodules of Z[x,y]

Let M = Z[1/2,1/5] (ring of polynomials evaluated at 1/2 and 1/5 with integer coefficients))

Then let K = Z[1/2] a submodule of M.

Does the following calculation hold for M/K?

Take 9/10 from M, then what is its congruence in M/K?

9/10 = 5/10 + 4/10 = 1/2 + 2/5 and since 1/2 is from K, then

9/10 is congruent to 2/5 + K in M/K?

A Page of Cups

A Tribute to Brunello's Sommelier


A Page of Swords

Lewis Carrol's first page from Alice Through the Looking Glass (and what she saw there)

White Pawn (Alice) to play, and win in eleven moves.


A Page of Pentacles

...because a library assistant is a valet of pages

knot slackened pentacle