Tuesday, September 7, 2021

Raiders of the Lost Symbol … Continues*

Filed under: General — m759 @ 7:12 PM

A Log24 search for "Watercourse" leads to . . .

("Watercourse" is in the Customer review link.)

The "five years ago" link leads to . . .


"What modern painters are trying to do,
if they only knew it, is paint invariants."

— James J. Gibson in Leonardo
(Vol. 11, pp. 227-235.
Pergamon Press Ltd., 1978)

An example of invariant structure:

The three line diagrams above result from the three partitions, into pairs of 2-element sets, of the 4-element set from which the entries of the bottom colored figure are drawn.  Taken as a set, these three line diagrams describe the structure of the bottom colored figure.  After coordinatizing the figure in a suitable manner, we find that this set of three line diagrams is invariant under the group of 16 binary translations acting on the colored figure.

A more remarkable invariance — that of symmetry itself — is observed if we arbitrarily and repeatedly permute rows and/or columns and/or 2×2 quadrants of the colored figure above. Each resulting figure has some ordinary or color-interchange symmetry.

This sort of mathematics illustrates the invisible "form" or "idea" behind the visible two-color pattern.  Hence it exemplifies, in a way, the conflict described by Plato between those who say that "real existence belongs only to that which can be handled" and those who say that "true reality consists in certain intelligible and bodiless forms."

* See that title in this journal.

Tuesday, October 28, 2014

Raiders of the Lost Symbol

Filed under: General,Geometry — m759 @ 5:00 PM

A print copy of next Sunday’s New York Times Book Review
arrived in today’s mail. From the front-page review:

Marcel Theroux on The Book of Strange New Things ,
a novel by Michel Faber —

“… taking a standard science fiction premise and
unfolding it with the patience and focus of a
tai chi master, until it reveals unexpected
connections, ironies and emotions.”

What is a tai chi master, and what is it that he unfolds?

Perhaps the taijitu  symbol and related material will help.

The Origin of Change

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

“Two things of opposite natures seem to depend
On one another, as a man depends
On a woman, day on night, the imagined

On the real. This is the origin of change.
Winter and spring, cold copulars, embrace
And forth the particulars of rapture come.”

Wallace Stevens,
“Notes Toward a Supreme Fiction,”
Canto IV of “It Must Change”

Tuesday, March 26, 2013

Raiders of the Lost Symbols

Filed under: General — m759 @ 10:09 AM

See Lines of Symbols in this journal.

Thursday, October 30, 2014


Filed under: General — m759 @ 5:09 PM

This journal Tuesday,  Oct. 28, 2014, at 5 PM ET:

“What is a tai chi master, and what is it that he unfolds?”

From an earlier post, Hamlet’s father’s ghost
on “the fretful porpentine”:

Hamlet , Act 1, Scene 5 —


“I could a tale unfold whose lightest word
Would harrow up thy soul, freeze thy young blood,
Make thy two eyes, like stars, start from their spheres,
Thy knotted and combinèd locks to part
And each particular hair to stand on end,
Like quills upon the fretful porpentine:
But this eternal blazon must not be
To ears of flesh and blood.”

Galway Kinnell:

“I roll
this way and that in the great bed, under
the quilt
that mimics this country of broken farms and woods”

— “The Porcupine”

For quilt-block designs that do not mimic farms or woods,
see the cover of Diamond Theory .  See also the quotations
from Wallace Stevens linked to in the last line of yesterday’s
post in memory of Kinnell.

“… a bee for the remembering of happiness” — Wallace Stevens

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