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.

Monday, August 10, 2009

Monday August 10, 2009

Filed under: General — Tags: — m759 @ 12:00 PM

Pictures Within Pictures

"The Chinese language is written in ideograms, pictures. Think of a DO NOT ENTER pictogram, a circle with a diagonal slash, a type of ideogram. It tells you what to do or not do, but not why. The why is part of a larger context, a bigger picture. Such is the nature of the Chinese language. Simple yet complex. Pictures within pictures."

Customer review at Amazon.com

See also the pictures in this journal on today's date five years ago.

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