Right angles everywhere (II), about the gnomon

In this post I shall write about the gnomon. According to wikipedia,

The gnomon is the part of a sundial that casts the shadow. Gnomon (γνώμων) is an ancient Greek word meaning “indicator”, “one who discerns,” or “that which reveals.”

In the next figure are collected the minimal ingredients needed for understanding the gnomon: the sun, a vertical shape and its horizontal shadow.

That is the minimal model of the ancient greek visual universe: sun, a man and its shadow on the beach. It is a speculation, but to me, a gnomon seems to be a visual atom.

Pythagoreans extracted from this minimal visual universe the pattern and used it for giving an explanation for the human vision, described by the next figure.

Here the sun is replaced by the eye (of a god, initially, but the pattern might apply to a mortal also), the light rays emanated by the sun are assimilated with the lines  of vision (from here the misconception that the ancient greeks really believed that the eyes shoot rays which illuminate the field of vision) and the indivisible pair man-shadow becomes the L-shape of a gnomon.  An atom of vision.

Here comes a second level of understanding the gnomon, also of pythagoreic flavor. I cite again from the wiki page:

Hero defined a gnomon as that which, added to an entity (number or shape), makes a new entity similar to the starting entity.

This justifies the Euclid’ picture of the gnomon, as a generator of self-similarity:

(image taken from the wiki page on gnomon)
So maybe the word “atom” is less appropriate than “generator”. In conclusion, according to ancient greeks, a gnomon (be it a triple sun-man-shadow or a pair eye – elementary L-shape) is the generator of the visual perception, via the mechanism of self-similarity.

In their architecture, they tried to make this obvious, readable.  Because it’s scalable (due to the relation with self-similarity), the architectural solution of constructing with gnomons  invaded the world.

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