I love this sweet combination of art and science:

Henry Hexham illustration forThe Principles of the Art Militaire, 1637

For me this drawing combines the beauty of the physical world (that funky little cannon could've been drawn by R. Crumb or George Herriman) with the beauty of the mathematical principles underlying that world. The artist who drew this had to labor under two sets of laws: the laws of perspective and the laws of physics. I respect the discipline required to make such pictures.

As far as we know, Pythagoras of Samos was the first human being to recognize the connection between mathematics and the design of the world, 2500 years ago. Arthur Koestler wrote about the awesome significance of that moment:
[Pythagoras'] influence on the ideas, and thereby on the destiny of the human race was probably greater than that of any single man before or after him.... [His] was the first successful reduction of quality to quantity, the first step towards the mathematization of human experience-- and therefore the beginning of science. Pythagoras discovered that the pitch of a note depends on the length of the string which produces it, and that concordant intervals in the scale are produced by simple numerical ratios.
Pythagoras took his new way of ordering the world and proceeded to go nuts with it, even using it to calculate what he believed would be the "music of the spheres"-- the musical hum of the planets in their orbit. (OK, OK, so not every new application was successful, but Pythagoras definitely set human science on its path.)

Bertrand Russell claimed, "Physics is mathematical not because we know so much about the physical world but because we know so little: it is only its mathematical properties that we can discover."
Russell may have been one heck of a mathematician, and he was certainly correct that quantifiable discoveries can be pure and true and beautiful, but his position reveals that he was no artist. An artist would've understood that art enables us to discover properties even beyond what math can confirm.

We have previously
talked on this blog about the beauty inherent in the rigorous craftsmanship of car illustrators who painted cars to satisfy not just the artistic taste of art directors but also the humorless committees of car company engineers, who rigorously inspected every detail of an illustration to make sure it conformed to the car's schematic diagrams. It was the job of these illustrators to combine math and art, and find the poetry in geometry.

Today, the processing powers of supercomputers have enabled us to merge numbers with shapes and colors in ways Pythagoras never dreamed of. The T square and triangle, primitive tools we employed for centuries, have been replaced by software. Cars, space ships and a wide variety of other images are now composed using CAD and CGI. But no matter how art and math have merged, always-- always-- the artist needs to be listening for that music of the spheres.

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