Moebius Transformations — And a Darwinian Snark

Found this elegant visual explanation of projection while asking the Internet to correct my spelling for Moebius.

Looking at this, I am glad I do not live in one of those non-Euclidean universes governed by Cthulhu (you know the ones, where parallel lines diverge, and no plane figures are congruent with any others of differing sizes).

Instead we live in a cosmos where math is lovely. Let us not in haste attribute to mere good luck and blind chance! Let us instead attribute our good fortune to blind Darwinian natural forces. Obviously, we were evolved to see the beauty in math.

Good thing Darwinian natural selection kills off in large numbers any organisms unable to appreciate the beauty in abstract mathematical imaginary constructs before breeding age.

Naturally, I cannot imagine what such a naturally selected reproductive or survival advantage would commit such culling with any statistical success, nor can I think of any experiment (nor thought experiment) to lend even the slightest weight of evidence for or against the claim — so this must mean that I am not well educated enough to grasp the sublime nuances of modern science.

Instead, I am one of those people who has read Darwin’s ORIGIN OF SPECIES, rather than one of those people who are under the impression that they have read Darwin’s ORIGIN OF SPECIES but in fact have not. Oddly, he never mentions descent with modification through natural selection as the sole source for every and any intellectual characteristic found at large on the human species. Fancy that!

So for whatever reason, we live in a cosmos where math is lovely.

It is almost as if it were designed that way, and we were designed with souls fit to perceive and admire such loveliness.

Here is a another animation showing some of the beauties of mathematics, but with no good explanation of the math. The music is less to my taste, and the introductory welcomes overstay their welcome, but the animation becomes interesting at about 1:50. I wish I could edit this just to show you the eye-catching parts, but that is beyond my leet skillz.

I believe ( I cannot be sure ) the animation was done by Jos Leys, who has a page here: