Sunday, April 08, 2007

Infinities within Infinities

Back in the late 1800's to early 1900's, a brilliant mathematician named Georg Cantor explored transfinite sets to see how they related to the concept of infinity. As seen above in iterations of the Menger Sponge (a 3D version of the Cantor Set), one sees, via Cantor's ideas, how infinities can reside within finite space without a care in the world. When Cantor's recursion is randomised and iterated via computer and applied to the real world, magic happens...

As seen in the beautiful Lorenz attractor, used in monitoring temperature variations in weather patterns, the notion of exact repeatability in open systems (in this case, temperature) is but a dream, something that is duplicated, among other things, in the variance of planet orbits, the growth of ferns or the dripping of a water faucet. Additionally, what is also seen from this research is the emergence of complex behavior coming out of seemingly simple systems, something that has forever changed how we view reality. "and so it goes." KV/Slaughterhouse Five"

No comments: