Nice weekend read....
Somewhat more to do with biology than mathematics, but the above article from Nautilus, on 'Nature as an IT wizard,' is simply too rich not to pass along. It crosses into information-processing, neuroscience, and even physics, with plenty of mathematical implications. Subtitle for the piece is, "Nature manages information, the currency of life, with exquisite efficiency." Three quick bits:
"Every organism is a brief upwelling of structure from chaos, a self-assembled wonder that must jealously defend its order until the day it dies. Sophisticated information processing is necessary to preserve and pass down the rules for maintaining this order, yet life is built out of the messiest materials: tumbling chemicals, soft cells, and tangled polymers."
"Not only does DNA store information at a density per unit volume exceeding any other known medium, it can achieve one quarter of the maximum information density allowed by the laws of physics (set by the entropy of a black hole). It’s so dense that all the world’s digital data could be stored in a dot of DNA the weight of eight paper clips. This remarkable storage density is paired with an equally remarkable reading mechanism."
"Why would nature use fractal geometry so regularly? Mathematically, fractals are interpreted as having a fractional dimension higher than the space they reside in: A fractal drawn on a two-dimensional sheet of paper, for example, has a higher dimension—say, 2.1. This is a useful feature, allowing nature to pack some part of a fourth dimension into three-dimensional space."