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"OH WATERS, TEEM WITH MEDICINE TO KEEP MY BODY SAFE FROM HARM, SO THAT I MAY LONG SEE THE SUN." - Rig Veda
Snow, tenderly caught by eddying breezes, swirled and spun in to and out of bright, lustrous shapes that gleamed against the emerald-blazoned black drape of sky and sparkled there for a moment, hanging, before settling gently to the soft, green-tufted plain with all the sickly sweetness of an over-written sentence.
Renormalization is a principled coarse-graining of space-time. It shows us how the small-scale details of a system may become irrelevant when looking at larger scales and lower energies. Coarse-graining is also crucial, however, for biological and cultural systems that lack a natural spatial arrangement. I introduce the notion of coarse-graining and equivalence classes, and give a brief history of attempts to tame the problem of simplifying and "averaging" things as various as algorithms and languages. I then present state-space compression, a new framework for understanding the general problem. At the end, I present recent empirical results, in an animal social system, that show evidence for the coupling of scales: the reaction of coarse-grained facts about a system "downwards" to influence the microphysics.