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Computational Mechanics

bactra.org · 1,709 words · saved by 1 readers

You go to the lab and you take your favorite set of measurements, until you can't stand it any more, and you want to make something of the data. You might look for structures or patterns in your data: these may even be those emergent properties so fabled in legend and philosophy. To do this, you need a way of characterizing different structures or patterns, and one of doing this is to write down a procedure which will reproduce the pattern, to a certain level of abstraction and accuracy. Fortunately there's a lot of theory on the subject of "effective procedures" in general: it's an off-shoot of mathematical logic called computation theory, or automata theory, which turns out to be equivalent to the theory of formal languages. The languages or automata form a hierarchy, in which those at the higher levels can do anything those at the lower levels can: Turing machines perch at the very top of the heap. (The most basic form of the hierarchy was discovered by Chomsky back when he worked f

Computational Mechanics Notebooks Computational Mechanics Last update : 12 Jul 1999 19:33 First version : (This notebook needs re-writing in a big way. Sorry; here's the old version, for what it's worth..) Here are two big fuzzy problems which come up in lots of areas of science: How do we find patterns in our data? How do some natural objects compute, or process information? Computational mechanics is a research program, developed by Jim Crutchfield and henchmen, which aims to address both of these problems with the same set of tricks. Since I think this is an under-appreciated line of resear

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