I've been studying Austrian Economics for the last few months and I was wondering how Austrians deal with chaos theory. Doesn't chaos theory/power laws/fractals/ect. tell us anything about economic phenomena, and if so, how is this reconciled with the Austrian a priori methodology?

I know that Murray N. Rothbard tackled chaos theory once (the article itself can be found in his book, "Making Economic Sense". Basically, chaos theory he argued helped to really destroy the credibility of mathematical economics, since even if a mathematical economist does find consequences of a butterfly flapping its wings, how can the even predict the existence of the butterfly in on spot in time and place, not to mention the milliions, if not billions of miniscule phenomenon that create ripple effects in society.

I know that Murray N. Rothbard tackled chaos theory once (the article itself can be found in his book, "Making Economic Sense". Basically, chaos theory he argued helped to really destroy the credibility of mathematical economics, since even if a mathematical economist does find consequences of a butterfly flapping its wings, how can the even predict the existence of the butterfly in on spot in time and place, not to mention the milliions, if not billions of miniscule phenomenon that create ripple effects in society.

Yes, that is the fatal flaw in mathematical economics--it uses the methods the natural scientists use to analyze perfectly controlled experiments, but on world phenomena subject to the butterfly effect and thus not controlled. No matter how many statistical tricks are used the results are not accurate.

Chaos theory basically says that some physical processes are deterministic yet unpredictable. A minuscule change in initial conditions can take the system in a completely different direction. Although the existence of chaotic attractors, zones where a system will never step out, allows some form of prediction. For example, in economics, even though we cannot predict how capitalism or socialism will organize an industry, we know that there specific paths that are impossible for either system and can be predictably excluded.

I find Stephen Wolfram's principle of computational equivalence more appealing. Economic processes are irreducibly complex computations, meaning that the only way to know how they will unfold is to watch them happen. Any attempt to predict the economy is naturally impossible.