SDB's recent wide ranging post on chaos theory got my creative juices flowing as I also have long been fascinated by chaos theory. In the pedantic column, the base of chaos theory is rightfully included in mathematics (I believe) though people seem to have discovered it in observing various disparate phenomena, from weather prediction to stock market behavior, to economics. The formulas they derived to talk about it really don't vary so a base science like math is a good place for it. Your mileage may vary.
One of the things about chaos theory and economics that I find highly useful in policy is how chaos theory affects statist economics. The natural order of things in economics seems to be a slow, secular form of progress with high variation, the boom and bust cycle. The busts, in particular, have very cruel and nasty results and a major form of human effort into the science of economics is how to ameliorate or end the bad effects of the busts. One of Marx's basic predictions regarding capitalist society is that the boom/bust cycle will grow ever wilder, to the point where the whole societal system cannot stand the magnitude of the economic perturbations and something else will arise to take its place, that something else being communism.
This kind of chaotic system perturbation is seen in biology in the way that heart attacks happen. Of course, like heart attacks, this is something that you want to avoid.
The empirical reality of a century of various economic experimentations across the world has given us a body of knowledge that demonstrates that Marx's analysis was fatally flawed. Any interference in correcting the busts seems to have two side effects. It reduces the booms, and it lowers the slope of the secular path in an unpredictable manner. You manage things too much, too long, and the secular upward path turns into a secular downward path and the natural virtuous circles of the economy turn into vicious circles as the country goes down the drain.
But "there is a lot of ruin in a nation" and free market advocates have long had poor records of predicting when, exactly the bad effects will come out. This is because, like everything else in the system, the side effects appear chaotically. But appear they will and it is a remarkable betrayal of the intergenerational societal compact to just kick the can down the road.
But we're all guilty of doing it.
We've fairly well enough established that total government control of the economy leads to horrendous negative effects. The two ideas left are lassez faire economics buttressed by a private charitable safety net and lightly managing the economy in order to pluck the economic goose but still get enough golden eggs to maintain the secular upward trend.
The problem is that politically, the temptation is always to pluck just a bit more in order to gain political advantage over your electoral rivals. Inevitably, this intersection of political interest and economic danger leads to US style stagflation and today's eurosclerosis.
For today's budding statist, the trick is to push out the economic bad news until after your political career is over. FDR's new deal is breaking down decades after he passed away and was enshrined as a great president. LBJ's great society ended up being a net negative to poor people sometime around Ronald Reagan's second term. Few curse him for the harm he has done to the poor and disadvantaged of today and tomorrow. The distance between cause and effect are too much for political purposes but the link is real.