rationalskepticism.org

archibald wrote:

Cito di Pense wrote:We do know what computationally-intractable problems are, and having a bunch of beardy guys sit around cogitating about human behavior is not likely to have more success than trying to compute it.

I didn't know this. But I now see the following:

"...consider a program that makes 2n operations before halting. For small n, say 100, and assuming for the sake of example that the computer does 1012 operations each second, the program would run for about 4 × 1010 years, which is the same order of magnitude as the age of the universe.
https://en.wikipedia.org/wiki/Computati ... actability

I'll agree with Cito and say that having even a basic understanding of complexity theory is a good thing(TM). For another reason, it'll give you ideas of the limits of, say, computer animation and what your iPhone can do.

Something somewhat related to complexity theory is chaos. Chaotic systems have the property that small changes to the input parameters get scaled up in a simulation into very large changes over time. Some systems are so chaotic that, even a change within your measurement error is going to completely flip your outputs over the timescale you're interested. This means that the simulation is utterly worthless. Hence, we don't ask weather forecasters for predictions more than a few days in advance.

Now suppose we have a model of human beings for making predictions. Even with magic beans computers, the model might exhibit such chaotic behaviour that it's impossible to get the inputs to a sufficient resolution to simulate it.

Artificially chaotic systems are used to generate "random" numbers. The numbers aren't random, of course, because they are generated by a deterministic procedure. But the benchmark for having a decent random number generator is that the problem of recognising that the data is actually algorithmically generated should be NP hard.