I have heard that the complex behavior of a flock of birds can be simulated with a computer programed with just four rules to govern the flock's behavior. An excellent example of how complexity can often be 'reduced' to relatively simple underlying principles capable of being expressed mathematically.
Of course, in this sort of case, no genuine reduction is taking place. Not anymore than calling the view from my window a "landscape" reduces the view to a landscape (whatever that is). But in other cases of reduction, it seems possible to argue there is a genuine reduction of one thing to some other, far simpler, thing. For instance, many very complex things can be reduced to the behavior of molecules.
However, even if we knew all the 'laws' 'governing' the behavior of something, we might still not be able to predict the behavior any given individual due to the number of variables involved. Try imagining all the things we know govern when and where an autumn leaf will fall. We know all sorts of things about what will influence its fall -- and we still cannot predict when and where it will fall.
But then you have the issue of 'emergent properties' at some point. So it's all very interesting. Of course, me -- I'd rather be watching strippers than thinking about these things, but the dancing girls won't be here for another two hours yet.
