[SomeStupidPoint]

Sort of by definition, you can't fully describe a random process. (A little fiddling actually turns that in to a pretty good definition of what a random process is, but that gets really technical, really quick.)

I doubt you'll find any better usage of randomness in other fields, and in many ways, "random" is used to censor things our theories can't represent, and wrap them in stochastic approximators. This is useful, because we can then use the stochastic models as a bound on the possible outcomes caused by things we can't model (for various reasons). This let's us calculate useful predictions involving things we don't or can't know.

I don't think randomness is a negative definition, just that our primary usage of the concept is boxing up unmodelable things.