Initial condition!

I was thinking how can we analyse some behavior without knowing the initial conditions of our dynamical variables. For instance, how can you interpret and evaluate some body's behavior without knowing his or her character?

To put my question in a more rigorous way, how much information one can extract from a short time interaction with a system? and how trustable is this data?

All we know of dynamical systems, a small part of which is mechanics, is applicable, just when one can fix the initial conditions. In another word, no initial condition means no prediction.

At the first look, you might say, I am not interested in studying systems that I don't know how they have started.
Nevertheless, not all physicists agree with you. Otherwise there was no "cosmology"!.