  We address the impossibility of achieving exact time reversal in a system
with many degrees of freedom. This is a particular example of the difficult
task of "aiming" an initial classical state so as to become a specific final
state. We also comment on the classical-to-quantum transition in any
non-separable closed system of $n \geq 2$ degrees of freedom. Even if the
system is initially in a well defined WKB, semi-classical state, quantum
evolution and, in particular, multiple reflections at classical turning points
make it completely quantum mechanical with each particle smeared almost
uniformly over all the configuration space. The argument, which is presented in
the context of $n$ hard discs, is quite general. Finally, we briefly address
more complex quantum systems with many degrees of freedom and ask when can they
provide an appropriate environment to the above simpler systems so that quantum
spreading is avoided by continuously leaving "imprints" in the environment. We
also discuss the possible connections with the pointer systems that are needed
in the quantum-to-classical "collapse" transitions.
