  This essay advocates the view that any problem that has a meaningful
empirical content, can be formulated in constructive, more definitely, finite
terms. We consider combinatorial models of dynamical systems and approaches to
statistical description of such models. We demonstrate that many concepts of
continuous physics --- such as continuous symmetries, the principle of least
action, Lagrangians, deterministic evolution equations --- can be obtained from
combinatorial structures as a result of the large number approximation. We
propose a constructive description of quantum behavior that provides, in
particular, a natural explanation of appearance of complex numbers in the
formalism of quantum mechanics. Some approaches to construction of discrete
models of quantum evolution that involve gauge connections are discussed.
