  We consider the problem of quantum behavior in the finite background.
Introduction of continuum or other infinities into physics leads only to
technical complications without any need for them in description of empirical
observations. The finite approach makes the problem constructive and more
tractable. We argue that quantum behavior is a natural consequence of
symmetries of dynamical systems. It is a result of fundamental impossibility to
trace identity of indistinguishable objects in their evolution - only
information about invariant combinations of such objects is available. We
demonstrate that any quantum dynamics can be embedded into a simple permutation
dynamics. Quantum phenomena, such as interferences, arise in invariant
subspaces of permutation representations of the symmetry group of a system.
Observable quantities can be expressed in terms of the permutation invariants.
