An active transformation of a physical system implies its motion. A passive transformation of the system is a change in the method of describing it. An analogy transformation means transition to another physical system, similar in some respect to the original one. In some cases transformations of one type may imitate those of another. The operation of particle permutation in quantum mechanics implies a passive transition to describing the same state of the system by a different method of introducing particle numbering. The problems of transitions from describing identical particles to describing different ones and that of ``explaining'' the probabilistic meaning of wave functions statistically are touched upon.