  It is proposed to define "quantumness" of a system (micro or macroscopic,
physical, biological, social, political) by starting with understanding that
quantum mechanics is a statistical theory. It says us only about probability
distributions. The only possible criteria of quantum behaviour are statistical
ones. Therefore I propose to consider any system which produces quantum
statistics as quantum ("quantumlike"). A possible test is based on the
interference of probabilities. I was mainly interested in using such an
approach to "quantumness" to extend the domain of applications of quantum
mathematical formalism and especially to apply it to cognitive sciences. There
were done experiments on interference of probabilities for ensembles of
students and a nontrivial interference was really found. One could say that the
quantum statistical behaviour might be expected. But the problem was not so
trivial. Yes, we might expect nonclassical statistics, but there was no reason
to get the quantum one, i.e., cos-interference. But we got it!
