  Von Neumann in 1932 was the first to outline the possible non existence of
dispersion free ensembles in quantum mechanics, and he used also such basic
evidence to give a preliminary proof on incompatibility between quantum
mechanics and (non-contextual) hidden variables theory. In the present paper we
give a detailed theoretical elaboration on the manner in which such fundamental
subject could be explored at perceptive and cognitive level in humans. We also
discuss a general design of the experiment that we have in progress so to give
direct indications to other researchers engaged in such field.
