Categorical Perception and Maximally Informative Observables

We formulate the problem of perception in the framework of information theory, and prove that categorical perception is equivalent to the existence of an observable that has the maximum possible information on the target of perception. We call such an observable maximally informative. Regardless whether categorical perception is real, maximally informative observables can form the basis of a theory of perception. We conclude with the implications of such a theory for the problem of speech perception.