  How are abstract concepts and musical themes recognized on the basis of some
previous experience? It is interesting to compare the different behaviors of
human and of artificial intelligences with respect to this problem. Generally,
a human mind that abstracts a concept (say, table) from a given set of known
examples creates a table-Gestalt: a kind of vague and out of focus image that
does not fully correspond to a particular table with well determined features.
A similar situation arises in the case of musical themes. Can the construction
of a gestaltic pattern, which is so natural for human minds, be taught to an
intelligent machine? This problem can be successfully discussed in the
framework of a quantum approach to pattern recognition and to machine learning.
The basic idea is replacing classical data sets with quantum data sets, where
either objects or musical themes can be formally represented as pieces of
quantum information, involving the uncertainties and the ambiguities that
characterize the quantum world. In this framework, the intuitive concept of
Gestalt can be simulated by the mathematical concept of positive centroid of a
given quantum data set. Accordingly, the crucial problem "how can we classify a
new object or a new musical theme (we have listened to) on the basis of a
previous experience?" can be dealt with in terms of some special quantum
similarity-relations. Although recognition procedures are different for human
and for artificial intelligences, there is a common method of "facing the
problems" that seems to work in both cases.
