this is a talk on heuristic aspects of idempotent mathematics in the spirit of current works of v.p. maslov and his collaborators. idempotent mathematics can be treated as a result of a dequantizati- on of the traditional mathematics as the planck constant tends to zero taking pure imaginary values. for example, the field of real numbers can be treated as a quantum object whereas idempotent semi- rings can be examined as \"classical\"" or \""semiclassical\"" objects