Proof as a path of light
pp. 195-222
in: Rossella Lupacchini, Giovanna Corsi (eds), Deduction, computation, experiment, Berlin, Springer, 2008Abstract
According to certain medieval philosophers, perspective is a "demonstrative science" as it reveals the connection between sensible and intelligible visions by means of the mathematical rules of geometric optics. Carrying over concepts and methods of the medieval perspectiva naturalis into a plane surface, the Renaissance perspectiva artificialis unfurls a new "pictorial" space. To appreciate the impact of quantum theory on determinism and computation issues this paper will adopt a "perspectival" approach: the architecture of the theory, first captured in the "real' three dimensional space, will lead us into a new "imaginary' space. Here the bilateral symmetry coupling any possibility with its negation, sized by "complex probability amplitudes", may dissolve the "ignorance' of classical probabilities as well as the "blindness' of finite mechanical procedures.