Abstract
From the projective space of the painting in the italian renaissance to the most complex models of contemporary mathematical physics, the idea of a priori construction of the space of all possible dynamics is incompatible with the unpredictability of the biological and social evolutions. This paper hints first to the joint birth of the early mathematical representations of actual infinity and of space, to be found in the italian renaissance painting. We then explore how this framed the mathematical approach to physics by the understanding of space and time as conditions of possibility for all physical dynamics. We finally challenge the construction of an a priori framing of the systems of life in pre-given spaces of possibilities and hint to a critical knowledge that combines science and philosophy in facing this challenge.
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