TY - Type of reference
TI - Mathematical Infinity “in prospettiva” and Spaces of Possibilities
AU - Giuseppe Longo
AB - The Italian Renaissance painters invented the first symbolic form for the mathematical concept of ’’actual’’ infinity : the projective point of the perspective. This was the result of a long debate on infinity, in philosophy, since Aristotle, and in theology, during the Middle Age, and had a major fall out in this early geometrization of space. In particular, this invention set the grounds for the construction of the infinite spaces of all possible physical dynamics. In spite of the diversity of the theories in physics (Classical, Relativistic, Quantum … theories), an a priori ’’phase space’’, as a generalization of the infinite Newtonian space-time, is a core presupposition of each theoretical frame. The problem will be posed of the pertinence of this construction as for historical sciences, biology in particular, where the “space of all possible paths” (the list of all phenotypes and their phylogenetic history) cannot be pre-given.
DO - 10.21494/ISTE.OP.2019.0415
JF - Art and Science
KW - Potential infinity, actual infinity, perspective, phase space, Evolution, Potential infinity, actual infinity, perspective, phase space, évolution,
L1 - https://www.openscience.fr/IMG/pdf/iste_artsci19v3n1_7.pdf
LA - en
PB - ISTE OpenScience
DA - 2019/09/19
SN - 2515-8767
TT - L’infini mathématique "in prospettiva" et les espaces des possibles
UR - https://www.openscience.fr/Mathematical-Infinity-in-prospettiva-and-Spaces-of-Possibilities
IS - Issue 1

VL - 3
ER -