Classical, Quantum and Biological Randomness as Relative Incomputability

In this paper we briefly discuss various forms of randomness that physics, mathematics and computing have proposed. Classical and quantum physics view randomness, that we describe as unpredictability in the intended theory, in di↵erent ways. Computing allows to discuss this issue in an abstract, yet very expressive mean, which yields useful hierarchies of randomness and may help to relate its various forms. We introduce then the open field of biological randomness—its peculiar nature and role in ontogenesis and in evolutionary dynamics (phylogenesis). Randomness does not oppose, but contributes to the organisms’ and populations’ structural stability, in contexts where the notion of probability, as measurement of randomness, is not well defined.