Randomness and Determination, from Physics and Computing towards Biology

Abstract. In this text we will discuss different forms of randomness in Natural Sciences and present some recent results relating them. In fi-nite processes, randomness differs in various theoretical context, or, to put it otherwise, there is no unifying notion of finite time randomness. In particular, we will introduce, classical (dynamical), quantum and al-gorithmic randomness. In physics, differing probabilities, as a measure of randomness, evidentiate the differences between the various notions. Yet, asymptotically, one is universal: Martin-Löf randomness provides a clearly defined and robust notion of randomness for infinite sequences of numbers. And this is based on recursion theory, that is the theory of effective computability. As a recurring issue, the question will be raised of what randomenss means in biology, phylogenesis in particular. Finally, hints will be given towards a thesis, relating finite time randomness and time irreversibility in physical processes1.