Giuseppe Longo introduces his paper ‘Quantifying the World and Its Webs: Mathematical Discrete vs Continua in Knowledge Construction’
This short paper is meant to be an introduction to the ‘Letter to Alan Turing’ that follows it. It summarizes some basic ideas in information theory and very informally hints at their mathematical properties. In order to introduce Turing’s two main theoretical contributions, in Theory of Computation and in Morphogenesis (an analysis of the dynamics of forms), the fundamental divide between discrete vs. continuous structures in mathematics is presented, as it is also a divide in his scientific life. The reader who is familiar with these notions, and is convinced that they (and their differences) are relevant in the mathematical understanding of phenomena, may skip this introduction and go directly to the Letter.