Building the World out of Information and Computation

Abstract

According to Pythagoras: All is Number, God is a Mathematician. Modern physics is in fact based on continuous mathematics, dierential and partial dierential equations, validating Pythagoras’ vision. In this essay we shall instead discuss a neo-Pythagorean ontology: All is Algorithm, God is a Programmer. In other words, can there be discrete computational models of the physical world? This is sometimes referred to as digital philosophy. There are in fact two books on digital philosophy, both in Italian: • Ugo Pagallo, Introduction to Digital Philosophy, from Leibniz to Chaitin • Andrea Vaccaro and Giuseppe Longo, Bit Bang: The Birth of Digital Philosophy Let’s review the development of digital philosophy. We’ll start, as is often the case, with Leibniz.