As a mathematician, I will focus on the consequences on knowledge construction of the very “mathematical structures” the new technologies of information are based on. The claim is that the use of discrete state (digital) devices both as mathematical models and as a knowledge paradigm in science and humanities is far from neutral. It will be then possible for the reader to develop some consequences of how the cultural and social relations may be affected by these technologies and their networks. In particular, these networks provide tools for knowledge as well as an image of the world; but, by their peculiar mathematical structure, the “causal relations” of phenomena, in all areas of knowledge, is often redesigned according to the relations proposed by the digital networks and their internal causality. I will discuss these issues in the informal style of a “personal letter” to Alan Turing. But let's first informally introduce some mathematical bases for this distant dialogue with the founding father of our computational universe...