 Real numbers are not accessible to us in finite computational processes yet they do play a role in our analysis of thermodynamic processes. The most elegant models of physical systems are based on functions in continuous spaces. In such models almost all points in space carry an infinite amount of information. Yet, the cornerstone of thermodynamics is that a finite amount of space has finite entropy. There is, on the basis of the theory of quantum information, no fundamental reason to assume that the expressiveness of real numbers is never used in nature itself on this level. This problem is related to questions studied in philosophy of mathematics (an intuitionistic versus a more platonic view). The issue is central in some of the more philosophical discussions on the nature of computation and information (Putnam 1988; Searle 1990). The problem is also related to the notion of phase transitions in the description of nature (e.g., thermodynamics versus statistical mechanics) and to the idea of levels of abstraction (Floridi 2002). 