Complexity concepts and the limitations of computable models

Abstract As they are implemented in modern computers, computable languages and computable models allow a new approach to logical and scientific thinking. Complexity and decidability problems imply some fundamental limitations to deterministic models. Some striking examples are given by large interactive programs. Different complexity concepts may be distinguished for the representations of data and for algorithms, with consequences relative to the feasibility of models. They are applied to various domains: history, power and politics, economy, and living beings.