Walter Fontana – Research

The formal structure of evolutionary theory is based upon the dynamics of (populations of) “individuals.” It therefore assumes the entities whose existence it is supposed to explain. At the heart of the existence problem is determining how biological organizations arise in ontogeny and in phylogeny. The research theme we called Algorithmic Chemistry (AlChemy) was an attempt at constructing a formal framework for thinking about molecular organization through an abstraction of chemistry. Our stance was to view molecules as rules of transformation and to exploit a mathematical theory of functions (λ-calculus) to represent abstract “molecules” that act upon one another generating new molecules or rules of transformation. Under suitable boundary conditions this model generates self-maintaining collectives of rules whose mutual transformations permit the continuous regeneration of these same rules. The “organization” of such a system is specified by the relationships of transformation that enable selfmaintenance, i.e. the algebraic structure of the system. This framework permits to address the robustness of organizations with respect to the elimination of components (self-repair), the addition of components not belonging to the organization (constrained extension) and the merger of autonomous organizations into higher-order structures (integration). 1 1 1 1 1 1