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 (lambda-calculus) to represent abstract “molecules” that act upon one another generating new molecules, that is, 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 self-maintenance, 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).
Although this particular model has slipped into the background, its basic vision remains intact. I keep gravitating back to the question of how the theoretical foundations of computation can help us represent and reason about biological processes. Computation is organization and the classical theory of computation (Turing, Hilbert, Church, and others) is but a theory of one very specific form of organization. Other forms will be discovered.
Key collaborator: Leo Buss (Yale)
selected papers:
Key collaborators: Peter Schuster (Vienna), Peter Stadler (Vienna), Lauren Ancel-Meyers (Austin)
selected papers:
