A quick introduction to the
Algorithmic Chemistry project
A number of complex systems have the feature that they are self-maintaining. The reader, for example, is a self-maintaining organization. In a biological context, self-maintenance means that simple chemical inputs are transformed through metabolic cycles into all those molecules that an organism needs to persist. Framed this way the term organization describes more than just a set of molecules, it refers also to a network of functional relationships that allows the persistence of an organism in spite of the fact that every single molecule may be continuously replaced. Common features of such systems include resistance to perturbation, extensibility, and history dependence. It is curious, given the importance of this topic, that there exists no scientific tradition in the formal study of self-maintenance. What would one wish of such a formalism? Minimally, we would like to know (1) What is required to produce a self-maintaining organization? (2) What classes of self-maintaining systems are possible? (3) What possible histories may be explored given a specific set of starting conditions?
We answer the first question by proposing a minimal theory of biological organization [papers]. We sought inspiration from chemistry asking, What is it about chemistry that allowed life? We claim that only two abstractions from chemistry are essential. First chemistry is constructive, i.e., the collision of molecules can generate new molecules. Second there exist equivalence classes such that many different reactions can produce the same stable products. We chose -calculus as a formal system because it captures these two abstractions, constructivism and equivalence relations and nothing more. By investigating the consequences of a many-body dynamical setting of -expressions we have generated a diversity of self-maintaining organizations with the desired properties, i.e., resistance to perturbation, extensibility, and history dependence [papers].
We call this a constructive dynamical system. In a conventional dynamical system all components and all interactions are given explicitly at the outset and the mathematical apparatus is used to compute, for example, equilibrium distributions of the components of the system. In contrast, the components of biological and chemical systems endogenously construct new components upon interaction. The information for this constructive action resides in their structure. The study of the possible organizations of such components hinges on the lawful association between structure and action. A major goal of the AlChemy project is to develop a formalization of the structure/action association called "chemistry" at a level of abstraction that is useful for understanding biological organization, its origin and evolution.
[Continue with an old (yet still valid) outline of our research vision.]