Computational Ontogeny

When the computer scientist seeks to model natural phenomena, he or she may select from two paths. Modeling may be by representation or by realization. This distinction is clarified by means of a simple physical example: an adiabatic pressure vessel. A representational model will in no way involve the operation of such a vessel even as a real gas law is observed (like van der Waals’ gas law), while it is precisely such operation that characterizes a realizational model, which involves the observation of a physical gas, lawful or not. With computational representation, notions such as temperature, pressure, rate, and so forth are abstracted, and the output data from the program constitute the model. With computational realization, on the other hand, it is the program itself that constitutes the abstract model. For computational theoretical biology, the paradigmatic results from the realization method came in one great moment of inspiration when John von Neumann (1951, 1966) conceived his model of machine self-replication. In this model, a configuration known as a universal constructor sets about the task of reading a coded description of some other configuration, the target construct, as expressed on an abstract tape, and according to that original description, produces that configuration. The universal constructor also duplicates the tape it is reading, and places the duplicate tape adjacent to the configuration it constructed upon reading the original tape. Many extensions of von Neumann’s work on the logically sufficient characters of self-replication are known. We may consider three examples. Elucidation of the minimal conditions for self-replication has reduced von Neumann’s universal construction from the status of a sufficient condition to the status of nonnecessity (see Langton 1984 and Smith 1992). Another concern of von Neumann (1966), that the description of a self-replicator cannot be generated by self-inspection, was refuted by Laing (1977), with examples coming from Ibánez et al. (1995). Vitányi (1973) considered mechanisms of sexual reproduction. Yet, within the von Neumann paradigm, no work beyond the threshold of self-replication is known; though now somewhat dated, Sipper (1998) provides a summary covering the first half-century of research into self-replication. Maynard Smith (1986: 99), speaking for the field of biology at large, lamented the lack of a machine embryology in artificial life models: