Evolution as a Random Walk on a High-Dimensional Manifold Defined by Physical Law: Implications for Open-Ended Artificial Life

Abstract

This short article presents a discussion of the underlying conditions under which natural evolution of life occurs and how these natural conditions may be extremely difficult to implement in artificial life (ALife) systems. In particular, the Darwinian concept of adaptation via natural selection may not have a complete or functional macro-level description that could be used to build any evolutionary environment that is defined at the agent-environment interaction level. Here we are specifically addressing open-ended evolution (Ruiz-Mirazo et al., 2004) in artificial systems (Standish, 2003; Nolfi, 2012; Mouret and Doncieux, 2012). One of the goals of ALife is to generate systems capable of sustained evolution of life-like complexity. Such systems, although artificial, could then be considered to produce real life of a kind (Pattee, 1987; Ray, 1993), as opposed to being just simulations of life. For evolutionary computing applications aimed at solving particular problems, a well-defined goal that is separate from survival in and of itself can be formalized into a selection criterion and used to evolve solutions (Oduguwa et al., 2005). However, in the case of open-ended evolution, many researchers now accept that agent-level definitions of fitness are unsuitable to drive differential selection and replication (Lynch, 2007; McShea, 1991; Lehman and Stanley, 2011). This includes even the most unbiased and high-level implicit fitness criteria in which replication is seemingly made to be a direct result of agent interaction with the environment (see for example Yaeger, 1994). Interestingly, concerns about the adequacy of neo-Darwinian and Darwinian theory to fully describe the evolution of life have come from several ALife researchers, often after attempting to implement evolving systems (Mitchell and Forrest, 1994; Lehman and Stanley, 2011; Watson, 2012; Nolfi, 2012). Ray, for example, indicates that there is something “oddly self-referential” about evolution (Ray, 1993). Dawkins describes how his views of natural biological evolution changed after playing around with ALife simulations (Dawkins, 2003). An underlying tenet of science is that all observable natural phenomena result from a fundamental set of physical laws and that physical law is essentially unchanging (Feynman, 1967; Zilsel et al., 2003). Such a set of laws, although not yet fully elucidated by physicists, is presumed to exist. If this were not the case, some fundamental cornerstones of science such as repeatability of experiments, as well as a host of epistemological underpinnings, would not hold. A consequence of the existence of such a set of elemental physical laws is that fundamental driving forces producing change in natural evolution result from or reflect the topology of a static space defined solely by unchanging physical law (Ray, 1993). In this sense (and noting that physics is thought to have an intrinsic stochastic aspect), evolution can be described as a random walk on a static manifold, one of extremely high dimensionality. The only fundamental nonrandom “force” driving change in nature is imparted by the underlying topology of this static extremely low-level and high-dimensional landscape. Furthermore, this low-level view of the universe is not mediated by a replication cycle per se. The discussion above implies that a system defined only in terms of a suitable set of elemental rules might in theory support open-ended evolution, and that our natural universe is an example of such a system. This raises the possibility that high-level representations (including the differential survival and replication paradigm upon which Darwinian evolution is based), while describing evolution sufficiently to generate simulations, might not fully functionally specify evolution to the degree needed to generate artificial realizations of evolution. (See Pattee (1987) for a discussion of the distinction between simulation and realization.) Below, we loosely summarize an argument that implies that high-level descriptions of complex systems are likely to be functionally incomplete. When complex systems with a high level of granularity are converted to lower levels of resolution, information is usually lost, even if overall patterns are seemingly more evident (Katsoulakis and Trashorras, 2006). Hence, if the behavior of a complex system is fully described (but not over-specified) at one level, it is in fact not likely to be fully described at a reduced level of resolution. The implication is that macrolevel traits in biological systems, being essentially extremely low-resolution views of matter/energy configurations, do not contain sufficient information to fully predict replication efficiency distributions (as generalizations of adaptive fitness landscapes (Wright, 1932) might have suggested). Relating variation in macro-level traits to replication efficiency would then not fully define the underlying forces driving evolution, not even in theory. In this case, the