What are some limitations to representing evolution in terms of functions?

In the Darwinian view, evolution is based on the idea of change accumulated over many generations, as nature selects from among variants in a population of replicators. The replicators which successfully pass their traits to subsequent generations will come to prevail in a population over time, even if their probabilities of surviving and leaving viable offspring are only slightly greater than those of competing variants.

If we think of a state space whose dimensions are the trait parameterizations of all replicators, then certain regions of that space will be more richly connected than others to larger or more remote areas of the space. Some choices result in designs that are more generative than others.

Associated with the state space is a set of functions that define the likelihood of each choice of parameter or each combination of choices. How generative or connected a region is depends on the functions associated with each point in the region. Most design choices result in unlikely or impossible replicators.

The degree of connectedness of a region is not necessarily tied to the success of the replicators that are instantiated from that region.

A region may be highly generative, leading to a profuse hierarchy of subordinate designs, but its replicators may be quite unsuccessful as they interact with their environment.

We can think of the environment abstractly as vectors, or maybe as a vector field, associated with the trait space. Each point in the trait space has an associated vector indicating the direction of a gradient. The gradient expresses increase or decrease in probability of stability. Stability, in turn, has some metric that can be defined, such as relative duration.

Because all the elements of these abstractions can be represented by values and by functions over those values, the abstractions could be modeled with software.

Would such software produce original and fundamentally surprising designs, as biological evolution does, or would the software simply unpack the information implicit in the outworking of the functions and values chosen for the parameters in the underlying abstraction?

Those choices of functions and values represent an external source of creativity. The magic of biological evolution also seems to spring from such choices, regardless of whether beneficial mutations actually exist in nature, as some biologists doubt, or whether new structures emerge because of nonlinear dynamical factors, as some biologists claim.

That predicament points to what we might call open algorithms. Open algorithms would be the ultimate in runtime polymorphism, if they could ever exist. Biological systems are contingent upon what in computer systems would be eliminated for being noise.

Computers can be made to accept and process noisy data, but not noisy functions.

Michael Webb, 2000

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