This paper is concerned with evolutionary systems and their evolvability. By ``evolutionary system'' we mean a system satisfying the abstract conditions for Darwinian evolution: reproduction with heritable variation, in a finite world, giving rise to natural selection. ``Evolvability'' is a more nebulous term; for our purposes, it roughly connotes the distinction between evolutionary systems which sustain a spontaneous and apparently open-ended growth of complexity--and those which do not. We have, by now, many examples of the latter, but only one of the former. We suspect this to be rather a deep problem; but we will attempt to scratch its surface by probing the relationship between certain distinguishable modes of reproduction and consequent evolutionary potential.
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