How does non-living matter exhibit open-ended evolution?

The most striking aspect of the phenomenon of life is that it appears to exhibit open-ended growth of complexity. What is the origin of this phenomenon and how can we construct models that recapitulate it? Life is composed of non-living matter; how does non-living matter exhibit open-endedness? In this talk, I will discuss a simple approach that uses an analogy with fluid turbulence to construct a dynamical model of an evolving ecosystem, which exhibits a limited form of open-ended evolution of complexity. The open-endedness can be demonstrated by scaling arguments. Whether life is truly open-ended can be addressed by studying the statistical properties of phylogenetic trees, and I show that there are analogues of scale interference in critical phenomena which reflect the indelible footprint of ecology on the large-scale structure of evolution. Lastly, I will consider the question of the control of open-ended evolution, and its implications for human health.