If emergence is not a real, existing phenomenon, but rather a description from a different perspective or a coordinate transformation or a state space transform or … something similar as indicated in my blog post Climbing Levels of Complexity , then it might be invertible.
What does that mean? As an example, starting with quantum theory, statistical mechanics and under technical assumptions like e.g. space being completely filled with matter we can get Hamiltonians describing phases like e.g. crystals. That might be the best understood example of emergence so far. On the other hand, we (considered as human beings) live in a world of solids, liquids and gases. Nevertheless we were able to derive the underlying quantum mechanical laws. From our description in terms of emergent properties we can go back to the ‘fundamental’ equations.
Evolution as a notion is not easy to grasp (for mathematicians). Could it be, just as a thought, that this is what evolution means: If we describe a system in terms of emergent laws such that one can get back (some) fundamental laws, then the system is called evolving.
That is bold, I know, but evolutionary adaption might exactly be that: Understanding the environment (which unfortunately evolves itself and thus creates troublesome circularities) in terms of the population and … as a gift … if halves the work we have according to my last post. If ‘life’ can be defined as emergent and evolving and if we have the transform governing emergent systems, then we are done. In the cases the transform is invertible we have ‘created’ life in the other cases not.
A truly random thought as long we we do not have the transform …