Complexity Theory in Biology and Technology: Broken Symmetries and Emergence

This paper discusses complexity theory, that is, the many theories that have been proposedfor emergence of complexity from the underlying physics. Our aim is to identify which aspects haveturned out to be the more fundamental ones as regards the emergence of biology, engineering, anddigital computing, as opposed to those that are in fact more peripheral in these contexts. In the caseswe consider, complexity arises via adaptive modular hierarchical structures that are open systemsinvolving broken symmetries. Each emergent level is causally effective because of the meshingtogether of upwards and downwards causation that takes place consistently with the underlyingphysics. Various physical constraints limit the outcomes that can be achieved. The underlying issueconcerns the origin of consciousness and agency given the basis of life in physics, which is structuredstarting from symmetries and variational principles with no trace of agency. A possible solution is toadmit that consciousness is an irreducible emergent property of matter.