Mikhail Prokopenko, Paul C. W. Davies, Michael Harré, Marcus Heisler, Zdenka Kuncic, Geraint F. Lewis, Ori Livson, Joseph T. Lizier, Fernando E. Rosas

We study open-ended evolution by focusing on computational and information-processing dynamics underlying major evolutionary transitions. In doing so, we consider biological organisms as hierarchical dynamical systems that generate regularities in their phase-spaces through interactions with their environment. These emergent information patterns can then be encoded within the organism’s components, leading to self-modelling “tangled hierarchies”. Our main conjecture is that when macro-scale patterns are encoded within micro-scale components, it creates fundamental tensions (computational inconsistencies) between what is encodable at a particular evolutionary stage and what is potentially realisable in the environment. A resolution of these tensions triggers an evolutionary transition which expands the problem-space, at the cost of generating new tensions in the expanded space, in a continual process. We argue that biological complexification can be interpreted computation-theoretically, within the Gödel–Turing–Post recursion-theoretic framework, as open-ended generation of computational novelty. In general, this process can be viewed as a meta-simulation performed by higher-order systems that successively simulate the computation carried out by lower-order systems. This computation-theoretic argument provides a basis for hypothesising the biological arrow of time.

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Kevin M. Stoltz, Cliff A. Joslyn

Boolean networks are a valuable class of discrete dynamical systems models, but they remain fundamentally limited by their inability to capture multi-way interactions in their components. To remedy this limitation, we propose a model of Boolean hypernetworks, which generalize standard Boolean networks. Utilizing the bijection between hypernetworks and bipartite networks, we show how Boolean hypernetworks generalize standard Boolean networks. We derive ensembles of Boolean hypernetworks from standard random Boolean networks and simulate the dynamics of each. Our results indicate that several properties of Boolean network dynamics are affected by the addition of multi-way interactions, and that these additions can have stabilizing or destabilizing effects.

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Sean M. Carroll & Achyuth Parola

We consider emergence from the perspective of dynamics: states of a system evolving with time. We focus on the role of a decomposition of wholes into parts, and attempt to characterize relationships between levels without reference to whether higher-level properties are “novel” or “unexpected.” We offer a classification of different varieties of emergence, with and without new ontological elements at higher levels.

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