Cardinality Leap for Open-Ended Evolution: Theoretical Consideration and Demonstration by "Hash Chemistry"
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Open-ended evolution requires unbounded possibilities that evolving entities can explore. The cardinality of those possibilities thus has a significant implication for the open-endedness of evolution. We propose that facilitating formation of higher-order entities is a generalizable, effective way to cause a "cardinality leap" in the set of possibilities that promotes open-endedness. We demonstrate this idea with a simple, proof-of-concept toy model called "Hash Chemistry" that uses a hash function as a fitness evaluator of evolving entities of any size/order. Simulation results showed that the number of individual entities involved in a single replication event gradually increased over time, indicating evolutionary appearance of higher-order entities. It was also observed that the cumulative number of unique replicating entities that appeared in evolution increased almost linearly along time without a bound, presenting a concrete example of open-endedness achieved by the cardinality leap.
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