Cardinality Leap for Open-Ended Evolution: Theoretical Consideration and Demonstration by "Hash Chemistry"

TL;DR

This paper introduces 'Hash Chemistry', a model demonstrating how increasing the complexity of entities through higher-order formations can significantly enhance the potential for open-ended evolution, as shown by unbounded growth in entity diversity.

Contribution

The paper proposes a general approach to promote open-ended evolution by enabling higher-order entity formation, demonstrated through a novel hash-based model called 'Hash Chemistry.'

Findings

Cumulative unique entities increased linearly over time.

Higher-order entities emerged naturally during evolution.

Control experiments with random evaluators did not show similar behaviors.

Abstract

Open-ended evolution requires unbounded possibilities that evolving entities can explore. The cardinality of a set 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 cumulative number of unique replicating entities that appeared in evolution increased almost linearly along time without an apparent bound, demonstrating the effectiveness of the proposed cardinality leap. It was also observed that the number of individual entities involved in a single replication event gradually increased over time, indicating evolutionary appearance of higher-order entities. Moreover, these behaviors were not observed in control experiments in which fitness evaluators were replaced by random number generators. This strongly suggests that the dynamics observed in Hash Chemistry were indeed evolutionary behaviors driven by selection and adaptation taking place at multiple scales.