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Durham University

Institute of Advanced Study

Normality, Magic, Miracle and Error: emergence along a reversibility spectrum

Formation of a butterfly from a pupa, extraction of a live dove from a magician’s empty hat, generation of new particles from high-energy particle collisions and spawning a new dream world from mind in sleep are all examples of a common, fuzzy notion called ‘emergence’. Emergence is intuitively defined in a subjective manner in various contexts, yet it eludes a universally acceptable objective definition. In this paper1 I pin the concept of emergence to the element of surprise in a phenomenon. I then propose a characterisation of emergence by first defining surprise in terms of an objective dimension called reversibility. Using this definition, I categorise the various notions of emergence into three main classes: (1) weak emergence in which the evolution from pre-emergence to post-emergence states is fully reversible and hence evokes the least amount of surprise, (2) quasi emergence in which the evolution from pre-emergence to post-emergence states holds surprise in the form of gaps in reversibility, but the gaps can be overcome via placeholders such as deterministic pseudo-randomness, and (3) strong emergence in which it is impossible to find any reversible description of evolution from pre-emergence states to post-emergence states, thereby making the element of surprise fundamental and impossible to redress. In fact, in the strong emergence case, the pre- and post-emergence states continue to co-exist despite an apparent transformation of the pre-emergence state to post-emergence state. These definitions are used to explain instances of emergence, organised along a continuous spectrum as normality, magic, miracle and error.


Vol 10 Article 17