Complexity vs Emergence: Quantifying Emergence in term of Persistent Mutual Information

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• Prof. R.C. Ball, Warwick U
• Thursday 11 March 2010, 13:45-15:00
• Theory Library.

If you have a question about this talk, please contact Dr Dimitri M Gangardt.

We define Persistent Mutual Information (PMI) as: the Mutual (Shannon) Information between the far past history of a system and its far future evolution. This quantifies how much past observations enable long term prediction, which we take as the primary signature of Emergent Behaviour. It is important to the definition of PMI that the mutual information between close times is excluded. This is the key distinction between PMI and a range of established Complexity Measures, and it means PMI has some robustness to superposed noise or chaotic behaviour. Note that purely chaotic behaviour has zero PMI . PMI quantifies Strong Emergence in the following sense: it captures the relationship (of past to future) for information which varies from one realisation of the system history to another. Thus ‘weakly emergent’ features which are reproducible from one realisation to another do not count, such as the system reliably ‘settling down’ to some fixed limit behaviour. It is only the variability of limit behaviour (from one realisation to another) which can count. We illustrate predictions of PMI for a variety of examples. The Logistic Map is informative and we compare with measured PMI data for this case. We show that measured PMI data captures not just the period doubling cascade but also the associated cascade of banded chaos, in which the band dynamics is detected as PMI and not the overlayer of chaotic decoration. Whilst our main focus is in terms of PMI over time, we can also extend the idea to PMI across space in extended systems as a generalisation of the notion of ordered phases.

This talk is part of the Theoretical Physics Seminars series.

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