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What is Emergence?

posted Oct 28, 2009, 5:02 AM by Olaf Bochmann   [ updated Oct 28, 2009, 4:29 PM ]
There are many views on what is emergence. At the same time it is one of the most seductive buzzwords in complex systems science. This summary is based on a talk from Robert MacKay, University of Warwick. It explains emergence as a property of a non-linear dynamical system, as non-unique statistical behavior without any topological reason.

History

  • Wikipedia: is the way complex systems and patterns arise out of simple interactions (e.g. a termite mound produced by a termite colony)
  • Aristotle, Metaphysics, Book 8: "... the totality is not, as it were, a mere heap, but the whole is something beside the parts ...", i.e., the whole is greater than the sum of the parts.
  • Anderson (1972), More is Different: "... the whole becomes not merely more, but very different from the sum of its parts."

Weak vs. Strong emergence

Chalmers (2002), Strong and Weak Emergence:
  • "... a high-level phenomenon is strongly emergent with respect to a low-level domain when the high-level phenomenon arises from the low-level domain, but truths concerning that phenomenon are not deducible even in principle from truths in the low-level domain." (most common in philosophical discussions)
  • "... a high-level phenomenon is weakly emergent with respect to a low-level domain when the high-level phenomenon arises from the low-level domain, but truths concerning that phenomenon are unexpected given the principles governing the low-level domain." (most common in recent scientific discussions on complex systems)
Q: Will something not deductible ever happen? It is unexpected to whom?

Dynamic Systems View

What emerges from a spatially extended dynamical system are probability distributions over space-time histories (space time phase) that arise from typical initial probabilities in the distant past. The amount of emergence is the "distance" of a space-time phase from the set of products for independent units. Strong emergence means non-unique space-time phase (but not due to decomposability).

Examples:
  • Climate is a probability distribution over space-time histories compatible with weather laws.
  • For equilibrium statistical mechanical systems the allowed probability distributions are the Gibbs phases for the energy \beta H (in units of temerature).
  • For Markov processes they are the Gibbs phases for -log p_{ij} (log of transitionprobabilities)
  • for deterministic dynamical systems with symbolic dynamics they are the Gibbs phases for log det Df^u (=SRB measures)
  • For spatially extended deterministic dynamical systems with symbolic dynamics they are the space-time Gibbs phases for tr (log Df^u)_{ss}.

Decomposability (we will not allow strong emergence to arrise from this):
  • Non-uniqueness can arise trivially for topological reasons, e.g. more than one attractor, or a 2-piece attractor - generally, because the system is decomposable.
  • A system with a space-time symbolic description is "indecomposable" if any allowable configurations on two sufficiently separated space-time patches can be joined into an allowable configuration ("specification property").
Proved examples of strong emergence:
  • ferromagnetic phase of 2D lsing model
  • ferromagnetic phase of Tom's NEC majority voter PCA
  • period-2 phases of Toom's NEC voter PCA
  • endemic infection v disease-free phases of contact processes
Crutchfield non-trivial collective behavior

Research Projects

  • make a zoo of possible phases
  • study their correlation structure
  • study robustness of phases/set of phases
  • universality classes/aggregation
  • bifurcations/scaling
  • control/optimization of phases
  • fit to data
  • develop in contexts with dynamic network
  • develop for game-theoretic contexts
  • What about systems that never settle down?

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