posted Oct 28, 2009, 5:02 AM by Olaf Bochmann
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updated Oct 28, 2009, 4:29 PM
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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 nonlinear dynamical system, as nonunique 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 "... a highlevel phenomenon is strongly emergent with respect to a lowlevel domain when the highlevel phenomenon arises from the lowlevel domain, but truths concerning that phenomenon are not deducible even in principle from truths in the lowlevel domain." (most common in philosophical discussions)
 "... a highlevel phenomenon is weakly emergent with respect to a lowlevel domain when the highlevel phenomenon arises from the lowlevel domain, but truths concerning that phenomenon are unexpected given the principles governing the lowlevel domain." (most common in recent scientific discussions on complex systems)
Q: Will something not deductible ever happen? It is unexpected to whom? Dynamic Systems ViewWhat emerges from a spatially extended dynamical system are probability distributions over spacetime histories (space time phase) that arise from typical initial probabilities in the distant past. The amount of emergence is the "distance" of a spacetime phase from the set of products for independent units. Strong emergence means nonunique spacetime phase (but not due to decomposability).
Examples:  Climate is a probability distribution over spacetime 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 spacetime Gibbs phases for tr (log Df^u)_{ss}.
Decomposability (we will not allow strong emergence to arrise from this):  Nonuniqueness can arise trivially for topological reasons, e.g. more than one attractor, or a 2piece attractor  generally, because the system is decomposable.
 A system with a spacetime symbolic description is "indecomposable" if any allowable configurations on two sufficiently separated spacetime 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
 period2 phases of Toom's NEC voter PCA
 endemic infection v diseasefree phases of contact processes
Crutchfield nontrivial collective behavior  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 gametheoretic contexts
 What about systems that never settle down?
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