Emergent Properties

In complexity theory. Logical analysis of the concept.

In Plato, e.g., the virtues of the ideal city in the Republic (doesn't Popper talk about this in his discussion of Plato?).

This is of course part of the continual argument about reductionism, and those most enamoured of emergent properties tend to be anti-reductionists. (I freely confess to being a reductionist, and thinking my opponents wooly-headed on this issue. For what follows, no warranty, express or implied, etc.) This term is used in a couple of senses, only one of which should trouble reductionists.

The weakest sense

Is also the most obvious. An emergent property is one which arises from the interaction of "lower-level" entities, none of which show it. No reductionism worth bothering with would be upset by this. The volume of a gas, or its pressure or temperature, even the number of molecules in the gas, are not properties of any individual molecule, though they depend on the properties of those individuals, and are entirely explicable from them; indeed, predictable well in advance.

Prediction

As above, but now we add the caveat that "the new property could not be predicted from a knowledge of the lower-level properties." Note that we cannot know that something is an emergent in this sense; we can only know that it cannot be predicted by us, with our current abilities. But "predict" is, here, ambiguous. It could mean foresee or prognosticate (i.e., make a statement about a future event which proves to be true), or it could mean deduce or explain --- what is sometimes called retrodiction. The "foresee" sense doesn't seem very important, because we typically invent a micro-level theory to explain an already-observed macro-level phenomenon. It is of course very nice indeed if the micro-theory predicts a new macro-phenomenon, which on investigation is found to happen; but this makes emergence an accidental result of what we happened to notice first.

Retrodiction or Explanation

"An emergent is a higher-level property, which cannot be deduced from or explained by the properties of the lower-level entities." This is almost troubling. The key is in "properties." Reductionists --- sane ones, anyhow --- don't deny that things interact; we spend a great deal of time worrying about those interactions. If by "properties" is meant just properties in the logical sense, then of course there are emergents, but so what? In this sense, pressure and volume are emergents.

On the other hand, if we are allowed both our properties and our relations, then "emergence" is a notion with teeth. The existence of any emergent properties, in this strong sense, would mean that universal reductionism is false. (Though it might be true locally, or for all other properties, or still be the most useful means of guiding inquiry, etc.) But, as above, I don't see how "X is an emergent property (strong sense)" could be established. At best we could say "X may be an emergent, since we have been unable to deduce it from the lower-level properties {Y}."

Does anyone know of any good candidates for this kind of emergent?

Addendum, April 2001: I'm pretty sure I know how to define "emergence," in the first, weakest, and most intelligble sense, in a quantitative, operational and objective way. One set of variables, A, emerges from another, B if (1) A is a function of B, i.e., at a higher level of abstraction, and (2) the higher-level variables can be predicted more efficiently than the lower-level ones, where "efficiency of prediction" is defined using information theory. See the concluding chapter of my dissertation, which unfortunately needs the previous chapters to be fully understood, but where I prove that, in a simple case (monoatomic ideal gas) thermodynamics emerges from statistical mechanics.

Addendum, December 2004: Since last updating this notebook, I have spent some time reading about the philosophers' notion of "supervenience", and feel either I'm very confused, or they are. A higher-level property is supposed to "supervene" on lower-level properties if differences at the higher level imply differences at the lower level, but not necessarily vice-versa. This is generally felt to let us admitting that the high-level, edifying properties are, indeed, related to the unedifying low-level ones, without having to embrace outright reductionism. But it seems to me to take about few lines of set theory to show that "supervenes on" means the same thing as "is a function of", and really that's all that reductionists ask for. So, like I said, I'm puzzled.

(For the record: Let's write lSu for the relationship "higher-level property u supervenes on low-level property l". The defining property of supervenience is that if u and v are not equal, then we cannot have lSu and lSv. So, if lSu and lSv, then u = v. But this establishes a many-one relationship mapping each low-level property to a unique high-level one, which is to say the high-level property is a function of the low-level property. Conversely, it is obvious that functional dependence implies supervenience. Hence, the two concepts are identical. QED.)

P. W. Anderson and D. L. Stein, "Broken Symmetry, Emergent Properties, Dissipative Structures, Life: Are They Related?", in F. E. Yates (ed.), Self-Organizing Systems: The Emergence of Order (pp. 445--457)
Fabio Boschetti's page on definitions of emergence
Markus Christen and Laura Rebecca Franklin, "The Concept of Emergence in Complexity Science: Finding Coherence between Theory and Practice", Proceedings of the SFI Complex Systems Summer School 2002 [Available in PDF.]
Joshua M. Epstein, "Agent-based Computational Models and Generative Social Science", Complexity 4:5 (1999): 41--60
Dror Givon, Raz Kupferman and Andrew Stuart, "Extracting macroscopic dynamics: model problems and algorithms", Nonlinearity 17 (2004): R55--R127 [PDF preprint]
Clark Glymour, "When Is a Brain Like the Planet?", Philosophy of Science 74 (2007): 330--347
John Holland, Emergence: From Chaos to Order [Review: Game Rules, or, Emergence according to Holland, or, Confessions of a Creative Reductionist]
Don Howard, "How to Think about Reduction and Emergence: Some Lessons from the Condensed Matter-Particle Physics Debate" [PDF. This is good, but I find it somewhat odd that Howard doesn't think of the quantum-state-of-the-multiparticle-system level as the lower one, to which descriptions in terms of individual particles reduces. Cf. Sewell.]
Manuel DeLanda, A New Philosophy of Society: Assemblage Theory and Social Complexity
Geoffrey L. Sewell, Quantum Mechanics and Its Emergent Macrophysics

CRS, "Functionalism, Emergence, and Collective Coordinates", Behavioral and Brain Sciences 27 (2004): 635--636 [PDF]
CRS and Cristopher Moore, "What Is a Macrostate? From Subjective Measurements to Objective Dynamics", cond-mat/0303625

Irene Appelbaum, "Two Conceptions Of The Emergence Of Phonemic Structure", Foundations of Science 9 (2004): 415--435 ["Lindblom's account of the emergence of phonemic structure is a central reference point in contemporary discussions of the emergence of language. ... [T]here are two distinct, and largely orthogonal conceptions of emergence implicit in Lindblom's account. According to one conception (causal emergence), the process by which minimal pairs are generated is crucial to the claim that phonemic structure is emergent; according to the other conception (analytic emergence), the fact that segments are an abstraction from the physical signal is what is crucial to the description of phonemic structure as emergent. The purpose of distinguishing rather than conflating these two conceptions of emergence is not ... to criticize [Lindblom] or to force us to choose between the two conceptions for consistency, but rather to give us a more detailed purchase on the notoriously thorny concept of emergent explanation."]
Robert W. Batterman, The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence
Robert C. Bishop and Harald Atmanspacher, "Contextual Emergence in the Description of Properties", phil-sci/2934
Fabio Boschetti, Mikhail Prokopenko, Ian Macreadie and Anne-Marie Grisogono, "Defining and detecting emergence in complex networks", KES 2005 [PDF]
Elena Castellani, "Reductionism, Emergence, and Effective Field Theories," physics/0101039
Jochen Fromm, "Types and Forms of Emergence", nlin.AO/0506028
Navot Israeli and Nigel Goldenfeld, "Coarse-graining of cellular automata, emergence, and the predictability of complex systems", nlin.CG/0508033
Michael Levin and Xiao-Gang Wen, "Photons and electrons as emergent phenomena", Reviews of Modern Physics 77 (2005): 871 ["Recent advances in condensed-matter theory have revealed that new and exotic phases of matter can exist in spin models (or more precisely, local bosonic models) via a simple physical mechanism, known as 'string-net condensation.' These new phases of matter have the unusual property that their collective excitations are gauge bosons and fermions. In some cases, the collective excitations can behave just like the photons, electrons, gluons, and quarks in our vacuum. This suggests that photons, electrons, and other elementary particles may have a unified origin --- string-net condensation in our vacuum. In addition, the string-net picture indicates how to make artificial photons, artificial electrons, and artificial quarks and gluons in condensed-matter systems."]
Kristie Lyn Miller, Issues In Theoretical Diversity: Persistence, Composition, and Time ["Our world is full of composite objects that persist through time: dogs, persons, chairs and rocks. But in virtue of what do a bunch of little objects get to compose some bigger object, and how does that bigger object persist through time? This book aims to answer these questions, but it does so by looking at accounts of composition and persistence through a new methodological lens. It asks the question: what does it take for two theories to be genuinely different, and how can we know whether what seems like metaphysical disagreement is really just semantic disagreement?"]
Jori E. Ruppert-Felsot, Olivier Praud, Eran Sharon, Harry L. Swinney, "Extraction of coherent structures in a rotating turbulent flow experiment", physics/0410161
Alex J. Ryan, "Emergence is coupled to scope, not level", Complexity 13 (2007): 67--77 = nlin.AO/0609011

CRS, "An Operational Test for Emergence Based on Statistical Complexity and Predictive Information" [Sucky title, I know]
CRS, "The Emergent Irrelevance of Quantum Mechanics to Biology" [for Derek Abbott's edited book on QM and life]

Notebooks

Emergent Properties