Emergence Explained Russ Abbott Dept. of Computer Science California State University, Los Angeles and The Aerospace Corporation What’s right and what’s wrong about reductionism Challenges for Biologically-Inspired Computing

Modeling problems The apparent impossibility of finding a non-arbitrary base level for our models. (Like a Mandelbrot set.) Don’t know how to build models in which the fundamental elements are far-from-equilibrium entities, i.e., elements that are based on processes rather than on structures. Don’t know how to model fitness except in terms of artificially defined functions or artificially defined fitness units. Don’t know how to build models that can notice emergent entities and characterize their (virtual) interactions.

Emergence the holy grail of complex system computing behavior at a larger scale [that] arises from the detailed structure, behavior and relationships on a finer scale. … how macroscopic behavior arises from microscopic behavior. the rest of the observable, exploitable order in the universe It is unlikely that a topic as complicated as emergence will submit meekly to a concise definition, and I have no such definition to offer. John Holland, Emergence: From Chaos to Order, 1998Emergence: From Chaos to Order

Emergence: making epiphenomena do real work. Higher level entities are real–not epiphenomenal and not just conceptual conveniences  They represent regions of reduced entropy.  They generally have a real internal design, whose components also are non-primitive entities. Interactions among non-primitive entities are virtual.  It's important that the interactions accomplish what they are supposed to accomplish within the design.  But ultimately, they are epiphenomenal. The only real action is at the very lowest level, i.e., quarks, etc. This leads to the modeling problems on the previous slide. E.g. biological arms races, co-evolution. Where I’m going

Is emergence (just) epiphenomenal? Epiphenomenon: a secondary phenomenon that is a by-product of another phenomenon.  “Genetic drift is an epiphenomenon of the basic components of replicating DNA, mutations, geography, and limiting resources.”  The elliptical shape of the earth’s orbit is an epiphenomenon of the force of gravity acting on a body in motion.  Imagine the earth as an agent that follows the rules of inertia and gravitational attraction.

Played on a rectangular grid.  A totalistic two-dimensional cellular automaton. A cell (agent) is either alive or dead. The 8 surrounding agents are an agent’s neighbors. Rules  A live agent with two or three live neighbors stays alive; otherwise it dies.  A dead agent with exactly three live neighbors is (miraculously) (re)born and becomes alive. The Game of Life

Gliders (waves of births and deaths—epidemics?) are (amazing) epiphenomena of the Game of Life rules—whose only(!) consequences are the switching on and off of agents. Gliders (and other epiphenomena) are causally powerless.  A glider does not change how the rules operate or which cells will be switched on and off.  A Game of Life run will proceed in exactly the same way whether one notices the gliders or not. Gliders exemplify emergence.  Gliders are not generated explicitly.  There is no glider algorithm.  Gliders are not visible in the rules.  Gliders are generated stigmergically. Epiphenomenal gliders All software is stigmergically epiphenomenal over the instruction execution cycle, which is stigmergically epiphenomenal over electron flows.

A Game of Life Turing Machine Amazing as they are, gliders are also trivial.  Once we know how to produce a glider, it’s simple to make them.  You generally don't do this with your models. Can build a library of Game of Life patterns. By suitably arranging these patterns, one can simulate a Turing Machine.  A second level of emergence.  Again, no algorithm; just stigmergy. What does it mean for epiphenomenal gliders and other epiphenomenal patterns to simulate a Turing Machine?

Design matters To prove that a Game-of-Life simulation of a Turing Machine works, one must reason about epiphenomenal interactions among epiphenomenal patterns.  Treat them as real. Implementations matter only as proof that the interactions are possible.

A Game of Life naturalist Find a lost tribe of Game of Life runs “in the wild.” Get a grant to study them. Figure out the Game of Life rules.  Your model can even explain gliders as emergents!  Publish your results. The rules do not explain the functionality of a Turing Machine simulation or a glider gun. Too teleological? Too artificial? Too designer-oriented? Design happens: things survive in the world if their designs work.  The designs must function at their own level.  Explaining the mechanisms that allow designs to be implemented is not enough.

Emergence: non-reductive regularity We have noticed a regularity: a Game-of-Life run simulating a Turing Machine or a glider gun. We can explain every step in that simulation by appeal to the Game-of-Life rules. Yet because the system has a design, its rules don’t explain what the system is doing functionally. Both  reductionism  the-whole-is-more-than-just-the-sum-of-its-parts. So emergence is any functionality—which is always more than the functionality’s implementation. (Functionalism)  Recall Shalizi’s definition of emergence as all the order in the universe above that of quarks/strings etc.

The emergence of complexity Anderson: The ability to reduce everything to simple fundamental laws [does not imply] the ability to start from those laws and reconstruct the universe. “More is Different,” Science, Condensed matter physics; super-conductivity; collective effects James Burke’s Connections; eBay market for virtual assets A non-reductive, contingent, stigmergic, historical process