Thursday, July 19, 2018

It's not complicated. It's Complex!

When is a system "complex"?
Even though we have intuition (e.g. complexity is associated with many interacting degrees of freedom) coming up with definitive criteria for complexity is not easy.

I just finished reading, Complexity: A Very Short Introduction, by John Holland.
His perspective is that a system is "complicated" if it has many interacting degrees of freedom, but is "complex" if in addition it exhibits emergent properties.
The criteria for emergence is the existence of new hierarchies, containing new entities or agents (defined by the formation of boundaries) that are coupled by new interactions, and described by new "laws".

Holland distinguishes complex physical systems (CPS) from complex adaptive systems (CAS).
The latter involve elements (agents) that can change (learn or adapt) in response to interactions with other agents.
Cellular automata and pattern formation in biology are CPS, whereas genetic algorithms, economics, and sociology are examples of CAS.

The book gives a rather dense (but worthwhile) introduction to key concepts in complexity theory including the emergence of specialists (e.g., division of labor, according to Adam Smith in economics), the role of diversity, co-evolution (e.g. Darwin's orchid and moth), and evolutionary niches (fixed points of Markov matrices!).

Holland smoothly flits backwards and forwards between examples in biology, economics, linguistics, and computer science.

Holland's definition of emergence is consistent with how I think in condensed matter. For example, the formation of weakly interacting quasi-particles in a Fermi liquid. The emergent "boundaries" define the spatial size of the quasi-particle.
What struck me is that the interactions should be viewed as emergent, just as much as the quasi-particles.
For example, if we start with quarks and QCD (quantum chromodynamics), then at "low" temperatures and densities, nucleons form and the nuclear force emerges.

2 comments:

  1. https://www.researchgate.net/figure/Intuition-of-what-should-be-complexity-at-least-asymptotically_fig1_302061783

    This paper with Fig 1 titled "Intuition of what should be complexity, at least asymptotically" sounds interesting

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