Thursday, September 28, 2017

Emergence in the Game of Life

How do complex structures emerge from simple systems?
How do you define emergence?

Conway's Game of life is a popular and widely studied version of cellular automata. It is based on four simple rules for the evolution of a two-dimensional grid of squares that can either be dead or alive. What is amazing is that distinct patterns: still lifes, oscillators, and spaceships can emerge.

Gosper's glider gun is shown below.

What does this have to do with strongly correlated electron systems?
The similarity is that one starts with extremely simple "rules": a crystal structure plus Coloumb's law and the Schrodinger equation (Laughlin and Pines' Theory of Everything) and complex structures emerge: quasi-particles, broken symmetry states, topological order, non-Fermi liquids, ...

Recently, Sophia Kivelson and Steven Kivelson [daughter and father] proposed the following definition:
An emergent behavior of a physical system is a qualitative property that can only occur in the limit that the number of microscopic constituents tends to infinity.
I think this would mean the properties above would not be classified as emergent. I am not sure I agree. I think I still prefer older broader definitions such as that of Michael Berry in terms of singular expansions or that of P. Luisi.
The definition also disagrees with Michael Polanyi, who argued that language and grammar are emergent.

1 comment:

  1. What's fascinating is cellular automata (even a simple 1D one) is Turing complete, which means, capability wise (not necessarily efficiency wise), the collection of these simple automatons have the same capability as the most advanced (non quantum) computer today.