Stephen Wolfram's A New Kind of Science (NKS) hit the bookstores in 2002 with maximum hype. His thesis is that the laws of physics can be generated by various cellular automata--simple programs producing complexity. Occasionally (meaning rarely) I look at the NKS blog and look for any new applications. I see nothing I consider meaningful. Is anyone aware of any advances in any physics theory resulting from NKS? While CA are both interesting and fun (John Conway, Game of Life), as a theory of everything, I see problems. The generator rules are deterministic, and they are local in that each cell state depends on its immediate neighbors. So NKS is a local deterministic model of reality. Bell has shown that this cannot be. Can anyone conversant with CA comment?
Answer
Wolfram's early work on cellular automata (CAs) has been useful in some didactical ways. The 1D CAs defined by Wolfram can be seen as minimalistic models for systems with many degrees of freedom and a thermodynamic limit. Insofar these CAs are based on a mixing discrete local dynamics, deterministic chaos results.
Apart from these didactical achievements, Wolfram's work on CAs has not resulted in anything tangible. This statement can be extended to a much broader group of CAs, and even holds for lattice gas automata (LGAs), dedicated CAs for hydrodynamic simulations. LGAs have never delivered on their initial promise of providing a method to simulate turbulence. A derivative system (Lattice Boltzmann - not a CA) has some applications in flow simulation.
It is against this background that NKS was released with much fanfare. Not surprisingly, reception by the scientific community has been negative. The book contains no new results (the result that the 'rule 110 CA' is Turing complete was proven years earlier by Wolfram's research assistant Matthew Cook), and has had zero impact on other fields of physics. I recently saw a pile of NKS copies for sale for less than $ 10 in my local Half Price Books store.
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