[On computational irreducibility and the predictability of complex physical systems] - A New Kind of Science: The NKS Forum

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On computational irreducibility and the predictability of complex physical systems

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Posted by: MikeHelland

Is anyone familiar with this paper?

Comments?

http://www.weizmann.ac.il/home/isra...l%20systems.pdf

"Can one predict the future evolution of a physical pro-
cess which is described or modeled by a computationally
irreducible (CIR) mathematical algorithm? For such sys-
tems, in order to know the system’s state after (e.g.) one
million time steps, there is no faster algorithm than to
solve the equation of motion a million time steps into the
future. Wolfram has suggested that the existence of CIR
systems in nature is at the root of our apparent inability
to model and understand complex systems [1, 2, 3, 4].
Complex physical systems that are CIR might there-
fore seem to be inherently unpredictable. It is tempting
to conclude from this that the enterprise of physics itself
is doomed from the outset; rather than attempting to
construct solvable mathematical models of physical pro-
cesses, computational models should be built, explored
and empirically analyzed. This argument, however, as-
sumes that infinite precision is required for the prediction
of future evolution. Usually coarse-grained or even statis-
tical information is sufficient: indeed, a physical model
is usually correct only to a certain level of resolution,
so that there is little interest in predictions from such a
model on a scale outside its regime of validity.
In this Letter, we report on experiments with near-
est neighbour one-dimensional cellular automata, which
show that because in practice one only seeks coarse-
grained information, complex physical systems can be
predictable and even computationally reducible at some
level of description. The implication of these results is
that, at least for systems whose complexity is the out-
come of very simple rules, useful approximations can be
made that enable predictions about future behavior."


Posted by: RLamy

Yes, it's an interesting paper, which has been discussed already on the "Pure NKS" forum (which is where it belongs IMHO). Their following paper, "Coarse-graining of cellular automata, emergence, and the predictability of complex systems" is more complete.




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