A New Kind of Finance

Finance has benefited from the Wolfram's NKS approach but it can and will benefit even more in the future, and the gains from the influence may actually be concentrated among practitioners who unintentionally employ those principles as a group.Comment: 13 pages; Forthcoming in "Irreducibility and Computational Equivalence: 10 Years After Wolfram's A New Kind of Science," Hector Zenil, ed., Springer Verlag, 201

Setting the demons loose: computational irreducibility does not guarantee unpredictability or emergence

A phenomenon resulting from a computationally irreducible (or computationally incompressible) process is supposedly unpredictable except via simulation. This notion of unpredictability has been deployed to formulate some recent accounts of computational emergence. Via a technical analysis of computational irreducibility, I show that computationally irreducibility can establish the impossibility of prediction only with respect to maximum standards of precision. By articulating the graded nature of prediction, I show that unpredictability to maximum standards is not equivalent to being unpredictable in general. I conclude that computational irreducibility fails to fulfill its assigned philosophical roles in theories of computational emergence

Coarse-graining of cellular automata, emergence, and the predictability of complex systems

We study the predictability of emergent phenomena in complex systems. Using nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's classification. The resulting coarse-grained CA that we construct are capable of emulating the large-scale behavior of the original systems without accounting for small-scale details. Several CA that can be coarse-grained by this construction are known to be universal Turing machines; they can emulate any CA or other computing devices and are therefore undecidable. We thus show that because in practice one only seeks coarse-grained information, complex physical systems can be predictable and even decidable at some level of description. The renormalization group flows that we construct induce a hierarchy of CA rules. This hierarchy agrees well with apparent rule complexity and is therefore a good candidate for a complexity measure and a classification method. Finally we argue that the large scale dynamics of CA can be very simple, at least when measured by the Kolmogorov complexity of the large scale update rule, and moreover exhibits a novel scaling law. We show that because of this large-scale simplicity, the probability of finding a coarse-grained description of CA approaches unity as one goes to increasingly coarser scales. We interpret this large scale simplicity as a pattern formation mechanism in which large scale patterns are forced upon the system by the simplicity of the rules that govern the large scale dynamics.Comment: 18 pages, 9 figure