1. Emergence and Universal Computation
- Author
-
Cassey Lee
- Subjects
Economics and Econometrics ,Kolmogorov complexity ,Ilya ,Gödel's incompleteness theorems ,Cellular automaton ,Epistemology ,symbols.namesake ,symbols ,Economics ,Gödel ,Einstein ,computer ,Axiom ,World view ,computer.programming_language - Abstract
Emergence refers to the spontaneous formation of higher level (macro) structures or patterns incomplex systems. Attempts to formalize the notion of emergence via algorithmic complexity theoryruns into the problem that the Kolmogorov complexity function is not computable. The reason for thismotivates a closer examination of the link between emergence and universal computation. FollowingWolfram’s pioneering work in the classification of cellular automata behavior, the research programsof Langton and Crutchfield, while incomplete, provide important insights to economists seeking tounderstand the relevance of emergence and universal computation to their discipline. They lead toquestions on the emergence of institutions and the concomitant changes in rule-based behavior on thepart of economic agents. 1. INTRODUCTION The twentieth century is replete with scientific and mathematical discoveriesthat have profoundly changed our world view. In physics, within a merecentury, our view of the cosmos changed from a classical (Newtonian) to arelativistic one following Einstein’s relativity theory in the early 1900s. Inmathematics, Hilbert’s faith in the closure of formal axiom systems fell apartwith Godel’s incompleteness theorem in the 1930s.Out of these ashes of lost deterministic foundations arose the sciences ofcomplex systems, first in the study of non-equilibrium thermodynamics(under the intellectual leadership of Ilya Prigogine in Brussels) and later, inbroader interdisciplinary terms, in New Mexico with the establishment of theSanta Fe Institute. Interestingly, a core element of this new paradigm—thenotion of emergence—reflects the passage of the sciences and mathematics
- Published
- 2022
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