Emergence and Universal Computation

Abstract

Emergence refers to the spontaneous formation of higher level (macro) structures or patterns in complex systems. Attempts to formalize the notion of emergence via algorithmic complexity theory runs into the problem that the Kolmogorov complexity function is not computable. The reason for this motivates a closer examination of the link between emergence and universal computation. Following Wolfram's pioneering work in the classification of cellular automata behavior, the research programs of Langton and Crutchfield, while incomplete, provide important insights to economists seeking to understand the relevance of emergence and universal computation to their discipline. They lead to questions on the emergence of institutions and the concomitant changes in rule-based behavior on the part of economic agents.

Segregation with social linkages: Evaluating Schelling’s model with networked individuals

“…Outlined in a series of papers (Schelling, 1969, 1971a, 1971b) and further elaborated in Schelling (2006), Schelling’s theory provided the foundation for large research in economics (Benito‐Ostolaza et al, 2015; Lee, 2004; Rosser, 2011; Sethi & Somanathan, 2004), sociology (Benard & Willer, 2007; Benenson et al, 2009; Fossett, 2011; Zhang, 2004), and social network analysis (de Marti & Zenou, 2017; Henry et al, 2011; Stadtfeld & Vörös, 2020).…”

Segregation with Social Linkages: Evaluating Schelling's Model with Networked Individuals

“…Outlined in a series of papers (Schelling, 1969(Schelling, , 1971a(Schelling, , 1971b and further elaborated in Schelling (2006), Schelling's theory provided the foundation for large research in economics (Benito-Ostolaza et al, 2015;Lee, 2004;Rosser, 2011;Sethi & Somanathan, 2004), sociology (Benard & Willer, 2007;Benenson et al, 2009;Fossett, 2011;Zhang, 2004), and social network analysis (de Marti & Zenou, 2017;Henry et al, 2011;Stadtfeld & Vörös, 2020). Schelling's simple mechanism was originally framed as a heuristic process of strategic reasoning, in which people leave their residence whenever they are a too small minority in their neighborhood.…”

From Swarm Simulations to Swarm Intelligence

“…Notably, emergent phenomena are key phenomena in all self-organizing systems such as collective intelligent behaviors of animal groups: flocks of birds, colonies of ants, schools of fish, swarms of bees, etc. Emergence is observed in the economy as well: macroeconomic fluctuations, traffic jams, hierarchy of cities, motion picture industry and mass protest behavior [18]. There are attempts to formalize the notion of emergence by algorithmic complexity theory.…”