Anticipatory Systems, Preferences, Averages: Inflation, Uncertain Phenomena, Management

TL;DR

This paper explores the complex, non-linear behavior of anticipatory systems, especially in economics, showing that traditional averaging methods fail for such systems and analyzing their responses to inflation and market dynamics.

Contribution

It introduces a formal analysis of anticipatory systems using generalized functions, revealing their non-linear nature and implications for economic modeling and inflation response.

Findings

Anticipatory systems exhibit highly non-linear and sensitive behavior.

Averages cannot be reliably computed for index complex systems.

Applications to economic inflation and production theory are demonstrated.

Abstract

Behavior of systems that are functions of anticipated behavior of other systems, whose own behavior is also anticipatory but homeostatic and determined by hierarchical ordering, which changes over time, of sets of possible environments that are not co-possible, is proven to be highly non-linear and sensitively dependent on precise parameters. Averages and other kinds of aggregates cannot be calculated for sets of measurements of behavior of systems, defined in this essay, that are "index complex" in this way. This includes many systems, for instance, social behavior, where anticipation of behavior of other individuals plays a central role. Anticipation of preferences of economic actors are discussed in this way. Analysis by way of generalized functions of complex variables is done for these kinds of systems, and equations of change of state are formally described. Behavior that comprises of responses to market interest rates is taken for example. Continuity assumptions in economics analyzed in this context. Anticipatory responses to inflation in economics are discussed. Applications to theory of production are presented.