The information requirements of complex biological and economic systems with algorithmic information theory

Abstract

This article interprets the natural laws creating and maintaining a complex system, such as an ecology or an economy, distant from equilibrium, as computations on a real world Universal Turing Machine (UTM). As a laboratory, UTM can simulate the real world UTM, from the perspective of algorithmic information theory, the number of bits in the shortest, appropriately coded binary algorithm that specifies a real world system on a laboratory UTM defines its algorithmic entropy and its information content. As only algorithmic entropy differences matter, and differences are UTM-independent, differences measured on the laboratory UTM align with entropy changes in the real world. The system's distance from equilibrium in bits defines its order. Computations require energy. Landauer's principle identifies the minimum energy per bit (or the real world equivalent) to drive the computation that creates and sustains a real world system in a homeostatic state distant from equilibrium. This high-grade energy carries the computational instructions that do work on the system, ejecting disorder as heat and waste. While replication algorithms drive the emergence of complex ecological systems (doi:10.1016/j.biosystems.2015.11.008), in economic systems, individual agent behaviour can be captured by computer algorithms akin to the perspective of an adaptive system paradigm. Rather than specifying detailed behavioural routines for an economy, a narrative is used to identify the information drivers that create an ordered far-from-equilibrium economic system. The narrative shows that, somewhat like the interdependence of species in a vibrant ecology, agents trade, utilise technology, and amalgamate to form more complex structures creating order and driving the economy further from equilibrium. An ordered economy is a better economy. Order-creating investments (infrastructure, machines etc.) enhance economic performance, in contrast to non-ordering investments that extract wealth from others, adding nothing.