A Theory of Emergence and Entropy in Systems of Systems

Systems of Systems (SOS) meet vital needs in our society by providing capabilities that are not possible by their discrete components or subsystems. Some SOS are engineered to produce predictable results, yet they can still display emergent behavior. These behaviors are often considered negative because they are not a function of the design. However, emergent behavior can also be serendipitous and produce unexpected positive results. The authors formalize a theory of emergence based on entropy. The theory has explanatory value for emergence as an ontological and phenomenological concept in systems of systems. © 2013 The Authors

Computationally Tractable Pairwise Complexity Profile

Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the information to describe a system as a function of the scale at which it is observed. We present a new formulation of the complexity profile, which expands its possible application to high-dimensional real-world and mathematically defined systems. The new method is constructed from the pairwise dependencies between components of the system. The pairwise approach may serve as both a formulation in its own right and a computationally feasible approximation to the original complexity profile. We compare it to the original complexity profile by giving cases where they are equivalent, proving properties common to both methods, and demonstrating where they differ. Both formulations satisfy linear superposition for unrelated systems and conservation of total degrees of freedom (sum rule). The new pairwise formulation is also a monotonically non-increasing function of scale. Furthermore, we show that the new formulation defines a class of related complexity profile functions for a given system, demonstrating the generality of the formalism.Comment: 18 pages, 3 figure

Eliminating the mystery from the concept of emergence

While some branches of complexity theory are advancing rapidly, the same cannot be said for our understanding of emergence. Despite a complete knowledge of the rules underlying the interactions between the parts of many systems, we are often baffled by their sudden transitions from simple to complex. Here I propose a solution to this conceptual problem. Given that emergence is often the result of many interactions occurring simultaneously in time and space, an ability to intuitively grasp it would require the ability to consciously think in parallel. A simple exercise is used to demonstrate that we do not possess this ability. Our surprise at the behaviour of cellular automata models, and the natural cases of pattern formation they mimic, is then explained from this perspective. This work suggests that the cognitive limitations of the mind can be as significant a barrier to scientific progress as the limitations of our senses

Measuring autonomy and emergence via Granger causality

Concepts of emergence and autonomy are central to artificial life and related cognitive and behavioral sciences. However, quantitative and easy-to-apply measures of these phenomena are mostly lacking. Here, I describe quantitative and practicable measures for both autonomy and emergence, based on the framework of multivariate autoregression and specifically Granger causality. G-autonomy measures the extent to which the knowing the past of a variable helps predict its future, as compared to predictions based on past states of external (environmental) variables. G-emergence measures the extent to which a process is both dependent upon and autonomous from its underlying causal factors. These measures are validated by application to agent-based models of predation (for autonomy) and flocking (for emergence). In the former, evolutionary adaptation enhances autonomy; the latter model illustrates not only emergence but also downward causation. I end with a discussion of relations among autonomy, emergence, and consciousness

The restrictions of the Maximum Entropy Production Principle

We tried to explain our point of view on this principle and answer a number of critical questions in this comment. It is the first time we have clearly presented all the existing restrictions of MEPP application and briefly explained them; this will help to avoid misunderstandings connected with its use.Comment: 7 pages, Added argument

Complexity and Information: Measuring Emergence, Self-organization, and Homeostasis at Multiple Scales

Concepts used in the scientific study of complex systems have become so widespread that their use and abuse has led to ambiguity and confusion in their meaning. In this paper we use information theory to provide abstract and concise measures of complexity, emergence, self-organization, and homeostasis. The purpose is to clarify the meaning of these concepts with the aid of the proposed formal measures. In a simplified version of the measures (focusing on the information produced by a system), emergence becomes the opposite of self-organization, while complexity represents their balance. Homeostasis can be seen as a measure of the stability of the system. We use computational experiments on random Boolean networks and elementary cellular automata to illustrate our measures at multiple scales.Comment: 42 pages, 11 figures, 2 table