Is it the right ansatz?

Open-Endedness for the Sake of Open-Endedness

Natural evolution keeps inventing new complex and intricate forms and behaviors. Digital evolution and genetic algorithms fail to create the same kind of complexity, not just because we still lack the computational resources to rival nature, but because (it has been argued) we have not understood in principle how to create open-ended evolving systems. Much effort has been made to define such open-endedness so as to create forms of increasing complexity indefinitely. Here, however, a simple evolving computational system that satisfies all such requirements is presented. Doing so reveals a shortcoming in the definitions for open-ended evolution. The goal to create models that rival biological complexity remains. This work suggests that our current definitions allow for even simple models to pass as open-ended, and that our definitions of complexity and diversity are more important for the quest of open-ended evolution than the fact that something runs indefinitely.

Levels of description: a novel approach to dynamical hierarchies

We present a novel formal interpretation of dynamical hierarchies based on information theory, in which each level is a near-state-determined system, and levels are related to one another in a partial ordering. This reformulation moves away from previous definitions, which have considered unique hierarchies of structures or objects arranged in aggregates. Instead, we consider hierarchies of dynamical systems: these are more suited to describing living systems, which are not mere aggregates, but organizations. Transformations from lower to higher levels in a hierarchy are redescriptions that lose information. There are two criteria for partial ordering. One is a state-dependence criterion enforcing predictability within a level. The second is a distinctness criterion enforcing the idea that the higher-level description must do more than just throw information away. We hope this will be a useful tool for empirical studies of both computational and physical dynamical hierarchies.

State aggregation and population dynamics in linear systems

We consider complex systems that are composed of many interacting elements, evolving under some dynamics. We are interested in characterizing the ways in which these elements may be grouped into higher-level, macroscopic states in a way that is compatible with those dynamics. Such groupings may then be thought of as naturally emergent properties of the system. We formalize this idea and, in the case that the dynamics are linear, prove necessary and sufficient conditions for this to happen. In cases where there is an underlying symmetry among the components of the system, group theory may be used to provide a strong sufficient condition. These observations are illustrated with some artificial life examples.

Toward a formalization of emergence

Emergence is a concept widely used in the sciences, the arts, and engineering. Some effort has been made to formalize it, but it is used in various contexts with different meanings, and a unified theory of emergence is still distant. The ultimate goal of a theory of emergence should include using emergence to model, design, or predict the behavior of multiagent systems. The author proposes a formal definition of a basic type of emergence using a language-theoretic and grammar systems approach. It is shown which types of phenomena can be modeled in this sense and what the consequences are for other more complex phenomena.

Defense of the ansatz for dynamical hierarchies

Gross and McMullin [Artificial Life, 7, 355-365] criticize the conclusions of our article on dynamical hierarchies [Artificial Life, 7, 329-353]. In this note we respond to their criticisms. After clarifying our ansatz, we argue that the simulations presented by Gross and McMullin present no evidence against the ansatz, in part because their simulations use a different simulation framework, and in part because their simulations are no less complex than ours. We also clarify why the micelles in our simulations are third-order emergent structures, and why we emphasize realism in our simulation.