Formal Definitions of Unbounded Evolution and Innovation Reveal Universal Mechanisms for Open-Ended Evolution in Dynamical Systems

Open-ended evolution (OEE) is relevant to a variety of biological, artificial and technological systems, but has been challenging to reproduce in silico. Most theoretical efforts focus on key aspects of open-ended evolution as it appears in biology. We recast the problem as a more general one in dynamical systems theory, providing simple criteria for open-ended evolution based on two hallmark features: unbounded evolution and innovation. We define unbounded evolution as patterns that are non-repeating within the expected Poincare recurrence time of an equivalent isolated system, and innovation as trajectories not observed in isolated systems. As a case study, we implement novel variants of cellular automata (CA) in which the update rules are allowed to vary with time in three alternative ways. Each is capable of generating conditions for open-ended evolution, but vary in their ability to do so. We find that state-dependent dynamics, widely regarded as a hallmark of life, statistically out-performs other candidate mechanisms, and is the only mechanism to produce open-ended evolution in a scalable manner, essential to the notion of ongoing evolution. This analysis suggests a new framework for unifying mechanisms for generating OEE with features distinctive to life and its artifacts, with broad applicability to biological and artificial systems.Comment: Main document: 17 pages, Supplement: 21 pages Presented at OEE2: The Second Workshop on Open-Ended Evolution, 15th International Conference on the Synthesis and Simulation of Living Systems (ALIFE XV), Canc\'un, Mexico, 4-8 July 2016 (http://www.tim-taylor.com/oee2/

Formal Definitions of Unbounded Evolution and Innovation Reveal Universal Mechanisms for Open-Ended Evolution in Dynamical Systems

abstract: Open-ended evolution (OEE) is relevant to a variety of biological, artificial and technological systems, but has been challenging to reproduce in silico. Most theoretical efforts focus on key aspects of open-ended evolution as it appears in biology. We recast the problem as a more general one in dynamical systems theory, providing simple criteria for open-ended evolution based on two hallmark features: unbounded evolution and innovation. We define unbounded evolution as patterns that are non-repeating within the expected Poincare recurrence time of an isolated system, and innovation as trajectories not observed in isolated systems. As a case study, we implement novel variants of cellular automata (CA) where the update rules are allowed to vary with time in three alternative ways. Each is capable of generating conditions for open-ended evolution, but vary in their ability to do so. We find that state-dependent dynamics, regarded as a hallmark of life, statistically out-performs other candidate mechanisms, and is the only mechanism to produce open-ended evolution in a scalable manner, essential to the notion of ongoing evolution. This analysis suggests a new framework for unifying mechanisms for generating OEE with features distinctive to life and its artifacts, with broad applicability to biological and artificial systems.The final version of this article, as published in Scientific Reports, can be viewed online at: http://www.nature.com/articles/s41598-017-00810-

The Physics of Open Ended Evolution

abstract: What makes living systems different than non-living ones? Unfortunately this question is impossible to answer, at least currently. Instead, we must face computationally tangible questions based on our current understanding of physics, computation, information, and biology. Yet we have few insights into how living systems might quantifiably differ from their non-living counterparts, as in a mathematical foundation to explain away our observations of biological evolution, emergence, innovation, and organization. The development of a theory of living systems, if at all possible, demands a mathematical understanding of how data generated by complex biological systems changes over time. In addition, this theory ought to be broad enough as to not be constrained to an Earth-based biochemistry. In this dissertation, the philosophy of studying living systems from the perspective of traditional physics is first explored as a motivating discussion for subsequent research. Traditionally, we have often thought of the physical world from a bottom-up approach: things happening on a smaller scale aggregate into things happening on a larger scale. In addition, the laws of physics are generally considered static over time. Research suggests that biological evolution may follow dynamic laws that (at least in part) change as a function of the state of the system. Of the three featured research projects, cellular automata (CA) are used as a model to study certain aspects of living systems in two of them. These aspects include self-reference, open-ended evolution, local physical universality, subjectivity, and information processing. Open-ended evolution and local physical universality are attributed to the vast amount of innovation observed throughout biological evolution. Biological systems may distinguish themselves in terms of information processing and storage, not outside the theory of computation. The final research project concretely explores real-world phenomenon by means of mapping dominance hierarchies in the evolution of video game strategies. Though the main question of how life differs from non-life remains unanswered, the mechanisms behind open-ended evolution and physical universality are revealed.Dissertation/ThesisDoctoral Dissertation Physics 201

Physical Universality, State-Dependent Dynamical Laws and Open-Ended Novelty

abstract: A major conceptual step forward in understanding the logical architecture of living systems was advanced by von Neumann with his universal constructor, a physical device capable of self-reproduction. A necessary condition for a universal constructor to exist is that the laws of physics permit physical universality, such that any transformation (consistent with the laws of physics and availability of resources) can be caused to occur. While physical universality has been demonstrated in simple cellular automata models, so far these have not displayed a requisite feature of life—namely open-ended evolution—the explanation of which was also a prime motivator in von Neumann’s formulation of a universal constructor. Current examples of physical universality rely on reversible dynamical laws, whereas it is well-known that living processes are dissipative. Here we show that physical universality and open-ended dynamics should both be possible in irreversible dynamical systems if one entertains the possibility of state-dependent laws. We demonstrate with simple toy models how the accessibility of state space can yield open-ended trajectories, defined as trajectories that do not repeat within the expected Poincaré recurrence time and are not reproducible by an isolated system. We discuss implications for physical universality, or an approximation to it, as a foundational framework for developing a physics for life

Emergence and algorithmic information dynamics of systems and observers

Previous work has shown that perturbation analysis in software space can produce candidate computable generative models and uncover possible causal properties from the finite description of an object or system quantifying the algorithmic contribution of each of its elements relative to the whole. One of the challenges for defining emergence is that one observer's prior knowledge may cause a phenomenon to present itself to such observer as emergent while for another as reducible. When attempting to quantify emergence, we demonstrate that the methods of Algorithmic Information Dynamics can deal with the richness of such observer-object dependencies both in theory and practice. By formalising the act of observing as mutual algorithmic perturbation, the emergence of algorithmic information is rendered invariant, minimal, and robust in the face of information cost and distortion, while still observer-dependent. We demonstrate that the unbounded increase of emergent algorithmic information implies asymptotically observer-independent emergence, which eventually overcomes any formal theory that an observer might devise to finitely characterise a phenomenon. We discuss observer-dependent emergence and asymptotically observer-independent emergence solving some previous suggestions indicating a hard distinction between strong and weak emergence

Open-Ended Evolution in Cellular Automata Worlds

Open-ended evolution is a fundamental issue in artificial life research. We consider biological and social systems as a flux of interacting components that transiently participate in interactions with other system components as part of these systems. This approach and the corresponding reasoning suggest that systems able to deliver open-ended evolution must have a representation equivalent of Turing machines. Here we provide an implementation of a such model of evolving systems using a cellular automata world. We analyze the simulated world using a set of metrics based on criteria of open-ended evolution suggested by Bedau et al. We show that the cellular automata world has significantly more evolutionary activity than a corresponding random shadow world. Our work indicates that the proposed cellular automata worlds have the potential to generate open-ended evolution according to the criteria that we have considered

Defining and simulating open-ended novelty: requirements, guidelines, and challenges

The open-endedness of a system is often defined as a continual production of novelty. Here we pin down this concept more fully by defining several types of novelty that a system may exhibit, classified as variation, innovation, and emergence. We then provide a meta-model for including levels of structure in a system’s model. From there, we define an architecture suitable for building simulations of open-ended novelty-generating systems and discuss how previously proposed systems fit into this framework. We discuss the design principles applicable to those systems and close with some challenges for the community

Emergence in artificial life

Even when concepts similar to emergence have been used since antiquity, we lack an agreed definition. However, emergence has been identified as one of the main features of complex systems. Most would agree on the statement ``life is complex''. Thus, understanding emergence and complexity should benefit the study of living systems. It can be said that life emerges from the interactions of complex molecules. But how useful is this to understand living systems? Artificial life (ALife) has been developed in recent decades to study life using a synthetic approach: build it to understand it. ALife systems are not so complex, be them soft (simulations), hard (robots), or wet (protocells). Then, we can aim at first understanding emergence in ALife, for then using this knowledge in biology. I argue that to understand emergence and life, it becomes useful to use information as a framework. In a general sense, I define emergence as information that is not present at one scale but is present at another scale. This perspective avoids problems of studying emergence from a materialist framework, and can be also useful in the study of self-organization and complexity.Comment: 28 pages, 1 figur