The concept of “autonomy,” once at the core of the original enactivist proposal in The Embodied Mind (Varela et al. in The embodied mind: cognitive science and human experience. MIT Press, Cambridge, 1991), is nowadays ignored or neglected by some of the most prominent contemporary enactivists approaches. Theories of autonomy, however, come to fill a theoretical gap that sensorimotor accounts of cognition cannot ignore: they provide a naturalized account of normativity and the resources to ground the identity of a cognitive subject in its specific mode of organization. There are, however, good reasons for the contemporary neglect of autonomy as a relevant concept for enactivism. On the one hand, the concept of autonomy has too often been assimilated into autopoiesis (or basic autonomy in the molecular or biological realm) and the implications are not always clear for a dynamical sensorimotor approach to cognitive science. On the other hand, the foundational enactivist proposal displays a metaphysical tension between the concept of operational closure (autonomy), deployed as constitutive, and that of structural coupling (sensorimotor dynamics); making it hard to reconcile with the claim that experience is sensorimotorly constituted. This tension is particularly apparent when Varela et al. propose Bittorio (a 1D cellular automata) as a model of the operational closure of the nervous system as it fails to satisfy the required conditions for a sensorimotor constitution of experience. It is, however, possible to solve these problems by re-considering autonomy at the level of sensorimotor neurodynamics. Two recent robotic simulation models are used for this task, illustrating the notion of strong sensorimotor dependency of neurodynamic patterns, and their networked intertwinement. The concept of habit is proposed as an enactivist building block for cognitive theorizing, re-conceptualizing mental life as a habit ecology, tied within an agent’s behaviour generating mechanism in coordination with its environment. Norms can be naturalized in terms of dynamic, interactively self-sustaining, coherentism. This conception of autonomous sensorimotor agency is put in contrast with those enactive approaches that reject autonomy or neglect the theoretical resources it has to offer for the project of naturalizing minds.

This article examines in some technical detail the application of Maturana and Varela’s biology of cognition to a simple concrete model: a glider in the game of Life cellular automaton. By adopting an autopoietic perspective on a glider, the set of possible perturbations to it can be divided into destructive and nondestructive subsets. From a glider’s reaction to each nondestructive perturbation, its cognitive domain is then mapped. In addition, the structure of a glider’s possible knowledge of its immediate environment, and the way in which that knowledge is grounded in its constitution, are fully described. The notion of structural coupling is then explored by characterizing the paths of mutual perturbation that a glider and its environment can undergo. Finally, a simple example of a communicative interaction between two gliders is given. The article concludes with a discussion of the potential implications of this analysis for the enactive approach to cognition.

Maturana and Varela’s concept of autopoiesis defines the essential organization of living systems and serves as a foundation for their biology of cognition and the enactive approach to cognitive science. As an initial step toward a more formal analysis of autopoiesis, this paper investigates its application to the compact, recurrent spatiotemporal patterns that arise in Conway’s Game of Life cellular automata. In particular, we demonstrate how such entities can be formulated as self-constructing networks of interdependent processes that maintain their own boundaries. We then characterize the specific organizations of several such entities, suggest a way to simplify the descriptions of these organizations, and briefly consider the transformation of such organizations over time. Relevance: The paper presents an analysis of a minimal concrete model of autopoiesis to provide a more rigorous foundation for the concept of autopoiesis and highlight its ambiguities and difficulties.

Beer R. D. (2020) Bittorio revisited: Structural coupling in the Game of Life. Adaptive Behavior 28(4): 197–212. https://cepa.info/7089

The notion of structural coupling plays a central role in Maturana and Varela’s biology of cognition framework and strongly influenced Varela’s subsequent enactive elaboration of this framework. Building upon previous work using a glider in the Game of Life (GoL) cellular automaton as a toy model of a minimal autopoietic system with which to concretely explore these theoretical frameworks, this article presents an analysis of structural coupling between a glider and its environment. Specifically, for sufficiently small GoL universes, we completely characterize the nonautonomous dynamics of both a glider and its environment in terms of interaction graphs, derive the set of possible glider lives determined by the mutual constraints between these interaction graphs, and show how such lives are embedded in the state transition graph of the entire GoL universe.

Gunji Y. & Nakamura T. (1991) Time reverse automata patterns generated by Spencer-Brown’s modulator: Invertibility based on autopoiesis. Biosystems 25(3): 151–177.

In the present paper the self-consistency or operational closure of autopoiesis is described by introducing time explicitly. It is an extension of Spencer-Brown’s idea of time, however. The definition of time is segregated into two parts, corresponding to the syntax and semantics of language, respectively. In this context, time reversibility is defined by the formalization of the relationship between time and self-consistency. This idea has also been discussed in the context of designation and/or naming. Here we will discuss it in the context of cellular automata and explain the structure of one-to-many type mappings. Our approach is the first attempt to extend autopoietic systems in terms of dynamics. It illustrates how to introduce an autopoietic time which looks irreversible, but without the concept of entropy.

Herr C. M. & Fischer T. (2013) Systems for Showing and Repurposing: A Second-Order Cybernetic Reflection on Some Cellular Automata Projects. Journal of Mathematics and System Science 3: 201–216. https://cepa.info/2323

Over the course of the past 70 years, the objectives of CA (cellular automata) research shifted from speculative and illustrative purposes without immediate goals outside of given implementations to the more utilitarian scientific and engineering objectives of simulating, controlling and predicting other phenomena. Looking back at our own 10-year history of CA related work, however, we recognize a generally inverse tendency from utilitarian objectives to finding more illustrative and speculative value. In this paper, we present a reflection on our own body of CA work, and we discuss the qualities of the various outcomes and insights we gained from a second-order cybernetic perspective. We argue that much of our own CA work may best be understood as creating machines for showing and for repurposing that allow their observers to gain new (second-order cybernetic) ways of seeing from interacting with them.

Purpose: The paper discusses the concept of a reflexive domain, an arena where the apparent objects as entities of the domain are actually processes and transformations of the domain as a whole. Human actions in the world partake of the patterns of reflexivity, and the productions of human beings, including science and mathematics, can be seen in this light. Methodology: Simple mathematical models are used to make conceptual points. Context: The paper begins with a review of the author’s previous work on eigenforms - objects as tokens for eigenbehaviors, the study of recursions and fixed points of recursions. The paper also studies eigenforms in the Boolean reflexive models of Vladimir Lefebvre. Findings: The paper gives a mathematical definition of a reflexive domain and proves that every transformation of such a domain has a fixed point. (This point of view has been taken by William Lawvere in the context of logic and category theory.) Thus eigenforms exist in reflexive domains. We discuss a related concept called a “magma.” A magma is composed entirely of its own structure-preserving transformations. Thus a magma can be regarded as a model of reflexivity and we call a magma “reflexive” if it encompasses all of its structure-preserving transformations (plus a side condition explained in the paper). We prove a fixed point theorem for reflexive magmas. We then show how magmas are related to knot theory and to an extension of set theory using knot diagrammatic topology. This work brings formalisms for self-reference into a wider arena of process algebra, combinatorics, non-standard set theory and topology. The paper then discusses how these findings are related to lambda calculus, set theory and models for self-reference. The last section of the paper is an account of a computer experiment with a variant of the Life cellular automaton of John H. Conway. In this variant, 7-Life, the recursions lead to self-sustaining processes with very long evolutionary patterns. We show how examples of novel phenomena arise in these patterns over the course of large time scales. Value: The paper provides a wider context and mathematical conceptual tools for the cybernetic study of reflexivity and circularity in systems.

Protevi J. (2009) Beyond autopoiesis: Inflections of emergence and politics in the work of Francisco Varela. In: Clarke B. & Hansen M. (eds.) Emergence and embodiment: New essays on second-order systems theory. Duke University Press, Durham: 94–112. https://cepa.info/4125

Excerpt: Francisco Varela’s work is a monumental achievement in twentieth-century biological and biophilosophical thought. After his early collaboration in neocybernetics with Humberto Maturana (autopoiesis), Varela made fundamental contributions to immunology (network theory), artificial life (cellular automata), cognitive science (enaction), philosophy of mind (neurophenomenology), brain studies (the brainweb), and East-West dialogue (the Mind and Life conferences). In the course of his career, Varela influenced many important collaborators and interlocutors, formed a generation of excellent students, and touched the lives of many with the intensity of his mind, the sharpness of his wit, and the strength of his spirit. In this essay, I will trace some of the key turning points in his thought, with special focus on the concept of emergence, which was always central to his work, and on questions of politics, which operate at the margins of his thought. I will divide Varela’s work into three periods – autopoiesis, enaction, and radical embodiment – each of which is marked by a guiding concept; a specific methodology; a research focus; an inflection in the notion of emergence; and a characteristic political question that specifies a scale of what I will call “political physiology” – that is, the formation of “bodies politic” at the civic, somatic, and “evental” scales. These terms refer to the formation of political states, politically constituted individuals, and their intersection in political encounters respectively.

Rocha L. M. (2000) Syntactic autonomy: Why there is no autonomy without symbols and how self-organizing systems might evolve them. In: Chandler J. & Van de Vijver G. (eds.) Closure: Emergent organizations and their dynamics. New York Academy of Sciences, New York: 207–223.

Two different types of agency are discussed that are based on dynamically coherent and incoherent couplings with an environment, respectively. I propose that until a private syntax (syntactic autonomy) is discovered by dynamically coherent agents, there are no significant or interesting types of closure or autonomy. When syntactic autonomy is established, then, because of a process of description-based selected self-organization, open-ended evolution is enabled. At this stage, in addition to dynamics, agents depend on localized, symbolic memory, thus adding a level of dynamic incoherence to their interaction with the environment. Furthermore, it is the appearance of syntactic autonomy that enables much more interesting types of closures among agents sharing the same syntax. To investigate how we can study the emergence of syntax from dynamic systems, experiments with cellular automata leading to emergent computation that solves nontrivial tasks are discussed. RNA editing is also mentioned as a process that may have been used to obtain a primordial biological code necessary for open-ended evolution.

Umpleby S. A. (2010) From complexity to reflexivity: Underlying logics used in science. Journal of the Washington Academy of Sciences 96(1): 15–26.

Current research on complexity can be thought of as the working out of ideas related to self-organizing systems, which were developed about 1960. Much more advanced technical means are now available, and the great accomplishment of the recent research has been the involvement of people from a wide range of disciplines in using modeling methods, such as cellular automata and genetic algorithms, which are a significant departure from previous methods. Research in reflexivity is less well known. Its origins can be traced back at least to 1975. Several reflexive theories have been proposed, for example by Argyris and Schon, von Foerster, Lefebvre, and Soros. The literatures in second order cybernetics and constructivism are very close to reflexivity, but the term “reflexivity” might attract wider interest. This presentation will describe the basic features of the theories of complexity and reflexivity, their early history, their evolution, and reactions to date. Although complexity is a major change from previous modeling methods, it does not violate any informal fallacies or any assumptions underlying the philosophy of science. Reflexivity does. Accepting reflexivity as a legitimate movement in science will require an expansion of the conception of science which still prevails in most fields. A shift from Science One to Science Two is now being discussed. This presentation will explain what is being proposed.