We introduce a spatial model of concentration dynamics that supports the emergence of spatiotemporal inhomogeneities that engage in metabolism–boundary co-construction. These configurations exhibit disintegration following some perturbations, and self-repair in response to others. We define robustness as a viable configuration’s tendency to return to its prior configuration in response to perturbations, and plasticity as a viable configuration’s tendency to change to other viable configurations. These properties are demonstrated and quantified in the model, allowing us to map a space of viable configurations and their possible transitions. Combining robustness and plasticity provides a measure of viability as the average expected survival time under ongoing perturbation, and allows us to measure how viability is affected as the configuration undergoes transitions. The framework introduced here is independent of the specific model we used, and is applicable for quantifying robustness, plasticity, and viability in any computational model of artificial life that demonstrates the conditions for viability that we promote.

Key words: autopoiesis, viability, robustness, plasticity, spatial dynamical system, metabolism

Living agency is subject to a normative dimension (good-bad, adaptive-maladaptive) that is absent from other types of interaction. We review current and historical attempts to naturalize normativity from an organism-centered perspective, identifying two central problems and their solution: (1) How to define the topology of the viability space so as to include a sense of gradation that permits reversible failure, and (2) how to relate both the processes that establish norms and those that result in norm-following behavior. We present a minimal metabolic system that is coupled to a gradient-climbing chemotactic mechanism. Studying the relationship between metabolic dynamics and environmental resource conditions, we identify an emergent viable region and a precarious region where the system tends to die unless environmental conditions change. We introduce the concept of normative field as the change of environmental conditions required to bring the system back to its viable region. Norm-following, or normative action, is defined as the course of behavior whose effect is positively correlated with the normative field. We close with a discussion of the limitations and extensions of our model and some final reflections on the nature of norms and teleology in agency.

Context: During the 1980s, Ernst von Glasersfeld’s reflections nourished various studies conducted by a community of mathematics education researchers at CIRADE, Quebec, Canada. Problem: What are his influence on and contributions to the center’s rich climate of development? We discuss the fecundity of von Glasersfeld’s ideas for the CIRADE researchers’ community, specifically in didactique des mathématiques. Furthermore, we take a prospective view and address some challenges that new, post-CIRADE mathematics education researchers are confronted with that are related to interpretations of and reactions to constructivism by the surrounding community. Results: Von Glasersfeld’s contribution still continues today, with a new generation of researchers in mathematics education that have inherited views and ideas related to constructivism. For the post-CIRADE research community, the concepts and epistemology that von Glasersfeld put forward still need to be developed further, in particular concepts such as subjectivity, viability, the circular interpretative effect, representations, the nature of knowing, errors, and reality. Implications: Radical constructivism’s offspring resides within the concepts and epistemology put forth, and that continue to be put forth, through a large number of new and different generations of theories, thereby perpetuating von Glasersfeld’s legacy.

Key words: radical constructivism, mathematics education, viability, reification, representation

Biology gives us numerous examples of self-assertional systems whose essence does not precede their existence but is rather revealed through it. Immune system is one of them. The fact of behaving in order not only to satisfy external constraints as a pre-fixed set of possible environments and objectives, but also to satisfy internal “viability” constraints justifies a sharper focus. Adaptability, creativity and memory are certainly interesting “side-effects” of such a tendency for self-consistency. However in this paper, we adopted a largely pragmatic attitude attempting to find the best hybridizing between the biological lessons and the engineering needs. The great difficulty, also shared by neural net and GA users, remains the precise localisation of the frontier where the biological reality must give way to a directed design.

Context: Meeting Ernst von Glasersfeld for the first time in 1985, when about 70% of his work had still to be conceived, written and published, was a great stroke of fortune for me; it was based on my collaboration with Silvio Ceccato that had started in 1981 and it profoundly influenced my contributions to radical constructivism in the following 25 years of our friendship. Problem: Presenting the details of how it all began can shed a light on the development of constructivist ideas. Method: Anecdotes from 1979 to 1985 about how I came to meet Silvio Ceccato in Milan in 1981 and the influence of these events on preparing the 1985 meeting with Ernst von Glasersfeld, also in Milan. Results: The article describes the timeline of 50 years of publications by von Glasersfeld, an anecdote about a connection between Ceccato and the University of Zurich in the 60s, the attempt to present Ceccato’s ideas as compatible and complementary with the neuroscience discourse in 1985, von Glasersfeld’s opinion about this attempt, and this attempt’s potential influence on the emergence of a new concept in neuroscience, “EEG microstates.” Implications: The events and facts reported in the article help us to understand some aspects of an early phase in the development of radical constructivism, especially the relationship between Ceccato, von Glasersfeld and other members of the Italian Operational School such as Bruna Zonta, Felice Accame, and the author himself.

Key words: history of science, operational methodology, Silvio Ceccato, neuroscience, single activity state, EEG microstate, viability

Open peer commentary on the article “Applying Radical Constructivism to Machine Learning: A Pilot Study in Assistive Robotics” by Markus Nowak, Claudio Castellini & Carlo Massironi. Upshot: Applying radical constructivism to machine learning is a challenge that requires us to dive very deeply into its theory of knowing and learning. We need to clarify its fundamental concepts, if possible, in operational terms. This commentary aims at outlining how this kind of clarification could look in the case of 3 such concepts: (a) the construction of experiential reality; (b) learning as a constructive activity; (c) the viability of conceptual structures.

Living systems employ several mechanisms and behaviors to achieve robustness and maintain themselves under changing internal and external conditions. Regulation stands out from them as a specific form of higher-order control, exerted over the basic regime responsible for the production and maintenance of the organism, and provides the system with the capacity to act on its own constitutive dynamics. It consists in the capability to selectively shift between different available regimes of self-production and self-maintenance in response to specific signals and perturbations, due to the action of a dedicated subsystem which is operationally distinct from the regulated ones. The role of regulation, however, is not exhausted by its contribution to maintain a living system’s viability. While enhancing robustness, regulatory mechanisms play a fundamental role in the realization of an autonomous biological organization. Specifically, they are at the basis of the remarkable integration of biological systems, insofar as they coordinate and modulate the activity of distinct functional subsystems. Moreover, by implementing complex and hierarchically organized control architectures, they allow for an increase in structural and organizational complexity while minimizing fragility. Finally, they endow living systems, from their most basic unicellular instances, with the capability to control their own internal dynamics to adaptively respond to specific features of their interaction with the environment, thus providing the basis for the emergence of minimal forms of cognition.

Key words: regulation, control, functional integration, organization, autonomy, cognition.

A theory of the central nervous system was formulated recently, in general thermodynamical terms. According to it, the function of a central nervous system, and more generally of living autopoietic units, is to minimize “surprise.” The nervous system fulfills its task, and the animal maintains its viability, by changing their inner organization or their ecological niche so as to maximize the predictability of what happens to them, and to minimize the correlative production of entropy. But what is the first-person correlate of this third-person description of the adaptation of living beings? What is the phenomenological counterpart of this state of minimal suprise? A plausible answer is that it amounts to a state of “déjà vu,” or to the monotony of habit. By contrast, says Henri Maldiney, surprise is lived as a sudden encounter with reality, a reality that is recognized as such because it is radically unexpected. Surprise is a concussion for the brain, it is a risk for a living being, but it can be lived in the first person as an awakening to what there is.

Key words: surprise, phenomenology, neurophenomenology, biological adaptation, homeostasy, neurobiology, disruption of expectations

This article revisits the concept of autopoiesis and examines its relation to cognition and life. We present a mathematical model of a 3D tesselation automaton, considered as a minimal example of autopoiesis. This leads us to a thesis T1: “An autopoietic system can be described as a random dynamical system, which is defined only within its organized autopoietic domain.” We propose a modified definition of autopoiesis: “An autopoietic system is a network of processes that produces the components that reproduce the network, and that also regulates the boundary conditions necessary for its ongoing existence as a network.” We also propose a definition of cognition: “A system is cognitive if and only if sensory inputs serve to trigger actions in a specific way, so as to satisfy a viability constraint.” It follows from these definitions that the concepts of autopoiesis and cognition, although deeply related in their connection with the regulation of the boundary conditions of the system, are not immediately identical: a system can be autopoietic without being cognitive, and cognitive without being autopoietic. Finally, we propose a thesis T2: “A system that is both autopoietic and cognitive is a living system.”

Key words: Autopoiesis, cognition, life, tessela- tion automaton, random dynamical system, boundary conditions

This Introduction is our attempt to clarify further the cluster of key notions: autonomy, viability, abduction and adaptation. These notions form the conceptual scaffolding within which the individual contribution contained in this volume can be placed. Hopefully, these global concepts represent fundamental signposts for future research that can spare us a mere flurry of modelling and simulations into which this new field could fall.

Key words: cognitivism, connectionism, enaction, autonomy, viability, abduction, adaptation