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

The paper looks at a combination of systems theory, cybernetics, and sociological theory in search of a tool for inquiring into contemporary social forms. The idea of observing networks, drawing on Heinz von Foerster’s and Niklas Luhmann’s notion of observing systems and Harrison C. White’s network calculus of identity and control, is outlined to enable basic sociological intuitions about social forms to be integrated with an understanding of both complexity and recursivity organizing our perspective on the human condition in a precarious world. Social forms are shown to gain robustness not from substantial identity but from relational ambiguity. Observing networks, or so the hypothesis goes, combine bodies, minds, society, and – soon perhaps – intelligent machines. The paper looks at how an understanding of complexity, recursivity, system, form, and network may help flesh out the calculus of our human condition.

Key words: complexity, form, network, recursivity, society, system

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.

Biological regulation is what allows an organism to handle the effects of a perturbation, modulating its own constitutive dynamics in response to particular changes in internal and external conditions. With the central focus of analysis on the case of minimal living systems, we argue that regulation consists in a specific form of second-order control, exerted over the core (constitutive) regime of production and maintenance of the components that actually put together the organism. The main argument is that regulation requires a distinctive architecture of functional relationships, and specifically the action of a dedicated subsystem whose activity is dynamically decoupled from that of the constitutive regime. We distinguish between two major ways in which control mechanisms contribute to the maintenance of a biological organisation in response to internal and external perturbations: dynamic stability and regulation. Based on this distinction an explicit definition and a set of organisational requirements for regulation are provided, and thoroughly illustrated through the examples of bacterial chemotaxis and the lac-operon. The analysis enables us to mark out the differences between regulation and closely related concepts such as feedback, robustness and homeostasis.

Open peer commentary on the article “Enactive Metaphorizing in the Mathematical Experience” by Daniela Díaz-Rojas, Jorge Soto-Andrade & Ronnie Videla-Reyes. Abstract: Díaz-Rojas, Soto-Andrade and Videla-Reyes advocate an approach to the teaching and learning of mathematics that emphasizes enaction, embodiment and metaphorization. I comment on their analysis of one of the illustrative examples, the handshake problem. First, I provide some historical context and rationale from mathematics education for how tasks such as the handshake problem have been used in studies of problem solving and why they also can be effective examples of rich problem-solving tasks that can be used in instructional settings. Then I comment on the robustness of the researchers’ analysis of the handshake problem by examining an extension problem, finding the number of diagonals in an n-sided polygon.

We introduce a series of evolutionary robotics simulations that address the behaviour of individuals in socially contingent interactions. The models are based on a recent study by Auvray, Lenay and Stewart [(2006) The attribution of intentionality in a simulated environment: The case of minimalist devices. In Tenth meeting of the association for the scientific study of consciousness, Oxford, UK, 23–26 June, 2006] on tactile perceptual crossing in a minimal virtual environment. In accordance, both the empirical experiments and our simulations point out the essential character of global embodied interaction dynamics for the sensitivity to contingency to arise. Rather than being individually perceived by any of the interactors, sensitivity to contingency arises from processes of circular causality that characterise the collective dynamics. Such global dynamical aspects are frequently neglected when studying social cognition. Furthermore, our synthetic studies point out interesting aspects of the task that are not immediately obvious in the empirical data. They, in addition, generate new hypotheses for further experiments. We conclude by promoting a minimal but tractable, dynamic and embodied account to social interaction, combining synthetic and empirical findings as well as concrete predictions regarding sensorimotor strategies, the role of time-delays and robustness to perturbations in interactive dynamics.

Key words: perceptual crossing, social contingency, agency, interaction dynamics, evolutionary robotics, simulation modelling.

To better understand selection processes in evolutionary systems (ecological to economic to social to artificial systems), the origins and role of diversity are examined in two systems that show increased group functionality (better performance, efficiency, robustness, adaptability, stability, etc.). Diversity was chosen as a clarifying concept, because it appears to have been largely ignored, or misunderstood. One system is a model of group selection within an ecosystem. The other is the group solution of a sequential problem using self-organizing dynamics in the absence of any selection. A comparison of the two systems show that while diversity is essential to both, improvement by natural selection is derived from consuming diversity, whereas improvement by noncompetitive self-organization is decreased by any reduction in diversity. The resulting perspective is that natural selection is a mechanism that increases the functionality of the individual (or groups within a larger system); noncompetitive self-organization of the system, without need for selection, increases the functionality of the whole above that of the individual or group. The two extreme roles for diversity are reconciled if natural selection is not strongly expressed in these systems-“survival of the fittest” becomes “survival of the adequate”-so that noncompetitive processes can occur. The resulting view of a mature ecosystem is an elastic web of interactions in which natural selection is dormant or retains the status quo. The processes of natural selection for individual or group improvement are activated only if environment changes are sufficient to break the elastic interconnections, as might occur in punctuated equilibria.

Context: Many recent research areas such as human cognition and quantum physics call the observer-independence of traditional science into question. Also, there is a growing need for self-reflexivity in science, i.e., a science that reflects on its own outcomes and products. Problem: We introduce the concept of second-order science that is based on the operation of re-entry. Our goal is to provide an overview of this largely unexplored science domain and of potential approaches in second-order fields. Method: We provide the necessary conceptual groundwork for explorations in second-order science, in which we discuss the differences between first- and second-order science and where we present a roadmap for second-order science. The article operates mainly with conceptual differentiations such as the separation between three seemingly identical concepts such as Science II, Science 2.0 and second-order science. Results: Compared with first-order science, the potential of second-order science lies in 1. higher levels of novelty and innovations, 2. higher levels of robustness and 3. wider integration as well as higher generality. As first-order science advances, second-order science, with re-entry as its basic operation, provides three vital functions for first-order science, namely a rich source of novelty and innovation, the necessary quality control and greater integration and generality. Implications: Second-order science should be viewed as a major expansion of traditional scientific fields and as a scientific breakthrough towards a new wave of innovative research. Constructivist content: Second-order science has strong ties with radical constructivism, which can be qualified as the most important root/origin of second-order science. Moreover, it will be argued that a new form of cybernetics is needed to cope with the new problems and challenges of second-order science.

Key words: Philosophy of science, methodology of science, first-order science, second-order science, Science 2.0, Science II, new cybernetics, second-order cybernetics, scientific novelty, re-entry

Upshot: In this response, I address the points raised in the commentaries, in particular those related to the scalability and robustness of the mechanism CALM, to its relation with the CAES architecture, and to the transition from sensorimotor to symbolic.