Open peer commentary on the article “Enactive Metaphorizing in the Mathematical Experience” by Daniela Díaz-Rojas, Jorge Soto-Andrade & Ronnie Videla-Reyes. Abstract: Welcoming their scholarly focus on metaphorizing, I critique Díaz-Rojas, Soto-Andrade and Videla-Reyes’s selection of the hypothetical constructs “conceptual metaphor” and “enactive metaphor” as guiding the epistemological positioning, educational design, and analytic interpretation of interactive mathematics education purporting to operationalize enactivist theory of cognition - both these constructs, I argue, are incompatible with enactivism. Instead, I draw on ecological dynamics to promote a view of metaphors as projected constraints on action, and I explain how mathematical concepts can be grounded in perceptual reorganization of motor coordination. I end with a note on how metaphors may take us astray and why that, too, is worthwhile.

There seem to be as many definitions of constructivism as there are minds to construct them. At least this is how it felt after reading the chapters by Duit (chap. 14), Saxe (chap. 15), and Spivey (chap. 16). Or perhaps there are as many questionings of constructivist ideas as practices in the field of education. For example, a teacher experiences a different set of constraints than a researcher or a designer, and these constraints in turn shape theories of learning in different ways.

Concurs with N. M. Agnew and J. L. Brown’s views that ontological and epistemological presuppositions impose certain constraints on the pursuit of knowledge. These authors have captured the constructivist thrust of G. A. Kelly’s (1955) psychology of personal constructs in their central theme.

This paper attempts to establish a systems-semiotic framework explaining creativity in the design process, where the design process is considered to have as its basis the cognitive process. The design process is considered as the interaction between two or more cognitive systems resulting in a purposeful and ongoing transformation of their already complex representational structures and the production of newer ones, in order to ful?ll an ill-defined goal. Creativity is considered as the result of an emergence of organizational complexity in each cognitive system participating in the design process, while it is trying to purposefully incorporate new constraints in its meaning structures. The meanings generated in each system are identi?ed as the contingent and anticipatory content of its representations, and where self-organization is the dominant process in which they are continuously involved. Furthermore, Peircean semiotic processes appear to provide the functionality needed by the emergent representational structures in order to complete the cycle of a creative design process. Creativity originates in the abductive stage of the semiotic process, the fallible nature of which is maintained in the proposed framework by the fact that the respective emergent representations can be mis?ts. The nodal points of the framework are identified and analyzed showing that a cognitive system needs the whole interactive anticipatory cycle in order to engage in a creative design process.

Key words: Anticipations, Creativity, Emergent Representations, Peircean Semiotic Processes, Self-organization

Upshot: Time constraints, locked curriculums, strict management, and possible anarchy in the classroom are some of the themes that originated from the commentaries. I argue that these challenges should be viewed holistically in the broader picture. I also question the educator’s role in mitigating these obstacles. My advice: Do it anyway.

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.

Key words: autopoiesis, enaction, structural coupling, cellular automata, enactivism

Open peer commentary on the article “Enaction as a Lived Experience: Towards a Radical Neurophenomenology” by Claire Petitmengin. Upshot: The neurophenomenological project is too ambitious technically, but highly appealing on the philosophical level, as can be learned from the extremely high ratio between theoretical and empirical work concerning neurophenomenology accumulated thus far. While “radical” neurophenomenology could possibly create, in highly unique projects, “mutual generative constraints,” will the hard problem be dissolved? I argue that although using micro phenomenology, as long as experimental designs inspired by front-loading phenomenological insights are reviewed by the regular scientific mind, the question of validating the phenomenology with objective measures remains, and will keep blocking the outbreak in this promising field. Since “we cannot solve our problems with the same level of thinking that created them,” it is timely for the scientific community to practice an attitude shift.

This paper is a practical guide to neurophenomenology. Varela’s neurophenomenological research program (NRP) aspires to bridge the gap between, and integrate, first-person (1P) and third-person (3P) approaches to understanding the mind. It does so by suggesting a methodological framework allowing these two irreducible phenomenal domains to relate and reciprocally support the investigation of one another. While highly appealing theoretically, neurophenomenology invites researchers to a challenging methodological endeavor. Based on our experience with empirical neurophenomenological implementation, we offer practical clarifications and insights learnt along the way. In the first part of the paper, we outline the theoretical principles of the NRP and briefly present the field of 1P research. We speak to the importance of phenomenological training and outline the utility of cooperating with meditators as skilled participants. We suggest that 1P accounts of subjective experience can be placed on a complexity continuum ranging between thick and thin phenomenology, highlighting the tension and trade-off inherent to the neurophenomenological attempt to naturalize phenomenology. We then outline a typology of bridges, which create mutual constraints between 1P and 3P approaches, and argue for the utility of alternating between the bridges depending on the available experimental resources, domain of interest and level of sought articulation. In the second part of the paper, we demonstrate how the theory can be put into practice by describing a decade of neurophenomenological studies investigating the sense of self with increasing focus on its embodied, and minimal, aspects. These aspects are accessed via the dissolution of the sense-of-boundaries, shedding new light on the multi-dimensionality and flexibility of embodied selfhood. We emphasize the evolving neurophenomenological dialogue, showing how consecutive studies, placed differently on the thin-to-thick 1P continuum, advance the research project by using the bridging principles appropriate for each stage.

Ten years ago, a group of researchers, led by Francisco Varela, were proposing an alternative vision of the immune system main behavior and function. I was part of this group. This new vision saw the immune system not as behaving distinctively with self and non-self or according to any dichotomy imposed a priori and from outside (the self-recognition vision), but rather as behaving in a unique way. From this indifferent behavior, any external impact would progressively been treated in two different ways, reactive and tolerant, but now, consequently and from inside the system (the self-assertion view). This paper will recall, through a very artificial simulation, the difference existing between these two visions. Also at that time, we believed that, from an engineering perspective, this new vision, emphasizing more the adaptability and the need for endogenous constraints than the recognition and the defensive ability, although less obvious to accept than the classical defensive one, should be more beneficial. These last ten years proved that we haven’t been convincing enough, and in this paper I resume the crusade.

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.