Ricard Solé, Manlio De Domenico

The path toward the emergence of life in our biosphere involved several key events allowing for the persistence, reproduction and evolution of molecular systems. All these processes took place in a given environmental context and required both molecular diversity and the right non-equilibrium conditions to sustain and favour complex self-sustaining molecular networks capable of evolving by natural selection. Life is a process that departs from non-life in several ways and cannot be reduced to standard chemical reactions. Moreover, achieving higher levels of complexity required the emergence of novelties. How did that happen? Here, we review different case studies associated with the early origins of life in terms of phase transitions and bifurcations, using symmetry breaking and percolation as two central components. We discuss simple models that allow for understanding key steps regarding life origins, such as molecular chirality, the transition to the first replicators and cooperators, the problem of error thresholds and information loss, and the potential for “order for free” as the basis for the emergence of life.

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Claudia Westermann

Constructivist Foundations 20(2): 67–71

Context: In 2024, we celebrated the 60th-anniversary meeting of the American Society for Cybernetics (ASC. In more than eighty, mostly participatory, sessions, the conference stretched over five days. Under the overarching theme “Living Cybernetics Playing Language,” the conference encouraged participants to reflect on cybernetics in everyday contexts, ranging from academic research to the building of communities. This special issue of Constructivist Foundations contains four target articles that emerged from this conference, and their related discussions. Problem: Sixty years after the foundation of the ASC, defining cybernetics is still a challenge. Diversity, one could say, has haunted cybernetics since its inception. There are many practices that refer to cybernetics in many disciplinary fields and contexts, but do these different practices share anything or do they rely on different aspects of (historical) cybernetic practices? Method: I present the contributions to this special issue as case studies of cybernetic practice and diversity and expose them to the questions mentioned above. Results: Cybernetic practices are as diverse in their methods as the disciplines to which they relate. And yet, as the study of the four target articles and the related commentaries show, these practices all embrace uncertainty. This embrace is the foundation for a particular technicity in which formation and reflexivity become intertwined and co-evolve. In its engagement with contemporary challenges, cybernetic technicity introduces recursive links setting relations across boundaries. Contemporary cybernetic practice, through varied approaches, is a living tradition of enacting open futures. Implications: Cybernetic thinking does not necessarily become detectable through a common vocabulary or set of references, but rather through a particular inherent logic, which links thinking and doing in a recursive co-evolving relationship. Constructivist content: The editorial discusses second-order approaches to cybernetics.

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Thomas F. Varley, Pedro A. M. Mediano, Alice Patania, Josh Bongard

The study of irreducible higher-order interactions has become a core topic of study in complex systems. Two of the most well-developed frameworks, topological data analysis and multivariate information theory, aim to provide formal tools for identifying higher-order interactions in empirical data. Despite similar aims, however, these two approaches are built on markedly different mathematical foundations and have been developed largely in parallel. In this study, we present a head-to-head comparison of topological data analysis and information-theoretic approaches to describing higher-order interactions in multivariate data; with the aim of assessing the similarities and differences between how the frameworks define “higher-order structures.” We begin with toy examples with known topologies, before turning to naturalistic data: fMRI signals collected from the human brain. We find that intrinsic, higher-order synergistic information is associated with three-dimensional cavities in a point cloud: shapes such as spheres are synergy-dominated. In fMRI data, we find strong correlations between synergistic information and both the number and size of three-dimensional cavities. Furthermore, we find that dimensionality reduction techniques such as PCA preferentially represent higher-order redundancies, and largely fail to preserve both higher-order information and topological structure, suggesting that common manifold-based approaches to studying high-dimensional data are systematically failing to identify important features of the data. These results point towards the possibility of developing a rich theory of higher-order interactions that spans topological and information-theoretic approaches while simultaneously highlighting the profound limitations of more conventional methods.

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Ori Livson, Mikhail Prokopenko

Incomputability results in formal logic and the Theory of Computation (i.e., incompleteness and undecidability) have deep implications for the foundations of mathematics and computer science. Likewise, Social Choice Theory, a branch of Welfare Economics, contains several impossibility results that place limits on the potential fairness, rationality and consistency of social decision-making processes. A formal relationship between Gödel’s Incompleteness Theorems in formal logic, and Arrow’s Impossibility Theorem in Social Choice Theory has long been conjectured. In this paper, we address this gap by bringing these two theories closer by introducing a general mathematical object called a Self-Reference System. Impossibility in Social Choice Theory is demonstrated to correspond to the impossibility of a Self-Reference System to interpret its own internal consistency. We also provide a proof of Gödel’s First Incompleteness Theorem in the same terms. Together, this recasts Arrow’s Impossibility Theorem as incomputability in the Gödelian sense. The incomputability results in both fields are shown to arise out of self-referential paradoxes. This is exemplified by a new proof of Arrow’s Impossibility Theorem centred around Condorcet Paradoxes.

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Takaya Arita, Wenxian Zheng, Reiji Suzuki, Fuminori Akiba

This study explored how large language models (LLMs) perform in two areas related to art: writing critiques of artworks and reasoning about mental states (Theory of Mind, or ToM) in art-related situations. For the critique generation part, we built a system that combines Noel Carroll’s evaluative framework with a broad selection of art criticism theories. The model was prompted to first write a full-length critique and then shorter, more coherent versions using a step-by-step prompting process. These AI-generated critiques were then compared with those written by human experts in a Turing test-style evaluation. In many cases, human subjects had difficulty telling which was which, and the results suggest that LLMs can produce critiques that are not only plausible in style but also rich in interpretation, as long as they are carefully guided. In the second part, we introduced new simple ToM tasks based on situations involving interpretation, emotion, and moral tension, which can appear in the context of art. These go beyond standard false-belief tests and allow for more complex, socially embedded forms of reasoning. We tested 41 recent LLMs and found that their performance varied across tasks and models. In particular, tasks that involved affective or ambiguous situations tended to reveal clearer differences. Taken together, these results help clarify how LLMs respond to complex interpretative challenges, revealing both their cognitive limitations and potential. While our findings do not directly contradict the so-called Generative AI Paradox–the idea that LLMs can produce expert-like output without genuine understanding–they suggest that, depending on how LLMs are instructed, such as through carefully designed prompts, these models may begin to show behaviors that resemble understanding more closely than we might assume.

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