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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THEOPI RADOS, et al.

SCIENCE 3 Apr 2025 Vol 388, Issue 6742 pp. 109-115

The advent of clonal multicellularity is a critical evolutionary milestone, seen often in eukaryotes, rarely in bacteria, and only once in archaea. We show that uniaxial compression induces clonal multicellularity in haloarchaea, forming tissue-like structures. These archaeal tissues are mechanically and molecularly distinct from their unicellular lifestyle, mimicking several eukaryotic features. Archaeal tissues undergo a multinucleate stage followed by tubulin-independent cellularization, orchestrated by active membrane tension at a critical cell size. After cellularization, tissue junction elasticity becomes akin to that of animal tissues, giving rise to two cell types—peripheral (Per) and central scutoid (Scu) cells—with distinct actin and protein glycosylation polarity patterns. Our findings highlight the potential convergent evolution of a biophysical mechanism in the emergence of multicellular systems across domains of life.

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Aaron Clauset, Barbara F. Walter, Lars-Erik Cederman, Kristian Skrede Gleditsch

Although very large wars remain an enduring threat in global politics, we lack a clear understanding of how some wars become large and costly, while most do not. There are three possibilities: large conflicts start with and maintain intense fighting, they persist over a long duration, or they escalate in intensity over time. Using detailed within-conflict data on civil and interstate wars 1946–2008, we show that escalation dynamics — variations in fighting intensity within an armed conflict — play a fundamental role in producing large conflicts and are a generic feature of both civil and interstate wars. However, civil wars tend to deescalate when they become very large, limiting their overall severity, while interstate wars exhibit a persistent risk of continual escalation. A non-parametric model demonstrates that this distinction in escalation dynamics can explain the differences in the historical sizes of civil vs. interstate wars, and explain Richardson’s Law governing the frequency and severity of interstate conflicts over the past 200 years. Escalation dynamics also drive enormous uncertainty in forecasting the eventual sizes of both hypothetical and ongoing civil wars, indicating a need to better understand the causes of escalation and deescalation within conflicts. The close relationship between the size, and hence the cost, of an armed conflict and its potential for escalation has broad implications for theories of conflict onset or termination and for risk assessment in international relations.

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