Recasting Arrow’s Impossibility Theorem as Gödelian Incomputability

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.

Read the full article at: arxiv.org

Assesing LLMs in Art Contexts: Critique Generation and Theory of Mind Evaluation

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.

Read the full article at: arxiv.org

A Test for Life Versus Non-Life

Carl Zimmer

For generations, physicists have puzzled over life. Their theories about matter and energy have helped them understand how the universe produced galaxies and planets. But physicists have struggled to understand how lifeless chemical reactions give rise to the complexity stored in our cells.

In a new book, “Life as No One Knows It: The Physics of Life’s Emergence,” out on Aug. 6, Sara Walker, a physicist at Arizona State University, offers a theory that she and her colleagues believe can make sense of life. Assembly theory, as they call it, looks at everything in the universe in terms of how it was assembled from smaller parts. Life, the scientists argue, emerges when the universe hits on a way to make exceptionally intricate things.

The book arrives at an opportune time, as assembly theory has attracted both praise and criticism in recent months. Dr. Walker argues that the theory holds the potential to help identify life on other worlds. And it may allow scientists like her to create life from scratch.

“I actually think alien life will be discovered in the lab first,” Dr. Walker said in an interview.

Read the full article at: www.nytimes.com

Book Review of “Life as no one knows it: the physics of life’s emergence”

Hector Zenil

Sara Walker’s Life as no one knows it arrives on the heels of extensive media coverage and promotional efforts that have catapulted it into bestseller status. I approached this book with a sense of anticipation, especially eager to explore her ideas on algorithmic probability and open-endedness–topics we briefly worked on together [1]. These areas of research are foundational to understanding life’s complexity and origins, and I had expected Walker’s book to delve into these subjects with depth and originality.

However, the book surprised me for other reasons–and unfortunately, not in a positive way. Rather than presenting her own work, much of the book focuses on the ideas of Leroy (Lee) Cronin, a chemist whose assembly theory (AT) has met with significant skepticism and criticism in the scientific community. The central thesis of AT is that the ability of life to make numerous copies of itself–or to utilize multiple copies of the resources it requires–is the defining feature of living systems. This concept, quantified through an “assembly index,” proposes that life’s complexity can be reduced to the mere counting of these copies. Note that it has been considered and disproven many times.

Cronin’s theory specifically has been disproven by multiple research groups [2,3,4], and the scientific merit of its approaches remains highly questionable. Walker, rather than scrutinizing or distancing herself from these ideas, devotes much of her book to promoting them without acknowledging the criticisms and counter-evidence.

Read the full article at: www.computingreviews.com

Tissue-like multicellular development triggered by mechanical compression in archaea

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.

Read the full article at: www.science.org