arXiv subjects

Ori Livson

Publications and source records attributed to Ori Livson.

5 recordsLinked to original sources

arXiv2026

Algorithmic bottlenecks in evolution: Genetic code, symbolic language, and the Great Filter hypothesis

The Great Filter hypothesis proposes that the emergence of technological societies capable of interstellar travel depends on a small number of exceptionally hard and highly improbable steps. Traditional versions of this hypothesis enumerate such "hard steps" along the trajectory from inanimate matter to complex technological societies but diverge in their explanations for why these particular steps should be so improbable. The theory of Major Evolutionary Transitions also faces challenges in identifying which steps should be considered universally "hard" across different evolutionary pathways. In contrast, we argue that two deeply structural obstacles dominate the evolutionary landscape: the coding threshold associated with the origin of genetic code, and the language threshold associated with the emergence of symbolic communication. We examine the developmental precursors of both transitions and analyze the underlying algorithmic bottlenecks: points at which evolving systems separate code from function, while entangling them within information hierarchies. Using a game-theoretic analysis of coupled signaling and coordination dynamics, we then argue that the corresponding multichannel games may exhibit saddle-type equilibria whose stable manifolds define narrow evolutionary paths, making the transitions intrinsically difficult to traverse. We conjecture that the so-called Great Filter is best understood not as a sequence of isolated improbable events, but as a nested structure of tangled information hierarchies. Under this conjecture, the rarity of advanced societies follows from the difficulty of crossing these coding thresholds in a competitive noisy environment. This hypothesis reframes the Great Filter as an algorithmic property of evolving systems, suggesting that only a small fraction of life may ever traverse the path toward technological societies capable of interstellar travel.

q-bio.PE↗

arXiv2026

The Non-Orientable Topology of Condorcet's Paradox

Preference cycles are prevalent in problems of decision-making, and are contradictory when preferences are assumed to be transitive. This contradiction underlies Condorcet's Paradox, a pioneering result of social choice theory, wherein intuitive and seemingly desirable constraints on decision-making necessarily lead to contradictory preference cycles. Topological methods have since broadened social choice theory and elucidated existing results. However, characterisations of preference cycles in topological social choice theory are lacking. In this paper, we address this gap by introducing a framework for topologically modelling preference cycles that generalises Baryshnikov's existing topological model of strict, ordinal preferences on 3 alternatives. In our framework, the contradiction underlying Condorcet's Paradox topologically corresponds to the non-orientability of a surface homeomorphic to either the Klein bottle or real projective plane, depending on how preference cycles are represented. These findings allow us to reformulate Arrow's Impossibility Theorem in terms of the orientability of a surface as well.

math.AT↗

arXiv2025

Arrow's Impossibility Theorem as a Generalisation of Condorcet's Paradox

Arrow's Impossibility Theorem is a seminal result of Social Choice Theory that demonstrates the impossibility of ranked-choice decision-making processes to jointly satisfy a number of intuitive and seemingly desirable constraints. The theorem is often described as a generalisation of Condorcet's Paradox, wherein pairwise majority voting may fail to jointly satisfy the same constraints due to the occurrence of elections that result in contradictory preference cycles. However, a formal proof of this relationship has been limited to D'Antoni's work, which applies only to the strict preference case, i.e., where indifference between alternatives is not allowed. In this paper, we generalise D'Antoni's methodology to prove in full (i.e., accounting for weak preferences) that Arrow's Impossibility Theorem can be equivalently stated in terms of contradictory preference cycles. This methodology involves explicitly constructing profiles that lead to preference cycles. Using this framework, we also prove a number of additional facts regarding social welfare functions. As a result, this methodology may yield further insights into the nature of preference cycles in other domains e.g., Money Pumps, Dutch Books, Intransitive Games, etc.

econ.TH↗

arXiv2025

Comparing and Contrasting Arrow's Impossibility Theorem and G\"odel's Incompleteness Theorem

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 various impossibility results that place limits on the potential fairness, rationality and consistency of social decision-making processes. However, a relationship between the fields' most seminal results: G\"odel's First Incompleteness Theorem of Formal Logic, and Arrow's Impossibility Theorem in Social Choice Theory is lacking. In this paper, we address this gap by introducing a general mathematical object called a Self-Reference System. Correspondences between the two theorems are formalised by abstracting well-known diagonalisation and fixed-point arguments, and consistency and completeness properties of provability predicates in the language of Self-Reference Systems. Nevertheless, we show that the mechanisms generating Arrovian impossibility and G\"odelian incompleteness have subtle differences.

math.LO↗

arXiv2024

Biological arrow of time: Emergence of tangled information hierarchies and self-modelling dynamics

We study open-ended evolution by focusing on computational and information-processing dynamics underlying major evolutionary transitions. In doing so, we consider biological organisms as hierarchical dynamical systems that generate regularities in their phase-spaces through interactions with their environment. These emergent information patterns can then be encoded within the organism's components, leading to self-modelling "tangled hierarchies". Our main conjecture is that when macro-scale patterns are encoded within micro-scale components, it creates fundamental tensions (computational inconsistencies) between what is encodable at a particular evolutionary stage and what is potentially realisable in the environment. A resolution of these tensions triggers an evolutionary transition which expands the problem-space, at the cost of generating new tensions in the expanded space, in a continual process. We argue that biological complexification can be interpreted computation-theoretically, within the Gödel--Turing--Post recursion-theoretic framework, as open-ended generation of computational novelty. In general, this process can be viewed as a meta-simulation performed by higher-order systems that successively simulate the computation carried out by lower-order systems. This computation-theoretic argument provides a basis for hypothesising the biological arrow of time.

q-bio.PE↗