Recursive numeral systems are highly regular and easy to process

TL;DR

This paper demonstrates that recursive numeral systems are highly regular and efficiently processed, with regularity explaining their natural shape and distinguishing them from less natural systems, using an MDL-based approach.

Contribution

It introduces an MDL-based framework to quantify regularity and processing efficiency in recursive numeral systems, explaining natural language patterns without ad-hoc constraints.

Findings

Recursive systems are more regular and efficient according to MDL measures.

Natural systems differ from theoretical ones mainly in regularity and processing complexity.

Regularity naturally constrains the shape of recursive numeral systems.

Abstract

Much recent work has shown how cross-linguistic variation is constrained by competing pressures from efficient communication. However, little attention has been paid to the role of the systematicity of forms (regularity), a key property of natural language. Here, we demonstrate the importance of regularity in explaining the shape of linguistic systems by looking at recursive numeral systems. Previous work has argued that these systems optimise the trade-off between lexicon size and average morphosyntatic complexity (Deni\'c and Szymanik, 2024). However, showing that only natural-language-like systems optimise this trade-off has proven elusive, and existing solutions rely on ad-hoc constraints to rule out unnatural systems (Yang and Regier, 2025). Drawing on the Minimum Description Length (MDL) approach, we argue that recursive numeral systems are better viewed as efficient with regard to their regularity and processing complexity. We show that our MDL-based measures of regularity and processing complexity better capture the key differences between attested, natural systems and theoretically possible ones, including "optimal" recursive numeral systems from previous work, and that the ad-hoc constraints naturally follow from regularity. Our approach highlights the need to incorporate regularity across sets of forms in studies attempting to measure efficiency in language.