How communicatively optimal are exact numeral systems? Once more on lexicon size and morphosyntactic complexity

2026-02-23

AI Summary

This study investigates whether exact numeral systems achieve an optimal trade-off in communicative efficiency between lexical inventory size and morphosyntactic complexity. Analyzing 52 phylogenetically diverse languages, the research introduces a refined annotation scheme that distinguishes predictable from unpredictable allomorphy and develops a more precise measure of morphological complexity. For the first time, it systematically evaluates the cross-linguistic communicative efficiency of numeral systems. The findings reveal that the numeral systems of most languages fall significantly below theoretical optimality, challenging prevailing assumptions in language evolution models that posit efficiency as a primary driving force. These results offer new empirical evidence for cognitive and historical inquiries into numeral system design and development.

Technology Category

• Natural Language Processing: Lexical Semantics and Morphology
• Cognitive Modeling & Cognitive Systems: Analogy
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Recent research argues that exact recursive numeral systems optimize communicative efficiency by balancing a tradeoff between the size of the numeral lexicon and the average morphosyntactic complexity (roughly length in morphemes) of numeral terms. We argue that previous studies have not characterized the data in a fashion that accounts for the degree of complexity languages display. Using data from 52 genetically diverse languages and an annotation scheme distinguishing between predictable and unpredictable allomorphy (formal variation), we show that many of the world's languages are decisively less efficient than one would expect. We discuss the implications of our findings for the study of numeral systems and linguistic evolution more generally.

Problem

• numeral systems
• communicative efficiency
• lexicon size
• morphosyntactic complexity
• linguistic evolution

Innovation

• numeral systems
• communicative efficiency
• morphosyntactic complexity
• allomorphy
• linguistic evolution