Rapid information gain explains cross-linguistic tendencies in numeral ordering

AbstractOne previously unexplained observation about numeral systems is the shared tendency in numeral expressions: Numerals greater than 20 often have the larger constituent number expressed before the smaller constituent number (e.g., twenty-four as opposed to four-twenty in English), and systems that originally adopt the reverse order of expression (e.g., four-and- twenty in Old English) tend to switch order over time. To explore these phenomena, we propose the view of Rapid Information Gain and contrast it with the established theory of Uniform Information Density. We compare the two theories in their ability to explain the shared tendency in the ordering of numeral expressions around 20. We find that Rapid Information Gain accounts for empirical patterns better than the alternative theory, suggesting that there is an emphasis on information front-loading as opposed to information smoothing in the design of large compound numerals. Our work shows that fine-grained generalizations about numeral systems can be understood in information-theoretic terms and offers an opportunity to characterize the design principles of lexical compounds through the lens of informative communication.

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