On Homophony and Rényi Entropy
This addresses a theoretical controversy in linguistics about language optimality, but the result is incremental as it refines existing debates without establishing a new paradigm.
The paper tackles the debate on homophony in natural languages by proposing a new information-theoretic quantification using sample Rényi entropy and re-evaluating prior claims, finding no clear pressure for or against homophony, which contrasts with previous findings.
Homophony's widespread presence in natural languages is a controversial topic. Recent theories of language optimality have tried to justify its prevalence, despite its negative effects on cognitive processing time; e.g., Piantadosi et al. (2012) argued homophony enables the reuse of efficient wordforms and is thus beneficial for languages. This hypothesis has recently been challenged by Trott and Bergen (2020), who posit that good wordforms are more often homophonous simply because they are more phonotactically probable. In this paper, we join in on the debate. We first propose a new information-theoretic quantification of a language's homophony: the sample Rényi entropy. Then, we use this quantification to revisit Trott and Bergen's claims. While their point is theoretically sound, a specific methodological issue in their experiments raises doubts about their results. After addressing this issue, we find no clear pressure either towards or against homophony -- a much more nuanced result than either Piantadosi et al.'s or Trott and Bergen's findings.