Text length strongly matters when analysing word frequency distributions

In a previous study, Aceves and Evans (AE) present a large-scale quantitative information-theoretic analysis of parallel corpus data in approximately 1,000 languages to show that there are apparently strong associations between the way languages encode information into words and patterns of communication, such as the configuration of semantic information. During the peer review process, one reviewer raised the question of the extent to which the presented results depend on different text lengths (see the Peer Review File). This is a very important question given that most, if not all, of the quantities associated with word frequency distributions vary systematically with text length. While AE claim that text length does not affect the results presented, I challenge this view by presenting analyses of AE's data and synthetic data that suggest that, contrary to AE's claim, both information density and semantic density are almost completely determined by text length. I also highlight that AE confuse the information-theoretic definition of information as established by Shannon with the everyday notion of information as knowledge or propositional content.