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One of the fundamental questions about human language is whether all languages are equally complex. Here, we approach this question from an information-theoretic perspective. We present a large scale quantitative cross-linguistic analysis of written language by training a language model on more than 6500 different documents as represented in 41 multilingual text collections consisting of ~ 3.5 billion words or ~ 9.0 billion characters and covering 2069 different languages that are spoken as a native language by more than 90% of the world population. We statistically infer the entropy of each language model as an index of what we call average prediction complexity. We compare complexity rankings across corpora and show that a language that tends to be more complex than another language in one corpus also tends to be more complex in another corpus. In addition, we show that speaker population size predicts entropy. We argue that both results constitute evidence against the equi-complexity hypothesis from an information-theoretic perspective.
A central goal of linguistics is to understand the diverse ways in which human language can be organized (Gibson et al. 2019; Lupyan/Dale 2016). In our contribution, we present results of a large scale cross-linguistic analysis of the statistical structure of written language (Koplenig/Wolfer/Meyer 2023) we approach this question from an information-theoretic perspective. To this end, we conduct a large scale quantitative cross-linguistic analysis of written language by training a language model on more than 6,500 different documents as represented in 41 multilingual text collections, so-called corpora, consisting of ~3.5 billion words or ~9.0 billion characters and covering 2,069 different languages that are spoken as a native language by more than 90% of the world population. We statistically infer the entropy of each language model as an index of un. To this end, we have trained a language model on more than 6,500 different documents as represented in 41 parallel/multilingual corpora consisting of ~3.5 billion words or ~9.0 billion characters and covering 2,069 different languages that are spoken as a native language by more than 90% of the world population or ~46% of all languages that have a standardized written representation. Figure 1 shows that our database covers a large variety of different text types, e.g. religious texts, legalese texts, subtitles for various movies and talks, newspaper texts, web crawls, Wikipedia articles, or translated example sentences from a free collaborative online database. Furthermore, we use word frequency information from the Crúbadán project that aims at creating text corpora for a large number of (especially under-resourced) languages (Scannell 2007). We statistically infer the entropy rate of each language model as an information-theoretic index of (un)predictability/complexity (Schürmann/Grassberger 1996; Takahira/Tanaka-Ishii/Dębowski 2016). Equipped with this database and information-theoretic estimation framework, we first evaluate the so-called ‘equi-complexity hypothesis’, the idea that all languages are equally complex (Sampson 2009). We compare complexity rankings across corpora and show that a language that tends to be more complex than another language in one corpus also tends to be more complex in another corpus. This constitutes evidence against the equi-complexity hypothesis from an information-theoretic perspective. We then present, discuss and evaluate evidence for a complexity-efficiency trade-off that unexpectedly emerged when we analysed our database: high-entropy languages tend to need fewer symbols to encode messages and vice versa. Given that, from an information theoretic point of view, the message length quantifies efficiency – the shorter the encoded message the higher the efficiency (Gibson et al. 2019) – this indicates that human languages trade off efficiency against complexity. More explicitly, a higher average amount of choice/uncertainty per produced/received symbol is compensated by a shorter average message length. Finally, we present results that could point toward the idea that the absolute amount of information in parallel texts is invariant across different languages.