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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.
In a recent article, Meylan and Griffiths (Meylan & Griffiths, 2021, henceforth, M&G) focus their attention on the significant methodological challenges that can arise when using large-scale linguistic corpora. To this end, M&G revisit a well-known result of Piantadosi, Tily, and Gibson (2011, henceforth, PT&G) who argue that average information content is a better predictor of word length than word frequency. We applaud M&G who conducted a very important study that should be read by any researcher interested in working with large-scale corpora. The fact that M&G mostly failed to find clear evidence in favor of PT&G's main finding motivated us to test PT&G's idea on a subset of the largest archive of German language texts designed for linguistic research, the German Reference Corpus consisting of ∼43 billion words. We only find very little support for the primary data point reported by PT&G.
Information theory can be used to assess how efficiently a message is transmitted on the basis of different symbolic systems. In this paper, I estimate the information-theoretic efficiency of written language for parallel text data in more than 1000 different languages, both on the level of characters and on the level of words as information encoding units. The main results show that (i) the median efficiency is ∼29% on the character level and ∼45% on the word level, (ii) efficiency on both levels is strongly correlated with each other and (iii) efficiency tends to be higher for languages with more speakers.