The choice associated with words is a fundamental property of natural languages. It lies at the heart of quantitative linguistics, computational linguistics and language sciences more generally. Information theory gives us tools at hand to measure precisely the average amount of choice associated with words: the word entropy. Here, we use three parallel corpora, encompassing ca. 450 million words in 1916 texts and 1259 languages, to tackle some of the major conceptual and practical problems of word entropy estimation: dependence on text size, register, style and estimation method, as well as non-independence of words in co-text. We present two main findings: Firstly, word entropies display relatively narrow, unimodal distributions. There is no language in our sample with a unigram entropy of less than six bits/word. We argue that this is in line with information-theoretic models of communication. Languages are held in a narrow range by two fundamental pressures: word learnability and word expressivity, with a potential bias towards expressivity. Secondly, there is a strong linear relationship between unigram entropies and entropy rates. The entropy difference between words with and without co-textual information is narrowly distributed around ca. three bits/word. In other words, knowing the preceding text reduces the uncertainty of words by roughly the same amount across languages of the world.

Automated Text Scoring (ATS) provides a cost-effective and consistent alternative to human marking. However, in order to achieve good performance, the predictive features of the system need to be manually engineered by human experts. We introduce a model that forms word representations by learning the extent to which specific words contribute to the text's score. Using Long-Short Term Memory networks to represent the meaning of texts, we demonstrate that a fully automated framework is able to achieve excellent results over similar approaches. In an attempt to make our results more interpretable, and inspired by recent advances in visualizing neural networks, we introduce a novel method for identifying the regions of the text that the model has found more discriminative.