Quantitative Linguistik
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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.
In der Korpuslinguistik und der Quantitativen Linguistik werden ganz verschiedenartige formale Maße verwendet, mit denen die Gebrauchshäufigkeit eines Wortes, eines Ausdrucks oder auch abstrakter oder komplexer sprachlicher Elemente in einem gegebenen Korpus gemessen und ggf. mit anderen Gebrauchshäufigkeiten verglichen werden kann. Im Folgenden soll für eine Auswahl dieser Maße (absolute Häufigkeit, relative Häufigkeit, Wahrscheinlichkeitsverteilung, Differenzenkoeffizient, Häufigkeitsklasse) zusammengefasst werden, wie sie definiert sind, welche Eigenschaften sie haben und unter welchen Bedingungen sie (sinnvoll) anwendbar und interpretierbar sind – dabei kann eine Rolle spielen, ob das Häufigkeitsmaß auf ein Korpus als Ganzes angewendet wird oder auf einzelne Teilkorpora. Zusätzlich zu den bei den einzelnen Häufigkeitsmaßen genannten Einschränkungen gilt generell der folgende vereinfachte Zusammenhang: Je seltener ein Wort im gegebenen Korpus insgesamt vorkommt und je kleiner dieses Korpus ist, desto stärker hängt die beobachtete Gebrauchshäufigkeit des Wortes von zufälligen Faktoren ab, d.h., desto geringer ist die statistische Zuverlässigkeit der Beobachtung.
Wenn alle Forschungsfragen gestellt, alle Hypothesen formuliert, alle Korpora kompiliert und alle Daten von Proband*innen gesammelt wurden, befinden Sie sich auf einer der letzten Etappen Ihrer linguistischen Studie: der Analyse der Daten. In diesem Kapitel werden Sie einige Werkzeuge kennenlernen, die Sie dabei unterstützen können. Hier nehmen wir an, dass Sie in irgendeiner Form eine quantitative statistische Auswertung vornehmen möchten, denn für qualitative Analysen sind die Werkzeuge, die wir Ihnen vorstellen werden, weniger bis gar nicht geeignet.
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.
Studying Lexical Dynamics and Language Change via Generalized Entropies: The Problem of Sample Size
(2020)
Recently, it was demonstrated that generalized entropies of order α offer novel and important opportunities to quantify the similarity of symbol sequences where α is a free parameter. Varying this parameter makes it possible to magnify differences between different texts at specific scales of the corresponding word frequency spectrum. For the analysis of the statistical properties of natural languages, this is especially interesting, because textual data are characterized by Zipf’s law, i.e., there are very few word types that occur very often (e.g., function words expressing grammatical relationships) and many word types with a very low frequency (e.g., content words carrying most of the meaning of a sentence). Here, this approach is systematically and empirically studied by analyzing the lexical dynamics of the German weekly news magazine Der Spiegel (consisting of approximately 365,000 articles and 237,000,000 words that were published between 1947 and 2017). We show that, analogous to most other measures in quantitative linguistics, similarity measures based on generalized entropies depend heavily on the sample size (i.e., text length). We argue that this makes it difficult to quantify lexical dynamics and language change and show that standard sampling approaches do not solve this problem. We discuss the consequences of the results for the statistical analysis of languages.
This paper argues that a lectometric approach may shed light on the distinction between destandardization and demotization, a pair of concepts that plays a key role in ongoing discussions about contemporary trends in standard languages. Instead of a binary distinction, the paper proposes three different types of destandardization, defined as quantitatively measurable changes in a stratigraphic language continuum. The three types are illustrated on the basis of a case study describing changes in the vocabulary of Dutch in The Netherlands and Flanders between 1990 and 2010.
Studying Lexical Dynamics and Language Change via Generalized Entropies: The Problem of Sample Size
(2019)
Recently, it was demonstrated that generalized entropies of order α offer novel and important opportunities to quantify the similarity of symbol sequences where α is a free parameter. Varying this parameter makes it possible to magnify differences between different texts at specific scales of the corresponding word frequency spectrum. For the analysis of the statistical properties of natural languages, this is especially interesting, because textual data are characterized by Zipf’s law, i.e., there are very few word types that occur very often (e.g., function words expressing grammatical relationships) and many word types with a very low frequency (e.g., content words carrying most of the meaning of a sentence). Here, this approach is systematically and empirically studied by analyzing the lexical dynamics of the German weekly news magazine Der Spiegel (consisting of approximately 365,000 articles and 237,000,000 words that were published between 1947 and 2017). We show that, analogous to most other measures in quantitative linguistics, similarity measures based on generalized entropies depend heavily on the sample size (i.e., text length). We argue that this makes it difficult to quantify lexical dynamics and language change and show that standard sampling approaches do not solve this problem. We discuss the consequences of the results for the statistical analysis of languages.
Large-scale empirical evidence indicates a fascinating statistical relationship between the estimated number of language users and its linguistic and statistical structure. In this context, the linguistic niche hypothesis argues that this relationship reflects a negative selection against morphological paradigms that are hard to learn for adults, because languages with a large number of speakers are assumed to be typically spoken and learned by greater proportions of adults. In this paper, this conjecture is tested empirically for more than 2000 languages. The results question the idea of the impact of non-native speakers on the grammatical and statistical structure of languages, as it is demonstrated that the relative proportion of non-native speakers does not significantly correlate with either morphological or information-theoretic complexity. While it thus seems that large numbers of adult learners/speakers do not affect the (grammatical or statistical) structure of a language, the results suggest that there is indeed a relationship between the number of speakers and (especially) information-theoretic complexity, i.e. entropy rates. A potential explanation for the observed relationship is discussed.