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Zipf's law of abbreviation, the tendency of more frequent words to beshorter, is one of the most solid candidates for a linguistic universal, in thesense that it has the potential for being exceptionless or with a number ofexceptions that is vanishingly small compared to the number of languages onEarth. Since Zipf's pioneering research, this law has been viewed as amanifestation of a universal principle of communication, i.e. the minimizationof word lengths, to reduce the effort of communication. Here we revisit theconcordance of written language with the law of abbreviation. Crucially, weprovide wider evidence that the law holds also in speech (when word length ismeasured in time), in particular in 46 languages from 14 linguistic families.Agreement with the law of abbreviation provides indirect evidence ofcompression of languages via the theoretical argument that the law ofabbreviation is a prediction of optimal coding. Motivated by the need of directevidence of compression, we derive a simple formula for a random baselineindicating that word lengths are systematically below chance, across linguisticfamilies and writing systems, and independently of the unit of measurement(length in characters or duration in time). Our work paves the way to measureand compare the degree of optimality of word lengths in languages.

Direct and indirect evidence of compression of word lengths. Zipf's law of abbreviation revisited