Online

Williams, Jake Ryland

Mathematics

2015

Ph. D.

Highly structured for efficient communication, natural languages are complex systems. Unlike in their computational cousins, functions and meanings in natural languages are relative, frequently prescribed to symbols through unexpected social processes. Despite grammar and definition, the presence of metaphor can leave unwitting language users "in the dark," so to speak. This is not problematic, but rather an important operational feature of languages, since the lifting of meaning onto higher-order structures allows individuals to compress descriptions of regularly-conveyed information. This compressed terminology, often only appropriate when taken locally (in context), is beneficial in an enormous world of novel experience. However, what is natural for a human to process can be tremendously difficult for a computer. When a sequence of words (a phrase) is to be taken as a unit, suppose the choice of words in the phrase is subordinate to the choice of the phrase, i.e., there exists an inter-word dependence owed to membership within a common phrase. This word selection process is not one of independent selection, and so is capable of generating word-frequency distributions that are not accessible via independent selection processes. We have shown in Ch. 2 through analysis of thousands of English texts that empirical word-frequency distributions possess these word-dependence anomalies, while phrase-frequency distributions do not. In doing so, this study has also led to the development of a novel, general, and mathematical framework for the generation of frequency data for phrases, opening up the field of mass-preserving mesoscopic lexical analyses. A common oversight in many studies of the generation and interpretation of language is the assumption that separate discourses are independent. However, even when separate texts are each produced by means of independent word selection, it is possible for their composite distribution of words to exhibit dependence. Succinctly, different texts may use a common word or phrase for different meanings, and so exhibit disproportionate usages when juxtaposed. To support this theory, we have shown in Ch. 3 that the act of combining distinct texts to form large 'corpora' results in word-dependence irregularities. This not only settles a 15-year discussion, challenging the current major theory, but also highlights an important practice necessary for successful computational analysis---the retention of meaningful separations in language. We must also consider how language speakers and listeners navigate such a combinatorially vast space for meaning. Dictionaries (or, the collective editorial communities behind them) are smart. They know all about the lexical objects they define, but we ask about the latent information they hold, or should hold, about related, undefined objects. Based solely on the text as data, in Ch. 4 we build on our result in Ch. 2 and develop a model of context defined by the structural similarities of phrases. We then apply this model to define measures of meaning in a corpus-guided experiment, computationally detecting entries missing from a massive, collaborative online dictionary known as the Wiktionary.