Quantifying Prosodic Variability in Middle English Alliterative Poetry

Interest in the mathematical structure of poetry dates back to at least the 19th century: after retiring from his mathematics position, J. J. Sylvester wrote a book on prosody called $\textit{The Laws of Verse}$. Today there is interest in the computer analysis of poems, and this paper discusses how a statistical approach can be applied to this task. Starting with the definition of what Middle English alliteration is, $\textit{Sir Gawain and the Green Knight}$ and William Langland's $\textit{Piers Plowman}$ are used to illustrate the methodology. Theory first developed for analyzing data from a Riemannian manifold turns out to be applicable to strings allowing one to compute a generalized mean and variance for textual data, which is applied to the poems above. The ratio of these two variances produces the analogue of the F test, and resampling allows p-values to be estimated. Consequently, this methodology provides a way to compare prosodic variability between two texts.