Mathematical philology: entropy information in refining classical texts' reconstruction, and early philologists' anticipation of information theory.

Philologists reconstructing ancient texts from variously miscopied manuscripts anticipated information theorists by centuries in conceptualizing information in terms of probability. An example is the editorial principle difficilior lectio potior (DLP): in choosing between otherwise acceptable alternative wordings in different manuscripts, "the more difficult reading [is] preferable." As philologists at least as early as Erasmus observed (and as information theory's version of the second law of thermodynamics would predict), scribal errors tend to replace less frequent and hence entropically more information-rich wordings with more frequent ones.

Stereoscopic comparison as the long-lost secret to microscopically detailed illumination like the Book of Kells'.

The idea that the seventh- and eighth-century illuminators of the finest few Insular manuscripts had a working knowledge of stereoscopic images (otherwise an eighteenth- and nineteenth-century discovery) helps explain how they could create singularly intricate, microscopically detailed designs at least five centuries before the earliest known artificial lenses of even spectacle quality. An important clue to this long-standing problem is that interlace patterns drawn largely freehand in lines spaced as closely as several per millimeter repeat so exactly across whole pages that repetitions can be free-fused to form microscopically detailed stereoscopic images whose relief in some instances indicates precision unsurpassed in astronomical instruments until the Renaissance. Spacings between repetitions commonly harmonize closely enough with normal interpupillary distances that copying disparities can be magnified tens of times in the stereoscopic relief of the images.

How science survived: medieval manuscripts' "demography" and classic texts' extinction.

Determining what fraction of texts and manuscripts have survived from Antiquity and the Middle Ages has been highly problematic. Analyzing the transmission of texts as the "paleodemography" of their manuscripts yields definite and surprisingly high estimates. Parchment copies of the foremost medieval textbooks on arithmetical and calendrical calculation closely fit age distributions expected for populations with logistic growth and manuscripts with exponential survivorship.