1. Mathematical diagrams are getting close attention, as Reviel Netz notes in The Archimedes Codex:
The scholars who edited mathematical texts in the nineteenth century were so interested in the words that they ignored the images. If you open an edition from that era, the diagrams you find are not based upon what is actually drawn in the original manuscripts. The diagrams represent, instead, the editor's own drawing. I was shocked to realize that and began to consider: should I produce, for the first time, an edition of the diagrams? (p. 30).2. Illustrations of texts have been re-assessed in many new ways, with the works of Kurt Weitzmann a half-century ago, Late antique and early Christian book illumination and Illustrations in roll and codex marking a starting point. I recently browsed through John Williams' Imaging the early medieval Bible (1999), which revises some of Weitzmann's ideas, and of course there are the more recent books of Jocelyn Penny Small, The Parallel Worlds of Classical Art and Text (2003), and of Michael Squire, Image and Text in Graeco-Roman Antiquity (2011), which debate whether book illustration was ever meant to depict what was in the text at all. But all of these books deal with the interplay between stories and pictures of people doing things.
3. Mental pictures of abstract matters are discussed in Mary Carruthers' books, particularly The Craft of Thought (1998), which explores the patristic and Roman Republican models of the medieval 'craft of memory' and thus casts some light on the place of visualizations in Late Antiquity:
Whereas ekphrasis always purports to be a meditative description of a painting, sculpture or the facade of a building, the initiating compositional pictura can also describe a schematized landscape in the form of a world map, or a figure like Lady Philosophy, or just about any of the formae mentis in common monastic use: a ladder, a tree, rotae, a rose-diagram. The rhetorical figures called ekphrasis and Bildeinsatz, in other words, are types of the cognitive, dispositive topos called pictura, which is the more general term. The most general terms of all for this cognitive instrument would include words like ratio and schema. (p. 200)
So visualizing things was a good way to start explaining them. However Carruthers is concerned with inner pictures, so her books yield very little about the ways that a real diagram or map could be employed for meditation or how it might be designed.
4. Small's other book, Wax Tablets of the Mind: Cognitive Studies of Memory and Literacy in Classical Antiquity (1997), explores the ways in which text could be said to visualize what was going on in people's heads, but once again does not deal with data visualization. Anna Catharina Esmeijer's Divina Quaternitas: a preliminary study in the method and application of visual exegesis tackles some of the same issues, but is of course mainly concerned with rather simple figures, not the complex abstraction of the Great Stemma.
Now obviously I have missed from this list a great many other learned books and articles. Many are listed on the further reading page of my website. But nowhere have I found a book or an article that goes to the heart of the issue. How the Latin writer could present mere words and numbers so pregnantly on the page so that the mere arrangement gave food for thought.
