Last year, the Israeli historian of mathematics Reviel Netz, who is professor of classics at Stanford University, spoke at the British Academy in London and offered an interesting new synthesis of his ideas on diagrams. As far as I know Netz has not paid any attention to the Great Stemma, but his thoughts on the Hellenistic intellectual world have a strong bearing on what followed on from it.
Netz is not only famous as the author of The Archimedes Codex, but also as the scholar who introduced in 1999 the idea that the geometrical diagrams in the works of Euclid, Archimedes and others should not be understood as after-the-fact explanations of geometrical discoveries or as mere ornaments to the text, but as integral to the logical proof, as snapshots of the discoveries themselves.
The geometers thought spatially, or diagrammatically, then honed the explanations in words afterwards.
Ideas evolve, and Netz seems to have moved onwards to a view that, in a sense, restores some of the primacy of text in that polarity. That would be my somewhat exaggerated take on what he was saying last year during Leaping out of the Page, a lecture in London that you can see on YouTube.
The question he explored in his 2013 March 14 presentation at the British Academy was: why are those Greek mathematical diagrams so bare, so sketchy, one might almost say, so rude?
Netz seeks to explain the fact that there is no evidence of anyone debating a better way to draw such diagrams (at 51.10 by elapsed time in the video) and he comes up with the following answer. Literary texts on papyrus in the classical period lack any word-breaks, paragraphs or illustrations. The readers had to inject all of that. The text they held in their hands was what Netz calls "schematic": rude cues for the educated reader to unlock and "perform" the text in his mind.
The diagrams conform with this: they are schematic too (52.18). Nothing more than that was expected of them. This seems to come out of ideas in Netz's book, Ludic Proof, in which he explored the startling similarities between Hellenistic poetry and mathematical texts from the same era.
So what could this reveal to us about Late Antique diagrams?
Firstly, it highlights the way in which Greek mathematical figures are so very different from Late Antique flow diagrams like the Great Stemma, the arbor porphyriana and the 37 stemmata of Cassiodorus. We may use the English term "diagram" for both types, but they do not belong to the same genera of things at all. The Late Antique graphics are startlingly new and creative, with no identifiable roots in mathematical techniques or any existing literary practices.
The idea of devoting an entire papyrus roll to a graphic without any accompanying text must have seemed strange and new-fangled to people when they first saw it.
Secondly, these observations reinforce our understanding that flow diagrams are part of the haptic world of things that we manipulate. Netz argues (24.57) that geometrical figures are cerebral and differ utterly from touchy-feely arithmetic: "When Greeks do counting, what they do is to operate on an abacus. They have counters that are being moved around on an abacus... You have a flat surface, and on this flat surface you are moving stuff."
Something parallel would have happened when the designer of a flow diagram was laying it out. He had to use counters or ostraca to plan it. Later on, the reader of the flow diagram will inevitably handle it too, putting fingertips on its "icons" and tracing its flows. The flow diagram is something everybody has an urge to manipulate, a Late Antique precursor to the iPad: it's a physical thing, designed to be not only looked at, but touched, and aimed at the "manual" user, even the semi-literate, not the cerebral reader showing off his paideia.
Netz stresses how, in Euclid or Archimedes, text and geometrical figures marry together. Papyri are one of the main media of Antiquity and a "happy" literary papyrus, as Netz calls it, always contains the same thing: column after column of text to be read left to right. The figures are subsumed into these slabs of text (which is why I say, not entirely seriously, that Netz now sees the text having primacy).
So my third reflection is on the thorough-going difference between the unidirectional content of a papryus book and the jump-in-anywhere nature of the first great infographic. The Great Stemma does not have any accompanying text: all its words are build directly into the drawing. It has no mandatory start or finish: you can read it from the right, or the left, or even upside-down.
From the point of view of traditional literary culture, the Great Stemma would have seemed to break every rule in the canon.
Leaping out of the Page: The Use of Diagram in Greek Mathematics. London: British Academy, 2013. https://www.youtube.com/watch?v=7hzzdLsTb5E&feature=youtube_gdata_player.
Netz, Reviel. Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic. 1st ed. Cambridge; New York: Cambridge University Press, 2009.
— The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History. Ideas in Context 51. Cambridge University Press, 1999.
Netz, Reviel, and William Noel. The Archimedes Codex. Revealing the Secrets of the World’s Greatest Palimpsest. London. Orion, 2007.
