Reasoning and symbolism in Diophantus 341
codex, and with the overall tenor of the culture with which it is associated: a
culture where writing as such becomes the centre of cultural life, with much
greater attention to its material setting. It is in this context that Diophantus
introduces his symbols: they are the product of the same culture that gave
rise to the codex.
Cognitively, we see that those symbols introduced by Diophantus are
indeed allographs. Th at is: they do not suppress the verbal reading of the
sign, but refer to it in a diff erent, visual way. It was impossible for a Greek
reader to come across the symbol Μ ο and not to have suggested to his mind
the verbal sound-shape ‘monad’. But at the same time, the symbol itself
would be striking: it would be a very common shape seen over and over
again in the text of Diophantus and nowhere else. It would also be a very
simple shape, immediately read off the page as a single visual object. Th us,
alongside the verbal reading of the object, there would also be a visual rec-
ognition of it, both obligatory and instantaneous. I thus suggest that what is
involved here is a systematic bimodality. One systematically reads the sign
both verbally and visually. One reads out the word; but is also aware of the
sign.
To sum up, then, Diophantus’ symbolism gives rise to a bimodal (verbal
and visual) parsing of the text (at the level of the noun-phrase). I shall
return to analyse the signifi cance of this in Section 4 below, where I shall
argue that this bimodality explains the function of Diophantus’ symbols
within his reasoning. Before that, then, let us acquaint ourselves with this
mode of reasoning.
3. Notes on reasoning in Diophantus
A sample of Diophantus
Th e following is a literal translation of Diophantus’ i .10. I follow Tannery’s
text, with the diff erence that, for each case where a symbol is available
(including alphabetical numerals which, when symbolic, I render by our
own Arabic numerals), I toss a couple of coins to decide whether I print it
as symbol or as resolved word. (25% I make to be full words, which is what
I postulate, for the sake of the exercise, might have been the original ratio.)
Th e translation follows my conventions from the translation of Greek
geometry,^13 including the introduction of Latin numerals to count steps of
construction and Arabic numerals to count steps of reasoning.
13 See Netz 2004.