340 reviel netz
used in Sanskrit mathematics. 10 Indo-European words are a concatena-
tion of prefi xes, roots and suffi xes. Each component is phonologically
autonomous, so that it is always possible to substitute some by alternative
symbols. A written word can thus naturally become a sequence concatenat-
ing symbols, or alphabetic representations, for prefi xes, roots and suffi xes.
Semitic words, on the other hand, are consonantal roots inside which are
inserted patterns of vocalic infi xes. Th e components cannot be taken apart
in the stream of speech, so that it is no longer feasible to substitute a word
by a concatenation of symbols, each standing for a root or a grammatical
element. Quite simply, the language does not function in terms of such con-
catenations. Arab translators, then, had naturally resolved standard Greek
abbreviations into their fully spelled out forms. But they did respect some
symbols: for instance, magical symbols, similar in character to those known
from Greek-era Papyri (though not derived from the Greek), are attested in
the Arabic tradition; 11 most famously, the Arabs had gradually appropri-
ated Indian numeral symbols. In such cases, the symbols were understood
primarily not as phonological units, but as written traces. I suggest that,
had Diophantus’ use of symbolism been as consistent as Tannery makes it,
an astute mathematical reader would recognize in it the use of symbolism
which goes beyond scribal expediency, and which is based on the written
trace – especially, given Diophantus’ own, explicit introduction of the
symbols. Th e Arab suppression of the symbolism in Diophantus suggests,
then, that they saw in it no more than the standard scribal abbreviation they
were familiar with from elsewhere in Greek writing.
I conclude with two comments, one historical, and the other cognitive.
Historically, we see that Diophantus’ symbols are rooted in a certain scribal
practice. Th is should be seen in the context of the long duration of Greek
writing. In antiquity, Greek writing was among the simplest systems in use
anywhere in human history: a single set of characters (roughly speaking,
our upper case), used with few abbreviations. Th rough late antiquity to the
early Middle Ages, the system becomes much more complex: the use of
abbreviations becomes much more common, and a new set of characters
(roughly speaking, our lower case) is introduced while the old set remains
in use in many contexts. In other words, the period is characterized by an
explosion in allography. 12 Th is may be related to the introduction of the10 See the lucid discussion in H1995: 87–90.
11 Canaan 1937 –8/2004, especially 2004: 167–75.
12 I t i s d i ffi cult to fi nd precise references for such claims that are rather the common stock of
knowledge acquired by palaeographers in their practice. Th e best introduction to the practices
of Greek manuscripts probably remains Groningen 1955. For abbreviations in early Greek
script, see McNamee 1982.