Why numerals?

Over the past few weeks in my new job, I have had many opportunities to introduce myself or be introduced as an expert in the ‘anthropology of mathematics’, which is probably the simplest and most accurate way to describe my work (although I also have strong research interests in other areas, such as writing systems and cross-cultural theory).  The comments I receive on this are mostly of two sorts:

(a) Oh, how interesting! I had never imagined there was such a thing!

(b) Oh, how interesting! Are there many people working in that field?

Both of these are perfectly understandable responses, because there aren’t really very many of us out there; perhaps a dozen working anthropologists who publish regularly on numerals, and a couple dozen more linguists.   There are many more anthropologists and linguists who at some point have written something on the subject, but aren’t specialists in the field.   But in comparison to, say, psychologists working on mathematical cognition, or to historians of mathematics, there aren’t too many of us.  And honestly, I’m okay with that, because it means that there are plenty of great questions that are completely untouched.

The question of why one would study the anthropology of mathematics is actually more interesting, from my perspective, and usually it doesn’t take much to get me onto that subject, particularly with people who answer (a).  For me, the fantastic thing about the subject is that it is so often taken for granted that there is one thing called ‘number’, or one thing called ‘mathematics’, and that there should be limited cross-cultural difference in the domain.   But at the same time, anthropologists generally work in domains where there is a lot of variability and assume that there are few or no constraints on human behavior, but in numeral systems there are all sorts of constraints, some evolutionary, some functional, and some social.  So teasing out the differences and similarities, without assuming in advance that the phenomenon is highly regular or highly variable, is fascinating stuff.   In other words, the fact that I am a comparativist (rather than a cultural particularist) and the fact that I study mathematics are closely linked.

The other really fascinating thing about number systems, for me, is that numbers can be represented using spoken or written language, but can also be represented using graphic numerical notation systems (like the set of signs, 0123456789, which laypeople generally call Arabic numerals but I call Western numerals).  So you have one system that has its origins in auditory media and is linked to linguistic abilities, and another that gets away from directly representing language and is trans-linguistic, but is nonetheless probably linked somehow to language.  So from an anthropological perspective, you have one linguistic and one non-linguistic (graphic) representation of number, which allows you to ask all sorts of interesting questions about the intersection of language and culture.

The last thing that is really cool about number is that within the domain of numerical notation, we have a pretty good database of all the numerical notation systems that have ever been used, and can without too much difficulty reconstruct the relationships between them (i.e. which systems are ancestral to which others, or which systems replaced which others).   This allows us not only to look at each system as a structured system of signs in a synchronic fashion (omitting the time dimension) but also to engage in a diachronic analysis, examining how systems interact and change over 5000 years of written history.   This is why I describe my forthcoming book as a ‘comparative history’.  But I’m writing about numbers, not about cross-cultural theory, which will have to be an essay for another day, because right now my book manuscript isn’t going to edit itself.

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