Interview by Grace East
Grace East: Reckonings whisks us away on a journey through time and space and introduces us to how people engage(d) with numbers in a huge variety of socio-historical contexts. Put simply: you seem to ask, “How are numbers used and why?” Toward the end of the book, you provide a nicely crystallized sentiment that runs throughout the text: “I see numerals as representational systems, related to practices of literacy and writing, not as computational systems” (150). Can you elaborate on this central idea and discuss a few key takeaways you hope readers will leave with after finishing this book?
Stephen Chrisomalis: I’ve been researching the anthropology of numbers for over twenty years now and one of the things that’s been most consistent is that, whenever I talk to people about my work, regardless of their discipline or theoretical orientation, they conflate numbers and math. And as it turns out, a lot of anthropologists got into the field in order to run as far away from mathematics as possible. Frankly anyone who has read anything I’ve ever written knows that my work requires much more knowledge of linguistics, semiotics, and philology than it does mathematics – which should make a whole different audience run in terror.
There is a pervasive Euro-American ideology that almost values or privileges innumeracy, as stridently argued by the mathematician John Allen Paulos. This is seen in the sort of person who is vaguely proud of not being able to calculate a tip or manage daily finances. I see that too. But I also see the corresponding ideology that numbers exist in this strange realm of mathematics, far removed from all other pursuits, only accessible to a special type of person. But in reality, numbers are everyday things, used by everyone to manage time, to make a list, or as any sort of label for things. In other words, they act as semiotic resources for managing practical socio-cognitive problems. In Reckonings, I show that refocusing attention on what people actually do with the numbers they’ve got, rather than focusing on them as an object of awe, is absolutely imperative for a discipline like anthropology, that still avoids the subject of numbers to a large degree.
Grace East: The ways in which language universals and particulars appear cross-linguistically serve as a frequent touchstone throughout the text. You use numbers as a specific lens through which to observe the parameters of human cognition. What is it about numbers that provides such a fitting representation of the complicated nature of identifying language universals as well as cognitive affordances and constraints?
Stephen Chrisomalis: Like a lot of people trained in linguistics in the 90s (and earlier), I could hardly escape the massive, almost hegemonic, Chomskyan view of linguistics, which regarded universals as widespread and grounded fully in the brain. Against this, in linguistic anthropology of course we had a more culturalist view, which regarded variation as the norm and universals, if present, as generally uninteresting. Neither of these positions (extremes, even caricatures, of course) ever appealed much to me, but they were there nonetheless in the background.
I began my work on numbers more than twenty years ago with the insight that number has two distinct sets of representations: number words (one two three) and number symbols (123), each of which occur very widely cross-culturally. And among users of numerical notation, the two systems co-occur in the same individuals. While each system has cross-linguistic and cross-cultural patterns, their patterns, structures, and regularities are not the same. You can’t predict the structure of a numerical notation from its users’ languages. Nevertheless, you can say a lot about what doesn’t occur in numerical notations; there are some powerful constraints, in other words. But these can’t come from a purported universal grammar, because they aren’t the same constraints that operate on linguistic numerals, and, frankly, because numerical notation isn’t a universal, but a product of specific social, technical, and historical contexts – largely those associated with the state.
So where do these regularities come from, if not hard-wired (a bad metaphor, if commonplace)? The key is partly that numerical notations are visual notations rather than auditory ones; their (relative) permanence and their dependence on visual processing make them different than number words. So the brain matters, but also it matters for what purposes and for what audiences writers are constructing these representations. That takes us back to the insight that numbers are for being seen and read, more than they are being manipulated as arithmetical objects. Once we understand that, we can incorporate activity and behavior into our analysis of why the patterns and structures that exist are there, both in number words and number symbols.
Grace East: I really enjoyed your chapters seeking to uncover why we don’t regularly use Roman numerals anymore, I think because it felt like we were along for the ride on a historical mystery quest. In these sections, you explain that the decline of Roman numerals must be accounted for based not on a retrospective conception of their utility (or lack thereof) in comparison to Western numerals, but rather an acknowledgement of the “confluence of specific economic, social, and communicative factors,” such as the invention of the printing press and increasing literacy rates (116). What about this historical quandary compelled you to look deeper for an answer? How can the lessons learned from these findings be applied more broadly, both within anthropology and outside of it?
Stephen Chrisomalis: If I were to write an article and claim that Facebook is the best of all possible social media, I would be rightly laughed out of the academy. But the claim that our current (Indo-Arabic / Western) numerals 0123456789 are the best ones possible, and that they replaced Roman numerals in Europe through a sort of survival of the fittest, is so widespread that I would say that in some sense it is the central myth about numbers. It’s this still-vital vestige of unilinear evolutionism, deeply unquestioned and surely ethnocentric, that has retained its acceptability in otherwise serious historical and social-scientific work.
But it also makes no sense to pretend like nothing happened at all over the last five hundred years, during which many, many numerical notations – not just the Roman numerals, but dozens of systems worldwide, have ceased to be used or are retained only for vestigial purposes. Without fetishizing modernity or treating it as a special object of anthropology, I ask, in Reckonings, if the Roman numerals were so bad, why were they retained as long as they were, and why only in the 15th and 16th centuries did they lose this purported notational contest. This builds on classic social science – think Immanuel Wallerstein or Eric Wolf – as well as discourse analysis on the ideologies underpinning the myth – in a way that I hope complements rather than challenges the cognitive approaches I use alongside them.
So for instance, as it turns out, no one in Western Europe seems actually to have complained about the inefficiency of Roman numerals (at least not in writing) until the late 17th century – long after they had been replaced throughout the continent. In fact, not until the 19th century did this kind of discourse become commonplace. The Roman numerals were replaced quietly, slowly, not by imperial fiat or by some cabal of number experts, but through the transformations in education, commerce, and literacy that accompanied mercantile capitalism between 1400 – 1600. That’s a time period – whether we call it late medieval or early modern, I don’t care – that precious few anthropologists devote much time or energy to, which I think is a serious mistake.
Grace East: One of my favorite takeaways from this book is that numbers are not objective abstractions, but rather socially and historically contingent human inventions and practices. To this end, I was particularly struck by the distinction you make between numerical recording (a final representation, like a written numeral) and numerical manipulation (the tools to do arithmetic, like an abacus). Can you talk more about how you arrived at the relationship between these and how it serves to impact our ideologies and biases around computation and cognition both diachronically and synchronically?
Stephen Chrisomalis: There’s a very famous story first told by the mathematician G.H. Hardy, about a visit to his ailing friend Srinivasa Ramanujan in the hospital. Hardy, upon arriving, recounted that he had taken a taxicab whose number was 1729, which he thought was very boring, only to be told by Ramanujan that it was very interesting indeed – the smallest number expressible as the sum of two cubes in two different ways. This anecdote was meant to impress the reader of the impressive intellect of Ramanujan, and while it may do so, it should also illustrate that for almost everyone else, including most mathematicians, 1729 is just the number of the cab, and its purpose is semiotic – a label, a name for the cab, whose purpose is to distinguish it from all others. It’s not that the rest of us aren’t doing anything with 1729 – it’s just that we aren’t computing with it.
The linkage between written numbers and arithmetic is a historically contingent one, dependent on widespread literacy and formal education and a social system that relies heavily on recorded computation. Most people historically who have had formal arithmetic education have separated the process of calculation – often with beads, boards, or other devices from the writing of results. There isn’t anything like Roman numeral ‘pen and paper’ calculation – although, for the record, I know of no fewer than five independent scholarly attempts over the past century to show how the Romans might have calculated using Roman numerals. But we know perfectly well how the Romans calculated – with the pebble-board abacus, just as the suan pan and soroban are still widely taught and used in China and Japan, respectively. The use of material engagement through these devices is ideologized as backward, although there is considerable evidence in the cognitive science literature for the inscription of abacus arithmetic in East Asia into powerful mental models – that is, algorithms.
What’s different about pen and paper is that your results (and your errors) have some permanence and can be scrutinized (by a teacher or supervisor), that makes it useful in a particular socioeconomic setting. The form factor of pen and paper (or chalk and board) arithmetic produces not simply a result but a means to a result, a written record. But in most historical settings, computation and recording have been separate activities, and so I want to make readers aware that this linkage is neither necessary nor inevitable.