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Re-counting the Cognitive History of Numerals

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In The MIT Press Reader Philip Laughlin, who acquires books for the MIT Press in the fields of Cognitive Science, Philosophy, Linguistics, and Bioethics, interviews Stephen Chrisomalis, Professor of Anthropology at Wayne State University and author of, among other books,Reckonings: Numerals, Cognition, and History.”

Those of us who learned arithmetic using pen and paper, working with the ten digits 0–9 and place value, may take for granted that this is the way it’s always been done, or at least the way it ought to be done. But if you think of the amount of time and energy spent in the early school years just to teach place value, you’ll realize that this sort of numeracy is not preordained.

Over the past 5,500 years, more than 100 distinct ways of writing numbers have been developed and used by numerate societies, linguistic anthropologist Stephen Chrisomalis has found. Thousands more ways of speaking numbers, manipulating physical objects, and using human bodies to enumerate are known to exist, or to have existed, he writes in his new book “Reckonings: Numerals, Cognition, and History.” Remarkably, each of the basic structures was invented multiple times independently of one another. In “Reckonings,” Chrisomalis considers how humans past and present have used numerals, reinterpreting historical and archaeological representations of numerical notation and exploring the implications of why we write numbers with figures rather than words. Drawing on, and expanding upon, the enormous cross-cultural and comparative literatures in linguistics, cognitive anthropology, and the history of science that bear on questions of numeracy, he shows that numeracy is a social practice.

Chrisomalis took time out from a busy end to the spring semester to field a few questions about his new book, his spirited defense of Roman numerals, his complicated relationships with mathematicians, and his thoughts on the validity of the Sapir-Whorf Hypothesis.


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Philip Laughlin
: We’ve worked with a number of linguists and anthropologists over the years but you are our first author to specialize in written numerical systems. What sparked your interest in this topic? Why are numerals an important area of research?

Stephen Chrisomalis: I first became interested in numerals when I wrote a paper in an undergraduate cognitive anthropology course in the mid-1990s. After moving away from the subject for a couple years, I came back to it when I was looking for a PhD topic along with my advisor, the late Bruce Trigger at McGill. This resulted in my dissertation, which later became my first book, “Numerical Notation: A Comparative History” (Cambridge, 2010). It was an unorthodox project for an anthropology department — neither strictly archaeological nor ethnohistorical nor ethnographic. But that was exactly the sort of creative project that it was possible to do at McGill at that time, and that sadly, given the exigencies of the modern job market, is almost impossible to imagine doing today.

What brought me to numerical notation as a dissertation subject is much of what still appeals to me about it now. We have evidence from over 100 different systems used across every inhabited continent over 5,000 years, including all the world’s literate traditions. Numbers are a ubiquitous domain of human existence, and written numerals are virtually everywhere that there is writing. While, of course, the historical and archaeological records are partial (which is in turn both exciting and frustrating), understanding their history and cross-cultural transmission is a tractable problem. We can tell, roughly, when and where they originate and how they relate to one another.

Also, every user of a numerical notation system is also a speaker of one or more languages, which lets us ask great questions comparing number words to numerical notation and to show how they interact. These questions can be as simple as “Do people say ‘two thousand twenty one’ or ‘twenty twenty one’?” and as big as “Were numbers first visual marks or spoken words?” As a linguist and an anthropologist, that’s very attractive. Because there is a significant and large literature on numerical cognition, the comparative, historical data I bring to the table is useful for testing and expanding on our knowledge in that interdisciplinary area.

PL: You had the cover image and title for this book in your head for years. Can you explain the significance of the watch and why you chose the title “Reckonings” in the first place? What were you trying to get across to potential readers with that evocative word?

SC: The title ‘Reckonings’ invokes the triple meaning of the word ‘reckon’ — to calculate, to think, and to judge — which parallels the three parts of the subtitle: “Numerals, Cognition, and History.” Reckoning is not mathematics, in its technical, disciplinary sense, but it reflects the everyday practices of working with and manipulating numbers. Then, in English and in other languages, we extend the verb for calculation to thinking in general — to reckon thus involves the more general cognitive questions I hope I’ve addressed. Finally, we come to reckoning as judgement — every numerical notation faces its own reckoning as users decide whether to adopt, transmit, and eventually, abandon it. As I spend a lot of time talking about the obsolescence of numeral systems, most notably but not limited to the Roman numerals, I wanted to echo this decision-making process of judgement by which users decide to abandon one notation in favor of another. “Reckonings” signals that the book might be about arithmetic — but it’s about a lot more than that.

The cover image of the book is a watch designed by the French watchmaker Jean-Antoine Lépine in 1788, now held at the British Museum (BM 1958,1201.289). Lépine was one of the first horologists to consistently use Western (commonly called Arabic) numerals instead of Roman numerals for hour markers, but in the 1780s he made a number of watches like this one, where he instead playfully mixed the two systems. The hybridity on this sort of artifact is visually striking and memorable to the viewer, both then and now. But actually, it isn’t as weird as it seems; we combine numerical representations all the time, like when we write something like “1.2 million” instead of “1,200,000.” Unlike the Roman numerals alone, which would be visually ‘unbalanced’ on a watch, this hybrid system expresses every number from 1 through 12 in no more than two digits. To me it embodies the passage of time in material form and the replacement of the Roman numerals. By the 1780s, they had been replaced for most purposes, but watch and clock faces are one of the places where, even today, they’re pretty common. As a sort of metonym for this historical process, the Lépine watch highlights that the decline and fall of the Roman numerals was not a slow, steady, predictable replacement, but one with many disjunctures.

PL: At the book launch, you talked a bit about the future of number systems, but with the caveat that you are not a “Futurologist.” So I’ll ask you to put on a historian’s hat instead: What kind of cultural changes are necessary for a society to switch from one number system to another? It seems to me that significant changes would have to happen at least at the political and economic level for one numerical system to supersede another, right?

SC: One of the key arguments in “Reckonings” is that . . .

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Written by Leisureguy

28 July 2021 at 11:49 am

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