Reckonings: Numerals, Cognition and History

by Stephen Chrisomalis, MIT Press, 2020, 264 pp. 
Hardcover, $35.00 ISBN 978-0-2362-04463-9 

Numbers are everywhere in our world, both literally and figuratively, but how much attention do any of us pay to their form or origins? The answer, on the basis of this work, is likely not enough. Stephen Chrisomalis, a professor of anthropology at Wayne State University, has written a compelling and thoroughly entertaining account of how numbers came to be used and represented, situating numeracy within a social and cognitive framing that sheds light on the peculiarly human shaping of numerals as communication.  

At the outset, the author establishes three understandings we might have of reckoning: as calculation, as thinking, and as evaluation. He wants us to recognize upfront that numbers provide a basis for the social practices that energize our world, from trade and calendaring to recipe-making and record-keeping. Our numbers both reflect and constrain our thinking, help us explain and share ideas, underlie our educational system, and highlight how our world view can both reflect and influence how groups make meaning of the world. This is no small challenge; the work crosses disciplinary lines to examine language as much as mathematics, psychology as well as history, but the ease with which Chrisomalis moves through these subjects takes the reader joyfully along, for the most part, without pause.  

The heart of the book is an examination of how our modern Western number system, with its decimal point and place values built around a limited set of individual numbers (0-9), came to replace the Roman numeral system that dominated the Western world for more than a millennium. Using this question as a launching pad, the author compares arguments for the cognitive efficiency of calculations, claims for the goodness of fit between the representation and the tasks people wanted to complete, explores the relative advantages of material technologies underlying numeracy, and reveals the cultural and political aims of advancing or managing a society through numeracy. In the end, no one explanation tells the full story, but along the way we learn that the transition from one dominant form to another took centuries, time during which many lives were lived under competing numerical systems, to the point where even now, where we might assume the Western form has won, so to speak, we still use Roman numerals for symbolic, ceremonial, or even traditional applications (such as numbering the forward of this book).  

While wrestling with these issues, we find the author comparing term frequency with Google’s Ngram Viewer (the co-occurrence of terms such as “clumsy” or “awkward” with “Roman numerals” seems to have reached a peak in the 1940s) or counting the appearance of Roman or Western numerals in early English printed books at the turn of the sixteenth century (Roman numerals even then still being more common), like a sleuth searching for signs in the messy records of human activity. The data is often fascinating, but a single interpretation is often elusive, and this is where the book reveals both its strengths and its limitations.  

In setting up the work, the author outlines the nature of constraints as helping us understand variability, and this is manifest in his representation of the many numbering systems that have been discovered as falling into five types. This launches comparisons and potential uses for each, which might then help us explain why some systems are more common than others. While a reader might hope there is some cognitive property of a system that is natural for us to prefer and thus to explain dominant types, the story here is that we are less the refiners of a natural representational numeracy than participants in the unfolding of very social dynamics. This is a rich tale, well told by the author, but it leaves tremendous room for interpretation and rationalizations after the fact. In attempting to explain the processes, the author moves into areas of technology adoption which he treats as a form of frequency dependence bias, with people making choices based on a mix of prestige, fashion, and how they see others behaving. It is this treatment that jars slightly, engaging in topics that are well-studied in communications and information but largely overlooking established theoretical models of diffusion and adoption that have been developed over decades to examine such phenomena.  

Obviously, while the history of number systems is emerging, data on the specifics of any system’s adoption and decline is sparse and any explanation likely speculative, but in places the author does seem to over-reach, hazarding guesses as to why both Roman and Western notations are found in early books or suggesting that Sequoyah, the creator of an original number system for the Cherokee language in the mid-nineteenth century, was not likely influenced by exposure to Caddoan languages, which shared a particular structural property. The author acknowledges, to his credit, that in key questions, the evidence offers little surety, but, on occasion, I found the basis for an interpretation or claim to be asserted too easily rather than cautiously inferred. When the story itself is so fascinating, dialing back on the theoretical claims would not have lessened the scholarly import of this work. As the final chapter indicates, there is little chance that the dominant numbering system we currently employ will be the last word (so to speak!), so we can anticipate changes ahead. The empirical record is still being generated. 

Minor quibbles aside, I strongly recommend this book for readers interested in the broad sweep of human history from an information lens and for those who might be curious in the origins of our translinguistic representations of quantity. Over seven chapters, the author covers a tremendous range of issues but constantly reminds us that numbers serve our needs and are, after all, human creations. The general properties of number systems and their role in human existence are fascinating, and Chrisomalis writes in a style that enlivens the topic and provokes the reader to think for themselves how numbers are both fixed and fluid in usage and time. Moreover, in its emphatic telling of a tale that weaves history with linguistics, politics with cognition, and text studies with computation, Reckonings serves as an enlightening example of how the fundamentals of information cannot be understood by a single discipline.

Andrew Dillon, School of Information, The University of Texas at Austin