Reckonings: Numerals, Cognition, and History by Stephen Chrisomalis (review)

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 up front 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 worldview 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 and 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 pages in the foreword 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 are 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 that he treats as a form of frequency dependence bias, with people making...