By the Numbers: Numeracy, Religion, and the Quantitative Transformation of Early Modern England by Jessica Marie Otis successfully presents both a descriptive history of numeracy in early modern England and the cultural impact of the emergence of numbers and calculations on the people and their faith during this era. She describes in the book the “ revolutionary shift in the way people used numbers during the early modern period” (13)
According to her GMU profile, Dr. Jessica Otis is an Associate Professor of History and Associate Director of the Roy Rosenzweig Center for History and New Media. Her background supports her qualifications for this publication. She received an MS in Mathematics and a PhD in History from the University of Virginia, and spent four years at Carnegie Mellon University Libraries as a Postdoctoral Fellow and Digital Humanities Specialist. Her ongoing research focuses on the Death by Numbers project, which seeks to transcribe and publish the Bills of Mortality to investigate how experiences of plague outbreaks connect with mentality among the people of early modern England.
In writing the book, Otis draws from many contemporary sources, including early modern math textbooks, diaries, sermons, pamphlets, and almanacs. To supplement this primary data, her notes and bibliography cite a broad range of current research and historical writing.
The first two chapters do an excellent job of explaining the history and the evolution of the operational use of numbers in early modern England. This includes outlining the three categories of methods for counting and calculation used in the sixteenth and seventeenth centuries. Otis breaks these down into three categories: the performative, object-based, and written symbols. The performative details how words and gestures were employed to allow people to count and calculated independent of physical aids, primarily focused on using 10 as the base associated with finger counting. With the object-based level of numeracy, people took the next conceptual step, relying on tally sticks and counters as tools for arithmetic. These methods began to be replaced in the eighteenth century with written symbols using words and both Roman and Arabic numerals.
As Arabic numerals became more common, Otis challenged historians such as Karl Menninger, who argued that the transition occurred because these symbols made calculation easier. She maintains that men and women initially “adopted Arabic numerals not for calculating but for recording” (44), with the qualification that, because Arabic numerals could be manipulated more easily, Roman numerals and tally sticks continued to be used for sensitive record-keeping. Ultimately, Otis shows that the opportunity to use Arabic numerals for both record-keeping and calculation tipped the scales in favor of this system.
Beyond the operational and adoption history of numeracy, the book shines in explaining the cultural shifts that numbers brought about in early modern England. Starting in chapter three, Otis addresses the cultural implications of the growing use of Arabic numerals for recording and calculation. For example, she notes that historians writing about education in the early modern period generally emphasize “the lack of a universal mathematical education” (80). However, Otis counters this view by arguing that “beginning in the 1580s, petty schools increasingly became a source of education in numeracy, arithmetic, and elementary accounting” (81). This change in the educational system was supported by the proliferation of textbooks and tutors, which hastened the overall adoption of Arabic numerals. She also draws on Mordecai Fingold’s research to support the teaching of mathematics, particularly at the university level. Likewise, the ultimate success of reforming the English calendar came after years of debate to address the “mathematical inconvenience” (114) of the Julian system. Math prevailed over the religious and political objections.
At an even deeper cultural level in chapter 5, Otis explains the practical implications of how faith, gaming, insurance, and tracking the plague affected society. Here, she highlights how By the Numbers produced a “quantitative transformation of early modern England, particularly its relationship with numeracy and religion” (11). She offers particular clarity and insight into how the clergy and Christian theology responded to the question of God’s providence and natural law, as seen in the debate between James Balmford and Thomas Gataker. The traditional view holds that God’s hand directs every event and interaction. However, calculations now showed predictable, quantifiable natural laws. For many, the resolution to this question was that “God employed intermediary forces, including so-called laws of nature. However, God was not in any way limited by these laws. He could, and did, violate them at will and function as a primary cause of earthly events” (120).
One area for future historical exploration of the implications of mathematical quantification for religion may be to assess its role in the emergence of the theology known as deism. This view holds that God created the universe to run according to natural laws but does not intervene in its daily operations, much like a watchmaker who builds a device and allows it to run on its own.
Finally, in chapter six, Otis explores both arithmetic and religion and examines the use of census data. In Old Testament times, King David’s taking a census brought punishment upon the nation of Israel. Once again, in early modern England, there was a potential conflict between numbering and faith. However, in this case, many clergy were able to distinguish the English census from the one in the Bible. As one pastor described it, David’s census was done “out of vain and ambitious ends” (142). In later years, census data went beyond serving fiscal and military purposes and also became a source for governing, known as political arithmetic.
By the Numbers presents an accessible history for both general readers and professional historians. The book offers a helpful perspective on how numeracy developed over time and was used by ordinary people in early modern England. More importantly, it highlights the cultural transformation it brought about in English society. A standout feature is Otis’s clear demonstration that men and women in the early modern period “developed a numerical worldview that existed within a framework defined by Christianity” (157). From much of our reading, including works by James Clark, Mark Stoyle, Lucy Mauffat Kaufman, Ian Gentles, and Andrea McKenzie, we see the central role that Christianity played in the day-to-day thoughts and actions of the people of this time. It makes sense, then, that the use and understanding of numbers and arithmetic would touch on people’s faith, bringing both challenges and opportunities. In her book, Otis captures and sensitively explores this transformation.