Otis 2024
Otis, Jessica Marie. By the Numbers: Numeracy, Religion, and the Quantitative Transformation of Early Modern England. Oxford: Oxford UP, 2024.
Introduction—“Number, Weight and Measure”: Numeracy in Early Modern England
This transformation in numerical practices was complex and wide-ranging in its impact on early modern society and thought. In part, it was a transfor- mation in symbolic systems—the culturally agreed upon symbols and syntax used to represent numbers. It was also a transformation in mathematical education, enabled by increasing literacy rates and the printing revolution. Most important, it was a transformation in technologies of knowledge, spe- cifically the way the people of early modern England conceived of and used numbers in th…
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This book demonstrates that the early modern period was a time of transition that fundamentally reoriented English ways of knowing about the world to rely increasingly on numbers.
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27Crucially, despite the common i termediary role played by words, the human understanding of quantity is abstract and largely independent of language.
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…early modern English nu- meracy can be provisionally defined as knowledge of a symbolic system for representing and manipulating numbers that is distinct from the English number words. While historically sensitive, this definition lumps together a wide variety of symbolic systems and obscures the differences between them. It is therefore useful to additionally treat each symbolic system as its own type of numeracy—e.g., hand gesture numeracy, tally stick numeracy, etc.—and to recognize the existence of early modern English numeracies, plural, within the overarching formula of early modern English numeracy, singul…
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Over the course of the early modern period, English men and women adopted Arabic numerals in a context-specific fashion, com- monly employing them side by side and interchangeably with other symbolic systems.
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During the late sixteenth and seventeenth centuries, many English account-keepers began to replace their existing object-based and literate arithmetical practices with new practices based on Arabic numerals.
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…they looked at the permanence of a system’s symbols when choosing a system for recording, and they developed strategies to in- crease symbols’ resistance to after-the-fact alterations. At the same time, they looked for the opposing characteristic of manipulability when choosing a system that would facilitate calculatio…
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remained conceptually distinct, people could employ different systems for each function, choosing the optimal system for the task at hand.
12 1. “The Dyuers Wittes of Man”: The Multiplicity and Materiality of Numbers
The main symbolic systems employed during the sixteenth and seven- teenth centuries can be roughly divided into three categories based on their most prominent material characteristics: performative, object-based, and written. Performative systems did not require the assistance of external phys- ical objects and could be employed under any circumstances. Object-based systems involved the alteration or manipulation of physical objects, which were invested with numerical meaning that persisted across…
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Written systems also involved the assistance of physical objects—commonly pen, ink, and paper. However, these objects were only a means to create and convey numerical symbols, not symbols themselves; the same symbols could be drawn on wax tablets or dust boards, engraved into wood and stone, or embroidered ont…
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The overwhelming majority of historical symbolic systems are base 10, and finger counting is the likely ultimate origin of this similarity. However, lan- guage is an important intermediary factor; in all known cases of independ- ently invented symbolic systems for numbers, the system has the same base as the number words in the culture’s nativ…