"Into the Mathematical Ocean": Navigation, Education, and the Expansion of Numeracy in Early Modern England and the Atlantic World (2015)
My dissertation follows two central lines of inquiry: first, why and when did the learning of mathematics increase in early modern England? Second, what were the economic and religious reactions to the spread of these new ideas and habits? I show that the largest growth in mathematical learning and study centered on elementary mathematics, especially spherical geometry and trigonometry, areas constitutive of technical navigation. I argue that the dramatic increase of naval and maritime commercial activity served as the chief impetus for the expansion of mathematical learning in the Atlantic world. Instruction in navigation, astronomy, and mathematical calculations became increasingly important in the 14th- 19th centuries with (a) the shift from coastal shipping, concentrated in the Mediterranean, to long-distance trade across the Atlantic and Indian oceans, and (b) the concurrent growth of the British Navy. I compare the impact of overseas trade not only between early modern England and the rest of Europe, but with that of the Ottoman Empire as well to show its decisive significance, not only economically but also intellectually and politically, for the growth of Atlantic trade. My research also demonstrates that the growth in the teaching of mathematics, which is widely assumed to have been fostered by institutions (especially the schools or the state), was in fact originally nurtured in informal and unstructured settings. Following this, I discuss the intertwined effects of the growth of mathematics on the economic and religious spheres. For centuries, religion was for many the primary guide to the natural world. In the course of the seventeenth- and eighteenth-centuries, however, people began to turn to natural philosophy to understand the natural world and so religion became more focused on ethics and morality as its special province. Furthermore, the ways in which these ethical and moral arguments were phrased began take on the model of mathematics. Morality had come to be widely viewed as something one could ideally present in an inarguable mathematical form. Examples include the work of Baruch Spinoza, Thomas Hobbes, Samuel Clarke, Gottfried Wilhelm Leibniz, Christian Wolff, and Francis Hutcheson, among others. Hutcheson, for instance, famously tried to demonstrate "The Manner of computing the Morality of Actions," in his I nquiry into Beauty and Virtue. I argue that the early Enlightenment introduction of quantificatory calculation to morality, what I term the "moral arithmetic," itself contributed to the rise of rationalistic, utilitarian, Benthamite thought. The "application of mathematics to the moral sciences," in the words of the pioneering economist Francis Edgeworth, was part of a larger attempt to rationally cement a new basis for morality, and helped lay the groundwork for modern economic analyses of human behavior.
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