England was a late starter in the empire-building project. By the late 16C Spain and Portugal had claimed much of South and Central America, and the French and Spanish were expanding their interests in North America. Queen Elizabeth encouraged exploration, elevating a young member of the landed gentry, Walter Ralegh, and awarding him exclusive patents for trade and exploration. With the wealth from his monopolies Sir Walter Ralegh funded three expeditions to North America. Ralegh had met a young Oxford graduate, Thomas Harriot, who was unusually talented in the skills essential for navigation in the 16C: mathematics and astronomy. Ralegh needed a navigational expert, and Herriot needed a patron. In addition to his navigational expertise, Harriot was also a teacher, linguist, and ethnographer. Eventually, Ralegh and Harriot became lifelong friends and associates.
Much is known about Ralegh, but Harriot is almost unknown. He did original research in mathematics, physics, astronomy, and linguistics. He was, arguably, the first European diplomat and linguist to a North American tribe. He left thousands of pages of manuscripts, but very little has been published. The only biography of Harriot was published more than 70 years ago. Recently his papers have been digitized and scholarly interest is increasing with recent monographs on Harriot’s work.
In 2019 the Oxford Press published Thomas Harriot: A Life in Science. The author, Robyn Arianrhod, has written what she describes as a popular treatment of Harriot’s life and work. Much of the book is, indeed, written for a popular audience, but Arianrhod is a mathematician and her treatment of the problems Harriot studied assumes her readers will have a working knowledge of high school algebra, geometry, trigonometry, and combinatorial mathematics. Extensive exhibits and graphs are provided. Arianrhod provides some background on Elizabethan and Jacobean England, so her book would be of interest to students of early modern England and England’s early colonial activities. The main audience, though, will be geographers and historians of science, mathematics, and navigation.
Harriot’s contributions are presented chronologically, so we begin with his work on navigation: refining navigational charts, improving instruments, and teaching Ralegh’s captains and navigators. He taught basic astronomy and how to use instruments and charts. A constant theme of Harriot’s life is his constant drive to improve accuracy and simplify. In the navigational context this means teaching consistent measurement practices, introducing easier to use and more accurate instruments, and ensuring that navigational tables are accurate. Arianrhod describes the navigational problems of the late 16C and shows how Harriot’s efforts over time improved accuracy.
Next, Arianrhod relates the expedition to establish a colony on Roanoke Island and Harriot’s activities in America. Harriot is the main interpreter. He learns the Algonquin language and teaches the Americans English. He records the culture of the tribe. Upon his return to England he writes up his observations and publishes them. The remainder of the book describes Harriot’s work to improve navigation and his own research into problems of mathematics and physics. As Harriot’s contributions accumulate and he is assured of continuing financial support more of his time is spent on more theoretical work. But he is always involved in helping his patrons with their practical problems, whether they involved navigation or plumbing.
One of the practical problems that Harriot worked on led to a theoretical problem that occupied him for years. The maps made by Mercator were a great boon to early navigators. They represented the earth’s spherical shape on a plane in such a way that it simplified practical navigation. But Mercator didn’t reveal how he made his maps. When Harriot finally understood the problem he was able to make his own maps faster and more accurately and to refine his navigational tables. Eventually Harriot’s improvements allowed a trained navigator to estimate their latitude to within a mile, a significant improvement in accuracy. He also worked on a construction project for his patron that required him to estimate water forces, flow rates and pressures, and specify pipe sizes. He was a general purpose analyst.
Harriot’s technique in solving problems was consistent: he tried to abstract away as many extraneous details as possible, collect data, and then try to develop a simple formulation of a more general problem. To collect data he would sometimes calculate hundreds of numbers in an effort to see patterns that he could use to imagine or infer a general solution.
As Harriot became more established he hired an assistant and spent more time on his own studies. Arianrhod describes these studies within the larger context of Jacobean political and religious intrigue. Under Elizabeth Harriot’s patrons were favored; under James they were persecuted. Harriot’s patronage and research continued throughout James’s reign, but with considerably more drama. Against this more stressful backdrop, Harriot does significant original work in optics (index of refraction, rainbows), spherical geometry, symbolic algebra, combinatorial mathematics, binomial theorem and applications, sums of infinite series, gravitation and motion, and much more. None of it was published in his lifetime and little of it was known to any except a few close friends. Arianrhod describes the nature of each problem that Harriot works on, provides a brief summary of the history of work on the problem, describes Harriot’s attempts to solve the problem, translates his results into contemporary concepts and notation, and describes subsequent developments. It’s an effective way to understand Harriot’s contributions.
Arianrhod devotes roughly equal attention to Harriot’s work and the social and political environment of England from roughly 1580 to 1620. Since little of Harriot’s research was known to his contemporaries it seems probable that he had little, if any, influence on the course of scientific development. His improvements to navigational practice were also unpublished, but copies of his more accurate charts and instruments, together with his trained navigators, probably helped improve navigational practices generally. His work shows that many of the problems he worked on were susceptible to existing or improved conceptual and analytical tools at least a generation before his more famous successors began publishing their results. Arianrhod shows how Harriot worked and gives examples from his notes. For those interested in how the process of scientific and technological discovery works, her examples will be instructive, and the social & historical context may provide useful context. For those interested in the social and cultural history of early modern England the contextual material will allow them to place this intellectual activity in its broader context.
