Robyn Arianrhod is an Australian historian of science. She was trained in mathematics at Monash University in Melbourne, Victoria, and remains an adjunct researcher there. Her most notable prior work, Einstein’s Heroes: Imagining the World through the Language of Mathematics (2005), focused on James Clerk Maxwell’s derivation of the laws of electromagnetism, and the concept of mathematics as the language of modern physics. The full extent of her powers of conceptual explication in mathematics, as well as her ability to convey the process and sensation of “discovering new math” to a lay audience, are on full display in Thomas Harriot: A Life in Science.
Arianrhod’s prologue frames her story as an archaeological dig in the British Library, where she undertakes the monumental task of organizing and reverse-engineering Harriot’s papers, attempting to gain insight into his creative process. In chapters one and two, she relates Harriot’s common birth, his attendance at Oxford via the surprisingly modern practice of need-based tuition, and his initial encounters with and patronage by Sir Walter Raleigh, against the backdrop of the Elizabethan Golden Age, the competition for naval power between the existing superpower Spain and the rising power of Britain, and the British desire to gain a colonial foothold in a New World thereto monopolized by Spain and Portugal. This motivates her discussion in chapters three and four of the practicalities of ocean navigation in the age of sail, and Harriot’s employment as Raleigh’s expert tutor in navigational techniques. In these chapters, she describes the development and transmission of millennia of astronomical knowledge underpinning the science of navigation, and their state of synthesis at the end of the 16th century. This magisterial technique, deployed time and again in the book, establishes the intellectual foundations upon which Harriot stood, and enables the reader to attempt an understanding of the practical problems Harriot needed to solve in the context of the knowledge that was available to him at the time — including logical, repeatable procedures amenable to reliable execution by non-experts.
Chapters five through eight chronicle the ill-fated Roanoke expedition and colony, while establishing Harriot’s status as a bona fide polymath capable of learning and documenting the Algonquin language and culture. In chapters nine and ten, she relates the defeat of the Spanish Armada, Raleigh’s shifting fortunes, the development of Harriot’s relationship with Northumberland, and, in a particularly compelling section, an illustration of Harriot’s interest in probability theory, likely spurred by Northumberland’s gambling habits. This vignette is an example of Arianrhod’s technique of motivating a theoretical tangent with a mundane scenario — providing insight into Harriot’s talent for abstraction and generalization.
In chapter eleven, Harriot and his patron Raleigh endure accusations of atheism, and Harriot survives Raleigh’s self-inflicted fall from grace at court via Northumberland’s gift of a life endowment, moving his residence from Raleigh’s estate in Devon to Northumberland’s, closer to London at Syon. In chapter twelve, Harriot painstakingly derives the law of refraction via experiment (1602), establishing his precedence over Snell (1621) by almost twenty years, and in chapter thirteen, he wrestles with the problem of projecting three-dimensional curves onto two-dimensional surfaces while measuring their length — of obvious import for the utility of flat maps in a time when globes were expensive and rare.
Chapter fourteen sees Raleigh’s fall from grace nearly complete, as the transition of power to James I in the wake of Elizabeth’s death leaves Raleigh imprisoned in the Tower of London for life. Chapter fifteen relates Harriot’s development of efficient algebraic notation and his brush with accusations of treason, as he is briefly detained in the wake of Guy Fawkes’ Gunpowder Plot, having done nothing more than attended a dinner party which happened to host one of the conspirators. After having been released, Harriot’s work on the physics of rainbows is repeatedly distracted and derailed by the continued capricious detention of Northumberland. This story illustrates the extreme precarity of court status and position during this tumultuous period in English history, and the resulting insecurity it generated for those of lesser status whose fortunes ebbed and flowed with their patron.
Chapter seventeen is a fascinating interlude detailing Harriot’s correspondence with Kepler, Kepler’s knowledge of Harriot’s domestic troubles, and their mutual frustration with their inability to theorize without fear of retribution. Of note, the role of the merchant Jan Erikson in shuttling letters between Kepler and Harriot illustrates the criticality of of early modern businessmen, transacting with wealthy patrons, in transmitting knowledge between scholars across Europe — especially prior to the development of reliable national postal services and a fully-fledged so-called “Republic of Letters”. Chapter 18 continues this dialogue concerning early notions of atomic theory, arising from Harriott and Kepler’s quest to understand why refraction occurs. While Kepler rejected the notion of atoms because he refused to acknowledge the concept of a pure vacuum, Harriot at points appeared to emphasize the role of empty space between particles of matter, between which light would “slip through”. While he did not fully grasp the profound truth just out of reach, his conception of empty space as playing a key role predated Ernest Rutherford’s discovery that atoms (and thus matter) are composed mainly of nothing — by nearly three centuries.
Arianrhod’s final chapters detail Harriot’s telescopic observations and theorizations on ballistic curves, roughly contemporaneous with Galileo’s work on similar problems. Again her strengths are clear — explaining the errors in reasoning committed by Harriot and Galileo, while making it clear that Newton could not have derived the concept of inertia without the half-correct notions hammered out by Galileo. She closes the book with an account of Raleigh’s ultimate fate on the scaffold and Harriot’s death from cancer at the hands of the pipe-smoking habit he’d acquired among the Algonquin. Her epilogue reads like a detective story, chronicling Harriot’s fall into obscurity, and in one particularly riveting sequence, historian Johannes Lohne’s chance encounter with a book owned by Harriot and containing Harriot’s marginalia, which spurred further investigation by Lohne and the modern era of Harriot scholarship.
Arianrhod’s dual themes are the case for Harriot’s sheer intellectual prowess, as well as an apologia of sorts for his failures to publish his work with sufficient frequency. After all, life in the shadow of the Elizabethan court was a stressful affair. The tragedy of Harriot’s life and obscurity throws the modern imperative for publication into stark relief — publish or perish, yes — but worse yet, publish or be guaranteed oblivion to posterity. This reader found only one major fault with Arianrhod’s work. Her endnotes contain exhaustively created and compiled diagrams illustrating the key mathematical concepts, and her mathematical prose would have been far easier to digest had it been interlaced with these diagrams. In their current position at the end of the book, they have far less impact than they otherwise could have had, and give the reader no respite from a textual onslaught of facts and logic that made her book a challenging slog at times, albeit a rewarding one.
