 Hi, I'm Peter Adamson and you're listening to the History of Philosophy podcast, brought to you with the support of the Philosophy department at King's College London and the LMU in Munich, online at historyofphilosophy.net. Today's episode, Nature's Mystery, Science in Renaissance England. Once that movie about John Dee has been made and swept the awards season, there will be public demand for a sequel. I suggest that the next movie should not be about Thomas Harriot. Not that his life was uneventful. He went to Virginia as a scientific advisor in the retinue of Walter Raleigh, becoming one of the first Europeans to learn a Native American language, Algonquian, and also one of the first to get cancer from enjoying tobacco. He was also arrested after another patron, Henry Percy, the Earl of Northumberland, was falsely suspected of being involved in the gunpowder plot to assassinate King James. There would be plenty of scientific achievements to present in the movie too. Harriot didn't just learn Algonquian, he devised a phonetic alphabet for recording it. He invented a groundbreaking system of mathematical notation, discovered the sign law of refraction, and made pioneering advances in the study of falling bodies and specific gravity. Harriot was also among the first to draw maps of the lunar surface and to see sunspots through a telescope. He beat Kepler to the realization that planets do not orbit in perfect circles. He was, in short, something of a one-man scientific revolution. The problem is just that such a movie project would shower on Harriot, the one thing he seemed most determined to avoid, publicity. Having made so many incredible discoveries, the sort of breakthroughs that would shortly be putting the light into enlightenment and transforming European history forever, he discussed them with a few close associates, wrote them down in manuscripts, put these in a drawer, and left it at that. His friend, William Lower, chided him for letting others claim credit for discoveries he had made earlier, including, according to Lower, the non-circular paths of the planets. This has ensured that his name is not a household one, at least not in my household. Before I came across him as the author of a report on the colony established at Virginia, I had never heard of him. Specialists on the history of science know better. They have been equally amazed by his prodigious mind and his failure to share its fruits with the world, and have discussed both at length. His decision not to publish has been given several explanations. Enjoying patronage as he did, he had no need to attract attention by making splashy announcements about his latest findings, and he had good reason to avoid notoriety as a target of rumors of atheism and then as collateral damage when his patron, Northumberland, was accused of conspiracy. But my favorite explanation is that it would simply have been very difficult to print his writings. They were full of diagrams and page after page of algebraic notations, more like a modern math textbook than the works of scientific prose produced by humanists only a few decades before. Indeed, we can better appreciate the achievements of Harriot and his peers at the end of the 16th century if we look back to the way science was conducted by English humanists a few decades earlier. Let's begin with a quote from Europe's most famous scholar of the early 16th century, Erasmus. In a passage I've mentioned before, one that praises Jean Colette and Thomas More, Erasmus poses the rhetorical question, what can be more acute, profound, and delicate than the judgment of Lenacre? The man being praised here was Thomas Lenacre. His major scientific contribution was to translate several works of Galen, including the philosophically significant On Temperaments and On the Natural Faculties. Lenacre was also a practicing doctor, but the editors of a collection of essays on him say in their introduction, nothing appears here on the subject of Lenacre's medical practice because nothing is known about it which would distinguish it from that of his contemporaries. So it is for his humanist philology that he is remembered today. Lenacre came by his expertise in ancient languages in the way customary for Englishmen of the time, he went to Italy. Having already begun to learn Greek at Oxford, he spent more than a decade in the cities of Florence, Rome, Padua, and Venice, and studied with the outstanding classicist Poliziano and the Byzantine emigre Demetrios Chalcocondylas. At Padua he attained a medical degree, at Venice he collaborated with the important book printer Aldus Manusius. After returning to England, he gave gifts to set up lectureships in medicine at Oxford and also served as the first president of the College of Physicians, which introduced much needed education and regulation in the field. A decade after Lenacre's death in 1524, Thomas Eliot, familiar to us as the author of the humanist political treatise Book of the Governor, published an accessible presentation of Greek medical theories called The Castle of Health. Eliot had learned about the topic from Lenacre himself and duly presented a thoroughly Galenic picture of health, its restoration, and maintenance, for example by suggesting appropriate diets for men and women of different humoral temperaments, none of which is to be sneezed at, unlike the cold you might catch if you don't eat warming foods to offset the phlegmatic mixture of your body. These humanists were making great strides in disseminating the scientific tradition of antiquity through translations, guides aimed at a popular audience, and the establishment of institutions for scientific study. But none of this looks much like the science of the 17th century, whereas Harriet's unpublished writings very much do. How can we explain this change? If I had to give a one-word answer, it would be mathematics. And if I had to give a two-word answer, it would be applied mathematics. Back in episode 361, I discussed how scholars of the Italian Renaissance lavished attention on the text of ancient mathematicians like Archimedes, Euclid, and Ptolemy, and then went on to explore concrete topics like the paths of falling bodies, timekeeping, and what we would now call a body's center of gravity. Things unfolded similarly in England, where Roger Ashen warned against the corrupting effect of focusing on pure mathematical sciences, as they sharpened men's wits over much, so they changed men's manners over sore, if they be not moderately mingled and wisely applied to some good use of life. For both pure and applied mathematics, English scholars took direct inspiration from their continental counterparts. The findings of Italian mathematicians like Regiomontanus, Niccolò Tartaglia, and Galileo were known to English scholars, and Harriet's work on algebra was based directly on the writings of the French mathematician Francois Viette. Harriet's way of symbolizing mathematical phenomena was strongly influenced by Viette, who also used letters for variables and was able to express geometrical shapes in algebraic terms. It's a long-standing cliché of historiography about early modern science that it developed outside the universities, which were still in the thrall of literally antiquated Aristotelian ideas. And I do mean long-standing. One contemporary praised the Elizabethan astronomer John Blaigrave for seeking knowledge outside the universities, commenting that, "...scholars have the books and practitioners the learning." That idea might seem to be supported by this story as I've been telling it, insofar as the mathematical exploration of nature grew out of humanism, not scholasticism. Harriet's enviable position as an independent researcher supported by Walter Raleigh and Henry Percy also fits with that narrative. Percy was dubbed the Wizard Earl for his intellectual proclivities and praised in a poem that contrasted the research he was sponsoring to the schoolmen's vulgar trodden paths. But as so often this neat story is only half true. Mathematics was a well-established subject at the universities of Oxford and Cambridge. We can see this from, for example, a document written by John Everard in 1598 detailing what he had to study at Cambridge. Yes, plenty of Aristotelian philosophy, with interpreters of both ancient and recent vintage literally running the gamut from A to Z, since Everard consulted commentaries ranging from Alexander of Aphrodisias to Zabarella. But also lectures on mathematics, which were held daily. The students could take instruction from such outstanding scholars as Henry Saville, who lectured on Ptolemy's astronomical work, the Almagest, enriching his presentation with information from up-to-date authors like Copernicus. He also taught optics, mechanics, trigonometry, and the history of ancient mathematics, for which he drew on Peter Rameis. To this day, there is a professorship of astronomy at Oxford named after Saville. It seems that practically every intellectual of the period was connected to the circle around Philip Sidney, and Saville was no exception. Sidney even supplied him with letters of introduction for a trip around Europe in 1581. Nonetheless, it has to be admitted that university teaching of the quadrivium, the traditional mathematical arts, was not at its best in the Elizabethan period. True, these lectures existed, and attendance was a requirement. Fines were levied on students who failed to turn up. But all too often, this meant that reluctant students were being bored to death by lecturers who also wished they were somewhere else. A number of them even petitioned to be excused from the chore. The aforementioned Henry Saville acknowledged all this in his own lectures, ranting about lazy students, that that went over well, and stating that he at least was glad to be there and to restore dignity to the mathematical lectures. Saville also pointed out the limits of a narrowly humanist approach to scientific texts. These disciplines call for more than expertise in ancient languages, they demand a philosophical mind. On balance then, it seems fair to conclude that the universities made some contribution to scientific and mathematical knowledge in this period without being the scene of the greatest breakthroughs. We can see this from the careers of John Dee and Thomas Harriot. Dee was educated at Cambridge, Harriot at Oxford, but Dee set up an independent facility at Morton Lake, while Harriot needed no institutional setting beyond the patronage he received from Raleigh and Percy. Nor was Harriot the only scholar associated with Percy. Modern historians speak of a whole Northumberland circle gathered around him, which besides Harriot included Walter Warner, Nathaniel Torperly, Robert Hughes, and Nicholas Hill. Percy's enthusiasm for the sciences continued undimmed even after he was imprisoned in the Tower of London in the wake of the gunpowder plot. He even kept scientific instruments in his rooms there. Instrumentation was crucial to Harriot's approach, since it allowed for mathematically precise observation of nature, which is really, to use an apt term, the constant that runs through all his most significant work. His combination of empiricism with calculation is already on show during his involvement with Raleigh's colonial project. For Raleigh's sea captains, Harriot wrote up easy-to-follow instructions for the use of navigational instruments. Underscoring that this was all a matter of applied mathematics, Richard Hachtluth praised Raleigh for engaging Harriot to show how to unite theory with practice. The same habits of mind guided Harriot in his dealings with the Native Americans that the group met in Virginia. He befriended some of them and showed a talent for linguistics. During his lifetime, Harriot's only published work was his propagandistic account of this journey, The Brief and True Report of Virginia, which came out in 1590. But the evidence of his manuscripts is more extraordinary. Here we find him inventing a new alphabet that could be used to write down Algonquian language. He also wrote other things down in this alphabet, meaning that it doubles as a kind of private code. This is recognizably the same man who made advances in algebraic notation and used meticulous measurement as his chief scientific method. Canons of science are not, as a rule, effusive, so we can take it as a lavish compliment when one of them says of Harriot's work in mathematics, In some of this he is startlingly original, in other parts good, and in the rest mostly pretty competent. Though he did do work in pure mathematics, our purposes and my ability to understand what is going on are better matched to his research on areas like projectile motion and specific gravity. The study of projectiles was of military significance because cannons were now a common weapon of war. Dee's protégé, Thomas Digges and his father, Leonard Digges, all applied geometrical analysis to understand the path described by a cannonball. Despite their interesting real-world applications, they were obliged to ignore many factors like wind resistance and the variable strength of the gunpowder. They were asking the more basic question of how the angle of the cannon's elevation affects the distance of the shot. Some had assumed that the cannonball moves straight for a while and is then captured by what we would now call gravity and pulled back to Earth. Harriot realized that instead, the cannonball's path is for its entire flight, the result of combining two other idealized motions. First, along a straight line, as fired from the cannon, and second, the free fall of the cannonball. Following his logic, he argued that the real trajectory would be a smooth but asymmetrical curve. Harriot's inquiries into falling bodies involved experiments in the sense that he set up and carefully measured real-world scenarios, rather than just sketching diagrams from his imagination. His neighbors were no doubt glad that these involved not cannons, but the quieter method of dropping metal bullets onto a set of scales. The idea was to see how far the bullet would have to fall before its velocity was sufficient to tip the scales for a certain counterweight. Similarly, he performed extensive observations to calculate the specific gravity of various substances like marble, diamond, crystal, and glass. Here he did not need to invent a new mathematical model for what was going on, but just to use the formula ascribed to Archimedes, you weigh a sample in air and water, and divide the weight in air by the difference between the two weights. Why you might ask, would it be useful to get exact values for the specific gravity of different materials? There are lots of applications, but if you worked at the King's treasury, the one that would interest you the most is that since different metals have different specific gravities, you can use this number to test the purity of a precious metal, like gold or silver. It's almost irresistible to compare and contrast Harriot's investigations to the work being done by Galileo at the same time. Galileo was also interested in the problem of falling bodies, and like him, Harriot was a convinced Copernican and early adopter of the telescope. Indeed there's a book about Harriot that calls him the English Galileo, but there's room for skepticism here. One obvious difference is that whereas Harriot left his ideas buried in manuscripts, Galileo was a genius of self-promotion who sought and achieved notoriety across Europe. That may indirectly confirm the hypothesis that Harriot's comfortable position was a factor in his choice not to publish. Since Galileo's situation was more precarious, he needed to convince an elite audience that he deserved the sort of support Harriot was already receiving. But more significant for us is a philosophical difference. Galileo was a true natural philosopher who made claims about the nature of the world, the kind of claims that could get him in trouble with the Pope. Harriot by contrast was largely content to make his observations and represent what he had seen using algebra and geometry. Perhaps Harriot thought that the mathematical model of the natural phenomenon is just that, a model, and that as a mathematician it was outside his sphere of competence to offer physical theories. This as you might recall would be the same line of thought Oseander used to diffuse the explosive implications of Copernicus. If that sort of methodological restraint was a general feature of Harriot's thought, then there was an important exception. He seems to have assumed that the bodies he was experimenting with are made of atoms. This would have been the theory underlying Harriot's work on specific gravities. It would also help to explain his interest in the geometrical question of how to pack together spherical bodies with the least space in between. But other members of the Northumberland circle, Walter Warner and Nicholas Hill, were much more forthright in their embrace of atomism. Hill wrote a book with the telling title Epicurean Philosophy which endorsed the idea that bodies are ultimately made of impenetrable and indivisible prime corpuscles whose different shapes allow them to entangle with one another, for instance with loops and hooks that become joined. As for Warner, he put forward a remarkable theory according to which atomic bodies influence one another through an all-purpose force that he called, well, force, in Latin vis. This force fills the otherwise empty space around atoms. It is responsible for all causal interaction and observable properties in bodies made from atoms, including color, hardness and softness, motion, and even weight. With this, Warner was anticipating something we more readily associate with early modern philosophers like John Locke, a contrast between the primary physical qualities of corpuscles and secondary qualities like color. Now, I don't want to deny that the Northumberland circle was anticipating early modern corpuscular theory or the mathematical analysis of nature. But as ever, we should remember that thinkers who may seem to us ahead of their time were also of their time. We saw in episode 398 that contemporaries on the continent like Schenck, Torelles, Gorleas, and Sennert were also experimenting with atomic theories. As for the use of mathematics to describe physical situations, that goes back to the Oxford calculators of the 14th century, and it's something we've seen in other authors. A particularly instructive parallel would be with John Dee, who incidentally knew Harriot, probably through their mutual friend Walter Raleigh. Though Dee is known to posterity mostly as a magician and Harriot mostly managed to avoid being known to posterity at all, they were both mathematicians who drew connections between math and other disciplines, especially alchemy and optics. Harriot, like Dee, performed alchemical experiments, and the atomic theory was a natural fit with alchemical thinking. After all, if everything is made of atoms, it should be possible to break down one substance and turn it into another by combining the atomic parts differently. The connections to optics may be even more important. The behavior of light, as with reflections from mirrors or the lengths of shadows, lends itself to being represented in geometrical diagrams. So it's natural that treatises on vision and light had always been written by mathematically inclined authors, starting in antiquity with Euclid and Ptolemy. They influenced medieval theorists of light like O'Kinde and Robert Grossnest, who, as I said last time, were in turn sources for John Dee's theory of rays. Walter Warner was also thinking of them when he devised his theory of the force that is propagated by atoms. The force emanates from the atom as light does from a light source. Harriot was very interested in optics. He wrote about such phenomena as the rainbow and, above all, the problem of refraction. It was in this context that he gave the clearest indication that he too was an atomist. For once, he did not confine his thoughts on this matter to private manuscripts. He didn't do anything so crass as to publish a book about it, of course, but he did put pen to paper to correspond with another scientist who was keenly interested in the behavior of light, none other than Johannes Kepler. So we can look ahead to the reflections of both men and a broader spectrum of thinkers on theories of light and vision, which I'll be illuminating next time here on the history of philosophy without any gaps.