This volume assembles ten studies of the life and work of Thomas Harriot (1560-1621). These are based on lectures that have been given annually at Oriel College, Oxford since 1990, by such authorities as Hugh Trevor Roper, David Quinn and John D. North. The contributions to Thomas Harriot. An Elizabethan man of science shed new light on all the main aspects of Harriot's life and stand as an important contribution to the re-evaluation of one of the most (...) gifted and intriguing figures in early modern British science. (shrink)

The contemplation of the end of life — life's ending — provokes the emotions of fear, alarm and despondency. Fears about the end of life are almost universal. The Stoic Zeno of Elea first analyzed the problem accurately when he pointed out what he thought the fundamental problems of human existence consisted of. He identified the fundamental anxieties as being fear of the gods and a fear of death. Both fears, he thought, could be therapeutically eliminated: fear of the gods (...) was pointless since they did not care about us, and fear of death could be rationalized away by reasonable philosophical argumentation. Without wishing to resurrect Zeno's arguments, one can safely say that he was spectacularly wrong in his view of the power of rational argument. The fears about life's ending are multifaceted. They consist of fears about the process of aging, the prospect of one's own dying and one's own death, and the fact that our lives and activities — as they are lived within the confines of our corporeal bodies — will come to an inevitable end.There are also problems and anxieties concerned with the fact that the passage of time and the visible effects it leaves on our physical selves make us conscious that, at some time or other, we are, like other material objects, subject to decay and wearing down. The process is a great equalizer and no one who lives long enough is spared the spectacle of witnessing and experiencing the gradual process of the decline of their physical powers and of their cognitive functions. No matter what sort of life has been led, the ending of that particular life is certain.In this paper I want to discuss some views about the nature of these fears about the later stages of life, aging, old age and death and their roots in the philosophical and metaphysical views we have come to endorse. (shrink)

Thomas Harriot was the finest English mathematician before Isaac Newton, but his work on the coinage of his country is almost unknown, unlike Newton’s. In the early 1600s Harriot studied several aspects of the gold and silver coins of his time. He investigated the ratio between the values of gold and silver, using data derived from the official weights of the coins; he used hydrostatic weighing to determine the composition of the coins; and he studied the methods used (...) to calculate how metals should be combined in order to produce the required standard of purity. This work required not only arithmetical skill, but also great insight into the relationships between the various quantities, and here his ‘greate invention of algebra’ played its part. The gold and silver coins were critically important in the national economy at that time, because they had intrinsic value and represented the country’s store of wealth. In his lifetime Harriot was supported by the patronage of Henry Percy, the Earl of Northumberland, who was a member of the Privy Council in 1604 when great changes to the English coinage were being made. After Harriot’s death his papers remained under the control of one of his executors, Sir Thomas Aylesbury, who became Master of the Tower Mint in 1635. These facts suggest that his work on the coins was considered to be important for practical reasons, not just academic ones. In this article the interplay between the scholarly work and its application to matters of national significance will be analysed in depth. The conclusions also throw some light on the long-standing mystery surrounding the fate of Harriot’s papers. (shrink)

Some time in the late 1590s, the Welsh amateur mathematician John Bulkeley wrote to Thomas Harriot asking his opinion about the properties of a truly gargantuan (but totally imaginary) plano-spherical convex lens, 48 feet in diameter. While Bulkeley’s original letter is lost, Harriot devoted several pages to the optical properties of “Mr Bulkeley his Glasse” in his optical papers (now in British Library MS Add. 6789), paying particular attention to the place of its burning point. Harriot’s calculational (...) methods in these papers are almost unique in Harriot’s optical remains, in that he uses both the sine law of refraction and interpolation from Witelo’s refraction tables in order to analyze the passage of light through the glass. For this and other reasons, it is very likely that Harriot wrote his papers on Bulkeley’s glass very shortly after his discovery of the law and while still working closely with Witelo’s great Optics; the papers represent, perhaps, his very first application of the law. His and Bulkeley’s interest in this giant glass conform to a long English tradition of curiosity about the optical and burning properties of large glasses, which grew more intense in late sixteenth-century England. In particular, Thomas Digges’s bold and widely known assertions about his father’s glasses that could see things several miles distant and could burn objects a half-mile or further away may have attracted Harriot and Bulkeley’s skeptical attention; for Harriot’s analysis of the burning distance and the intensity of Bulkeley’s fantastic lens, it shows that Digges’s claims could never have been true about any real lens (and this, I propose, was what Bulkeley had asked about in his original letter to Harriot). There was also a deeper, mathematical relevance to the problem that may have caught Harriot’s attention. His most recent source on refraction—Giambattista della Porta’s De refractione of 1593—identified a mathematical flaw in Witelo’s cursory suggestion about the optics of a lens (the only place that lenses appear, however fleetingly, in the writings of the thirteenth-century Perspectivist authors). In his early notes on optics, in a copy of Witelo’s optics, Harriot highlighted Witelo’s remarks on the lens and della Porta’s criticism (which he found unsatisfactory). The most significant problem with Witelo’s theorem would disappear as the radius of curvature of the lens approached infinity. Bulkeley’s gigantic glass, then, may have provided Harriot an opportunity to test out Witelo’s claims about a plano-spherical glass, at a time when he was still intensely concerned with the problems and methods of the Perspectivist school. (shrink)

From the early eighteenth century onward, primacy for the invention of binary numeration and arithmetic was almost universally credited to the German polymath Gottfried Wilhelm Leibniz (1646–1716). Then, in 1922, Frank Vigor Morley (1899–1980) noted that an unpublished manuscript of the English mathematician, astronomer, and alchemist Thomas Harriot (1560–1621) contained the numbers 1 to 8 in binary. Morley’s only comment was that this foray into binary was “certainly prior to the usual dates given for binary numeration”. Almost thirty years (...) later, John William Shirley (1908–1988) published reproductions of two of Harriot’s undated manuscript pages, which, he claimed, showed that Harriot had invented binary numeration “nearly a century before Leibniz’s time”. But while Shirley correctly asserted that Harriot had invented binary numeration, he made no attempt to explain how or when Harriot had done so. Curiously, few since Shirley’s time have attempted to answer these questions, despite their obvious importance. After all, Harriot was, as far as we know, the first to invent binary. Accordingly, answering the how and when questions about Harriot’s invention of binary is the aim of this short paper. (shrink)

In a manuscript summary, probably written in 1619, of his otherwise unknown earlier work on the oblique impact of elastic spheres, Thomas Harriot gives a largely ‘correct’ theory for their subsequent motion. He derives various consequences from his theory, but gives little indication of the observations or the first principles on which it may have been based. The text of the summary, and of some related fragments, is given.

Decades before Newton’s Principia ushered in the age of modern science, Aristotelian physics faced a serious challenge against its weakest point, in the quest to construct a new theory of projectile motion. Yet how were such new principles of motion conceived, without reference to an established theory of mechanics? This paper explores the conceptual space between the rejection of Aristotle’s physics and the appearance of Newton’s physics in which people such as Harriot and Galileo sought new ways to understand (...) mechanical phenomena. This paper seeks to show that both Harriot and Galileo looked to the zeitgeist of accepting the law of reflection as a law of oblique projection-rebound for all material bodies, for their foundational conceptual resource. The kinematics and dynamics of light’s compound, oblique motion had been developed over centuries within optics, and constituted the ‘ideal’ resource for novel analyses of oblique projectile motion. Whereas Harriot’s inclusion of air resistance restricted the generalizability of optical principles to his simplest case, the upright parabola, Galileo’s idealized analysis of projectile motion in a vacuum represented all cases of projectile motion as upright parabolas. He was thus able to generalize these optical principles to projectile motion per se. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Imagined Apotheoses: Drake, Harriot, and Ralegh in the AmericasWilliam M. HamlinPerhaps the two best known stories of Europeans being taken for gods by non-European peoples are those of Hernan Cortés in Mexico and Captain James Cook in Hawaii. Separated by two hundred sixty years, five thousand miles, and vast differences in cultural and linguistic context, these two incidents nonetheless share many traits in the conventional telling. Cortés and (...) Cook were both strong leaders, for instance, both capable of inspiring devotion among their subordinates. Both men became amateur ethnographers during their lengthy sojourns away from Europe, both sought to promote an image of respectful rather than rapacious foreign incursion, and both are said to have been taken for returning gods by the native peoples among whom they landed: Cortés for the Toltec culture-hero and demigod Quetzalcoatl, Cook for the Hawaiian deity Lono. Click for larger view View full resolutionFigure 1.“The Far Side” cartoon by Gary Larson. Courtesy of Chronicle Features, San Francisco.Recent scholarly studies and debates—among them the rather strident dispute between Gananath Obeyesekere and Marshall Sahlins over the alleged deification of Cook by eighteenth-century Hawaiians—have opened up these returning-god theories to skeptical critique and detailed justification; but such discussions have had little, if any, impact on popular imagination. 1 [End Page 405] Indeed, the idea that redoubtable European explorers can be (and often are) perceived as supernatural beings by non-European “primitives” has been uncritically perpetuated to this day by filmmakers, fantasists, writers of popular history, and purveyors of cultural literacy. E. D. Hirsch, Jr., for instance, informs our children that Caribbean islanders encountered by Columbus “asked if he had come from heaven”—the implication being, of course, that they took him for a god. 2 And in the recent film, 1492: Conquest of Paradise, we hear the indefatigable Admiral (played by Gerard Depardieu) claim that “on every island the natives welcome us with great generosity and trust.... Because of our appearance, we have been mistaken for gods, and are treated accordingly.” 3 Fortunately, we also have a “Far Side” parody of the cultural conceit on which such ideas in part rely, but the cartoon serves as well to demonstrate just how thoroughly the conceit has permeated our collective awareness (see figure 1). 4 Click for larger view View full resolutionFigure 2.“It’s against my programming to impersonate a deity.” From The Return of the Jedi, dir. Richard Marquand, Lucasfilm, Ltd., 1983. All Rights Reserved. Courtesy of Lucasfilm, Ltd.Let me offer just one other example. Near the end of the popular 1983 film The Return of the Jedi, the forest-dwelling Ewoks begin to chant and salaam upon first glimpsing the golden robot C-3PO, who in turn tells his captured comrades, “I do believe they think I am some sort of god.” When Han Solo sarcastically asks the robot to use his “divine influence” to help extricate them from their predicament, C-3PO replies that such an action would be improper: “It’s against my programming to impersonate a deity.” Here we see, embedded within a film romance, both the classic trope of the apotheosized foreigner and the related motif of the foreigner’s reluctance to [End Page 406] play the god-role (see figure 2). It is worth noting, however, that while C-3PO may be unwilling to exploit the Ewoks’ misperception, Luke Skywalker is not; he uses the “Force” to convince the Ewoks of the robot’s magical prowess and, more to the point, to perpetuate their misapprehension. 5What I wish to suggest in this essay is that certain habitual Western assumptions or conceits regarding cross-cultural encounters—assumptions which have been usefully termed “myth models” inasmuch as they condition human perception and find frequent discursive expression—coexist easily but in fact disjunctively with certain other ideological structures in many early modern travel narratives and colonial accounts. Obeyesekere, in his provocative book on the supposed deification of Captain Cook in Hawaii, has linked such myth models to the conceptual structures of the longue durée as characterized by Fernand Braudel, and it is possible that they may also be... (shrink)

'The Greate Invention of Algebra' casts new light on the work of Thomas Harriot, an innovative thinker and practitioner in several branches of the mathematical sciences, including navigation, astronomy, optics, geometry, and algebra. Although on his death Harriot left behind over four thousand manuscript sheets, much of his work remains unpublished. This book focuses on one hundred and forty of Harriot's manuscript pages, those concerned with the structure and solution of equations. The original material has been carefully (...) ordered, translated, and annotated to provide the first complete edition of his work on this subject, and an extended introduction provides the reader with a lucid background to the work and explains its contents. Illustrations from the manuscripts provide fascinating reference material. The appendix discusses correlations between Harriot's manuscripts and the texts of his contemporaries Viète, Warner, and Torporley. The clear and concise exposition makes this an excellent reference volume for historians of mathematics and those interested in the history of science. This is an important new resource for understanding the development of algebra in seventeenth-century England. (shrink)

This is a book review-article. No abstract is required by me.

Recent influential criticisms attack the reputation of Thomas Harriot by citing the contents of his ethnographic and economic survey, A briefe and true report of the new found land of Virginia, first published in 1588. This interpretation makes Harriot, together with Shakespeare and others, agents of a colonialist project. But profound differences are indicated in the comparison of the relatively unbiased depiction and analysis by Harriot and his artist collaborator John White with the interpretations of America and (...) Americans by some of their contemporaries. A briefe and true report conveys, and John White's drawings support, insight into particular non-European features of the cultural and economic lives of the Algonquian peoples. On the contrary, Captain Arthur Barlowe's Discourse and the illustrations by Theodore de Bry for the 1600 edition of Harriot's book instance romanticizing, stereotyping, and unanalytic condescension very unlike Harriot's and White's. These differences prove the faultiness of the recent assessment. (shrink)

The manuscripts of Harriot discussed in this paper are essentially rough notes marginal to his systematic treatment of algebra, of which a small part was published posthumously. The central theme is the sign-rule for multiplication; but the incidentals open up an aspect of symbolism in mathematics entirely new for the time. A more restricted aspect of the same theme was touched on by Commandino in his Euclid, quoted by Harriot as rightly blaming ‘those that thinke that minus per (...) minus shal produce plus’; Commandino's authority was Cardano, in a similarly marginal departure from his great Ars magna, the de Aliza, which Harriot also cites in the same reference. The ostensible motivation, to preserve intact the Euclidean tradition in geometry, plays a very minor role in Harriot's notes. The basic aim, to elude the fatal link with imaginaries, they do touch on. More dimly underlying the arguments are the crucial logical facets of the problem, which Harriot faced with a greater conceptual clarity, formulating in words, however, only his own conclusion: the choice of sign-rule is the user's—a fact not fully recognised by mathematicians generally until the 19th century. (shrink)

Torporley's ‘Congestor analyticus’, completed in 1627 in the library of the Earl of Northumberland at Petworth, was seen by Rigaud in the 1830s among the mathematical manuscript collection of the Earl of Macclesfield. Torporley's additional copy of the introductory part, preserved at Sion College, has been used for the present report. Torporley's prime objective was the presentation of some of Harriot's work. His first example concerns a classical problem in number theory. The complete solution, by an inductive process based (...) on tables of differences, is given in a few folios of the British Library collection of Harriot manuscripts. Torporley's transcription and commentary contrast forcibly today with the immediate illuminating impact of Harriot's original. (shrink)

Summary This paper investigates the fate of Thomas Harriot's algebra after his death in 1621 and, in particular, the largely unsuccessful efforts of seventeenth-century mathematicians to promote it. The little known surviving manuscripts of Nathaniel Torporley have been used to elucidate the roles of Torporley and Walter Warner in the preparation of the Praxis, and a partial translation of Torporley's important critique of the Praxis is offered here for the first time. The known whereabouts of Harriot's mathematical papers, (...) both originals and copies, during the seventeenth century and later are summarised. John Wallis's controversial 1685 account of Harriot's algebra is examined in detail and it is argued that John Pell's influence on Wallis was far more significant than has previously been realised. The paper ends with a reassessment of Harriot's underrated and important contribution to the development of modern algebra. (shrink)

This article addresses research that deals with approaches to psychological and social trauma and ways to manage its disruptive power. In the first instance I apply this to the life of my great-grandmother in order to help understand why her life became unbearably difficult, the treatment she received as a female ‘hysteric’ in the 1940s and most importantly the impact that her life has continued to have through four generations of family life. In the second instance, I apply trauma theory (...) to the history of forgetting women and its implications for feminist action and recovery with specific reference to Feminist Theology. I suggest that there are powerful connections between the individual and collective forgetting of women’s lives, and that this forgetting is premised on forms of symbolic violence. I turn to the work of psychiatrists Judith Herman, and Russell Meares and feminist theologian Elisabeth Schüssler Fiorenza, in order to provide an account of forgetting, remembering and finally recovery. (shrink)

The article reflects on a 2006 keynote about sex and religion discussing a topic the author has addressed as a central issue. Although the author has been involved in what has been known as the field of women and religion for decades, theory that is now emerging under the rubric of what is at times called ‘critical religion’, has led her to a different approach to the topic. The article reflects on the past and moves forward to introduce this trajectory (...) of theory. The hope is to convince the reader that thinking critically about sex and religion together is a new and necessary adventure. (shrink)

Galileo’s telescopic lunar observations, announced in Siderius Nuncius (1610), were a triumph of observational skill and ingenuity. Yet, unlike the Medicean stars, Galileo’s lunar “discoveries” were not especially novel. Indeed, Plutarch had noted the moon’s uneven surface in classical times, and many other renaissance observers had also turned their gaze moonward, even (in Harriot’s case) aided by telescopes of their own. Moreover, what Galileo and his contemporaries saw was colored by the assumptions they already had. Copernicans assumed the moon (...) was a terrestrial satellite, thus Galileo saw its mountains and Kepler “saw” the dwellings of its inhabitants. Aristotelians assumed the moon was a perfect sphere, so they saw differences in density and rarity in the lunar body. Theory corrected the results of observation, so Galileo’s lunar observations, like those that had come before, proved nothing. Yet this failure contained the germ of Galileo’s success, since the Siderius Nuncius gave observation a rhetorical force it did not have before. Observers on all sides set out to see for themselves what Galileo reported. Hence, all parties now had to answer to what they saw, whatever they believed. Thus, the Siderius Nuncius ultimately changed the grounds upon which natural philosophical argument and debate was carried out. In this new empirical arena, the Galilean science would eventually prevail. (shrink)

Gottfried Wilhelm Leibniz is the self-proclaimed inventor of the binary system and is considered as such by most historians of mathematics and/or mathematicians. Really though, we owe the groundwork of today’s computing not to Leibniz but to the Englishman Thomas Harriot and the Spaniard Juan Caramuel de Lobkowitz, whom Leibniz plagiarized. This plagiarism has been identified on the basis of several facts: Caramuel’s work on the binary system is earlier than Leibniz’s, Leibniz was acquainted—both directly and indirectly—with Caramuel’s work (...) and Leibniz had a natural tendency to plagiarize scientific works. (shrink)