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Introduction - Thomas Harriot Summer Series 2021
- 1. Thomas Harriot Summer Series Introduction Friday, June 18, 2021
- 2. Thomas Harriot (1560-1621) Brief biography 2 1560: Born in Oxfordshire 1577: Matriculates at Oxford (St Mary’s Hall: Oriel College) from 1580: Humphrey Gilbert (to ‘83), Walter Raleigh 1584: First Virginia voyage 1585-6: Harriot in Virginia (Roanoke) 1588/90: A brief and true report of the New Found Land of Virginia from c. 1593: Henry Percy, 9th Earl of Northumberland. → Sion House 1597: First optical experiments July 22, 1601: discovers “law of refraction” 1603: Raleigh imprisoned in Tower 1605: Northumberland imprisoned in Tower 1606-9: Harriot writes to Kepler about refraction July 1609: Makes first ever telescopic map of the moon July 1621: Dies after long illness
- 4. Harriot’s Manuscripts ● Rediscovered 1784, in Petworth House (seat of the Egremonts, successors to the Percys, Earls of Northumberland). ● Papers of “modern interest” separated by Franz von Zach. ● Harriot said to anticipate and surpass both Galileo and Kepler. ● Debacle of attempted publication in Oxford at Clarendon Press. See Jackie Stedall, “Thomas Harriot (1560-1621): History and Historiography” 4
- 5. 1794-8: Verdict of Abraham Robertson, Savilian Professor of Geometry “Every thing depending upon the composition and resolution of forces is so much better understood, and more clearly treated, since the discoveries of Sir Isaac Newton, that it would suffer much upon comparison with modern publications. The subject is more fully and elegantly handled in Keill’s Introduction to Natural Philosophy. [The papers on] the spots of the sun. I do not think that Harriott ever intended them for publication; nor do I think that the publication of them now would either satisfy rational curiosity, or contribute, in the smallest degree, to the advancement of astronomy. Upon the whole it is my opinion that the publication of the papers mentioned in this report could only tend to prove that Harriott was very assiduous in his mathematical studies, and in his observations of the heavenly bodies; it could not contribute to the advancement of science.” 5
- 6. Current State of Manuscripts ● Zach’s “significant” papers returned to Petworth House (where they still are). ● Remainder (the vast bulk) donated to British Museum (BL); divided into 8 volumes along subject lines: MSS Additional 6782-9. ● Other material found in BL in Harley fondo; and in Bodleian Library, Rigaud fondo. ● Papers in Sion College (now in Lambeth Palace). ● Until recently, only place to see all papers (almost) together: University of Delaware Special Collections, Shirley collection. 6
- 7. Modern publications ● Committee formed in 1975 to publish a 7-volume edition of Harriot’s papers. ● Editions of small treatises found among the papers (on collision of bodies) ● Matthias Schemmel: The English Galileo: Thomas Harriot’s work on motion as an example of preclassical mechanics ● Janet Beery and Jackie Stedall: Thomas Harriot’s doctrine of triangular numbers: the “Magisteria magna” (interpolation methods) 7
- 8. Front page of Harriot project (hosted at MPIWG) 8
- 11. Exploring some of the mathematical papers 11
- 12. A network of manuscript pages 12
- 13. Manuscript and text view 13
- 14. Full manuscript view ... 14
- 15. … in extraordinary resolution 15
- 17. Harriot teaches navigation to Raleigh’s sailors (1595 and 1584) MS Add. 6788, fol. 491 17 “How to know your course to sayle to any place assigned; & in sayling to make true recconing to find where you are at any time; & how farre from any place desired.”
- 18. Everyday life in Virginia Watercolor by John White (1585/6) 18
- 19. Watercolors by John White (1585/6) 19 Everyday life in Virginia
- 20. 20 The Harriot/White Map of Virginia White’s Watercolor de Bry’s Engraving
- 21. “Most things they saw with us, as Mathematical instruments, sea compasses, the virtue of the loadstone in drawing iron, a perspective glass whereby was shown many strange sights, burning glasses, wildfire works, guns, books, writing and reading, spring clocks that seem to go of themselves, and many other things that we had, were so strange to them, and so far exceeded their capacities to comprehend the reason and means how they should be made and done, that they thought they were rather the works of gods than of men, or at the leastwise they had been given and taught us of the gods. Which made many of them to have such opinion of us, as that if they knew not the truth of god and religion already, it was rather to be had from us, whom God so specially loved than from a people that were so simple, as they found themselves to be in comparison of us. Whereupon greater credit was given to that we spoke of concerning such matters.” (A brief and true report, 1588) 21 Harriot: Science and Imperialism in the New World
- 22. Harriot’s algebraic phonetic alphabet for the Algonquin language 22 MS Add. 6782, fol. 337r
- 23. Westminster School 23 1585 version in papers of Richard Busby An universall Alphabet conteyninge six & thirty letters, whereby may be expressed the lively image of mans voyce in what language soever; first devised upon occasion to seeke for fit letters to expresse the Virginian speche. 1585. Beginning of Lord’s Prayer “Matthew Royden” (a poet, and one of Harriot’s friends from Oxford, and through the early 1580s)
- 24. MS Add. 6789, fol. 390 24 Harriot’s “cipher” “An yris videtur in punkto yunionis - No.” (“Is a rainbow seen at the point of union? No.”)
- 25. Harriot the Mathematical Explorer
- 26. A desire to find a way to the interior of things … 26 MS Add. 6789, fol 336
- 27. 27 … and to transform messy reality into algebra and calculation Giulio Parigi, Palazzo degli Uffizi, c. 1600 MS Add. 6789, fol. 116
- 28. Seeing the world through a mathematical lens 28 MS Add. 6788, fols 411r-v
- 29. Harriot on the Burning Mirror 29 MS Add. 6789, fol 390
- 30. MS Add. 6789, fol 116 30 Harriot’s innovation: a “functional” approach
- 31. MS Add. 6789, fol. 116v 31 Mathematics and the imagination “If the sun’s diameter were 2° 46′ 40″, it would burn up everything on earth. I should give some thought to this question: how big would the apparent diameter be in the sphere of Venus and Mercury?”
- 32. 1. How many people fit on the globe? 2. Mr Bulkeley’s Glass: Refraction, mathematics, and the imagination 3. Mapping the Moon 4. Billiard Balls: Collision and Stacking – mathematical model making 5. Conic sections – tools for exploring mathematics and nature 6. Binary numbers, combinations – and divination Themes of the next six meetings
Hinweis der Redaktion
- This was in preparation for Raleigh’s first expedition in search of El Dorado. These lectures are based on a book Harriot wrote, now lost, entitled Arcticon, which he wrote in 1584 to train the sailors for the first Virginia expedition. Throughout these lectures, he refers to his teaching “11 years ago.”
- Harriot traveled to the New World in two principal capacities: First, as a kind of mathematical consultant. He was to continue his navigational work while at sea; and, after arrival in Virginia, to map the territory. While in Virginia, as well as surveying the land mathematically, he very likely worked with the “alchemist” and metallurgist who came to look for precious metals and minerals. Secondly, he was there as an interpreter. The previous reconnaissance trip, in 1584, had brought back two young Native American men, from whom Harriot had learned the Algonquin language to the point of fluency. On the 1585-6 trip, he was the expedition’s only link between the Europeans and the natives. A lot went wrong on this journey, and the year-long stay was punctuated by constant friction between the native Americans and the English – mainly because of the heavy-handed and brutal approach of the leaders of the expedition. Harriot, as his later writing shows, was deeply disappointed; he became close to the native Americans, as did his closest companion on this journey, the artist John White. The two of them recorded, portrayed, and mapped the new land around the English settlement at Roanoke.
- Beautifully naturalistic paintings. Were damaged in a flood in the 19th century - were apparently once even more vivid, with details picked out in gold and silver.
- Here we have the original White map, plotted mathematically by Harriot – and the engraved version from Theodore de Bry’s 1590 America, which reproduced White’s watercolor, and included a text by Harriot, which we’ll look at in a moment.
- Why algebraic? On the one hand, the symbols are in fact based on the standard (at that time) symbols used for algebraic unknowns.
- In another sense, this fuller description of the system shows that it transferred to the realm of language the goals of algebra - As Viète put it, To solve every problem, through a completely universal method of substituting tokens for magnitudes and numbers. Here, we have a universal alphabet, rationally designed to express any language whatsoever.
- And he continued to use the alphabet as a private cipher in his manuscripts.
- The Harriot who set out to explore nature was the same Harriot whose curiosity guided him in the New World. He first became interested in optics, because he was obsessed with the question of the structure of matter. He was convinced that the world was made of atoms; but how can we peer beneath the surface of things and detect those atoms and their arrangement? Optics seemed to offer a way in: especially the phenomenon of refraction, which he portrays here (as he does very often) as the result of collisions with unseen obstacles.
- Other side of Harriot: quantification and reduction to symbols. We already saw that impulse with the alphabet. In general, Harriot transformed geometrical problems into algebraic, and then numerical ones.
- What makes Harriot so interesting? The mathematization (or, more specifically, arithmetization) of the world. Rainstorm in Durham House, Raleigh’s London residence.
- This is the geometrical model, known to several optical theorists before Harriot.
- Here is one of about 20 sheets on the concave spherical mirror, all filled with calculations of this kind. What is Harriot doing here? First, he has turned the geometrical model he got from his predecessors, into a trigonometric function. In other words, he can plug into a formula the value for the ray entering the mirror, and get out of it a number that told him where on the central axis of the mirror it was reflected to. Actually, he went a little further than that. He realized that the sun’s rays don’t hit the mirror precisely in parallels, but as rays that diverge ever so slightly – by about half a degree at most, the apparent size of the sun in the sky. No one had thought of this before (and no one would, again, until Descartes some 30 years later). The practical consequence of this was that any burning instruments, mirror or lens, however fabulously precise, would always be limited by the sloppy, divergent light it had to work with. The dreams of burning ships across a harbor were just dreams. So Harriot put all of that too, into a formula, which is what he’s calculating here. He’s actually doing the same calculation here over and over again, trying to find the right value, until here [CLICK] he gets as close as he can to .5. And what does this represent? If we imagine holding the mirror up to the sun, and tilting it ever so slightly back and forth, this tells us where the very edge of the extended, diverging sunbeam passes through the focus of the mirror. And then [CLICK] we have a calculation that Harriot does again and again on many pages, to find the intensity of the burning. What he finds is that, within a very small area, close to the center of the mirror, there is considerable heat generated. But this falls off rapidly with distance – and, because of the nature of the sunbeam, much faster than anyone had suspected. He had, implicitly, disproved one of the great optical fantasies of his day. I say implicitly, because these pages are typical: all we have are the calculations, without explanation. My job is to reconstruct the geometrical framework in which these numbers make sense – and then, using what I know of the culture of the time, explain why these calculations might have been significant.