July 14, 2008
TMA 2.1
This was a gobbet question concerning an extract from John Dee’s preface to the first Engish translation of Euclid’s elements mathematics. I won’t quote it, as it is quite long.
John Dee on navigation
The extract is taken from John Dee’s Mathematicall praeface to Henry Billingsley’s English translation of Euclid’s Elements of 1570. In this preface (together with his ‘Groundplatt’ diagram) he is giving a schematic overview of the mathematical sciences, both pure (“Principall”) and applied (“Derivative”). In the extract he is discussing navigation in relation to mathematics. In the course of the extract he gives a definition of the art of navigation (finding sailing routes between arbitrary places, and determining position at sea); he relates this art to various parts of mathematics; he gives a long list of instruments used in navigation; and he argues for the particular importance of navigation to England as an island nation.
In discussing the arts pertaining to navigation he is indicating what knowledge a master pilot—as a practitioner—needs. He gives four specific arts (“Hydrographie, Astronomie, Astrologie, and Horometrie”), these being founded on the “Principall” sciences of geometry and arithmetic. The instruments he lists are those a pilot should be able to use (and make).
Of these arts, hydrography relates to plotting routes and understanding charts; with the attendant difficulties of considering spherical geometry whilst dealing with flat maps. The abilities to make astronomical observations and to reckon time would be used at sea in determining a ship’s position and bearing. It is not clear why Dee includes astrology in the list: Dee’s sympathies in this area are well known, but he does not expand on the topic. It is possible that he meant nothing more than knowledge of the constellations and the movements of the planets.
Billingsley’s translation made Euclid accessible to unlatined English-speakers for the first time. And for Dee to emphasise the usefulness of mathematical understanding puts him in the tradition of Robert Recorde, who would put similar ‘pitches’ to his potential readers in his vernacular mathematical works.
The book, and Dee’s preface, was not specifically aimed at navigational practitioners: The Elements is a work of pure geometry. Dee makes it clear that geometry, together with arithmetic, is the foundation of all the navigational arts, but does not indicate to what extent pilots should study its principles. Perhaps Dee’s intended audience here consists of those who might study geometry in order to further its application, continuing Dee’s work in devising useful arts for practitioners to learn.
Dee was an ardent admirer of the ancients, and so it is fitting that he would choose a translation of the most famous of Greek mathematical texts as the vehicle for this mathematical manifesto. The recovery and publication of Greek texts had been the object of programmatic effort in Italy around this time. (Francesco Maurocilo was a little earlier. Federigo Commandino was a contemporary with whom Dee had corresponded concerning a possible lost work of Euclid.) The motivation was the perceived superiority of the ancients over Islamic and mediaeval authors. This program included Italian translations, as Dee notes in his preface, although Commandino’s Italian version of The Elements was not published until 1575.
Dee’s preface is not particularly concerned with promoting the content of one particular book, as being either profitable for practitioners or edifying for scholars. He is proposing a systematization of all mathematics that (as shown on his Groundplatt) would encompass both theoretical, Euclidean geometry and the practical arts of navigation (and much else besides). His vision could be taken as pedagogical reform in the manner of his friend Peter Ramus: the Groundplatt is a ‘dialectic’ presentation such as Ramus might produce, and is described by Dee in a Ramist turn of phrase as being “somewhat Methodically contrived”. It could also be taken as the outline of a program of research, such as the ones Descartes and Frances Bacon would later produce.
Navigation was an increasingly important matter in England at this time, with the growth in trade and the exploration of the New World, as Dee suggests in this extract. He mentions devices he invented for the Moscovy Company, a trading company to whom Dee was a technical advisor. Recorde had previously acted in a similar capacity, writing instructional books for their navigators’ use. Works that follow up Dee’s remarks on navigation in the preface included William Bourne’s A regiment for the sea and Dee’s own General and rare memorials pertayning to the perfect arte of navigation. Dee’s friend Mercator devised a projection most suitable for navigational charts, the basis of which was later worked out by Edward Wright and Thomas Harriot.
It is appropriate that Dee should include a list of instruments in his account of navigational knowledge. Practical mathematics is primarily carried out by various sorts of practitioner, rather than by scholars, and instruments were an important part of this. Certain trades had always had their instruments, but around this period there was an increased inventiveness. This became more pronounced slightly later, with more mathematically sophisticated instruments devised by people such as Edmund Gunter of Gresham College.
Dee is well known as a sympathiser of hermetic philosophy, a form of neoplatonism common in the early Renaissance. Dee’s work on navigation exemplifies the fact that hermeticism—unlike Platonism proper—tended not denigrate worldly matters, and that it emphasised the power that knowledge brings.
Thoughts
Oh dear, this is very flat, isn’t it? I think this was my first attempt to write methodically: making sure I had things to say about all the things that needed them (author, target audience, relevant mathematical traditions, etc) and then just stringing them together. It might be inevitable that an answer to this sort of question will be a sequence of facts and observations that lacks any real point.
And I do bang on about mathematical practice and practitioners. There’s one learning outcome that I’ve definitely demonstrated. (Not that MA290 was like that.)
These days Dee is mainly remembered for conjuring spirits with Edward Kelley. I still find it surprising that in his day he was a key figure in English mathematics. It is even more surprising that he was friends with Peter Ramus, scourge of all dunsicality (and called “the pedant of France” by Giordano Bruno). Even though I should know better, I find it hard not to think in terms of an anachronistic distinction between respectable science and occultism. (Although I recall that Ramists were, for example, against the teaching of astrology, but not because it was diabolical, or even because it was false, but because in their classification it was a ‘specific’ rather than a ‘general’ art.)
I have a vague theory about the different perception of John Dee and Isaac Newton. At some point, presumably during 18th century, the connection between early modern science and occultism became an embarrassment. Because Dee’s occult interests were well known his importance as a mathematician had to be played down. Whereas Newton was firmly at the heart of the scientific pantheon, so his interest in alchemy had to be treated as peripheral. (There’s a similar story with Johannes Kepler.)
[At this point I was going to go on about the relative obscurity of Thomas Harriot being less due to his association with the “School of Night” than his failure to publish on his most important work, but I'm getting off topic.]
Posted by robin2 at July 14, 2008 09:12 PM