Isaac Newton: The Last Lone Genius?

The Friday before last, with much advanced publicity, the BBC broadcast a new documentary film biography of Isaac Newton with the title The Last Magician. This phrase is part of a famous quote by John Maynard Keynes, “not the first scientist but the last magician”, describing his feeling upon reading the Newtonian alchemical manuscripts that he acquired at the auction of the Portsmouth family Newton papers in 1936.  This of course together with the advanced advertising for the programme signalled that we were due for a fresh dose of “did you know that Newton was a secret alchemist?” A phenomenon that Rebekah “Becky” Higgitt has blogged on informatively in the past.

Based on quotes from Newton’s own writings and correspondence as well of those of his contemporaries the programme was in its basics factually correct. As usual for BBC historical documentaries it was well-produced and excellently filmed and thus pleasant to watch. The basic structure was the direct quotes being spoken by actors in costume and commented upon by five more or less experts. These were the historians of science Rob Iliffe head of the Newton Papers editing project and a genuine Newton expert, Patricia Fara author of an excellent book on the changing image of Newton down the centuries and Lisa Jardine expert on Renaissance history of science, as well as popular science writer James Gleick author of a competent popular Newton biography and astrophysicist turned novelist Stuart Clark.

Given all of these preconditions it should have been an excellent hours entertainment for a historian of science like myself, unfortunately it turned out to be a major disappointment for two reasons. The programme deliberately created two principle impressions that were and are fundamentally wrong.

The first of these turned up in the pre-programme publicity but also featured prominently fairly early in the documentary in what seems at first glance to be a fairly harmless statement:

By the age of 21, he had rejected 2,000 years of scientific orthodoxy…

This brief phrase contains two claims one implicit and one explicit. The implicit claim is how wonderful Newton was to take such a bold step when he was only 21 years old. Anyone who has spent anytime at all looking at the history of mathematics knows that mathematicians tend to be very precocious. Pascal wrote the paper that gained him entry to the top flight of seventeenth century mathematics at the age of sixteen. In the nineteenth century the teenage William Rowan Hamilton was trotted out in public like a circus pony to display his brilliance. The stories are legion and there is absolutely nothing unusual in Newton intellectual development it’s par for the course for a highly talented mathematician.

As Becky put it very succinctly in a tweet what they are actually saying here is that there had been no science since Aristotle, which is of course complete rubbish. The scientific orthodoxy of the day, which was by the way on the verge of disappearing, of which more shortly, came into being in the thirteenth century when Albertus Magnus and his pupil Thomas Aquinas created a synthesis of Catholic theology and Aristotle’s philosophy with the addition of Ptolemaic geocentric astronomy. This synthesis is known as Scholastic or Aristotelian physics or natural philosophy. However as Edward Grant, one of the leading experts on medieval science, points out Aristotelian philosophy is not Aristotle’s philosophy. It is also important to note that Aristotelian philosophy was never carved in stone but in fact changed and developed continuously over the next four hundred years. Examples of major changes are the work of the Oxford Calculatores and the Paris Physicists in the fourteenth century. The Aristotelian physics of the fifteenth century is a very different beast to that of the thirteenth century. The geocentric astronomy produced in the middle of the fifteenth century by Peuerbach and Regiomontanus differed substantially from that of the first Ptolemaic translations of the twelfth century.

Added to all this change and development the first seeds of what would become modern science began to poke their slender stems out of the substrate of scientific innovation around the beginning of the fifteenth century. By 1661 when Newton went up to university Keplerian heliocentric astronomy had become the new orthodoxy and Aristotelian physics was being pushed out by the new physics developed by mathematicians such as Tartaglia and Benedetti in the sixteenth century and Stevin, Galileo, Borelli, Descartes, Pascal, Huygens and others in the seventeenth. One should bear in mind that the Leopoldina, the Accademia del Cimento, the Royal Society and the Acadédemie des Sciences all institutions dedicated to the propagation and development of the new science were founded in 1652, 1657, 1660 and 1666 respectively. The young Newton did not like some Carrollian hero draw his Vorpal Blade to slay the Jabberwock of ancient Greek science but like any bright young academic would do jumped on the band wagon of modern science that was speeding full speed ahead into the future.

We now turn to what I see as the most serious failing of the documentary expressed in the question posed in the title of this post. For the best part of an hour the documentary banged on about Newton’s solitude, his isolation his lone path to the secrets of nature. We were presented with the ultimate lone genius of the history of science. It went so far that the only other contemporary researchers mentioned by name were Descartes in passing and Hooke purely in a negative light. The way that the programme was structured created a totally false impression of Newton’s scientific endeavours.

We actually know very little about Newton’s time as a student though it is safe to say that he was more the type to curl up in front of the fire with a good book on a Friday evening than to go to the latest rave at which ever student hostelry was in that term. As a fellow we know that he communicated and worked together with other scholars such as Isaac Barrow so to talk of total solitude as the documentary did is wrong. After he emerged from obscurity at the beginning of the 1670s with his reflecting telescope and his famous paper on the phenomenon of colours he was in no way isolated. Even if Cambridge was somewhat off the beaten track in those days Newton corresponded with other scholars in Britain and also abroad as can easily be seen in his voluminous correspondence as edited by Turnbull. He was also often visited by other mathematical scholars such as Halley or John Collins. When he left Cambridge to go to London he became positively gregarious. Maintaining a town house with his niece Catherine Barton, a renowned social beauty, as his housekeeper where he received and entertained visitors. At the Royal Mint, which he attended daily, he was surrounded by a large staff. After 1703 he presided over the weekly meetings of the Royal Society and on other evenings surrounded by his acolytes he held court in one or other of the then fashionable London coffee bars.

More important for me was the totally false impression created by the documentary of Newton’s mathematical and scientific work. Anyone being introduced to Newton for the first time would come away with the impression that he revolutionised mathematics, physics and astronomy in a superhuman solo endeavour completely isolated from the rest of the late seventeenth century intellectual world.

We got presented with Newton in 1666 creating a completely new branch of mathematics, he only actually started it then and it took a number of years to develop. At no point was any other mathematician mentioned. The fact that Newton either, directly or indirectly, knew of and built on the previous work in this field of Kepler, Cavalieri, Fermat, Pascal, Descartes, van Schooten, Barrow and others was quietly swept under the carpet. Even worse no mention what so ever of Leibniz who independently developed the same mathematics almost at the same time from the same sources. This of course led eventually to the most notorious priority dispute in the history of science involving many of the leading mathematicians of Europe.

The same thing occurred with the presentation of his work in optics, no mention of Kepler, Schiener, Descartes, Grimaldi, Gregory, Hooke, Huygens or anybody for that matter. Isaac apparently did it all alone in isolation.

This form of presentation continued with his greatest work the Principia. We got each of the famous laws of motion presented individually but no hint of the fact that the first was taken from Beeckman by way of Descartes, the second from Huygens and the third from his readings in alchemy. We were told that he derived the law of gravity from his three laws but no mention was made of the fact that the concept of the law of gravity was common, much discussed intellectual property in academic circles at the time. No mention of the contributions made to the substance of the Principia by the work of Kepler, Galileo, Cassini, Halley and above all Flamsteed. We had the strange spectacle of Hooke famous accusation of Newton having stolen his law of gravity and plagiarised him delivered in a passionate speech to the Royal Society in 1660 but no mention what so ever that Hooke’s accusation had more than a little substance. Hooke and Newton had corresponded on the subject in the early 1680s and Hooke had already formulated a concept of universal gravity before Newton. This correspondence was with certainty one of the spurs that led Newton to write the Principia although Hook’s claims as to the extent of his contribution are wildly exaggerated.

Isaac Newton did not live and work in an intellectual vacuum as was very strongly implied either deliberately or accidently through bad scripting by this documentary. He was part of a strong multi-faceted scientific community who supplied both the scaffolding and a significant part of substance of Newton’s life work in mathematics, physics and astronomy. He was in no way a lone genius but a highly significant cog in a large intellectual endeavour.

There was a time some decades back when some historians of science went so far as to decry the Principia as purely a work of synthesis with only a very small original contribution from Newton. This view was shown to be exaggerated and invalid and has been dropped but the opposite point of view implied by this documentary of the Principia as being alone the work of Newton’s genius is even more false.

Before I close there are a couple of small points from the film that I think should be mentioned. As is all too often the case we had the tired old statement that after Newton became President of the Royal Society he produced no more original scientific work. This was as always made without explicit comment but with a strong implicit negative aura. Dear people, when Isaac Newton became President of the Royal Society in 1703 he was already sixty years old. He had written and published two of the most important major scientific works in the history of mankind, his Principia and his Optics, as well as vast quantities of, largely unpublished, absolutely world-class mathematics, which he did however circulate in manuscript amongst his acolytes. What more did you expect him to do (FFS)?

I noted four major scientific/historical errors during the film, a fairly low quota; there may have been others. We of course get introduced to Newton’s reflecting telescope, the invention that first made him known to the world at large, but then we get informed that this instrument played a major role in marine navigation in the eighteenth century. Now whilst it is true that the reflecting telescope, mostly Gregorian’s and not Newtonian’s, had become the instrument of choice for astronomers by the middle of the eighteenth century they were for several good reasons not used for navigation on ships. Firstly reflecting telescopes whilst in principle smaller than refracting ones don’t telescope and so are more massive and cumbersome than the classical marine telescope. Secondly until the nineteenth century reflecting telescopes had metal mirrors made of so-called speculum metal an alloy that unfortunately was very susceptible to corrosion necessitating regular re-polishing. The salt-water atmosphere of sea voyages would have been very adverse for such mirrors requiring almost daily re-polishing and thus completely impractical.

The next error I spotted was a real howler. A voice over informed the viewer that, “for centuries light was considered the purest form of energy in the universe.” Really? Although etymologically derived from an ancient Greek word the physics concept of energy was first appeared in the nineteenth century, as did the recognition that light is a form of energy. Nuff said.

Moving along the historical time scale in the opposite direction voice over informed us the Newton’s Principia made possible the accurate prediction of comets and eclipses. Now the former is indeed true although the credit should properly go to Halley who first showed that some comets were periodical and obeyed Newton’s law of gravity. The latter is however again a real history of science howler. The Babylonians could accurately predict lunar eclipses in about the fifth century BCE and the ability to accurately predict solar eclipses was also developed in antiquity. No need to wait for Newton.

My final error is the one that as a historian of science causes me the most concern. Whilst discussing Newton’s alchemy voice over stated correctly Newton’s alchemical belief that light and matter are both products of some as yet undiscovered primal alchemical substance. The claim was immediately made that Newton had anticipated Einstein’s famous E = MC²! This claim being, to my surprise, repeated by Rob Iliffe an excellent historian of science. Now I’m not a big fan of the Kuhn/Feyerabend principle of the incommensurability of scientific theories. This says that one can’t compare scientific theories because the definitions of the concepts that they contain differ and are thus not comparable. Newton’s concept of force is not Maxwell’s concept of force for example. However I think that here we have a genuine case of incommensurability. The metaphysical concepts behind Newton’s alchemical theory and the metaphysical concepts behind Einstein’ theory of relativity are in no way comparable. It is not even comparing apples with oranges; it’s comparing apples with bicycles!

On the whole I think what was superficially a very good and certainly an excellently produced documentary failed miserably as a piece of history of science for the reasons that I have outlined above. Maybe I’m being too harsh but on the whole I don’t think so. For me the very strong emphasis of the biography of Newton as some sort of lone genius whether intended or an accidental product of ill considered scripting made this documentary next to worthless as a contribution to popular history of science.

 

 

What was when modern?

Darin Hayton has a short post discussing a review of John Hessler’s A Renaissance Globemaker’s Toolbox, a new book about the cartographical endeavours of the Renaissance mathematicus Johannes Schöner.  As well as being the addressee of Rheticus’ Naratio Prima, the first published account of Copernican heliocentricity, Schöner played a very central roll in the history of globe making as well as the evolution of cartography in the sixteenth century and it is with this aspect of his life that the new book is concerned. Schöner put together a private bound volume of cartographical material that he used for his own work. This volume contained, amongst other things, the only known copy of the first map to name the newly discovered western continent America, Martin Waldseemüller’s 1507 map of the world, that was purchased by the Library of Congress for ten million dollars in 2003. In his latest book Hassel analyses all the cartographical material contained in Schöner’s “toolbox” to develop a picture of how he worked. I might write more about this book when I’ve read it, I ordered it today, but here I’m concerned with one troubling paragraph of the review to which Darin has already drawn attention in his post. The reviewer, John Wilford, wrote at the end of his piece the following:

Nothing in the book points up more clearly Schöner’s pivotal place in a world in transition from the medieval to the modern than his residual interest in astrology and his awakening curiosity when he apparently heard reports of a new theory being formulated by a Polish Catholic cleric. A brilliant young student of Schöner’s, Georg Joachim Rheticus, went to see Copernicus in 1539 and learned more about the Earth orbiting the Sun. Rheticus then composed a short treatise, written in the form of a letter to his teacher, “most illustrious and learned” Johannes Schöner.

In his post Darin comments on this paragraph thus:

Schöner’s interest in that “new theory being formulated by a Polish Catholic cleric” probably owed more to his interest in astrology and making astrological prognostications than the modernity we see in Copernicus’s theory. Along with his prognostications and calendars, Schöner also wrote books on astrology before and after Copernicus’s De revolutionibus was published, notably his Opusculum Astrologicum in 1539 and De iudiciis nativitatum Libri Tres in 1545. Schöner might also have been the author of a horoscope cast for Copernicus. Judging from the table of contents, Hessler spends some time assessing Schöner’s astrology. Schöner’s interest in astrology shouldn’t diminish our interest in him, but it should, perhaps, prompt us to wonder about the labels “modern” and “medieval” and the work they do for us…

Darin criticism is right on the button and in what follows I would like to expand upon it somewhat and expose what I see as a common misconception concerning the history of astrology.

Darin is perfectly correct when he surmises that any interest that Schöner had in the work of Copernicus was almost certainly motivated by his very active interest in astrology and it should be noted that Schöner’s “brilliant young student”, Georg Joachim Rheticus, who famously undertook the arduous journey to Frauenburg to visit Copernicus did so after spending several months in Nürnberg studying astrology under Schöner. The central section of Rheticus’ Naratio Prima consists of an excurse on what he sees as a confirmation of an astrological cyclical theory of history, popular at the time amongst Renaissance scholars, delivered by Copernicus’ theory of the precession of the equinoxes. However I see a major problem in Wilford’s labelling of Schöner’s astrology as medieval.

Schöner’s astrology is Renaissance astrology and it is for various reasons a very different beast to medieval astrology. His astrological practice cannot and should not be seen, as Wilford wishes us to do so, as a residual left over from earlier times but as the, for the sixteenth century, central and actual activity of the working Renaissance mathematicus; Schöner’s astrology was modern.

European horoscope astrology, there are other sorts that I won’t discuss here, began life in Greece sometime in the fifth and fourth centuries BCE, combing elements of earlier Egyptian and Babylonian systems of prognostication. Its fortunes waxed and waned over the following centuries and reached a zenith in the work of Ptolemaeus in the second century CE. From here like all the other sciences of antiquity, and its adherents certainly regarded it as a science, it went into decline, almost disappearing completely in the Early Middle Ages. Although it should be pointed out that those works of astronomy from antiquity that remained known in this period such as Martianus Capella’s De nuptiis Philologiae et Mercurii and Microbius’ Commentarii in Somnium Scipionis are strongly astrological.

With the first major revival of learning at the beginning of the High Middle Ages, twelfth and thirteenth centuries, and the rise of the European universities astrology enjoyed a rather dubious reputation. It stood in conflict with the dominating Catholic theology. Horoscope astrology with its seemingly deterministic prognostications appeared to contradict the central Church tenet, the belief in free will.

With the advent of Humanist Renaissance in the fifteenth century astrology enjoyed a major revival centred around astro-medicine, or as it was also known iatro-mathematics, a discipline that like astrology had its roots in fourth century BCE Greece. This form of medicine believed that the causes and cures of diseases were controlled by celestial influences and that a medicus must study the horoscopes of both the patient and the disease to determine the correct course of treatment. Chairs of astrology were established at the Northern Italian humanist universities and also in Cracow in Poland, later in other parts of Europe. By the end of the century astrology was the central discipline studied and practiced by the Renaissance mathematicus. This revival in the fortunes of astrology was also made possible because the new astrologers interpreted horoscopes as being indicative and no longer deterministic. That is a horoscope indicated a possible course for the future but one that could be altered by the subject of the horoscope if he took the right actions. Actions defined by the astrologer, of course, for a further fee.

In the sixteenth century at the start of the Reformation Philipp Melanchthon, who was responsible for the curricular of the Lutheran Protestant schools and university, established chairs for mathematics in all of the Protestant educational establishments to further the study of astrology of which he was a passionate adherent. Johannes Schöner professor for mathematics at the Egidian Oberschule in Nürnberg was one of the first of those appointees. Favoured for his already excellent reputation as an astrologer. Far from being a medieval residue Renaissance astrology, as practiced by Schöner, was a cutting edge academic discipline and for its time the epitome of modern.

Astrology was also not in the process of dying off following Schöner’s own demise in 1547 it continued to be a central field of study for the cartographers and astronomers who created the modern disciplines over the next hundred years. Both Gemma Frisius and Gerard Mercator, who are regarded as two of the principle founders of modern cartography and who were both highly influenced by Schöner’s work, were highly respected practicing astrologers. Rheticus the midwife of Copernican heliocentricity who became a medicus practicing astro-medicine in Cracow in the later part of his life gained a European wide reputation for his astrological prognostica. Michael Maestlin, Kepler’s teacher, and Tycho Brahe, his most significant employer, who each made important contribution to the evolution of the new astronomy were both practicing astrologers who regarded astrology as central to their astronomical research. Kepler himself, probably the most important of the modern astronomers, was also a passionate believer in celestial influence even if he rejected the traditional horoscope astrology and wished to replace it with one of his own devising. Finally even Galileo Galilei, supposedly the first really modern “scientist” taught astrology to the medicine student at the University of Padua a discipline that he himself obviously believed in as evidenced by the horoscopes that he drew up for his own family. This list of sixteenth and early seventeenth century astrologers is of course not exhaustive but merely an indication of just how deep the study and practice of astrology was embedded in the work of a Renaissance mathematicus.

Astrology first went into decline and lost its social and academic status in the second half of the seventeenth century with the general decline of the scholastic Aristotelian philosophy and with it the Renaissance belief in the micro-cosmos/ macro-cosmos philosophy, the fundamental justification for celestial influence and astrology.

Returning to the starting point of this post I hope I have made clear with my brief exposition of the history of European horoscope astrology that Schöner’s “residual interest in astrology” in no way indicates his “pivotal place in a world in transition from the medieval to the modern” as there was nothing medieval about his astrological activities for they were in themselves a sign of modernity in the sixteenth century.

Killed by Homeopathy

The mathematician, philosopher and logician George Boole died on the 8^th December 1864. What most people don’t realise is that he was in all probability killed by homeopathy.

In 1849 Boole, a self-taught mathematician and school master, was appointed Professor of Mathematics at the newly founded Queen’s College Cork and it was here in 1850 that he first met Mary Everest, niece of the military surveyor Colonel George Everest after whom the mountain is named, who was visiting another of her uncles, John Ryall who was Professor of Greek at Cork.  The family name, by the way, is pronounced Eve – rest and not Ever – rest. From 1852 on George became Mary’s maths tutor and when her father died in 1855 the two of them married. Despite a fairly large difference in age it was a happy marriage that produced five rather special daughters, who I might blog about another time.

Mary Everest Boole was a highly intelligent woman who after the death of her husband, she lived for another 52 years, would go on to become a noted educationalist who today is something of a feminist icon. She had, however, at least one fatal flaw. Mary’s father had been a devoted disciple of Samuel Hahnemann and she spent a large part of her childhood living in Hahnemann’s house in France where she too became an adherent of his medical philosophy.

The Boole’s lived outside of Cork and one day when walking home from work George got drenched in a downpour and developed a chill. Mary following Hahnemann’s guiding principle that “like cures like” wrapped her ailing husband in wet bed sheets. George developed pneumonia and died. This story is not based on hearsay or a popular myth but the written testimony of one of their daughters who never forgave her mother for having, in her opinion, killed her father.

The next time somebody tells you that homeopathy is harmless you can tell them that it killed one of the greatest mathematical minds of the nineteenth century on whose algebraic logic both the soft- and the hardware of your computer function.

The other professor of mathematics at Wittenberg.

Anybody who knows a bit about the history of astronomy in the early modern period or who has wasted their time and money reading Dava Sobel’s last perversion of the history of science will know that Copernicus was finally persuaded to publish his De Revolutionibus by Georg Joachim Rheticus who was professor of mathematics at the University of Wittenberg. To be precise he was appointed professor for the lower mathematics, i.e. arithmetic and geometry, by Phillip Melanchthon in 1536. In the same year Melanchthon appointed Erasmus Reinhold, who was born on 22^nd October 1511, professor for the higher mathematics, i.e. astronomy and music. Like his colleague Rheticus, Reinhold made a significant, but less well-known, contribution to the reception of Copernicus’ heliocentricity.

Reinhold was the son of Johannes Reinhold, a tax collector, from Saalfeld in Thüringen. He entered the University of Wittenberg as a student in the winter semester 1530/31 graduating MA in 1535 and as already noted above being appointed professor in 1536. He remained in Wittenberg the rest of his life serving terms as dean of the faculty of arts and as rector of the university. He died in 1553 probably of tuberculosis. He was respected as a practicing astronomer and was considered and excellent teacher.

To understand Reinhold’s contribution to heliocentricity one first has to consider the function of mathematical astronomy. Since at least the first algebraic astronomical models of the Babylonians up to the seventeenth century the main function of mathematical astronomy was to supply accurate predictions of the positions of celestial bodies and the occurrence of celestial phenomena such as lunar and solar eclipses; this data then being utilised by astrologers, navigators, cartographers and others. The mathematical models of the cosmos produced by Ptolemaeus and others described and traced the movement of the various heavenly bodies, in order to make the positional predictions those movements had to be turned into data tables showing the weekly/daily/hourly positions of those bodies; these list of data are known as planetary tables or ephemerides. Various sets of tables that had been calculated for the geocentric models were already in existence and their inaccuracies were one of the major driving forces behind moves to reform mathematical astronomy throughout the fifteenth and sixteenth centuries of which Copernicus’ De revolutionibus was one result. Copernicus had not calculated planetary tables for his heliocentric model and this task fell to Erasmus Reinhold.

Using modified versions of the models supplied by Copernicus, in his magnum opus, Reinhold calculated the first ever set of heliocentric planetary tables, financed by and dedicated to Albrecht Duke of Prussia, they were titled the Prutenicae Tabulae Coelestium Motuum, which translates as the Prussian Tables of Celestial Motion. They were originally destined to be published by Johannes Petreius, who had published De revolutionibus, but he died before they were finished and so the first edition was published by Ulrich Morhard in Tübingen in 1551. Morhard’s widow produced a reprint of the first edition in 1562. A second edition was edited by Michael Maestlin, Kepler’s teacher, in Tübingen in 1571. A third edition was published in Wittenberg in 1585.

The tables were eagerly awaited by the sixteenth century astronomical community, irrespective of whether they believed in heliocentricity or not, with the hope that Copernicus’ new mathematical models would deliver more accurate predictive data than the older tables based on the geocentric models. Unfortunately this proved not to be the case. In some aspects the new tables were better than their predecessors, in others about the same and in some even worse. This failure to deliver was due to the fact that the data on which the Copernican models were constructed was the same defective or inaccurate data as that on which the earlier geocentric models had been constructed. It also severed to slow down the acceptance of a heliocentric cosmology.

The inability of both the geocentric and the heliocentric planetary tables to deliver accurate celestial predictions is what started off a young Tycho Brahe (who died 24 October 1601) on his twenty-plus years programme of astronomical observation in order to obtain a new accurate set of basic data on which to construct planetary orbit models. It was using Tycho’s vast collection of data that Kepler was able to construct his elliptical heliocentric astronomy. The tables that Kepler then calculated using his models and Tycho’s data, the Tabulae Rudolphinae or Rudolphine Tables named after the German Emperor römisch-deutsche Kaiser Rudolph II who financed them, finally did the trick. Compared with all of their predecessors the Rudolphine Tables were extremely accurate and they were the major factor in persuading people to adopt a heliocentric cosmology and in fact a Keplerian elliptical world view and not a Copernican one as is often falsely claimed.

An Italo-Chinese Jesuit

The first history of science post that I wrote for The Renaissance Mathematicus was about the Jesuit mathematicus and educational reformer Christoph Clavius and his introduction of the mathematical sciences into the curricula of the European Catholic schools, colleges and universities at the beginning of the seventeenth century. My post ends with a brief list of some of the most prominent Jesuit and non-Jesuit beneficiaries of Clavius’ mathematical education programme in the seventeenth century. One of the earliest of Clavius’ graduates, who studied under the master himself in Rome, was the Italian Jesuit mathematicus Matteo Ricci who was born 6^th October 1552.

Ricci entered the Jesuit order in 1571 and studied mathematics, astronomy and cartography amongst other things under Clavius at the Collegio Romano. After graduation in 1577 he applied and was accepted to serve in the Jesuit mission to India. As was usual he was first sent to Coimbra in Portugal to prepare for his Asian service and then in 1578 he sailed to the Jesuit mission in Goa. From here Ricci was sent to Macao in China in 1582. In 1583 he was invited by the Chinese governor to settle in Zhaoqing. Ricci succeeded in becoming accepted into Chinese society, where all other Europeans in the early modern period had failed, by accommodating to Chinese mores and habits. He clothed himself as a Buddhist monk and learnt to speak, read and write Classical Chinese; even writing the first Chinese-Portuguese dictionary. Even given his gentle accommodative approach it took Ricci nineteen years to gain access to Beijing and the centre of Chinese power. From 1588 until his death in 1610 he was the leader of the Jesuit mission to China.

During his time in Zhaoqing Ricci produced the first modern Chinese map of the world based on the world map of Abraham Ortelius thereby introducing the Chinese to America for the first time.

1604 Japanese copy of Ricci’s Chinese World Map

Later he went on to produce the first modern map of the Far East

Ricci’s Far East Map

With the help of his Chinese Christian converts Ricci produced a Chinese translation of the first six books of Clavius’ annotated edition of the Elements of Euclid thus introducing the Chinese to Western mathematics.

 Ricci and his  prominent convert, Xu Guangqi (Copperplate print from Athanasius Kircher’s China illustrata, 1667

Through his knowledge of astronomy Ricci succeeded in becoming appointed as an advisor to the Chinese government. The mathematical abilities that Ricci acquired from Clavius made it possible for him as the first European in the early modern period to penetrate Chinese society and to build a bridgehead for the Jesuit mission to China. Ricci successors in this mission, in particular Ferdinand Verbiest and Adam Schall von Bell, building on Ricci’s successes introduced modern European astronomy, including Copernican heliocentricity, into China.

Transmission of scientific knowledge from one culture to another plays an important role in the history of science. Till about the thirteenth century CE the Chinese were scientifically and technically well in advance of Europe but by the seventeenth century they were lagging well behind. The Jesuit mission to China in the seventeenth century brought the Chinese up to date on the newest developments in Western mathematics, astronomy and cartography. The door to this transmission of knowledge was opened by Matteo Ricci.

It’s silly questions time again: “Was Newton a scientist or a sorcerer?

Back in May the Guardian art critic Jonathan Jones asked, “Is Leonardo da Vinci a great artist or a great scientist?” making, as I pointed out at the time, a serious category mistake. Something must be in the drinking water at the Guardian because now Stuart Clark on the Guardians Science Blogs is asking “Was Newton a scientist or a sorcerer?” making, you guessed it, a serious category mistake. As my Internet friend Tom Levenson, who is himself something of a Newton expert, pointed out on twitter Gotta stop with “Scientist and/or sorcerer” nonsense. Newton never saw himself in those terms… In fact Tom’s tweet says it all but for those not in the know, who might want to learn more, I will elaborate.

For all those at the back who haven’t been paying attention Newton cannot have been a scientist because the term was first coined by William Whewell in 1833 and did not come into common usage until around 1870. There are those who will immediately say that Newton thought like a modern scientist so it doesn’t matter if the term is anachronistic he was one, so there. The problem with this claim is that it’s based on a very limited knowledge of Newton, his life, his work and the way he thought. Put very simply Newton did not think like a modern scientist, which brings us to the second prong of Stuart Clark’s dichotomy.

Clark calls Newton a sorcerer because he was a practicing alchemist, which displays an immense ignorance of the world of seventeenth century thought on his part. A sorcerer is a practitioner of magic in fact a practitioner of black magic and that is a very, very different thing from an alchemist. What follows is a brief outline as to why Clark’s appellation is so inappropriate (with apologies to all serious historians of alchemy, astrology and natural magic for a totally inadequate explanation of these disciplines in the early modern period).

In the early modern period there are three so-called occult (occult just means hidden or concealed) sciences: astrology, natural magic and alchemy all of which found their legitimacy in the micro-cosmos macro-cosmos philosophy. This cosmology says as above so below or the world we live in is a reflection of the heavens. Astrology investigates the connections between the heavens and the earth and tries to define the heavenly or celestial influences. Both natural magic and alchemy are methods that try or at least hope to directly influence or manipulate those influences. Practitioners of all three disciplines distance themselves clearly from demonic or black magic that tries to manipulate nature through demonic powers. A sorcerer is a user of demonic magic.

Newton rejected both astrology and natural magic and is also on record as not believing in witches or ghost so I think we can safely say he also rejected demonic magic, so he definitely wasn’t a sorcerer. He was however a convinced alchemist. This was not a mild side-line or passing fantasy as some commentators on Clark’s post would like to believe, the study of alchemy was his main occupation six months of the year for about thirty years. Also this was not after he ceased doing scientific work as many sources would have you believe but parallel to his main period of scientific activity between 1666 and 1696 when he gave up academia to move to London and the Royal Mint. It is important to understand that for Newton and his fellow alchemists, which included Robert Boyle and John Locke, alchemy was an epistemic discipline that is a branch of knowledge like optics or mechanics.

So Newton was neither a scientist nor a sorcerer so what was he? We have already seen he was a committed alchemist, what else?

Newton was Lucasian Professor of Mathematics at Cambridge so it is safe to call him a mathematician. To find out what he was we can look at his two principle publications The Optics and Principia. The Optics is basically a book on geometrical optics, which was then still a sub-discipline of mathematics, in fact Newton in his roll as professor lectured on optics, so this can safely be subsumed under his roll as mathematician. The Principia is actually titled Philosophiæ Naturalis Principia Mathematica or in English The Mathematical Principles of Natural Philosophy, all of which tells us that Newton was a natural philosopher. So we have mathematician and natural philosopher. However the title of his main work tells us that he was a representative of a fairly new breed of academic the mathematical natural philosopher. Newton wasn’t the first of this genus, which had slowly evolved since sometime in the High Middle Ages, Galileo, Kepler, Borelli and Huygens being other examples from the seventeenth century.

Maybe we could restate Clarks question as “Was Newton a mathematical natural philosopher or an alchemist?” but should we do so we would be again doing Newton an injustice. We are back to the reason that Newton did not think like a modern scientist. For Newton his theological studies (that I haven’t dealt with here) and his alchemical studies were an integral part of his natural philosophical investigations, in fact they were at the very heart of those investigations so to present these two aspects of his work as a dichotomy would be totally false.

In his blog post Clark quotes a footnote from Richard Westfall one of the deans of Newton studies:

“My modes of thought are so far removed from those of alchemy that I am constantly uneasy in writing on the subject … [Nevertheless] my personal preferences cannot make more than a million words he wrote in the study of alchemy disappear.”

He then goes on to quote novelist Rebecca Stott:

“Westfall admitted to wishing that he could make those million words disappear.”

This is a complete misrepresentation. It was one of Westfall’s doctoral students Betty Jo Teeter Dobbs who wrote the definitive account of Newton’s alchemical studies The Foundations of Newton’s Alchemy, or the Hunting of the Green Lyon and also the definitive account of how his alchemy fitted into his approach to knowledge The Janus Faces of Genius: The Role of Alchemy in Newton’s Thought. Both books are highly recommended for anybody who wishes to know more about Isaac the Alchemist.

For an excellent short account of the misrepresentation of Newton’s alchemical activities I recommend this post from last year by Rebekah “Becky” Higgitt at he blog Teleskopos: Newton and alchemy: a constant surprise?

Addendum: As Ian Hopkinson correctly pointed out on Twitter Newton is of course a Fig Roll.

The Virgin Queen was in reality John Dee in drag.

The rumbling you can hear in the background is the HISTSCI HULK playing skittles with some skyscrapers. He’s all riled up and wants to place a big green foot in Carole Jahme’s butt and propel her into publishing purgatory. What has Ms Jahme done to provoke the wrath of the big green HISTSCI destroyer? Damon Albarn’s so-called Opera Dr Dee is being revived in London and Ms Jahme wrote an introductory preview posted last Monday on the Guardian’s website. This preview is unfortunately a mixture of exaggerations, half-truths and fantasies that is a blot on the Guardian’s reputation for good journalism. Now it could be argued in her defence that several of the false claims made in her article are also made in the video interview with the director of the piece Rufus Norris and the Public Astronomer at the Royal Observatory Marek Kukula at the head of the article and that they are also to blame for this piece of shoddy journalism. However there is a thing in writing in general and in journalism in particular that seems to be going out of fashion called fact checking, something that Ms Jahme apparently can’t be bothered to waste her time on. I did consider letting the big green monster loose on her but didn’t fancy the job of cleaning up the carnage so I’ve decided to expose some of Ms Jahme’s worst history of science sins myself.

Before I deal with any detail from the article I would like to address the premise given by Norris for the opera itself. He, and Albarn in previous interviews, create the impression that Dee is somehow a neglected figure, particularly as a mathematicus (which is what he was), I beg to differ. There are at least eight monographs that deal with large parts or the whole of Dee’s biography as well as several monographs that deal with wider contexts of Elizabethan culture that have Dee as a central figure. A couple of these works deal explicitly with Dee as a Renaissance scientific figure. There is also a volume of academic papers on Dee as well as academic annotated editions of his principle works. Already in the 1930s, as modern history of science was beginning to emerge, historians of astronomy, geography and navigation devoted quite a considerable amount of attention to Dee. There are articles on Dee in the Encyclopaedia Britannica, the Dictionary of Scientific Biography, the New Oxford dictionary of Biography and in the Internet at MacTutor and on Wikipedia, some of them quite substantial. I do not think Dee has been neglected, in fact I can’t think of another scientific figure of his stature who has been covered in anything approaching the expansive extant to which Dee has been. This brings us to the next problem, what is Dee’s scientific stature. Just as it is easy to underestimate Dee’s importance and influence in the development of the mathematical sciences in late sixteenth century England it is also possible to overestimate them and in my opinion both in the video and the article this is done. Dee played a role as a teacher and facilitator along with Robert Recorde, Leonard Digges, Thomas Digges, Thomas Harriot, Edward Wright and others in introducing the mathematical sciences into Britain but he made no original contributions to the mathematical sciences himself. He is not a Kepler, Galileo, Descartes or Huygens and he is certainly not one of the giants on whom shoulders Newton stood as claimed by Norris in the interview. Dee is an important figure but he is no more important than at least a dozen of his contemporaries who have received not even ten per cent of the scholarly attention that Dee has.

John Dee

Now to Ms Jahme who tells us that:

Dee was a larger-than-life magus figure. He was probably the inspiration for Christopher Marlowe’s character Doctor Faustus, Ben Jonson’s The Alchemist and Shakespeare’s Prospero.

We’ve been here before as the opera was premiered in Manchester but it is worth re-examining these claims. Marlow’s Faustus is of course based on the real life German magus Dr Johann Georg Faust whose fictionalised life story was a sixteenth century best seller. Ben Johnson’s The Alchemist is a satire on alchemy and alchemists in general, of which Dee was only one of many, and whilst Dee is not name-checked in the piece his medium Edward Kelly is. The claim that Dee is Prospero is old and there is no evidence to support it. Frances Yates one of the real experts for sixteenth century alchemy and magic thinks that Prospero is Giordano Bruno but addresses the claim for Dee pointing out that Dee and Bruno share many key characteristics. I think Prospero is probably a composite figure with elements of Bruno, Dee, Faust, Kelly, Robert Fludd, Cornelius Agrippa, Oswald Croll and a dozen other less well-known contemporary hermetic figures. Instantly identifying Prospero with Dee is in my opinion an act of hagiography and a failure to recognise just how widespread hermeticism was at the end of the sixteenth and beginning of the seventeenth centuries.

Ms Jahme informs us that:

Dee taught Raleigh and Drake “the perfect art of navigation” for calculating longitude from lunar distance observation, which helped facilitate the establishment of the British Empire.

Dee was certainly one of the mathematical practitioners teaching navigation and cartography to English sea captains in the sixteenth century along with Thomas Digges, Harriot, Wright and others but he did not teach Drake or Raleigh. I don’t actually know who, if anyone, taught Drake but if it had been Dee I’m sure I would have read about it in my studies and I haven’t. Raleigh and his ship’s captains were of course instructed not by Dee but by his friend Thomas Harriot who even accompanied the ill fated expedition to establish a colony on Roanoke Island in Virginia, as a sort of scientific officer. Dee instructed Martin Frobisher and other captains of the Muscovy Company in their attempts to discovery either a North-West or a North-East passage to China.

There is more to come Ms Jahme continues with the following:

Infamous in his lifetime, Dee was a risk-taker and exceptional scholar. With his eye on the court he rejected the comfort of university tenure at Cambridge, preferring to collate and categorise his data independently. A serious bibliophile, his private library became the largest in Britain. Dee charted the movement of the planets and in his early career toured Europe giving talks on astronomy – a form of science outreach that was entirely new.

We have here four claims of which two are true, one shows a complete lack of understanding of sixteenth century intellectual culture and one is complete rubbish. The first sentence and the statement about Dee’s love of books are both correct. The statement about university tenure is quite frankly bizarre. It seems to assume that Mediaeval Cambridge was like a modern university. Dee had a fellowship at Trinity but after graduating MA he left the university, as he apparently did not wish to study for a doctorate. Accepting a life as fellow and under-reader in Greek would have been tantamount to giving up before he started, not the comfort of university tenure but a dead end in badly paid futility. However it is the final sentence that this time takes the prize for wrongness. Jahme has exaggerated and misinterpreted a moderately false statement of Norris’ and made a real mess out of it.

In the period of his life that he dedicated to the study of the mathematical sciences Dee made three trips to the European continent; these were not lecture but study tours. Such tours were common practice in the High Middle Ages and the Renaissance with young scholars travelling from university to university to study manuscripts not available in their home university libraries and to meet, study under and discuss or dispute with other scholars. Norris says that this was unique for an English mathematical practitioner at this time and although rare it was not unique. Henry Savile, who would later use his fortune to found the chairs for geometry and astronomy in Oxford, is a contemporary of Dee’s who also undertook such a study tour of the continent. Norris also claims that this was a lecture tour and it is this that Jahme falsely makes unique. On his first trip of only a few months in 1547 Dee studied in Louvain under Gemma Frisius and Gerald Mercator. He returned to Louvain for further studies in 1548 and staid until 1550. Here I would like to correct another of Norris’ false statements. He claims in the video interview that Dee’s range of subjects mathematics, astronomy, astrology, geography, cartography, navigation and history was unusually wide and unique. This is simply not true. This is the normal range of study of the Renaissance mathematicus and is exactly what Dee would have studied with Frisius and Mercator in Louvain. When he left Louvain Dee went to Paris were he did indeed lecture, not on astronomy, but Euclidian geometry. Again this is not out of the ordinary, the visiting scholar demonstrating his own learning to his hosts, nothing new or unusual here. His third trip abroad in 1562 to 1564 was to visit other scholars such as Gesner in Switzerland or the Italian mathematician Commandino with whom he published the translation of a Greek mathematical text.

He was opposed to a tiered system of education where those without classical scholarship were held back, so when his translation of Euclid’s mathematics was complete he made the arcane information accessible to non-university-taught artisans and craftsmen. In his General and Rare Memorials Pertaining to the Perfect Arte of Navigation, he advocated the usefulness of mathematics as a “Publick Commodity”.

In the above quote Jahme has got something right for a change. Dee, following Robert Recorde, is one of the founders of the so-called English School of Mathematics; a group of mathematical practitioners who made their knowledge available in the vernacular. However Dee, unlike Digges for example, also wrote extensively in Latin for an educated public. The paragraph does however contain one serious error. Although Dee wrote his very famous preface for the first English translation of Euclid’s Elements, the translation itself was not by Dee but by Henry Billingsley.

We now come to what I regard as the weirdest claim made by Jahme:

His students include Francis Bacon, promoter of the “scientific method”, and the astronomer Thomas Diggs, who believed the universe to be infinite.

Thomas Digges was not only Dee’s student but also his foster son and he was indeed the first modern astronomer to propose an infinite universe. Although Dee was instrumental in spreading knowledge of Copernican heliocentricity in England he does not appear to have been a totally convinced Copernican. Digges, however, was a totally convinced Copernican who also published the first ever partial translation into the vernacular of De revolutionibus. Now I wouldn’t claim to be an expert on either Dee or Bacon but I have read an awful lot about and by both of them and I have never ever come across the claim that Bacon was a student of Dee’s. If we look at this rationally it also seems highly unlikely. Dee was absolutely convinced that mathematics was the most important discipline of all and was the number one propagator of the works of Copernicus in Britain. Bacon rejected both mathematics and heliocentricity so it does no appear very likely that he was Dee’s student. I will happily admit that I haven’t really researched this properly but a quick search revealed that Dee mentions Bacon just once in his diary. The then 21 year old accompanied somebody else who was visiting Dee in Mortlake in 1583. Bacon never mentions Dee at all in his voluminous writings! I did stumble across one website that actually claimed the fact of Dee’s absence from Bacon’s writings as proof that Bacon was Dee’s disciple! On that basis I could prove literally anything!

It is to the enigmatic Dr John Dee that we must look for the origins of Britain’s contribution to modern Western science, yet Dee has been largely left out of the history books – why?

Both of the claims made in the quote above are simply false and two wrongs definitively do not make a right. This post is already over long but there are two short claims made by Ms Jahme that I wish to include before I close my demolition of her pitifully bad piece of history of science journalism. She writes:

In 1600, astronomer Giordano Bruno was burnt at the stake for daring to say the sun was a star.

And a few lines further on:

Within Dee’s lifetime Copernicus’s sun-centric theories would be strengthened by Galileo’s discoveries.

Giordano Bruno was not an astronomer and he was burnt for his religious opinions and not for his cosmological ones. The reports are not totally in agreement but Dee died in either 1608 or 1609. Galileo first published his telescopic discoveries in 1610 so not in Dee’s lifetime.

It would appear that one qualifies as a history of science writer these days when one is good at making things up so I’ve decided to stop being a pedant and to go with the flow. My next work will be the sensational discovery that Elizabeth the Virgin Queen was in reality Renaissance magus John Dee in drag! Remember you read it here first.

Mapping the history of triangulation

One of my interests as a historian of practical mathematics is the history of the invention of triangulation and its applications in both cartography and geodesy, a subject on which I have, in the meantime, read a small library of academic books and papers. Now, at first glance, it would seem that the measuring of large triangles across the landscape is not the sort of exciting scientific endeavour that would inspire an author to put pen to paper or fingers to keyboard to produce a work of popular science history, however appearances can be deceptive. I possess five popular historical volumes on the application of triangulation to the solution of geodetic and cartographic problems, of which I have read the first three They are John Keay, The Great Arc: The Dramatic Tale of How India was Mapped and Everest was Named, HarperCollins, 2000, Ken Alder, The Measure of All Things: The Seven Year Odyssey and Hidden Error That Transformed the World, Free Press, 2002, Rachel Hewitt, Map of a Nation: A Biography of the Ordnance Survey, Granta Books, 2010, Larrie D. Ferreiro, Measure of the Earth: The Enlightenment Expedition that Reshaped the World, Basic Books, 2011 and Paul Murdin, Full Meridian of Glory: Perilous Adventures in the Competition to Measure the Earth, Copernicus Books, 2009. The first, as the title says, deals with the measurement of the meridian arc in India in the 19^th century and the resulting mapping of this sub-continent. The second deals with the re-measurement of the meridian arc in France to determine the basic unit of the metre for the metric system in the late 18^th century. The third is self-explanatory but also includes the measurement of a meridian arc in Britain. The last two deal with the history of the measurement, mostly by the French, of meridian arcs in France, Peru and Lapland to determine whether the earth is a prolate or an oblate spheroid, a story that I have already blogged about.

Given the fact that triangulation is a very major, or even the major, player in all of these books one could as reader expect the authors to have researched and in their respective books to explain the historical origins of this technique or methodology. This expectation is not really fulfilled. Let us examine what each of them has to say on the subject.

Paul Murdin writes the following:

[Willebrod] Snell (sic)[1] had proposed the technique of triangulation as a way to measure the relative locations of points on the surface of the Earth (Smith 1986). The method, which is still the standard one, starts by the surveyors measuring a reference line between two stakes on a flat plain using standard sized sticks or chains (Fig. 7). A third stake is placed somewhere else on the plain at a significant location. From each end of the line, a surveyor sights the stake at the other end as well as the third stake, measuring the angle between with a theodolite. [emphasis in original] The third stake is located relative to the other two by trigonometry of the triangle. From the reference points the surveyor can also sight natural vertical features in the landscape.  […]  All these features can be located relative to the others building a chain of triangles across the country – hence the term triangulation (Murdin, p. 15)

Snell’s techniques were demonstrated by relatively small-scale projects by him and other Dutch cartographers. The first survey by triangulation is regarded to be Snell’s survey prior to 1615 of the Netherlands from Alkmaar via Amsterdam, Leiden, Utrecht, Dordrecht and Breda to Bergen-op-Zoom, accumulating an overall distance of 120 km. (Murdin p. 17)

Although he doesn’t actually directly say so Murdin implies that the technique of triangulation was invented by Snel; it wasn’t. Although Snel was almost certainly the first to measure a meridian arc using triangulation he certainly wasn’t the first to carry out a triangulation survey. I have included so much of the first quote because it saves me the bother of explaining the basic principles of triangulation. Let see whether Ferreiro does any better.

Writing about The Academy of Science’s proposal to extend Picard’s first triangulation survey in the late 17^th century he writes:

The method for carrying out long-distance surveys had been around for several centuries and used a basic Euclidean premise: Given two angles of a triangle and the length of one side, the remaining sides and angles can be computed. This principle can be employed to measure over long distances by establishing a geodesic chain of triangles between two fixed points.

 Here nobody in credited with the invention and the couple of lines quoted contain a number of serious errors. The method had not been around for several centuries but was, as we will see, invented in the first half of the 16^th century. It does not use a basic Euclidean premise. Given two angles and one side of a triangle one can construct the triangle using Euclidean geometry but if you wish to compute the rest of the triangle, and the subsequent chain of triangles, which is indeed what is done in triangulation, you need trigonometry, which you will search for in vain in the Elements of Euclid. The oldest surviving source for trigonometry is Ptolemaeus’ Syntaxis Mathematiké from the middle of the 2^nd century CE more than 400 years later than Euclid. The trigonometry used in the Early Modern Period for triangulation came into Europe from India via the Islamic Empire during the High Middle Ages.

How do our other authors fair fare? Alder like Murdin plumps incorrectly for Snel, also misspelling his name:

The modern technique for using triangles to measure earthly distances, however, was introduced in 1617 by Willebrod Snell, “The Dutch Eratosthenes,” on the frozen fields outside Leyden, and his [my emphasis] method persisted for the next 360 years.

To be fair to both Murdin and Alder many academic sources, that should know better, attribute the invention of triangulation to Snel.

Keay ignores the subject completely giving a brief description of the principles of the technique but wasting no thoughts on its origins. Of our five authors only Hewitt gets the attribution right, she writes:

Triangulation had first emerged as a map-making method in the mid sixteenth century when the Flemish mathematician Gemma Frisius set out the idea in his Libellus de locorum describendum ratione (Booklet concerning a way of describing places),…

So who was Gemma Frisius?

Gemma Frisius 17th C woodcut

E. de Boulonois

He was born Jemma Reinierzoon or Jemma son of Reinier to poor parents in Dokkum in Friesland on 9^th Dec 1508. His nom de plume Gemma Frisius is a Latinised onomatopoeic version of his birth name plus the toponym Frisius for Friesland. His parents died whilst he was still very young and he moved to relatives in Groningen, where he was educated in a cloister school. On 26^th February 1926 1526 he matriculated as a poor scholar at the University of Louvain where he graduated Master of Arts in 1528. In 1529 there followed one of the strange unexplained episodes in the history of science. In 1924 1524 the then young German graduate of the University of Vienna Peter Apian published his Cosmographia, a textbook on astronomy, astrology, surveying, cartography and other aspects of applied astronomy. Apian not only wrote this book but printed and published himself, as part of his efforts to establish himself as a scientific publisher. In 1529 a second improved edition of Apian’s Cosmographia was published but not by Apian, the second and all the subsequent highly successful extended and improved thirty-two editions of this book, in many different languages, were edited by Gemma Frisius. This was one of the most successful mathematical textbooks published in the sixteenth century and it is not known why Gemma and not Apian edited and published all but the original edition.

Following up on his edition of Apian’s Cosmographia Gemma Frisius began to make printed terrestrial and celestial globes moving the tradition of their manufacture from Nürnberg to the northern Germanic area and through his pupil Gerard Mercator into Holland, where the Dutch would dominate the European globe making industry for most of the seventeenth century. He also set up as an instrument maker and through his own efforts and those of his nephews, the Arsenius brothers, Louvain became a major centre for high quality mathematical instruments.

In 1934 1534 he married and started to study medicine, graduating MA in 1536, which allowed him to practice medicine, going on to obtain his MD in 1541. At some point he became Professor of Medicine at the University of Louvain. During his medical studies he famously helped his fellow medical student Andreas Vesalius to steal a corpse from the gallows to conduct a bit of illicit dissection. Vesalius would of course go on to publish the most famous anatomy book of all times, his De fabrica, in 1543, in which he praises Gemma as a doctor and a mathematician.

Teaching medicine at the university, Gemma only taught mathematics privately producing in his time several famous pupils. I have already mentioned Gerard Mercator possibly the most well know of Gemma’s students but amongst other names known only to historians of mathematics and astronomy can be found the name of John Dee who came to Louvain after graduating at Cambridge to study at the feet of the master.

Gemma published nothing on medicine but lots of works on mathematics including, alongside the Cosmographia, the most successful arithmetic textbook of the sixteenth century. His Radio astronomico, a handbook on a new form of cross-staff of his own invention, published in 1545, contains the earliest printed, largely positive, discussion of Copernicus’ De revolutionibus.

Gemma was very successful and highly respected in his own lifetime and was one of the leading mathematical practitioners of Europe when he died of kidney stones on 25^th May 1555 not yet 47 years old.

Many of his innovations in the mathematical sciences were published as appendices to his various editions of the Cosmographia and it is here attached to the 1533 third edition (Gemma’s second) that we find the Libellus de locorum describendum ratione, his pamphlet outlining completely and in detail the technique of triangulation.

Gemma himself did not enjoy good health and was a thinker and not a doer so he almost certainly didn’t carry out any surveying work himself. We do know that Mercator used Gemma’s method when he surveyed the Duchy of Lorraine later in the century. Tycho Brahe who knew Gemma’s work well being a customer of his instrument workshop also conducted a survey of his island of Hven using Gemma’s triangulation, which was never actually finished. Willebrod Snel would also have been well acquainted with Gemma’s work and it is almost certainly the Libellus that was the source of his knowledge of triangulation.

Some sources claim rather vaguely that triangulation was acquired by the Europeans from the Arab mathematicians during the Renaissance but fail to give any source for these claims or to reference any Arabic works on the subject. More directly some sources claim that the great Islamic scholar al-Biruni, who wrote extensively on geography and geodesy, used triangulation. This claim is simply false. He used geometrical methods to determine the longitude and latitude of various cities but his calculations did not just use triangles and he had no measured base line and made no sightings. He merely constructed geometrical models of the positions of the towns respective to each other based on travellers’ tales of the scale of their separations.

Historically there is very little doubt that the technique of triangulation emerged once and once only in a pamphlet written and published by Gemma Frisius in 1533. It is a strange fact that relatively insignificant scientific discoveries and inventions proudly carry the names of their discoverers and inventors but most people, including the people who write books about it, never stop to consider who invented triangulation, which until the invention of GPS, was the only tool, and a very powerful one, capable of producing accurate maps with their incredible economic, political, military and scientific significance. Gemma Frisius belongs in the pantheon of great modern scholars for his invention and not forgotten and ignored even by those who earn money writing about the incredible applications that this invention made possible.

 

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[1] Snel is written with only one ‘l’, a common mistake in English texts. In his Latin publications Snel Latinised his name, as had his father also an academic mathematician, as Snellius. English authors translating back into the vernacular made the mistake of retaining the second ‘l’.

It’s not the Mercator projection; it’s the Mercator-Wright projection!

500 years ago on 5^th March 1512 Gerard de Kremer was born in Rupelmonde, in those days a town in the Spanish Netherlands today in Belgium. He is of course much better known through his Latinised pseudonym Mercator.

In German a Kremer or Krämer is a shopkeeper, a grocer and Latinised it becomes Mercator, the root of course of the English words merchant, mercantile, merchandise etc. In modern German a Krämerladen is a corner-shop. Mercator turns up for the first time in a scientific context as an assistant globe-maker to Gemma Frisius in Leuven between 1534 and 1537. Gemma Frisius was professor of medicine at the University of Leuven and was a leading European mathematicus.

Under his tuition Mercator learnt mathematics, astronomy, astrology, surveying, instrument and globe making and cartography. As a pupil and later colleague of Frisius Mercator became part of an important circle of mathematical practitioners that included the Englishman John Dee and the Dutchman Abraham Ortelius.

In his own right Mercator became one of the leading European instrument and globe makers, surveyors, and cartographers but in this post I just want to take a brief look at the thing for which he is most famous the Mercator projection.

As you probably know it is impossible to cut open a sphere and spread it out flat. This is a major problem for cartographer because of course the world is a sphere, at least theoretically. In reality it resembles a rather lumpy distorted potato but cartographers treat it as an idealised oblate spheroid. Over the centuries cartographers developed mathematical methods of transferring the surface of the sphere onto a flat sheet of paper, parchment or what ever. These methods are known as projections because that is exactly what they are. On selects a viewpoint inside or outside the sphere and projects the points on its surface along the lines of sight onto a flat surface. One such projection is the cylindrical projection in which the sphere is conceived of as being inside a cylinder and all points on the spheres surface are projected from the middle of the sphere onto the inside of the cylinder which is then rolled out flat.

The problem is that all projections distort if some way the surface of the sphere. A cartographer has to choose the projection, which best conserves that aspect of the map that he wishes to emphasise.

In the Renaissance the age of exploration, which had been kick-started by the Portuguese King Henry the Navigator (who coincidentally was born on 4^th March 1394) in the 15^th century,

the mathematicians were called upon to develop new methods of astral and mathematical navigation and new forms of cartography. Mercator’s teacher Gemma Frisius for example invented triangulation for surveying and cartography and first suggested the chronometer method of determining longitude. One of the central problems that needed to solved was what path does a compass bearing follow on a globe and how would it be possible to represent that compass bearing as a straight line on a sea chart?

The first part of the problem was solved by the Portuguese mathematicus Pedro Nunes one of the leading mathematical practitioners of the age. Nunes was professor of mathematics at the University of Coimbra and Royal Cosmographer to the Portuguese Crown.

Nunes demonstrated that a constant compass bearing on a globe follows a segment of a spiral and not a great circle as had been previously assumed. Such lines are technically known as loxodromes or rhumb lines.He also knew that in order to make a constant compass bearing on a sea-chart a straight line then the lines of longitude and latitude must be straight parallel lines but he was not able to work out how the lines of latitude needed to be spaced. This was the problem that was first solved by Mercator and led to the Mercator projection.

The Mercator projection is basically a cylindrical projection in which the distances between the lines of latitude are adjusted according to a special mathematical formula.

Mercator printed and published a world map constructed according to this method of projection in 1569 but he did not explain the mathematical rules on which it was based. He was a professional cartographer and globe maker and he probably hoped that if he kept his method secret then the people who wished to take advantage of this new development would have to order their maps and charts from him.

We know from their unpublished papers that both of the English mathematicians John Dee

and Thomas Harriot

independently solved the mathematical problem of the projection but like Mercator neither of them made the knowledge public. We can however assume that both of them made use of this knowledge when teaching navigation and cartography, Dee to the pilots of the Muscovy Company and Harriot to Walter Raleigh’s sea captains.

The first person to publish the mathematical method of constructing such a chart was another English mathematicus Edward Wright in his book Certaine Errors in Navigation, first published in 1599.

It is because of this that modern historians of cartography say that the correct name for this type of map projection is the Mercator-Wright Projection.

If you go to John D. Cook’s Endeavour Blog and follow the links you can find out all about the maths of the Mercator-Wright projection. There’s a link to a Mercator projection xkcd cartoon too!

Midwifery in the evolution of science

In the history of science there are some well known cases of scholars who acted as midwives for more prominent colleges helping or even leading them to present their epoch making work to the general public. The most famous case is probably Edmund Halley who not only posed the question that provoked Newton to write his Principia but saw the book through the press, even paying the publishing cost out of his own pocket because the Royal Society had notoriously spent all of its funds publishing a book on fish. Another scientific midwife in the Early Modern Period was Georg Joachim Rheticus who was born on 16^th February 1514. It was the young Rheticus who travelled to Frombork in Ermland and persuaded Copernicus to publish his De revolutionibus and took the manuscript personally to the printer publisher Johannes Petrejus in Nürnberg, although he didn’t stay to see it through the press.

Born Georg Joachim Iserin in the town of Feldkirch in Austria his father, also Georg, was the town medicus and his mother Thomassina de Porris was a minor Italian aristocrat. However despite his privileged birth his childhood was anything but smooth. As he was only fourteen years old his father was found guilty of stealing from his patients and sentence to death. As part of his sentence his name was banned in perpetuity and Georg Joachim Iserin became Georg Joachim de Porris. Georg Joachim was lucky in that he found the support and friendship of Achilles Pirmin Gasser his father’s successor as town medicus. Gasser arranged for the youth to attend school in Zurich where he sat on the school bench next to Conrad Gessner who would go on to become one of the leading naturalists of the age and remained a friend for life. In 1531 Gasser sent him to his own alma mater Luther’s university in Wittenberg. Here his talent for mathematics was recognised and supported by Phillip Melanchthon. As he graduated MA in 1536 Melanchthon appointed him professor for the lower mathematics. It was during his time as a student in Wittenberg that he adopted the toponym Rheticus based on the name of the Roman province containing Feldkirch, Rhaetia.

In 1538 Rheticus took leave of absence from the university to go on an extended study tour of Southern Germany. Such tours were common practice on the mediaeval university and he went with the support of and letters of introduction from Melanchthon. The first station on his journey was Nürnberg where he studied astrology with Johannes Schöner the professor of mathematics at the local gymnasium and a good friend of Melanchthon. Here he got to know Nürnberg’s comparatively large mathematical community including Johannes Petrejus the leading European publisher of mathematical texts. After several months in Nürnberg he moved on to Tübingen and the rector of the university there, Joachim Camerarius the Elder, Melanchthon’s close friend and later biographer. Camerarius had been rector of the gymnasium in Nürnberg before being appointed rector in Tübingen and was a close friend of both Petrejus, for whom he had worked as an editor, and Schöner.  Rheticus also had a letter of introduction to Peter Apian in Ingolstadt but it is doubtful whether he ever went there.

Sometime in his travels Rheticus heard of an astronomer in Ermland who had supposedly developed a completely new system of the world. Curious to discover what this man had to offer Rheticus decided to go and seek him out. After a visit to Gasser in Feldkirch he set off on the long journey to Frombork. The Ermlander astronomer was of course Copernicus who was already sixty-six years old as the young Wittenberg professor arrived at his door in 1539. Rheticus spent most of the next two years persuading the older man to revise and prepare his manuscript for publication and to allow him to take the manuscript to Pertrejus in Nürnberg to be printed. In 1540 Rheticus published his own account of Copernicus’ work the Narratio prima (first report) in the form of an open letter addressed to Johannes Schöner. In 1541 he published, as a separate work, a revised version of the trigonometry sections of De revolutionibus. In 1542 he finally brought Copernicus’ manuscript to Petrejus’ workshop in Nürnberg and the process of printing could begin. Rheticus had intended to see the work through the press himself but Melanchthon demanded that he take up his new position as professor of mathematics in Leipzig where Camerarius was now rector. Andreas Osiander took over the job of editing Copernicus’ manuscript with consequences that would echo down the centuries.

Rheticus’ work as midwife was over and his life would lead him along a complex and at times sad path, which I will deal with another time. Without Rheticus’ intervention Copernicus’ legendary book might never have seen the light of day so he deserves to have a higher profile in the history of science than he does.