New lecturing attire

I have acquired a new T-shirt from the good folks at the History of Alchemy Podcasts, which will be worn with pride whilst lecturing on the history of alchemy (and other topics).

The elegant piece of attire can be witnessed below modelled by the lecturer in person on the market place in Erlangen this very Saturday.

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Should you wish to also acquire such an elegant object of haut-couture and thereby support the excellent work of the History of Alchemy Podcasts then you can do so here. If you don’t already listen to the History of Alchemy Podcasts you should!

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A spirited defence

After I had, in my last blog post, mauled his Scientific American essay in my usual uncouth Rambo style, Michael Barany responded with great elegance and courtesy in a spirited defence of his historical claims to which I now intend to add some comments, thus extending this exchange by a fourth part.

On early practical mathematicians Michael Barany acknowledges that their work is for the public good but argues correctly that that doesn’t then a “public good”. I acknowledge that there is a difference and accept his point however I have a sneaky feeling that something is only referred to as a “public good” when somebody in power is trying to put one over on the great unwashed.

Barany thinks that the Liber Abbaci and per definition all the other abbacus books, only exist for a closed circle of insider and not for the general public. In fact abbacus books were used as textbooks in so-called abbacus schools, which were small private schools that taught the basics of arithmetic, algebra, geometry and bookkeeping open to all who could pay the fees demanded by the schoolteacher, who was very often the author of the abbacus book that he used for his teaching. It is true that the pupils were mostly the apprentices of tradesmen, builders and artists but they were at least in theory open to all and were not quite the closed shop that Michael Barany seems to be implying. In this context Michael Barany says that Recorde’s Pathway to Knowledge, a book on elementary Euclidean geometry, is eminently impractical. However elementary Euclidean geometry was part of the syllabus of all abbacus schools considered part of the necessary knowledge required by artist and builder/architect apprentices. In fact the first Italian vernacular translation of Euclid was made by Tartaglia, an abbacus schoolteacher.

Michael Barany makes some plausible but rather stretched argument to justify his couterpositioning of Recorde and Dee, which I don’t find totally convincing but slips into his argument the following gem. If you don’t like Dee as your English standard bearer for keeping mathematics close to one’s chest, try Thomas Harriot. Now I assume that this flippant comment was written tongue in cheek but just in case.

Michael Barany’s whole essay contrasts what he sees as two approaches to mathematics, those who see mathematics as a topic for everyone and those who view mathematics as a topic for an elitist clique. In the passage that I criticised in his original essay he presented Robert Recorde as an example of the former and John Dee as a representative of the latter. A contrast that he tries to defend in his reply, where this statement about Harriot turns up. Now his elitist argument is very much dependent on a clique or closed circle of trained experts or adepts who exchanged their arcane knowledge amongst themselves but not with outsiders. A good example of such behaviour in the history of science is alchemy and the alchemists. Harriot as an example of such behaviour is a complete flop. Thomas Harriot made significant discoveries in various fields of scientific endeavour, mathematics, dynamics, chemistry, optics, cartography and astronomy, however he never published any of his work and although he corresponded with other leading Renaissance scholars he also didn’t share his discoveries with these people. A good example of this is his correspondence with Kepler, where he discussed over several letters the problem of refraction but never once mentioned that he had already discovered what we now know as Snell’s Law. Harriot remained throughout his life a closed circle with exactly one member, not a very good example to illustrate Michael Barany’s thesis.

I claimed that there was no advance mathematics in Europe from late antiquity till the fifteenth century. Michael Barany counters this by saying: This cuts, for instance, the rich history of Islamic court mathematics out of the European history in which it emphatically belongs; it doesn’t cut it. Ignoring Islamic Andalusia, Islamic mathematics was developed outside of Europe and although it started to reappear in Europe during the twelfth and thirteen centuries during the translator period nobody within Europe was really capable of doing much with those advanced aspects of it before the fifteenth century, so I stand by my claim.

We now turn to Michael Barany’s defence of his original: In the seventeenth century’s Scientific Revolution, the new promoters of an experimental science that was (at least in principle) open to any observer were suspicious of mathematical arguments as inaccessible, tending to shut down diverse perspectives with a false sense of certainty. This he contrast with a, in his opinion, eighteenth century where mathematicians help sway over the scientific community. I basically implied that this claim was rubbish and I still stand by that to that, so what does Michael Barany produce in his defence.

In my original post I listed seven leading scholars of the seventeenth century who were mathematicians and whose very substantive contributions to the so-called scientific revolution was mathematical, on this Barany writes:

Thony pretends that naming some figures remembered today both for mathematics and for their contributions to the scientific revolution contradicts this well-established historical claim.

The, without any doubt, principle figures of the so-called scientific revolution are just some figures! Interesting? So what is Michael Barany’s well-established historical claim? We get offered the following:

Following Steven Shapin and many who have written since his classic 1988 article on Boyle’s relationship to mathematics, I chose to emphasize the conflicts between the experimental program associated with the scientific revolution and competing views on the role of mathematics in natural philosophy.

What we have here is an argument by authority, that of Steven Shapin, whose work and the conclusions that he draws are by no means undisputed, and one name Robert Boyle! Curiously a few days before I read this, science writer, John Gribbin, commentated on Facebook that Robert Hooke had to work out Boyle’s Law because Boyle was lousy at mathematics, might this explain his aversion to it? However Michael Barany does offer us a second argument:

But to take just his most famous example, Newton’s prestige in the Royal Society is generally seen today to have had at least as much to do with his Opticks and his other non-mathematical pursuits as with his calculus, which contemporaries almost uniformly found impenetrable.

Really? I seem to remember that twenty years before he published his Opticks, Old Isaac wrote another somewhat significant tome entitled Philosophiæ Naturalis Principia Mathematica [my emphasis], which was published by the Royal Society. It was this volume of mathematical physics that established Newton’s reputation, not only with the fellows of the Royal Society, but with the entire scientific community of Europe, even with those who rejected Newton’s central concept of gravity as action at a distance. This book led to Newton being elected President of the Royal Society, in 1704, the same year as the Opticks was published. The Opticks certainly enhanced Newton’s reputation but he was already considered almost universally by then to be the greatest living natural philosopher.

Is the Opticks truly non-mathematical? Well, actually no! When it was published it was the culmination of two thousand years of geometrical optics, a mathematical discipline that begins with Euclid, Hero and Ptolemaeus in antiquity and was developed by various Islamic scholars in the Middle Ages, most notably Ibn al-Haytham. One of the first mathematical sciences to re-enter Europe in the High Middle Ages it was propagated by Robert Grosseteste, Roger Bacon, John Peckham and Witelo. In the seventeenth-century it was one of the mainstream disciplines contributing to the so-called scientific revolution developed by Thomas Harriot, Johannes Kepler, Willebrord van Roijen Snell, Christoph Scheiner, René Descartes, Pierre Fermat, Christiaan Huygens, Robert Hooke, James Gregory and others. Newton built on and developed the work of all these people and published his results in his Opticks in 1706. Yes, some of his results are based on experiments but that does not make the results non-mathematical and if you bother to read the book you will find more than a smidgen of geometry there in.

In my opinion trying to recruit Newton as an example of non-mathematical experimental science is an act of desperation.

To be fair to Michael Barany the division between those who favoured non-mathematical experimental science and the mathematician really did exist in the seventeenth century, however it was largely confined to England and most prominently in the Royal Society. This is the conflict between the Baconians and the Newtonians that I have blogged about on several occasions in the past. Boyle, Hooke and Flamsteed, for example, were all Baconians who, following Francis Bacon, were not particularly fond of mathematical proofs. This conflict has an interesting history within the Royal Society, which led to disadvantages for the development of the mathematical sciences in England in the eighteenth century.

When the Royal Society was initially founded some mathematician did not become members because of the dominance of the Baconians and that despite the fact that the first President, William Brouncker, was a mathematician. Later under Newton’s presidency the mathematicians gained the ascendency, but first in 1712 after an eight-year guerrilla conflict between Newton and Hans Sloane, a Baconian and the society’s secretary. Following Newton’s death in 1727 (ns) the Baconians regained power and the result was that, whereas on the continent the mathematical sciences flourished and evolved throughout the eighteenth century, in England they withered and died, leading to a new power struggle in the nineteenth century featuring such figures as Charles Babbage and John Herschel.

To claim as Michael Barany does that this conflict within the English scientific community meant that mathematics played an inferior role in the seventeenth century is a bridge too far and contradicts the available historical facts. Yes, the mathematization of nature was not the only game in town and interestingly non-mathematical experimental science was not the only alternative. In fact the seventeenth century was a wonderful cuddle-muddle of conflicting meta-physical views on the sciences. However whatever Steven Shapin might or might not claim the seventeenth century was a very mathematical century and mathematics was the principle driving force behind the so-called scientific revolution. As a footnote I would point out that many of the leading experimental natural philosophers of the seventeenth century, such as Galileo, Pascal, Stevin and Newton, were mathematicians who interpreted and presented their results mathematically.

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Some rather strange history of maths

Scientific American has a guest blog post with the title: Mathematicians Are Overselling the Idea That “Math Is Everywhere, which argues in its subtitle: The mathematics that is most important to society is the province of the exceptional few—and that’s always been true. Now I’m not really interested in the substantial argument of the article but the author, Michael J. Barany, opens his piece with some historical comments that I find to be substantially wrong; a situation made worse by the fact that the author is a historian of mathematics.

Barany’s third paragraph starts as follows:

In the first agricultural societies in the cradle of civilization, math connected the heavens and the earth. Priests used astronomical calculations to mark the seasons and interpret divine will, and their special command of mathematics gave them power and privilege in their societies.

We are taking about the area loosely known as Babylon, although the names and culture changed over the millennia, and it is largely a myth, not only for this culture, that astronomical calculations were used to mark the seasons. The Babylonian astrologers certainly interpreted the divine will but they were civil servants who whilst certainly belonging to the upper echelons of society did not have much in the way of power or privilege. They were trained experts who did a job for which they got paid. If they did it well they lived a peaceful life and if they did it badly they risked an awful lot, including their lives.

Barany continues as follows:

As early economies grew larger and more complex, merchants and craftsmen incorporated more and more basic mathematics into their work, but for them mathematics was a trick of the trade rather than a public good. For millennia, advanced math remained the concern of the well-off, as either a philosophical pastime or a means to assert special authority.

It is certainly true that merchants and craftsmen in advanced societies – Babylon, Greece, Rome – used basic mathematics in their work but as these people provide the bedrock of their societies ­– food, housing etc. – I think it is safe to say that their maths based activities were in general for the public good. As for advanced maths, and here I restrict myself to European history, it appeared no earlier than 1500 BCE in Babylon and had disappeared again by the fourth century CE with the collapse of the Roman Empire, so we are talking about two millennia at the most. Also for a large part of that time the Romans, who were the dominant power of the period, didn’t really have much interest in advance maths at all.

With the rebirth of European learned culture in the High Middle ages we have a society that founded the European universities but, like the Romans, didn’t really care for advanced maths, which only really began to reappear in the fifteenth century. Barany’s next paragraph contains an inherent contradiction:

The first relatively widespread suggestions that anything beyond simple practical math ought to have a wider reach date to what historians call the Early Modern period, beginning around five centuries ago, when many of our modern social structures and institutions started to take shape. Just as Martin Luther and other early Protestants began to insist that Scripture should be available to the masses in their own languages, scientific writers like Welsh polymath Robert Recorde used the relatively new technology of the printing press to promote math for the people. Recorde’s 1543 English arithmetic textbook began with an argument that “no man can do any thing alone, and much less talk or bargain with another, but he shall still have to do with number” and that numbers’ uses were “unnumerable” (pun intended).

Barany says, “that anything beyond simple practical math ought to have a wider reach…” and then goes on to suggest that this was typified by Robert Recorde with his The Grounde of Artes from 1543. Recorde’s book is very basic arithmetic; it is an abbacus or reckoning book for teaching basic arithmetic and book keeping to apprentices. In other words it is a book of simple practical maths. Historically what makes Recorde’s book interesting is that it is the first such book written in English, whereas on the continent such books had been being produced in the vernacular as manuscripts and then later as printed books since the thirteenth century when Leonardo of Pisa produced his Libre Abbaci, the book that gave the genre its name. Abbaci comes from the Italian verb to calculate or to reckon.

What however led me to write this post is the beginning of Barany’s next paragraph:

Far more influential and representative of this period, however, was Recorde’s contemporary John Dee, who used his mathematical reputation to gain a powerful position advising Queen Elizabeth I. Dee hewed so closely to the idea of math as a secret and privileged kind of knowledge that his detractors accused him of conjuring and other occult practices.

Barany is contrasting Recorde, man of the people bringing mathematic to the masses in his opinion with Dee an elitist defender of mathematics as secret and privileged knowledge. This would be quite funny if it wasn’t contained in an essay in Scientific American. Let us examine the two founders of the so-called English School of Mathematics a little more closely.

Robert Recorde who obtained a doctorate in medicine from Cambridge University was in fact personal physician to both Edward VI and Queen Mary. He served as comptroller of the Bristol Mint and supervisor of the Dublin Mint both important high level government appointments. Dee acquired a BA at St John’s College Cambridge and became a fellow of Trinity College. He then travelled extensively on the continent studying in Leuven under Gemma Frisius. Shortly after his return to England he was thrown into to prison on suspicion of sedition against Queen Mary; a charge of which he was eventually cleared. Although consulted oft by Queen Elizabeth he never, as opposed to Recorde, managed to obtain an official court appointment.

On the mathematical side Recorde did indeed write and publish, in English, a series of four introductory mathematics textbooks establishing the so-called English School of Mathematics. Following Recorde’s death it was Dee who edited and published further editions of Recorde’s mathematics books. Dee, having studied under Gemma Frisius and Gerard Mercator, introduced modern cartography and globe making into Britain. He also taught navigation and cartography to the captains of the Muscovy Trading Company. In his home in Mortlake, Dee assembled the largest mathematics library in Europe, which functioned as a sort of open university for all who wished to come and study with him. His most important pupil was his foster son Thomas Digges who went on to become the most important English mathematical practitioner of the next generation. Dee also wrote the preface to the first English translation of Euclid’s Elements by Henry Billingsley. The preface is a brilliant tour de force surveying, in English, all the existing branches of mathematics. Somehow this is not the picture of a man, who hewed so closely to the idea of math as a secret and privileged kind of knowledge. Dee was an evangelising populariser and propagator of mathematics for everyman.

It is however Barany’s next segment that should leave any historian of science or mathematics totally gobsmacked and gasping for words. He writes:

In the seventeenth century’s Scientific Revolution, the new promoters of an experimental science that was (at least in principle) open to any observer were suspicious of mathematical arguments as inaccessible, tending to shut down diverse perspectives with a false sense of certainty.

What can I say? I hardly know where to begin. Let us just list the major seventeenth-century contributors to the so-called Scientific Revolution, which itself has been characterised as the mathematization of nature (my emphasis). Simon Stevin, Johannes Kepler, Galileo Galilei, René Descartes, Blaise Pascal, Christiaan Huygens and last but by no means least Isaac Newton. Every single one of them a mathematician, whose very substantial contributions to the so-called Scientific Revolution were all mathematical. I could also add an even longer list of not quite so well known mathematicians who contributed. The seventeenth century has also been characterised, by more than one historian of mathematics as the golden age of mathematics, producing as it did modern algebra, analytical geometry and calculus along with a whole raft full of other mathematical developments.

The only thing I can say in Barany’s defence is that he in apparently a history of modern, i.e. twentieth-century, mathematics. I would politely suggest that should he again venture somewhat deeper into the past that he first does a little more research.

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Uccello and the Problem of Space

Nice post on Renaissance master of linear perspective Uccello

In the Dark

The other night I was watching an old episode of the detective series Lewis and it reminded me of something I wanted to blog about but never found the time. The episode in question, The Point of Vanishing, involves a discussion of a painting which can be found in the Ashmolean Museum in Oxford:

Uccello_TheHunt

I won’t spoil the plot by explaining its role in the TV programme, but this work – called “The Hunt in the Forest” or “The Night Hunt” or some other variation on that title –  is by one of the leading figures of the Early Renaissance, Paolo Uccello, who was born in Florence and lived from about 1396 until 1475. He was most notable for his explorations of the use of perspective in painting, and specifically in “The Problem of Space”, i.e. how to convey the presence of three dimensions when the paint is…

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Not a theology student

On the 10 August 1591 (os) (according to Max Caspar, 11 August according to Owen Gingerich!) Johannes Kepler graduated MA at the University of Tübingen. This is a verified undisputed historical fact, however nearly all secondary sources go on to state that he then went on to study theology, his studies being interrupted, shortly before completion, when he was appointed school teacher and district mathematicus in Graz. A post he took up on 11 April 1594. The part about the theology studies is however not true. This myth was created by historians and it would be interesting to trace who first put it out in the world and it is also interesting that nobody bothered to check this claim against the sources until Charlotte Methuen published her Kepler’s Tübingen: Stimulus to a Theological Mathematics in 1998.

Johannes Kepler Source: Wikimedia Commons

Johannes Kepler
Source: Wikimedia Commons

One reason for the lack of control is because the version with the theology studies seems so plausible. At medieval universities all student started their studies with the seven liberal arts graduating BA, in Kepler’s case in 1588 having matriculated two years earlier. Those, who stayed on at the university now intensified those studies graduating MA, essentially a teaching qualification. Those, who now wished to continue in academia had, in the normal run of events, the choice between taken a doctorate in law, medicine or theology. We know that Kepler was initially very disappointed with his appointment as a school teacher for mathematics because he would have preferred to become a Protestant pastor, so it would seem logical that because he stayed on at the university after graduating MA he must have studied theology. However appearances can be, and in this case are, deceptive. The problem is that Tübingen, or at least the Tübinger Stift in which Kepler studied was not a conventional medieval university.

A major problem that the Lutheran Protestant Church faced following the Reformation was finding enough pastors to run their churches and enough schoolteachers for their schools. In areas that converted to Protestantism the churches naturally had Catholic priest many of whom were not prepared or willing to convert and the education system, including both schools and universities, was firmly in the hands of the Catholic Church. This meant that the Lutheran Church had to build its own education system from scratch. This was the task taken on by Phillip Melanchthon, whom Luther called his Preceptor Germania – Germany’s schoolteacher – a task that he mastered brilliantly.

The state of Baden-Württemberg, one of the largest and most important early Protestant states gasped here the initiative, setting up a state sponsored school and university system to educate future Protestant schoolteachers and pastors. The Tübinger Stift was established in 1536 for exactly this purpose. The Dukes of Württemberg also provided stipends for gifted children of less wealthy families to enable them to attend the Stift. Kepler was the recipient of such a stipend.

Tübinger Still (left and University (right) Source: Kepler-Gesellschaft e.V.

Tübinger Still (left) and University (right)
Source: Kepler-Gesellschaft e.V.

All the students did a general course of studies, which upon completion with an MA qualified them to become either a schoolteacher or a pastor depending on the positions required to be filled, when they graduated. Allocation was also to some extent conditioned by the abilities of the individual student. Upon completion of their MAs student remained at the university receiving instruction in the various practical aspects of their future careers, teaching practice, basic theology for sermons and so forth until a suitable vacancy became available. Only a very, very small percentage of these students formally matriculated for a doctorate in theology, an unnecessary qualification for a simple pastor. Most Catholic priest of the period also did not possess a doctorate in theology. Kepler was not one of those who chose to do a doctorate in theology but was simply a participant in the general career preparation course for schoolteachers and pastor; a course for which there were no formal final exams or qualifications.

Kepler had been in this career holding pattern, so to speak, for not quite three years when the Evangelical Church authorities in Graz asked the University in Tübingen to recommend a new mathematics teacher for their school. After due consideration the university chose Kepler, who had displayed a high aptitude for mathematics, for the position. After some hesitation Kepler accepted the posting. He could have refused but it would not have placed him as a stipendiary in a very good position with the authorities. He was also free to leave the system and return to civil life but this would have meant having to reimburse his stipend.

It was clear from the beginning of his studies that he could, or would, be appointed either a schoolteacher or a pastor but the young Johannes had set his heart on serving his God as a pastor and was thus initially deeply disappointed by his appointment. The turning point came in Graz when he realised, in a moment of revelation, that he could best serve his God, a geometrical creator, by revealing the mathematical wonders of that creation. And so he dedicated his life to being God’s geometer, a task that he fulfilled with some distinction.

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Getting Kepler wrong

In recent times a bit of philosophy of science bun fight took place on the Intertubes. It started off in the New York Times with an opinion piece by James Blachowicz entitled, There is no Scientific Method. The title is actually a misnomer, as what Blachowicz actually argues is that the problem solving procedure usually called the scientific method is not unique to science. I’m not going to discuss it here but it is hardly an original theory, in fact I’ve argued something very similar myself in the past. I will, however, say that I don’t think that Blachowicz argues his case very well. Above all I think that his final three paragraphs in which he explains why, if the method is not exclusive to science, science is different to other form of knowledge are pretty crappy and largely wrong. Someone who also disparages those final three paragraphs in physics blogger Chad Orzel, who has written a pretty nifty book about the scientific method himself.[1] Chad wrote a post on his Uncertain Principles blog entitled, Why Physicists Disparage Philosophers, In Three Paragraphs, which if your read or have already read Blachowicz’s opinion piece you should definitely also read.

Chad was not the only physicist who weighed in on Blachowicz’s opinion piece with Ethan Siegel posting on his Forbes blog, Starts with a Bang, a rejoinder entitled Yes, New York Times, There Is a Scientific Method. In his piece Blachowicz illustrates his interpretation of the use of the scientific method in actual science with a brief discussion of Kepler’s search for the shape of the orbit of Mars using Tycho Brahe’s observational data as extensively described by Kepler in his Astronomia Nova in 1609. Here are the actual paragraphs from Blachowicz:

Now compare this with a scientific example: Johannes Kepler’s discovery that the orbit of Mars is an ellipse.

In this case, the actual meaning of courage (what a definition is designed to define) corresponds with the actual observations that Kepler sought to explain — that is, the data regarding the orbit of Mars. In the case of definition, we compare the literal meaning of a proposed definition with the actual meaning we want to define. In Kepler’s case, he needed to compare the predicted observations from a proposed explanatory hypothesis with the actual observations he wanted to explain.

 Early on, Kepler determined that the orbit of Mars was not a circle (the default perfect shape of the planetary spheres, an idea inherited from the Greeks). There is a very simple equation for a circle, but the first noncircular shape Kepler entertained as a replacement was an oval. Despite our use of the word “oval” as sometimes synonymous with ellipse, Kepler understood it as egg-shaped (in the asymmetrical chicken-egg way). Maybe he thought the orbit had to be lopsided (rather than symmetrical) because he knew the Sun was not at the center of the oval. Unfortunately, there is no simple equation for such an oval (although there is one for an ellipse).

When a scientist tests a hypothesis and finds that its predictions do not quite match available observations, there is always the option of forcing the hypothesis to fit the data. One can resort to curve-fitting, in which a hypothesis is patched together from different independent pieces, each piece more or less fitting a different part of the data. A tailor for whom fit is everything and style is nothing can make me a suit that will fit like a glove — but as a patchwork with odd random seams everywhere, it will also not look very much like a suit.

The lesson is that it is not just the observed facts that drive a scientist’s theorizing. A scientist would, presumably, no more be caught in a patchwork hypothesis than in a patchwork suit. Science education, however, has persistently relied more on empirical fit as its trump card, perhaps partly to separate science from those dangerous seat-of-the-pants theorizings (including philosophy) that pretend to find their way apart from such evidence.

Kepler could have hammered out a patchwork equation that would have represented the oval orbit of Mars. It would have fit the facts better than the earlier circle hypothesis. But it would have failed to meet the second criterion that all such explanation requires: that it be simple, with a single explanatory principle devoid of tacked-on ad hoc exceptions, analogous to the case of courage as acting in the face of great fear, except for running away, tying one’s shoelace and yelling profanities.

 It is here that Ethan launches his attack accusing Blachowicz of not having dug deep enough and of misrepresenting what Kepler actually did. After posting a picture of Kepler’s wonderful 3D model of his Platonic cosmos:

Kepler

Ethan posted the following:

Kepler’s original model, above, was the Mysterium Cosmographicum, where he detailed his outstandingly creative theory for what determined the planetary orbits. In 1596, he published the idea that there were a series of invisible Platonic solids, with the planetary orbits residing on the inscribed and circumscribed spheres. This model would predict their orbits, their relative distances, and — if it were right — would match the outstanding data taken by Tycho Brahe over many decades.

But beginning in the early 1600s, when Kepler had access to the full suite of Brahe’s data, he found that it didn’t match his model. His other efforts at models, including oval-shaped orbits, failed as well. The thing is, Kepler didn’t just say, “oh well, it didn’t match,” to some arbitrary degree of precision. He had the previous best scientific model — Ptolemy’s geocentric model with epicycles, equants and deferents — to compare it to. In science, if you want your new idea to supersede the old model, it has to prove itself to be superior through experiments and observations. That’s what makes it science. And that’s why the ellipses succeeded, because they gave better, more accurate prediction than all the models that came before, including Ptolemy’s, Copernicus’, Brahe’s and even Kepler’s own earlier models.

Unfortunately Ethan has hoisted himself with his own petard. He has not dug deep enough and what he presents here is presentist interpretation of what Kepler actually thought and did over a period of around thirty years. I will explain.

At the various stages of Kepler’s development that Ethan sketches Kepler is dealing with and providing answers for different non-exclusive question, which don’t replace each other sequentially.

At the beginning Kepler was looking for an answer to the question, why there are only six planets? In the Copernican system the seven planets of the Greek’s had been reduced to six as the Earth and the Sun exchanged places and the Moon became the Earth’s satellite (a word that Kepler would coin later with reference to the newly discovered moons of Jupiter). This metaphysical question seems rather strange to us today but it fitted into Kepler’s metaphysics. Kepler was deeply religious and his God was a rational, logical creator of a mathematical (read geometrical) cosmos. Kepler’s cosmos was also finite, so there were and could only be six planets. He was later mortified when Galileo announced the discovery of four new celestial bodies and infinitely relieved when there turned out to be satellites and not planets. Kepler’s answer to his question was the model shown above with the spheres of the six planets inscribing and circumscribing the five regular Platonic solids. There are, and can only be, only five regular Platonic solids therefore there can only be six planets, Q.E.D. Using the available data on the size of the planetary orbits Kepler turned his vision into a mathematical model of the cosmos and discovered that it fit roughly but not accurately enough. His passion for precision and accuracy was a major driving force throughout Kepler’s scientific career. Kepler was aware that Tycho had been collecting new more accurate astronomical data for thirty years and this was one of his major reasons for wanting to work with Tycho in Prague; the other reason was that Kepler, as a Protestant who refused to convert to Catholicism, was being expelled from Graz and desperately needed a new job.

In Prague Tycho, who thought he had been plagiarised by Ursus, was not prepared to hand over his precious data to a comparative stranger and instead gave Kepler a couple of commissions. The first was to write an account of Tycho’s dispute with Ursus, which Kepler did producing a classic in the history and philosophy of science, which unfortunately was not published at the time. Kepler second task was to determine the orbit of Mars based on Tycho’s observational data. At this time, this had nothing to do with his previous work in the Mysterium Cosmographicum. Famously, what Kepler thought would be a simple mathematical exercise taking a couple of weeks turned into a six year battle to tame the god of war, published in all its gory detail in his Astronomia nova in 1609. Having at some point abandoned the traditional circular orbits Kepler hit upon his oval, meaning egg shaped rather than elliptical, orbit and calculated it using Tycho’s data. His calculations displayed eight arc minutes of error in places, that’s eight sixtieths of one degree, a level of accuracy way above anything that either Ptolemaeus or Copernicus had ever produced. He had superseded the old model easily to quote Ethan, however eight arc minutes of error was an affront to Kepler’s love of accuracy and in his opinion an insult to Tycho’s observational accuracy, so it was back to the drawing board. In his further efforts Kepler finally discovered his first two laws of planetary motion and his elliptical orbits[2]. This set of answers were however to a different set of questions to those in the Mysterium Cosmographicum and in no way were considered to replace them.

Throughout his life Kepler remained convinced that his Platonic model just required fine-tuning, which he meant quite literally. Already in the Mysterium Cosmographicum he muses about the Pythagorean music of the spheres and his magnum opus, the Harmonices Mundi published in 1619, is a truly amazing conglomeration of plane and spherical geometry, music theory, astrology and astronomy containing many gems but most famous for his third law of planetary motion, the harmonic law. Throughout all of this work the Platonic solids model of the Mysterium Cosmographicum remained Kepler’s vision of the cosmos and in 1621 he published a revised and extended version of his first book confirming his belief in it. It is this combination of, from our point of view, weird Renaissance heuristics, Platonic solids, harmony of the spheres, combined with the high level highly accurate modern science that it generated, the laws of planetary motion etc., that led Arthur Koestler to title his biography of Kepler, The Watershed. He saw Kepler as straddling the watershed between the Middle Ages and the Early Modern Period with one foot planted firmly in the past and the other striding determinedly into the future. The inherently contradictory duality is what leads presentists such as Ethan to misunderstand and misrepresent Kepler. He didn’t replace his metaphysical Platonic solids model of the cosmos with his mathematical elliptical model of the planetary orbits but considered them as equal parts of his whole astronomical/cosmological vision. We do not have Ethan’s Whig march of progress of one model replacing another but rather a Renaissance concept of the cosmos that can only be considered on its own terms and simply doesn’t make sense if we try to interpret it from our own modern perspective.

Since I started writing this post there have been two further contributions to the debate that inspired it. On the bigthink Jag Bhalla interviews Rebecca Newberger Goldstein on the topic under the title, What’s Behind A Science vs. Philosophy Fight?

On The Multidisciplinarian, William Storage, in his The Myth of Scientific Method, takes apart Ethan’s (mis)use of Galileo in his contribution. This one is highly recommended

 

[1] Chad Orzel, Eureka! Discover Your Inner Scientist, Basic Books, New York, 2014

[2] As I’ve said more than once in the past the best account of Kepler’s Astronomia nova is James R. Voelkel, The Composition of Kepler’s Astronomia nova, Princeton University Press, 2001

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Filed under History of Astronomy, Myths of Science

Words matter

This morning, as usual, I caught the beginning of Thought for the Day on BBC Radio’s Today Programme (I know, I know), as I was preparing to leave my flat at 7:50 am. This morning the speaker, Bishop James Jones, took as his topic Yorkshire Day, the yearly celebration of God’s own county, as the natives like to call it. Bishop Jones, informed us that Yorkshire has 10% of the population of the UK (it’s actually nearer to 7% but who’s quibbling) and then went on to say, “Yorkshire is the most British region in the UK with over 40% of the population having Anglo-Saxon ancestry.

Now I’ve got nothing against Yorkshire, some of my best friends live there, but I fail to see how being of Anglo-Saxon descent makes somebody most British, in fact when I heard this my inner historian cringed. For those of my readers who are not up on the etymology of the terms of parts of the UK and its populations I will explain why this is fundamentally wrong. If the speaker had said most English I probably wouldn’t have reacted the way I did, as the words England and English are in fact derived from our Angle ancestors – England being Angle-Land. The problem is equating Britain or British with Anglo-Saxon.

The first mention of the origin of word Britain turns up in the reports of the Greek geographer explorer Pytheas of Massalia who voyaged around the British Isles in about 300 BCE and referred to them as the Prettanikē or something similar (Pytheas’ original writings are lost and we only have later secondary accounts of his report). This evolves to Britannia in the writings of Latin scholars. Now Pytheas undertook his voyages about four hundred years before Tacitus makes the first know reference to the Anglii, then still firmly on the continent, in his Germania and at least eight hundred years before the Angles invaded North East England.

Possible locations of the Angles, Saxons and Jutes before their migration to Britain. Source: Wikimedia Commons

Possible locations of the Angles, Saxons and Jutes before their migration to Britain.
Source: Wikimedia Commons

Viewed historically, the term British references the pre-Germanic pre-Roman, Celtic, population of the British Isles in contrast to the term English, which references the Germanic post Roman invaders. Etymologically the phrase of Anglo-Saxon descent would at best indicate most English and definitely not most but rather least British.

Angles, Saxons and Jutes throughout England Source: Wikimedia Commons

Angles, Saxons and Jutes throughout England
Source: Wikimedia Commons

 

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Filed under Odds and Ends