There is no such thing as Greek science.

I’m pretty certain that a fair number of people reading the title of this post will be going, ‘what the hell is he talking about? We heard all about Greek science at primary (grade) school, secondary school, high school, college, university” or “I’ve read about Greek science in that popular history of science book, popular science journal, that website, on Wikipedia, in that magazine at the hairdressers!” “Of course there is such a thing as Greek science you can hear/read about it all over the place. Has he gone barmy or something?” Others are probably thinking he’s about to go on about how the word science when used for the ancient Greeks is anachronistic and we shouldn’t call it science but … This chain of thought is in fact correct but is not the topic of this post. In fact for the moment I’m quite happy to use the word science in this context as a shorthand way of describing all of the intellectual disciplines practiced by the ancient Greeks that are related to the disciplines that we call the sciences today, even if this usage is more than somewhat anachronistic. What I’m objecting to, in fact rejecting is the whole term ‘Greek science’ it doesn’t exist has never existed and its usage leads to a series of dangerous misconceptions; dangerous that is for our understanding of the history of western science. Why do I say this and what misconceptions?

The usage of the term Greek science implies that there is a coherent, albeit, abstract object that can be indicated by this term, no such object has ever existed. This becomes very obvious if one takes the time to look closely at what is usually labelled Greek science.

If we look at the time dimension we are talking about a set of activities that begins some what earlier than six hundred BCE with the earliest of the so-called pre-Socratic philosophers i.e. Thales and co. It carries on in the western world until the death of the last of the so-called encyclopaedists Isidore of Seville in 632 C. That is a time span of more than twelve hundred years. Just to put that in perspective, if we go back twelve hundred and fifty years from today Pippin the Short, the first of the Carolingians to become King of the Franks, was on the throne. His son Karl der Große, or Charlemagne, as the English call him, might be better known to you. Twelve hundred years is a lot of human history and a lot can happen in a time span that long.

A geographical examination yields a similar result. The pre-Socratics lived in what became known as Asia Minor and is now part of Turkey. It stretches over the Greek island and mainland in its development to Southern Italy. It took in the whole of the Hellenistic Empire of Alexander the Great and later the whole of the Roman Empire. Our last representative Isidore, as his name tells us, lived in Seville in Spain. Up till now I’ve not mentioned the final Greek Empire, Byzantium, which begins when the Roman Emperor Constantine moved his capital from Rome to Constantinople and ended with the fall of that noble city to the Turks in 1453. It occupied a large part of what is now Turkey. Geo-politically over our twelve hundred plus years we progress from ancient Greek culture through Hellenistic culture, on to Romano-Hellenistic culture and finishing up in post-classical Roman late antiquity or the Early Medieval period. It should be clear by now that to refer to Greek science is a fairly pointless exercise from the point of view of time, geography, and politics and culture. It’s about as meaningless as referring to European science and using the term to designate some sort of coherent whole beginning with Charlemagne and going up to the present and encompassing the whole of the continent of Europe. That coherent whole simply doesn’t exist.

Of course the time, special and politico-cultural dimensions are only part of the problem and not even the most important part. Despite the vast diversity that we have just sketched people still insist in talking about a single coherent science and it is here that the real damage caused by misconception takes place. Let us start with one typical example to illustrate what I mean. In popular presentations of the study of the theory of optics I constantly stumble across statement of the type, ‘the Greeks believed that we see by beams projected from the eyes to the objects perceived’. Such standpoint is know technically as an extramission theory of vision and is indeed one of the theories of vision proposed and discussed by the ancient Greeks. The important phrase here is ‘one of the theories’; the various groups in ancient Greece proposed at least five different contrasting, conflicting and contradictory theories of vision over a number of centuries that they investigated and discussed. These theories were then taken up and debated further by both the Islamic and the European scholars in the Middle Ages. We don’t have a case of ‘the Greeks thought/believed this’ but rather the Atomists believed this, the Platonists believed this, the Aristotelians believed this, the Stoics believe this and the mathematical optical theorists believed this. In other words we have conflicting competing theories presented by different schools of thought each of which was different at different times and often in different areas during those twelve hundred years that Greek culture existed. Those who just present the extramission theory as being what the Greeks thought seem to be motivated by presenting the Greeks in a bad light. Look how stupid the Greeks were, they actually believed that the eyes send out rays of fire enabling people to see.

One could of course argue that this is one example and doesn’t necessarily represent the whole of Greek science but it does. The list of groups that I named as holding differing theories of vision is basically the list of principle schools of thought within ancient Greek culture who developed and presented views on a multitude of scientific topics throughout the Greek cultural period. They are others who didn’t necessarily have views on optics, such as the Pythagoreans, but did develop theories in other areas. Each of the named schools came into being and enjoyed a period of prominence as their ideas were shiny new and stimulating then falling somewhat into the background as new schools emerged with other shiny new ideas.

A second example is provided by the disciplines of astronomy and cosmology. It is a commonplace that the Greeks believed the heavens to be divided into two spheres, the sublunar and the supralunar, the latter being perfect and the former corruptible. They, the Greeks, also believed that comets being corruptible inhabit the sublunar sphere. These views are not the views of the Greeks but of Aristotle and the Aristotelians. Another school of thought the Stoics regarded the entire heavens to be of one nature with no division and comets to be phenomena of the supralunar region. The Stoics and there cosmology were in general more dominant in later antiquity than the Aristotelians.

The opinion that the views of the Aristotle were those of the Greeks comes from adoption of those views by Europeans in the High Middle Ages and the misconception that they and they alone dominated European thought until deposed by the ‘modern’ astronomy in the Early Modern Period. In fact modern research into the history of astronomy has revealed that a renaissance of the Stoic cosmology in Europe in the fifteenth and sixteenth centuries played a significant role in the so-called astronomical revolution.

I could go on producing examples from every branch of Greek knowledge that display the diversity of Greek thought across the centuries. Even the much-quoted Greek mathematics was in reality a varying range of diverse and oft conflicting schools. The two most famous Greek mathematicians Euclid and Archimedes represent two conflicting approaches to the subject, Euclid synthetic, Archimedes analytical. These two fundamentally different approaches resurfaced in conflict with each other during the seventeenth century following the renaissances of synthetic Euclidian mathematics in the fifteenth century and analytic Archimedean mathematics in the sixteenth century.

Any extensive in depth survey of science carried out in the Greek language in the Mediterranean region in antiquity should convince anybody that there never was anything that could reasonably be called Greek science and we should all endeavour to stop using the term and instead talk about the Platonic theory of vision, Aristotelian cosmology, Euclidian geometry or whatever label correctly identifies the topic under discussion. By pure chance Mary Beard, a leading British classicist, tweeted the following statement during the week that perfectly sums up the message of this post in 140 characters:

 

Afraid I bridle at generalising “did THE GREEKS think?” M Finley always said “which Greeks? when?” Not unitary culture – @wmarybeard

 

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Emmy the student and Emmy the communist!

Emmy Noether’s birthday on 23 March saw her honoured with a Google Doodle, which of course led to various people posting brief biographies of Erlangen’s most famous science personality or drawing attention to existing posts in the Internet.

Emmy Google Doodle

Almost all of these posts contain two significant errors concerning Emmy’s career that I would like to correct here. For those interested I have written earlier posts on Emmy’s family home in Erlangen and the problems she went through trying to get her habilitation, the German qualification required to be able to teach at university.

The first oft repeated error concerns Emmy’s education and I quote a typical example below:

Today she is celebrated for her contributions to abstract algebra and theoretical physics, but in 20th-century Bavaria, Noether had to fight for every bit of education and academic achievement. Women were not allowed to enrol at the University of Erlangen, so Noether had to petition each professor to attend classes.

As a teenager Emmy displayed neither an interest nor a special aptitude for mathematics but rather more for music and dance. She attended the Städtische Höhere Töchterschule (the town secondary girls’ school), now the Marie-Therese-Gymnasium, and in 1900 graduated as a teacher for English and French at the girls’ school in Ansbach. In 1903 she took her Abitur exam externally at the Königlichen Realgymnasium in Nürnberg. The Abitur is the diploma from German secondary school qualifying for university admission or matriculation. Previous to this she had been auditing some mathematics courses in Göttingen as a guest student with the personal permission of the professors whose courses she visited, hence the claim above. However she had become ill and had returned home to Erlangen. In 1903 the laws were changed in Bavaria allowing women to register at university for the first time. Emmy registered as a regular student at the University of Erlangen in 1903 and graduated with a PhD in mathematics in 1907, under the supervision of Paul Gordon, in invariant theory. She was only the second woman in Germany to obtain a PhD in mathematics. In 1908 she became a member of the Circolo Matematico di Palermo and in 1909 a member of the Deutschen Mathematiker-Vereinigung. In 1909 Hilbert and Klein invited her to come to the University of Göttingen, as a post-doc researcher. It was here in 1915 that Hilbert suggested that she should habilitate with the well know consequences.

Emmy remained in Göttingen until the Nazis came to power in 1933. She held guest professorships in Moscow in 1928/29 and in Frankfort am Main in 1930. She was awarded the Ackermann-Teubner Memorial Prize for her complete scientific work in 1932 and held the plenary lecture at the International Mathematical Congress in Zurich also in 1932. In 1933 when the Nazis came to power she was expelled from her teaching position in Göttingen and it is here that the second oft repeated error turns up.

On coming to power the Nazis introduced the so-called Gesetz zur Wiederherstellung des Berufsbeamtentums, (The Law for the Restoration of the Professional Civil Service). This was a law introduced by the Nazis to remove all undesirables from state employment, this of course meant the Jews but also, socialists, communists and anybody else deemed undesirable by the Nazi Party. Like many of her colleges in the mathematics department at Göttingen Emmy was removed from her teaching position under this law. In fact the culling in the mathematics department was so extreme that it led to a famous, possibly apocryphal, exchange between Bernhard Rust (and not Hermann Göring, see comments) and David Hilbert.

Rust: “I hear you have some problems in the mathematics department at Göttingen Herr Professor”.

Hilbert: “No, there are no problems; there is no mathematics department in Göttingen”.

The Wikipedia article on the history of the University Göttingen gives the story as follows (in German)

Ein Jahr später erkundigte sich der Reichserziehungsminister Bernhard Rust anlässlich eines Banketts bei dem neben ihm platzierten Mathematiker David Hilbert ob das mathematische Institut in Göttingen durch die Entfernung der jüdischen, demokratischen und sozialistischen Mathematiker gelitten habe. Hilbert soll in seiner ostpreußischen Mundart (laut Abraham Fraenkel, Lebenskreise, 1967, S. 159) erwidert haben: „Jelitten? Dat hat nich jelitten, Herr Minister. Dat jibt es doch janich mehr.“

The source here is given as Abraham Fraenkel in his autobiography Lebenkreise published in 1967.

This translates as follows:

One year later [that is after the expulsions in 1933] the Imperial Education Minister Bernhard Rust, who was seated next to the mathematician David Hilbert at a banquet, inquired, whether the Mathematics Institute at Göttingen had suffered through the removal of the Jewish, democratic and socialist mathematicians. Hilbert is said to have replied in his East Prussian dialect” Suffered? It hasn’t suffered, Herr Minister. It doesn’t exist anymore”

It is usually claimed that Emmy lost her position because she was Jewish, a reasonable assumption but not true. Emmy lost her position, like many other in Göttingen, because the Nazis thought she was a communist. Like many European universities in the 1920s and 30s Göttingen was a hot bed of radical intellectual socialism. Emmy had been a member of a radical socialist party in the early twenties but changed later to the more moderate SPD, who were also banned by the Nazis. However it was her guest professorship in Moscow that proved her undoing. Because she reported positively on her year in Russia the Nazis considered her to be a communist and this was the reason for her expulsion from the university in 1933.

Initially Emmy, after her expulsion, actually applied for a position at the University of Moscow but the attempts by the Russian topologist Pavel Alexandrov to get her a position got bogged down in the Russian bureaucracy and so when, through the good offices of Hermann Weyl, she received the offer of a guest professorship in America at Bryn Mawr College she accepted. In America she taught at Bryn Mawr and the Institute of Advanced Studies in Princeton but tragically died of cancer of the uterus in 1935.

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Calendrical confusion or just when did Newton die?

Today there is general agreement throughout the world that for commercial and international political purposes everybody uses the Gregorian calendar, first introduced into the Catholic countries of Europe in 1582. However Europeans should never forget that for other purposes other cultures have their own calendars often wildly at odds with the Gregorian one. Tomorrow is for example the Persian New Year’s a festival, which marks the first day of spring. The Persian calendar is not only used in Iran but in many other countries that were historically under Persian influence. Tomorrow also marks the first day of the year 1394 for Persians. Earlier all cultures used their own calendars a bewildering array of lunar calendars, lunar-solar calendars and pure solar calendars making life very difficult for both astronomers and historians. Trying to find out what a given date in an original document is, or better would have been, on our ‘universal’ Gregorian calendar is often a complex and tortuous problem. Astronomers whose observations of the heavens need to span long periods of time solved the problem for themselves by introducing a standard calendrical scale into which they then converted all historical astronomical data from diverse cultures. Throughout late antiquity, the Islamic Empire and well into the European Early Modern Period astronomers used the Egyptian solar calendar for this purpose. You can still find astronomical dates given according to this system in Copernicus’ De revolutionibus. In modern times they introduced the Julian day count for this purpose.

Within Europe the most famous calendrical confusion occurred in the early centuries following the introduction in Catholic countries of the Gregorian calendar. Exactly because it was Catholic most Protestant states refused, at first, to introduce it, meaning that Europe was running on two different time scales making life difficult for anybody having to do outside of their own national borders, in particular for traders. This problem was particularly acute in The Holy Roman Empire of German States that patchwork of small, medium and large states, principalities and independent cities that occupied most of middle Europe. Neighbouring states were often of conflicting religious affiliation meaning that people living in the border regions only needed to go a couple of kilometres down the road to go ten days backwards or forwards in time. The only people who were happy with this system were the calendar makers who could sell two sets of calendars Gregorian, so-called new style or ‘ns’ and Julian, so-called old-style or ‘os’. Some enterprising printer publishers even printed both calendars in one pamphlet, for a higher price of course.

Within Germany the problem was finally solved at the end of the seventeenth century, largely due to the efforts of Erhard Weigel who campaigned tirelessly to get the Protestant states to adopt the Gregorian calendar, which they finally did on 1 January 1700. England as usual had to go its own way.

Although John Dee, the court advisor on all things mathematical, recommended the adoption of the Gregorian calendar in the sixteenth century the Anglican Bishops blocked its adoption because it came from the Pope and the Anglican Church couldn’t be seen cowing down to the Vatican. Even when the Protestant German states finally accepted that adopting the Gregorian calendar was more rational than any religious prejudices the English still remained obdurate, not prepared to have anything to do with Catholicism. England final came into line in 1752. So what about Isaac Newton?

Many Internet sources are saying that Isaac Newton died on 20 March almost none of them say whether this is new-style or old-style. Most of the sources give 1727 as the year of death a few 1726. Most sources give Newton’s life span as 1642–1727, others 1642–1726 and yet others 1643–1727, what is going on here?

Isaac Newton was born 25 December 1642 according to the Julian calendar that is old-style. If converted to the Georgian calendar, we have to add ten days, and so his date of birth was 4 January 1643 new-style. Things become slightly more complicated with his date of death. Newton died 20 March 1726 according to the Julian calendar that is old-style. Converting to the Georgian calendar we now have to add eleven days because the Julian calendar has slipped another day behind the Gregorian one so his date of death is 31 March 1727 new-style. Wait a minute we just jumped a year what happened here? When Julius Caesar introduced the solar calendar in Rome he moved the New Year from the traditional Roman spring equinox, 25 March, to the first of January. During the Middle Ages the Church moved the New Year back to 25 March. With the adoption of the Gregorian calendar New Year’s Day moved back to 1 January. However England still retaining the medieval version of the Julian calendar kept 25 March as New Year’s Day. Thus at the time of Newton’s death 1727 started on 25 March in England meaning that Newton died 20 March 1726 (os).

Just to summarise if you wish to correctly quote Newton’s dates of birth and death then they are 25 December 1642 – 20 March 1726 (os) or 4 January 1643 – 31 March 1727 (ns).

 

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Filed under History of Astronomy, Newton

The continuing saga of io9’s history of science inanities.

I made a sort of deal with myself to, if possible, avoid io9 and above all the inane utterances of Esther Inglis-Arkell. Unfortunately I fell for a bit of history of science click bait on Twitter and stumbled into her attempt to retell the story of the degenerating relations between Isaac Newton and John Flamsteed, the Astronomer Royal. I say attempt but that is actual a misuse of the word because it somehow implies making an effort, something that Ms Inglis-Arkell is not willed to do. Her post resembles something half read, half understood and then half forgotten spewed out onto the page in a semblance of English sentences. It in no way approaches being something that one could honestly label history of science story telling even if one were to stretch this concept to its outer most limits.

I have blogged on the relations between Newton and Flamsteed on a number of occasion but let us look at Ms Inglis-Arkell miserable attempt at telling the story and in so doing bring the correct story out into the open. Our storyteller opens her tale thus:

Isaac Newton reached the level of genius in two different disciplines: physics and making people miserable. This is a tale of his accomplishments in the latter discipline. The object of his scorn, this time, is a poor astronomer named John Flamsteed, who made the mistake of not being agreeable enough.

I tend to dislike the term genius but if one is going to apply it to Newton’s various activities then one should acknowledge that as an academic he also reached the level of genius as a mathematician, as a theoretical astronomer and as an instrument maker and not just as a physicist. Credit where credit is due. On the subject of his making people miserable, John Flamsteed was anything but a saint and as I pointed out in an earlier post, Grumpy old astronomers behaving badly or don’t just blame Isaac!, in the dispute in question both of them gave as good as he got.

We now get to the factual part of the story where our storyteller displays her grasp of the facts or rather her lack of one:

Flamsteed and Newton started their acquaintance on good terms. They spent the 1680s happily corresponding about two lights in the sky, seen in 1680, which were either two comets or one comet that made two trips by Earth. This got Flamsteed interested in cataloguing [sic] the heavens. If enough information was compiled about the lay of the night sky, astronomers would be able to understand all kinds of things about the shape of the universe and how its various pieces worked. By the mid-1690s, Flamsteed was the Astronomer Royal and was making a star catalogue which he would publish when it was completed.

Remember that bit about half read and half forgotten? John Flamsteed had been installed by Charles II as Astronomer Royal for the newly commissioned Royal Observatory at Greenwich on 22 June 1675 “forthwith to apply himself with the most exact care and diligence to the rectifying the tables of the motions of the heavens, and the places of the fixed stars, so as to find out the so-much desired longitude of places, for the perfecting the art of navigation.” Not by the mid-1690s as Ms Inglis-Arkell would have us believe. I love the bit about how, astronomers would be able to understand all kinds of things about the shape of the universe and how its various pieces worked”, Which basically just says that she doesn’t have a clue what she’s talking about so she’ll just waffle for a bit and hope nobody notices. The Observatory itself wasn’t finished till 1685 but by the beginning of the 1680 Flamsteed was already busily fulfilling his obligations as official state astronomical observer.

The early 1680s saw a series of spectacular comets observable from Europe, and Flamsteed along with all the other European astronomers devoted himself to observing their trajectories and it was a conjecture based on his observations that led to his correspondence with Newton. He observed two comets in 1680, one in November and the second in mid December. Flamsteed became convinced that they were one and the same comet, which had orbited the sun. He communicated his thoughts by letter to Isaac Newton (1642–1727) in Cambridge, the two hadn’t fallen out with each other yet, and Newton initially rejected Flamsteed’s findings. However on consideration he came to the conclusion that Flamsteed was probably right and drawing also on the observations of Edmund Halley began to calculate possible orbits for the comet. He and Halley began to pay particular attention to observing comets, in particular the comet of 1682. By the time Newton published his Principia, his study of cometary orbits took up one third of the third volume, the volume that actually deals with the cosmos and the laws of motion and the law of gravity. By showing that not only the planets and their satellite systems obeyed the law of gravity but that also comets did so, Newton was able to demonstrate that his laws were truly universal. Note that Flamsteed two-in-one comet was orbiting the sun and not “one comet that made two trips by Earth”; this will come up again in the next paragraph:

Newton, meanwhile, believed that returning comets might be drawn to the Earth by some mysterious force. They might circle the Earth, in fact, the way the Moon circled the Earth. Perhaps, the force that drew the Moon and the comets might be the same. Newton wanted to study his “Moon’s Theory,” and to do so he needed the information in Flamsteed’s catalogue, incomplete though it was. Newton had risen to the rank President of the Royal Society of London for Improving Natural Knowledge; the titles might leave one in doubt as to who had the power, but Newton’s fame and connections far outstripped Flamsteed’s. When Isaac Newton wanted information from the catalogue, he wanted it immediately, whether it was published or not.

The opening sentences of this paragraph are a confession of complete incompetence for somebody, who, if I remember correctly, has a degree in physics. We are of course talking about the force of gravity, so why not call it that? Anyone who has studied physics at school knows that according to the law of gravity any two bodies “attract each other” something that Newton had spelled out very clearly in his Principia, which was published in 1687 before the dispute that Inglis-Arkell is attempting to describe took place. So the comets are not being “drawn to the Earth by some mysterious force”. In fact they are not being drawn to the Earth at all and there are certainly not circling it. Flamsteed’s careful observations and astute deduction had correctly led Newton to the conclusion that the force of gravity causes some comets to orbit the sun. As we shall see shortly when Newton and Flamsteed got in each others hair about Newton’s need for fresh observational date on the moon he was still Lucasian Professor of Mathematics in Cambridge and still ten years away from becoming President of the Royal Society. However before I go into detail let us look at Inglis-Arkell’s account of the affair.

You can get a lot done when you’re friends with the Queen, but it still took a lot of time for Isaac Newton to get what he wanted from John Flamsteed. First Flamsteed sent assistants’ work instead of his own. Newton was exasperated with the mistakes they had made. Newton wrote nasty letters. Flamsteed wrote nasty diary entries. Newton turned to the royal Prince George, asking him to order Flamsteed to write a book that would include all his current data. Flamsteed just couldn’t get it together to produce the book, much as he must have wished to comply with his Prince’s order.

Newton inspected the Royal Observatory. Flamsteed guarded the equipment so jealously that the two physically fought over it. Flamsteed ended that day with a very smug diary entry declaring that the “instruments… were my own.”

Now the Astronomer Royal was not only disobeying Isaac Newton but the actual Royals, and so it’s impressive that Flamsteed managed to keep his prestigious appointment. He didn’t lose his position or his data for over a decade. It wasn’t until 1712 that Newton was able to influence Queen Anne and Prince George enough to force Flamsteed to publish his data in a small volume. Still, Flamsteed was bitter at the defeat.

Our intrepid wanna-be historian of science has conflated and confused three separate struggles between the two protagonists into one, getting her facts wrong along the way and even making thinks up, not a very good advertisement for a website that wishes to inform its readers or maybe this is one of their sci-fi contributions.

Let us take a look at what really happened. In an incredible tour de force Newton wrote and published his Principia in the three years between 1684 and 1687 and as I noted above Flamsteed’s recognition that some comets orbit the sun went on to play a central role in this ground-breaking work. In his magnum opus Newton was able to demonstrate that the whole of the then known cosmos lay under the rule of the law of gravity. It determined the elliptical orbits of the planets around the sun as well as the orbits of the then known satellites of Jupiter and Saturn. It converted the comets from irregular prophets of doom into celestial objects with regular but extremely long orbits. Everything seemed to fit neatly into place in a clockwork cosmos. Well almost everything! The earth’s closest neighbour appeared not to want to obey the dictates of gravity. Although Newton managed to get a fairly good approximation of a gravity-determined orbit for the moon it wasn’t anywhere near as good as he would have liked.

The problem lies on the size of the moon. Having an unusually large mass for a satellite the moon is involved in a gravitational system with both the earth and the sun, the classical three-body problem. As a result its orbit is not a smooth ellipse but being pulled hither and thither by both the earth and the sun its orbit contains many substantial irregularities making it very difficult to calculate. There is in fact no general analytical solution to the three-body problem, as was finally proved in the nineteenth century by Henri Poincaré. The physicist or astronomer is forced to calculate each irregularity step by step, the situation that Newton found himself in whilst writing the Principia.

In 1693 Newton was contemplating a second edition of the Principia and decided to tackle the moon’s orbit anew. This required new observational data and the person who was in procession of that data was Flamsteed. Newton never the most diplomatic of men at the best of times was even more grumpy than usual in the early 1690s. He was recovering from what appears to have been some sort of major mental breakdown, he was tackling one of the few mathematical problem that would always defeat him (the moon’s orbit, which was finally solved by Laplace in his Exposition du système du monde at the end of the eighteenth century), and he was frustrated by his situation in Cambridge and was looking for a suitable position in recognition of his, in the meantime, considerable status in London. The latter would be solved by Charles Montagu appointing him Warden of the Mint in 1696. His approach to Flamsteed to obtain the data that he required was high handed to say the least. Flamsteed, also an irritable man, who was overworked, underpaid and underfinanced in his efforts to map the entire heavens, was less than pleased by Newton’s imperious demands but delivered the requested data none the less. Newton failed to solve his problem and blaming Flamsteed and his data demanded more. Flamsteed feeling put upon grumbled but delivered; and so the pair of grumpy old men continued, each developing an intense dislike of the other. In the end Newton’s demands became so impossible that Flamsteed started sending Newton raw observational data letting him calculate the lunar positions for himself. It is difficult to say where this vicious circle would have led if Newton had not lost interest in the problem and shelved it, and the plans for a second edition of Principia, in 1695. By now the two men were totally at loggerheads but would have nothing more to do with each other for the next nine years.

In 1704 Newton, by now Master of the Mint and resident in London, was elected President of the Royal Society. On 12 April 1704 Newton took a boat down the river from the Tower of London, home of the Mint, to Greenwich, home of the Royal Observatory, to visit Flamsteed. Surprisingly amicable Newton suggested to Flamsteed that he should speak to Prince George of Denmark, Queen Anne’s consort, on Flamsteed’s behalf about obtaining funds to have Flamsteed’s life work published. Flamsteed was agreeable to having his work published especially as his critics, most notably Edmond Halley and David Gregory, were pointing out that he had nothing to show for almost thirty years of endeavour. However he would have preferred to deal with the matter himself rather than have Newton as his broker. Newton spoke to Prince George and obtained the promise of the necessary funds. Meanwhile Flamsteed drew up a publication plan for his work. He wanted three volumes with his star catalogue the high point of his work in the third and final volume. Newton had other plans. He set up an editorial board at the Royal Society consisting of himself, David Gregory, Christopher Wren, Francis Robartes and John Arbuthnot to oversee the publication. Flamsteed, the author and also a member of the Royal Society, was not included. Newton ignored Flamsteed’s wishes and declared that the star catalogue would be printed in volume one. Newton commissioned a printer to print sample sheets, however Flamsteed found them to be of poor quality and wished to find a new printer. Newton ignored him and gave the printer the commission to print the work ordering Flamsteed to supply the introductory material for the first volume.

One major problem was that the star catalogue was at this time not complete. Flamsteed kept stalling declining to supply with Newton with the catalogue until he could complete it. He needed to calculate the stellar positions from the raw observational data. Newton promised him the money to pay the computers and actually obtained the money from Prince George. Flamsteed employed the computers to do the work and paid them out of his own pocket requesting restitution from Newton. Newton refused to pay up. So the whole sorry affair dragged on until Prince George died in 1708 with which the project ground to an end. If Flamsteed had grown to dislike Newton in the 1690s he truly hated him now.

Things remained quiet for two years then at the end of 1710 John Arbuthnot, who was physician to Queen Anne, suddenly announced that Anne had issued a warrant that appointed the president and others as the council of the Royal Society saw fit to be ‘constant Visitors’ of the Royal Society. As used here visitor means supervisor and it effectively meant that Newton was now Flamsteed’s boss. With their newly won authority Newton and his cronies did everything in their power to make life uncomfortable for Flamsteed over the next few years. On 26 October 1711 Newton summoned Flamsteed to a meeting in Crane Court, the home of the Royal Society, to inform him of the state of the observatory instruments. Here we meet a classic of institutional funding. The Crown had paid to have the Royal Observatory built and having appointed Flamsteed to run it the Crown paid his wages, on a very miserly level, however no money was ever supplied for instruments and so Flamsteed had bought his instruments with his own money. When Newton demanded account of the state of the instruments Flamsteed could prove that they were all his own private property and thus no concern of Newton’s. Newton was far from pleased by this defeat. He now ordered the Royal Ordnance to service, repair and upgrade the instruments and thus to win official control over them. Unfortunately the Ordnance, which, like the Mint, occupied the Tower of London didn’t like Newton so taking sides with Flamsteed informed Newton that there were no funds available for this work. A minor victory for Flamsteed but he had already suffered a major defeat. Before discussing this I should point out that contrary to Ms Inglis-Arkell’s claims, at no time did the elderly combatants resort to any form of physical contact.

On 14 March 1711 Arbuthnot had informed Flamsteed that the Queen had commanded the complete publication of his work; the brief reprieve brought about by the death of Prince George was over. Although the star catalogue, which was all that Newton was interested in publishing, was now finished Flamsteed at first prevaricated again. Arbuthnot wrote to Flamsteed requesting him to deliver up the catalogue, Flamsteed declined with further excuses. Newton exploded and shot off a letter ripping a strip of Flamsteed for defying a Royal command and the fight was now effectively over. Flamsteed met with Arbuthnot and handed over the manuscript requesting conditions concerning the printing and editing to which Arbuthnot acquiesced and promptly ignored. Flamsteed went ballistic, as he discovered that printing was going ahead without his knowledge and even worse his manuscript was being edited by Edmond Halley! Flamsteed by now hated Newton but he reserved his greatest loathing for Halley. It has been much speculated why Flamsteed had such an extreme aversion to Halley but it went so far that he refused to use his name and only referred to him as Reimers after Nicolaus Reimers Bär, whom Flamsteed believed had plagiarised his hero Tycho and was thus the most despicable person in the history of astronomy. Flamsteed had lost all down the line and in 1712 his star catalogue appeared in a large folio volume (not the small volume claimed by Inglis-Arkell). Deeply bitter Flamsteed now swore to publish his life’s work in three volumes, as he had originally planned in 1704, at his own expense and began with the preparation. It should be noted that far from ‘Newton being able to influence Queen Anne and Prince George enough to force Flamsteed to publish his data’, Prince George had by now been dead for four years!

However Newton might have won a victory but he hadn’t yet won the war and the tide began finally to turn in Flamsteed’s favour. In 1714 Queen Anne died and was succeeded on the throne by George I, Elector of Hanover. The succession also brought with it a change of government. Now Inglius-Arkell claims that George didn’t like Newton but this is not true. He greatly respected Newton who had long been regarded as the greatest natural philosopher in Europe; he even forced his librarian, Gottfried Wilhelm von Leibniz, who would have loved to have moved to London to escape his Hanoverian backwater (no offense intended to Hannover or the Hanoverians), to stay at home so as not to offend Newton, who was at war with Leibniz when he wasn’t battling Flamsteed. However the succession and the change of government did mean a loss of influence for Newton. In early 1715 Charles Montagu, Lord Halifax, one of the most powerful politicians in England during the previous twenty years and Newton’s political patron, died. Charles Paulet, 2nd Duke of Boulton, the Lord Chamberlin, was a friend of Flamsteed’s and on 30 November 1715 he signed a warrant ordering Newton to return the three hundred remaining copies of the printed star catalogue to Flamsteed. He “made a Sacrifice of them to Heavenly Truth”; i.e. he burnt them.

Flamsteed continued with his project to publish his life’s work at his own expense but died in 1719 before he could finish the project. His widow with the willing help of his two assistants Joseph Crosthwait and Abraham Sharp finished the job and his three-volume Historia coelestis britannica was finally published in 1725, followed by his charts of the constellations the Atlas coelestis, edited by his widow and James Hodgson in 1727. Together they form a fitting monument to one of history’s greatest observational astronomers. Flamsteed had written a long preface for the Historia describing, from his standpoint, in great detail his twenty year long war with Newton but this did not make it into the final printed edition, probably because Newton, by now a living legend, was still very much alive. It only resurfaced a hundred years later. Flamsteed got his revenge, from beyond the grave, on Halley, who followed him as Astronomer Royal. As already explained above, Flamsteed’s observational instruments were his own personal property so when he died his widow stripped the observatory bare leaving Halley an empty building in which to pursue his new office.

The whole, more than twenty year long, farce is one of the more unsavoury episodes in the history of science and certainly not how one would expect two senior officers of state to behave. It is clear that Newton caries most of the blame although Flamsteed was not exactly a model of virtue deliberately fanning the flames through renitent and provocative behaviour. In particular his behaviour towards Halley, who was more than qualified and very capable of editing the star catalogue, was extremely childish and inexcusable.

You might think that I am being very unfair to Ms Inglis-Arkell having turned her very brief account into an overlong post but that is actually the point and her central failure, ignoring all of the factual errors in her version of the story. What I have laid out here are only the bare bones of the whole story, if I were to go into real detail this post would be ten times longer than it already is. Ms Inglis-Arkell attempt to reduce a highly complex series of episodes out of the history of science to a couple of hundred words in a throwaway post could only end in a level of distortion that makes the whole exercise a complete waste of time, effort (not that she seems to expended much of that) and cyberspace.

 

 

 

 

 

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Filed under Early Scientific Publishing, History of Astronomy, History of science, Newton

Discovery is a process not an act.

This morning somebody on Twitter tweeted that William Herschel discovered the planet Uranus on this day in 1781. A typical tweet amongst history of science fans on Twitter, who like to acknowledge and celebrate births, deaths, inventions and discoveries in what amounts to a rolling history of science calendar. On this occasion my history of science soul sisterTM, Rebekah “Becky” Higgitt, who’s quite knowledgeable about eighteenth-century astronomy, tweeted, quite correctly, that Herschel initially thought he had discovered a comet and it was Nevil Maskelyne, who first suggested that he had in fact observed a new planet and not a comet. She then asked if we should not then say that it was Nevil Maskelyne who discovered Uranus and not Herschel? Becky could be considered a bit biased having fairly recently devoted several years of her life to the study of the life and work of Maskelyne and also having edited a, highly recommended, book on the man. Herschel fans might thus feel justified in dismissing her comment and maintain their position than it was the Hanoverian musician turned amateur astronomer who discovered the first new planet to be observed since antiquity. Rather than trying to stoke the fires of a discovery priority dispute, of which there are all too many in the history of science, I think this an opportunity to look critically at what the term discovery actually means in the history of science.

For some reason we love to hang a specific date, even better the exact time, when a discovery of science was made in the history of science. In fact I have about a running metre of books within arms reach of this computer full of such information. William Herschel discovered Uranus on 13 March 1781, Galileo Galilei discovered the moons of Jupiter on 7 January 1610, Simon Marius did the same just one day later, Johannes Kepler discovered his third law of planetary motion on 8 March 1618 and so on and so forth. However this accurate pinning of scientific or technological discoveries onto the ribbon of time creates a very false impression of what discovery is and this was exactly the point that Becky was trying to make on Twitter, which in turn led to me writing this post. Discovery is not a single act by a single person for which it is possible to give a stopwatch accurate moment of discovery but is rather a process spread over a period of time, which can in fact take several years and which almost always involves quite a large number of people.

To illustrate what this means let us take a closer look at Galileo’s epoch making discovery of the four largest (actually it was only three on the first day) moons of Jupiter. On 7 January 1610 whilst observing the planet Jupiter Galileo noted three stars that roughly formed a line with the middle axis or equator of the planet. When he observed again on the following evening they were still there. You might ask so what? Stars belong to the sphere of fixed stars, which are so called because they ‘always’ remain in the same place, whereas planets are called planets (the Greek for wanderer) because they move around with reference to the fixed stars. This being the case Galileo’s three new stars that he had recorded should have changed their position relative to Jupiter, or more accurately Jupiter should have changed its position relative to the three stars. Galileo was astute enough to realise that he was on to something and continued to observe and record the now four new stars and Jupiter over the following nights. The new stars did change their positions relative to Jupiter but not in the way he would have expected if they were fixed stars plus they always stayed in the vicinity of the planet. With time and enough observations Galileo realised that the four new objects were in fact orbiting Jupiter. He had discovered Jupiter’s four largest moons, or had he?

Science requires that new discoveries can be repeated by other independent practitioners/observers and discoveries are only confirmed and thus accepted when this has taken place. Now as stated above Simon Marius in Ansbach had also first observed the moons of Jupiter just one day later on 8 January 1610 and like Galileo had continued to observe them and had also reached the conclusion that they were orbiting the planet. This would have been the necessary confirmation that Galileo required but Marius only published his observations four years later, in 1614, leading Galileo, who by this time had long been acknowledged as the discoverer to denounce Marius as a plagiarist. Back in 1610 when Galileo fist published his observations on 14 March, in his Sidereus Nuncius, people were, not surprisingly, rather sceptical about his claims.

As I have recorded on several occasions on this blog it was the Jesuit mathematician astronomers under Christoph Clavius at the Collegio Romano who provide the necessary independent confirmation of his observations but this was not a simple process. At first the Jesuits did not have a telescope powerful enough to resolve the moons of Jupiter and their initial attempts to construct one failed. However Grienberger and Lembo persevered with assistance from Galileo, from afar by post, and in the end they were able to confirm all of Galileo’s observations. Another aspect of this discovery was to prove that they were actually moons orbiting Jupiter the four new objects needed to be observed consistently and accurately in order to determine their orbits so that one could predict their positions at any given time. Both Galileo and Marius undertook this task, Marius’ results were more accurate than those of his Tuscan rival, but it was first Cassini several decades later who, with much superior telescopes at his disposal, was able to produce tables of the orbits accurate enough to truly satisfy the requirements of the astronomical community.

It would now seem that we are finished with our tale of the discovery of the four moons of Jupiter but there is another extremely important factor that needs to be addressed. New discoveries often involve new methods and/or new scientific instruments, without which the discovery would not have been possible. This was very much the case with the discovery of the moons of Jupiter, which was only made possible by the very recently invented, September 1608, telescope. Any such new methodology or instrumentation must be clearly and convincingly shown to provide objective verifiable facts based on solid scientific theory. No such demonstration of objective scientific reliability existed at this point in time for the telescope. In fact all those in 1610, who doubted the telescopes ability to deliver objective verifiable scientific facts, and who tend to get ridiculed by the cheerleaders of scientism today, were perfectly correct to do so. Galileo, who when it came to optics was a tinkerer rather than a theorist, was not in the position to deliver the very necessary scientific theory of the telescope. Enter Johannes Kepler.

Kepler had already ready written extensively on theoretical optics including one of the earliest scientific analysis of how lenses functions. He was also an unabashed cheerleader for Galileo’s telescopic discoveries, sight unseen, writing the first positive, rather gushing in fact, review of Sidereus Nuncius, which Galileo used for his own propaganda purposes. Kepler realised at once that in order to confirm those discoveries a theoretical description of how the telescope functions was necessary and he sat down and wrote one. His Dioptrice, which explains the science of single lenses, the convex/concave two lens Dutch telescope used by Galileo, the convex/convex two lens astronomical or Keplerian telescope, the three lens terrestrial telescope and even the telephoto lens, was published in 1611. Galileo, arrogant and egoistical as ever, dismissed it as unreadable but it successfully silenced those who doubted the scientific objectivity of the telescope.

All of the factors that I have described above played an important and indispensible part in the discovery of the four largest moons of Jupiter. What we have here is not the act of one person at a specific point in time, in this case Galileo’s first observation of those three stars, but a chain of intertwined events or a process spread over a period of several years. There is nothing exceptional in the discovery of the moons of Jupiter but all scientific and technological discoveries involve a similar complex process carried out by a group of people over a period of time. Discovery is not the single act of a single person but a process involving several and sometimes many people spread over a period of time. The anniversaries that we like to celebrate are mostly just the starting point to that process.

 

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Why The Imitation Game is a disaster for historians.

I made the mistake, as a former professional historian of logic and meta-mathematics and, as a consequence, an amateur historian of the computer, of going to the cinema to watch the Alan Turing biopic The Imitation Game. I knew that it wouldn’t be historically accurate but that it would be a total historical disaster and, as I said on leaving the cinema, an insult to the memory of both Alan Turing and the others who worked in Bletchley Park surprised even me, a dyed in the wool, life-long cynic.

As I ventilated my disgust over the next few days on Twitter some, quite correctly, took me to task, informing me that it is a film and not a history book and therefore one shouldn’t criticise it for any inaccuracies that it contains. This attitude is of course perfectly correct and I would accept it,m if only the people who watch the film, who unlike myself are not knowledgeable historians, would view the film in this way; unfortunately they don’t.

The pre-release publicity for the film emphasised very intensely that the film tells a “true” story. This is screwed back somewhat in the film itself which opens with the claim that it is “based on a true story”. Unfortunately people simply ignore the “based on” and as I left a full cinema, at the end of the film, people all around me were saying to each other, “Wow, I didn’t know that. It’s a true story, you know?” and other similar expressions. This was compounded by both the Golden Globes and the Oscars, as the film won the awards of the respective organisations for best-adapted script! The film is supposedly based on Andrew Hodges’ Alan Turing biography, The Enigma. This book, which I read when it was first published, is one of the best biographies of a scientist that I’ve ever read, superbly researched, meticulously detailed and a real pleasure to read. Hodges is apparently prohibited by a gag clause in his contract for the film rights to his book from commenting on the film. “Take this large sum of money son and shut your mouth whilst we destroy your book!” It is not much of an exaggeration to say that the adaption consists of dumping the factual content of the book, plus several of the central characters, and writing a piece of third rate fiction using the names of some of the figures in Hodges’ biography. If that’s the film industries definition of ‘best adapted’ I don’t won’t to know what they consider to be the ‘worst adapted’.

I’m not going to go into great detail about everything that is wrong with the film because to a certain extent others have already done the work for me. The film almost completely ignores the contributions of the Poles in breaking the Enigma Codes (note the plural, there was more than one, another thing that doesn’t get mentioned in the film). They only get mentioned in a passing half sentence, which I strongly suspect almost all viewers failed to notice. You can read about the Polish contribution here, here and here. A short, general but largely accurate account of Turing’s involvement can be read here. There is a biting general criticism of the film on Ursula Writes, and another slightly less acerbic by L. V. Anderson on the Slate website. Another demolition job both of the Imitation Game and the Hawking biopic The Theory of Everything is on the Nature website by Colin Macilwain.

In case anybody doubts that the lay public think that the film is a ‘true’ story I have extracted part of a fairly typical critique of the film from the website of G. B. Hatch

I wanted to see this film the minute I heard about it. The plot sounded very intriguing. I had never learned about Alan Turing, and I now believe every History teacher should be showing this film while teaching WWII. Alan Turing and his team are some of the heroes of WWII that didn’t need to fire a single shot. This film, like “Argo”, is a great historical thriller based on a story that had remained confidential for several decades. This film is “The Imitation Game”.

“The Imitation Game” tells the true story of Alan Turing (played by Benedict Cumberbatch), a brilliant yet socially awkward British mathematician who is hired as a German code-breaker during WWII. He sets out to create a machine that will crack the Enigma Code, a German code that many claim as unbreakable. With the help of fellow code-breaker Joan Clarke (played by Keira Knightley), Turing invents this machine, which he calls ‘Christopher’, while also trying to hide his homosexuality which was illegal at the time. The film perfectly blends intensity and humor, while also transitioning between the past, present, and future.

As can be clearly seen Mr (or is that Ms?) Hatch is convinced that the film tells a true story and even goes so far as to suggest that the film should be used in school history lessons!

The historian is clearly presented by a dilemma when the film industry decides to make a film about a well-researched and well-documented historical episode. Almost without exception the scriptwriters decide that history is too complex, too boring, not sexy enough or whatever. They throw out ninety per cent of the historical facts and write there own ‘better than reality’ version usually retaining not much more that the names of the historical characters. They then add a bucket full of false historical touches, such as horns on Viking helmets, that everybody knows are “true”. The whole thing is then packaged up by the advertising department as the “amazing unknown true story of”! If the historian complains he gets firmly put in his place by people telling him “it’s only a film”. If he doesn’t complain he can listen to all those film goers sitting around in bars and cafés saying, “Did you know Alan Turing won the Second World War almost single handed!”

What ever else you have no hope of winning if you are a historian.

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A Swiss Clockmaker

We all have clichéd images in our heads when we hear the names of countries other than our own. For many people the name Switzerland evokes a muddled collection of snow-covered mountains, delicious superior chocolates and high precision clocks and watches. Jost Bürgi who was born in the small town of Lichtensteig, in the  Toggenburg region of the canton of St. Gallen on 28 February 1552 fills this cliché as the most expert clockmaker in the sixteenth century. However Bürgi was much more that just a Swiss clockmaker, he was also an instrument maker, an astronomer, a mathematician and in his private life a successful property owner and private banker, the last of course serving yet another Swiss cliché.

As we all too many figures, who made significant contributions to science and technology in the Renaissance we know next to nothing about Bürgi’s origins or background. There is no known registration of his birth or his baptism; his date of birth is known from the engraving shown below from 1592, in which the portrait was added in 1619 but which was first published in 1648. That the included date is his birthday was confirmed by Bürgi’s brother in law.

Bramer1648

His father was probably the locksmith Lienz Bürgi but that is not known for certain. About his education or lack of it nothing is known at all and just as little is known about where he learnt his trade as clockmaker. Various speculations have been made by historians over the years but they remain just speculations. The earliest documentary proof that we have of Bürgi’s existence is his employment contract when he entered the service of the Landgrave Wilhelm IV of Hessen-Kassel as court clockmaker, already twenty-seven years old, on 25 July 1579. Wilhelm was unique amongst the German rulers of the Renaissance in that he was not only a fan or supporter of astronomy but was himself an active practicing astronomer. In his castle in Kassel he constructed, what is recognised as, the first observatory in Early Modern Europe.

Wilhelm IV. von Hessen-Kassel Source: Wikimedia Commons

Wilhelm IV. von Hessen-Kassel
Source: Wikimedia Commons

He also played a major role in persuading the Danish King Frederick II, a cousin, to supply Tycho Brahe with the necessary land and money to establish an observatory in Denmark. In the 1560s Wilhelm was supported in his astronomical activities by Andreas Schöner, the son of the famous Nürnberger cartographer, globe and instrument maker, astronomer, astrologer and mathematician Johannes Schöner. He also commissioned the clockmaker Eberhard Baldewein (1525-1593) to construct two planet clocks and a mechanical globe.

 

Eberhart Baldewein Planet clock 1661 Source: Wikimedia Commons

Eberhart Baldewein Planet clock 1661
Source: Wikimedia Commons

The planet clock shows the positions of the sun, moon and the planets, based on Peter Apian’s Astronomicom Caessareum, on its various dials.

 

Eberhard Baldewein Mechanical Celestial Globe circa 1573

Eberhard Baldewein Mechanical Celestial Globe circa 1573 The globe, finished by Heinrich Lennep in 1693, was used to record the position of the stars mapped by Wilhelm and his team in their observations.

These mechanical objects were serviced and maintained by Baldewein’s ex-apprentice, Hans Bucher, who had helped to build them and who had been employed by Wilhelm, for this purpose, since 1560. When Bucher died in 1578-1579 Bürgi was employed to replace him, charged with the maintenance of the existing objects on a fixed, but very generous salary, and commissioned to produce new mechanical instruments for which he would be paid extra. Over the next fifty years Bürgi produced many beautiful and highly efficient clocks and mechanical globes both for Wilhelm and for others.

Bürgi Quartz Clock 1622-27 Source: Swiss Physical Society

Bürgi Quartz Clock 1622-27
Source: Swiss Physical Society

 

 

 

 

 

Bürgi Mechanical Celestial Globe 1594 Source: Wikimedia Commons

Bürgi Mechanical Celestial Globe 1594
Source: Wikimedia Commons

 

 

Jost Bürgi and Antonius Eisenhoit: Armillary sphere with astronomical clock made 1585 in Kassel, now at Nordiska Museet in Stockholm. Source Wikimedia Commons

Jost Bürgi and Antonius Eisenhoit: Armillary sphere with astronomical clock made 1585 in Kassel, now at Nordiska Museet in Stockholm.
Source Wikimedia Commons

Bürgi was also a highly inventive clockmaker, who is credited with the invention of both the cross-beat escapement and the remontoire, two highly important improvements in clock mechanics. In the late sixteenth century the average clocks were accurate to about thirty minutes a day, Bürgi’s clock were said to be accurate to less than one minute a day. This amazing increase in accuracy allowed mechanical clocks to be used, for the first time ever, for timing astronomical observations. Bürgi also supplied clocks for this purpose for Tycho’s observatory on Hven. In 1592 Wilhelm presented his nephew Rudolph II, the German Emperor, with one of Bürgi’s mechanical globes and Bürgi was sent to Prague with the globe to demonstrate it to Rudolph. This was his first contact with what would later become his workplace. Whilst away from Kassel Bürgi’s employer, Wilhelm died. Before continuing the story we need to go back and look at some of Bürgi’s other activities.

As stated at the beginning Bürgi was not just a clockmaker. In 1584 Wilhelm appointed the Wittenberg University graduate Christoph Rothmann as court astronomer. From this point on the three, Wilhelm, Rothmann and Bürgi, were engaged in a major programme to map the heavens, similar to and just as accurate, as that of Tycho on Hven. The two observatories exchanged much information on instruments, observations and astronomical and cosmological theories. However all was not harmonious in this three-man team. Although Wilhelm treated Bürgi, whom he held in high regard, with great respect Rothmann, who appears to have been a bit of a snob, treated Bürgi with contempt because he was uneducated and couldn’t read or write Latin, that Bürgi was the better mathematician of the two might have been one reason for Rothmann’s attitude.

In the 1580s the itinerant mathematician and astronomer Paul Wittich came to Kassel from Hven and taught Bürgi prosthaphaeresis, a method using trigonometric formulas, of turning multiplication into addition, thus simplifying complex astronomical calculations. The method was first discovered by Johannes Werner in Nürnberg at the beginning of the sixteenth century but he never published it and so his discovery remained unknown. It is not known whether Wittich rediscovered the method or learnt of it from Werner’s manuscripts whilst visiting Nürnberg. The method was first published by Nicolaus Reimers Baer, who was then accused by Tycho of having plagiarised the method, Tycho claiming falsely that he had discovered it. In fact Tycho had also learnt it from Wittich. Bürgi had expanded and improved the method and when Baer also came to Kassel in 1588, Bürgi taught him the method and how to use it, in exchange for which Baer translated Copernicus’ De revolutionibus into German for Bürgi. This was the first such translation and a copy of Baer’s manuscript is still in existence in Graz. Whilst Baer was in Kassel Bürgi created a brass model of the Tychonic geocentric-heliocentric model of the cosmos, which Baer claimed to have discovered himself. When Tycho got wind of this he was apoplectic with rage.

In 1590 Rothmann disappeared off the face of the earth following a visit to Hven and for the last two years of Wilhelm’s life Bürgi took over as chief astronomical observer in Kassel, proving to be just as good in this work as in his clock making.

Following Wilhelm’s death his son Maurice who inherited the title renewed Bürgi’s contract with the court.

 

Kupferstich mit dem Porträt Moritz von Hessen-Kassel aus dem Werk Theatrum Europaeum von 1662 Source: Wikimedia Commons

Kupferstich mit dem Porträt Moritz von Hessen-Kassel aus dem Werk Theatrum Europaeum von 1662
Source: Wikimedia Commons

However Maurice did not share his father’s love of astronomy investing his spare time instead in the study of alchemy. Bürgi however continued to serve the court as clock and instrument maker. Over the next eight years Bürgi made several visits to the Emperor’s court in Prague and in 1604 Rudolph requested Maurice to allow him to retain Bürgi’s services on a permanent basis. Maurice acquiesced and Bürgi moved permanently to Prague although still remaining formally in service to Maurice in Kassel. Rudolph gave Bürgi a very generous contract paying him 60 gulden a month as well as full board and lodging. As in Kassel all clocks and globes were paid extra. To put that into perspective 60 gulden was a yearly wage for a young academic starting out on his career!

In Prague Bürgi worked closely with the Imperial Mathematicus, Johannes Kepler. Kepler, unlike Rothmann, respected Bürgi immensely and encouraged him to publish his mathematical works. Bürgi was the author of an original Cos, an algebra textbook, from which Kepler says he learnt much and which only saw the light of day through Kepler’s efforts. Kepler was also responsible for the publication of Bürgi’s logarithmic tables in 1620.

 

Bürgi's Logarithmic Tables Source: University of Graz

Bürgi’s Logarithmic Tables
Source: University of Graz

This is probably Bürgi’s greatest mathematical achievement and he is considered along side of John Napier as the inventor of logarithms. In many earlier historical works Bürgi is credited with having invented logarithms before Napier. Napier published his tables in 1614 six years before Bürgi and is known to have been working on them for twenty years, that is since 1594. Bürgi’s fan club claim that he had invented his logarithms in 1588 that is six years earlier than Napier. However modern experts on the history of logarithms think that references to 1588 are to Bürgi’s use of prosthaphaeresis and that he didn’t start work on his logarithms before 1604. However it is clear that the two men developed the concept independently of each other and both deserve the laurels for their invention. It should however be pointed out that the concept on which logarithms are based was known to Archimedes and had already been investigated by Michael Stifel earlier in the sixteenth century in a work that was probably known to Bürgi.

Through his work as clock maker Bürgi became a very wealthy man and invested his wealth with profit in property deals and as a private banker lending quite substantial sums to his customers. In 1631 Bürgi, now 80 years old, retired and returned ‘home’ to Kassel where he died in January of the following year shortly before his 81st birthday. His death was registered in the Church of St Martin’s on the 31 January 1632. Although now only known to historians of science and horology, in his own time Bürgi was a well-known and highly respected, astronomer, mathematician and clock maker who made significant and important contributions to all three disciplines.

 

 

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