The emergence of modern astronomy – a complex mosaic: Part XLIII

The Moon is the Earth’s nearest celestial neighbour and the most prominent object in the night sky. People have been tracking, observing and recording the movements of the Moon for thousands of years, so one could assume that calculating its orbit around the Earth should be a reasonable simple matter, however in reality it is anything but.

The problem can be found in the law of gravity itself, which states that any two bodies mutually attract each other. However, that attraction is not restricted to just those two bodies but all bodies attract each other simultaneously. Given the relative masses of somebody standing next to you and the Earth, when calculating the pull of gravity on you, we can, in our calculation, neglect the pull exercised by the mass of your neighbour. With planets, however, it is more difficult to ignore multiple sources of gravitational force. We briefly touched on the gravitational effect of Jupiter and Saturn, both comparatively large masses, on the flight paths of comets, so called perturbation. In fact when calculating the Earth orbit around the Sun then the effects of those giant planets, whilst relatively small, are in fact detectable.

With the Moon the problem is greatly exacerbated. The gravitation attraction between the Earth and the Moon is the primary force that has to be considered but the not inconsiderable gravitational attraction between the Sun and the Moon also plays an anything but insignificant role. The result is that the Moon’s orbit around the Sun Earth is not the smooth ellipse of Kepler’s planetary laws that it would be if the two bodies existed in isolation but a weird, apparently highly irregular, dance through the heavens as the Moon is pulled hither and thither between the Earth and the Sun.

Kepler in fact did not try to apply his laws of planetary motion to the Moon simply leaving it out of his considerations. The first person to apply the Keplerian elliptical astronomy to the Moon was Jeremiah Horrocks (1618–1641), an early-convinced Keplerian, who was also the first person to observe a transit of Venus having recalculated Kepler’s Rudolphine Tables in order to predict to correct date of the occurrence. Horrocks produced a theory of the Moon based on Kepler’s work, which was far and away the best approximation to the Moon’s orbit that had been produced up till that time but was still highly deficient. This was the model that Newton began his work with as he tried to make the Moon’s orbit fit into his grand gravitational theory, as defined by his three laws of motion, Kepler’s three laws of planetary motion and the inverse square law of gravity; this would turn into something of a nightmare for Newton and cause a massive rift between Newton and John Flamsteed the Astronomer Royal.

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Portrait of Newton at 46 by Godfrey Kneller, 1689 Source: Wikimedia Commons

What Newton was faced with was attempting to solve the three-body problem, that is a general solution for the mutual gravitational attraction of three bodies in space. What Newton did not and could not know was that the general analytical solution simple doesn’t exist, the proof of this lay in the distant future. The best one can hope for are partial local solutions based on approximations and this was the approach that Newton set out to use. The deviations of the Moon, perturbations, from the smooth elliptical orbit that it would have if only it and the Earth were involved are not as irregular as they at first appear but follow a complex pattern; Newton set out to pick them off one by one. In order to do so he need the most accurate data available, which meant new measurement made during new observations by John Flamsteed the Astronomer Royal.

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Source: Wikimedia Commons

For Newton solving the lunar orbit was the most pressing problem in his life and he imperiously demanded that Flamsteed supply him with the data that he required to make his calculations. For Flamsteed the important task in his life, as an observational astronomer, was to complete a new star catalogue on a level of observational accuracy hitherto unknown. The principle interests of the two men were thus largely incompatible. Newton demanded that Flamsteed use his time to supply him with his lunar data and Flamsteed desired to use his time to work on his star catalogue, although to be fair he did supply Newton, if somewhat grudgingly with the desired data. As Newton became more and more frustrated by the problems he was trying to solve the tone of his missives to Flamsteed in Greenwich became more and more imperious and Flamsteed got more and more frustrated at being treated like a lackey by the Lucasian Professor. The relations between the two degenerated rapidly.

The situation was exacerbated by the presence of Edmond Halley in the mix, as Newton’s chief supporter. Halley had started his illustrious career as a protégée of Flamsteed’s when he, still an undergraduate, sailed to the island of Saint Helena to make a rapid survey of the southern night skies for English navigators. The men enjoyed good relations often observing together and with Halley even deputising for Flamsteed at Greenwich when he was indisposed. However something happened around 1686 and Flamsteed began to reject Halley. It reached a point where Flamsteed, who was deeply religious with a puritan streak, disparaged Halley as a drunkard and a heathen. He stopped referring him by name calling him instead Reymers, a reference to the astronomer Nicolaus Reimers Ursus (1551–1600). Flamsteed was a glowing fan of Tycho Brahe and he believed Tycho’s accusation that Ursus plagiarised Tycho’s system. So Reymers was in his opinion a highly insulting label.

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Portrait of Edmond Halley painted around 1687 by Thomas Murray (Royal Society, London) Source: Wikimedia Commons

Newton only succeeded in resolving about half of the irregularities in the Moon’s orbit and blamed his failure on Flamsteed. This led to one of the most bizarre episodes in the history of astronomy. In 1704 Newton was elected President of the Royal Society and one of his first acts was to call Flamsteed to account. He demanded to know what Flamsteed had achieved in the twenty-nine years that he had been Astronomer Royal and when he intended to make the results of his researches public. Flamsteed was also aware of the fact that he had nothing to show for nearly thirty years of labours and was negotiating with Prince George of Denmark, Queen Anne’s consort, to get him to sponsor the publication of his star catalogue. Independently of Flamsteed, Newton was also negotiating with Prince George for the same reason and as he was now Europe’s most famous scientist he won this round. George agreed to finance the publication, and was, as a reward, elected a member of the Royal Society.

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Prince George of Denmark and Norway, Duke of Cumberland Portrait by Michael Dahl c. 1705 Source: Wikimedia Commons

Newton set up a committee, at the Royal Society, to supervise the work with himself as chairman and the Savilian Professors of Mathematics and Astronomy, David Gregory and Edmond Halley, both of whom Flamsteed regarded as his enemies, Francis Robartes an MP and teller at the Exchequer and Dr John Arbuthnotmathematician, satirist and physician extraordinary to Queen Anne. Although Arbuthnot, a Tory, was of opposing political views to Newton, a Whig, he was a close friend and confidant. Flamsteed was not offered a place on this committee, which was decidedly stacked against him.

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David Gregory Source: Wikimedia Commons

Flamsteed’s view on what he wanted published and how it was to be organised and Newton’s views on the topic were at odds from the very beginning. Flamsteed saw his star catalogue as the centrepiece of a multi-volume publication, whereas all that really interested Newton was his data on the planetary and Moon orbits, with which he hoped to rectify his deficient lunar theory. What ensued was a guerrilla war of attrition with Flamsteed sniping at the referees and Newton and the referees squashing nearly all of Flamsteed wishes and proposals. At one point Newton even had Flamsteed ejected from the Royal Society for non-payment of his membership fees, although he was by no means the only member in arrears. Progress was painfully slow and at times virtually non-existent till it finally ground completely to a halt with the death of Prince George in 1708.

George’s death led to a two-year ceasefire in which Newton and Flamsteed did not communicate but Flamsteed took the time to work on the version of his star catalogue that he wanted to see published. Then in 1710 John Arbuthnot appeared at the council of the Royal society with a royal warrant from Queen Anne appointing the president of the society and anybody the council chose to deputise ‘constant Visitors’ to the Royal Observatory at Greenwich. ‘Visitor’ here means supervisor in the legal sense. Flamsteed’s goose was well and truly cooked. He was now officially answerable to Newton. Instead of waiting for Flamsteed to finish his star catalogue the Royal Society produced and published one in the form that Newton wanted and edited by Edmond Halley, the man Flamsteed regarded as his greatest enemy. It appeared in 1712. In 1713 Newton published the second edition of his Principia with its still defective lunar theory but with Flamsteed name eliminated as far as possible.

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John Arbuthnot Portrait by Godfrey Kneller Source: Wikimedia Commons

The farce did not end here. In 1714 Queen Anne died and the Visitor warrant thus lost its validity. The Tory government fell and the Whigs regained power. Newton’s political sponsor, Charles Montagu, 1st Earl of Halifax, died in 1715 leaving him without a voice in the new government. Flamsteed, however, was friends with the Lord Chamberlain, Lord Boulton. On 30 November 1715 Boulton signed a warrant ordering Newton and co to hand over the remaining 300 copies of their ‘pirate’ catalogue to Flamsteed.  After some procrastination and some more insults aimed at Flamsteed they finally complied on 28 March 1716. Flamsteed “made a Sacrifice of them to Heavenly truth”, that is he burnt them. Flamsteed had in the mean time published his star catalogue at his own expense and devoted the rest of his life to preparing the rest of his life’s work for publication. He died in 1719 but his widow, Margaret, and two of his former assistants, Joseph Crosthwait and Abraham Sharp, edited and published his Historia coelestis britannia in three volumes in 1725; it is rightly regarded as a classic in the history of celestial observation. Margaret also took her revenge on Halley, who succeeded Flamsteed as Astronomer Royal. Flamsteed had paid for the instruments in the observatory at Greenwich out of his own pocket, so she stripped the building bare leaving Halley with an empty observatory without instruments. For once in his life Newton lost a confrontation with a scientific colleague, of which there were quite a few, game, set and match

The bitter and in the end unseemly dispute between Newton and Flamsteed did nothing to help Newton with his lunar theory problem and to bring his description of the Moon’s orbit into line with the law of gravity. In the end this discrepancy in the Principia remained beyond Newton’s death. Mathematicians and astronomers in the eighteen century were well aware of this unsightly defect in Newton’s work and in the 1740s Leonhard Euler (1707­–1783), Alexis Clairaut (1713–1765) and Jean d’Alembert (1717–1783) all took up the problem and tried to solve it, in competition with each other.  For a time all three of them thought that they would have to replace the inverse square law of gravity, thinking that the problem lay there. Clairaut even went so far as to announce to the Paris Academy on 15 November 1747 that the law of gravity was false, to the joy of the Cartesian astronomers. Having then found a way of calculating the lunar irregularities using approximations and confirming the inverse square law, Clairaut had to retract his own announcement. Although they had not found a solution to the three-body problem the three mathematicians had succeeded in bringing the orbit of the Moon into line with the law of gravity. The first complete, consistent presentation of a Newtonian theory of the cosmos was presented by Pierre-Simon Laplace in his Traité de mécanique céleste, 5 Vol., Paris 1798–1825.

Mathematicians and astronomers were still not happy with the lack of a general solution to the three-body problem, so in 1887 Oscar II, the King of Sweden, advised by Gösta Mittag-Leffler offered a prize for the solution of the more general n-body problem.

Given a system of arbitrarily many mass points that attract each according to Newton’s law, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converge uniformly.

Nobody succeeded in solving the challenge but Henri Poincaré’s attempt to find a solution although not successful, contained enough promising leads that he was awarded the prize. As stated a solution to the problem was found for three bodies by Karl F Sundman in 1912 and generalised for more than three bodies by Quidong Wang in the 1990s.

The whole episode of Newton’s failed attempt to find a lunar theory consonant with his theory of gravitation demonstrates that even the greatest of mathematicians can’t solve everything. It also demonstrates that the greatest of mathematicians can behave like small children having a temper tantrum if they don’t get their own way.

 

 

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Filed under History of Astrology, History of Mathematics, History of Physics, Newton

A scientific Dutchman

For many decades the popular narrative version of the scientific revolution started in Poland/Germany with Copernicus moving on through Tycho in Denmark, Kepler in Germany/Austria, Galileo et al in Northern Italy, Descartes, Pascal, Mersenne etc., in France and then Newton and his supporters and opponents in London. The Netherlands simply didn’t get a look in except for Christiaan Huygens, who was treated as a sort of honorary Frenchman. As I’ve tried to show over the years the Netherlands and its scholars–Gemma Frisius, Simon Stephen, Isaac Beeckman, the Snels, and the cartographers–actually played a central role in the evolution of the sciences during the Early Modern Period. In more recent years efforts have been made to increase the historical coverage of the contributions made in the Netherlands, a prominent example being Harold J Cook’s Matters of Exchange: Commerce, Medicine and Science in the Dutch Golden Age.[1]

A very strange anomaly in the #histSTM coverage concerns Christiaan Huygens, who without doubt belongs to the seventeenth century scientific elite. Whereas my bookcase has an entire row of Newton biographies, and another row of Galileo biographies and in both cases there are others that I’ve read but don’t own. The Kepler collection is somewhat smaller but it is still a collection. I have no idea how many Descartes biographies exist but it is quite a large number. But for Christiaan Huygens there is almost nothing available in English. The only biography I’m aware of is the English translation of Cornelis Dirk Andriesse’s scientific biography of Christiaan Huygens, The Man Behind the Principle.[2] I read this several years ago and must admit I found it somewhat lacking. This being the case, great expectation have been raised by the announcement of a new Huygens biography by Hugh Aldersey-Williams, Dutch Light: Christiaan Huygens and the Making of Science in Europe.[3]

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So does Aldersey-Williams fulfil those expectations? Does he deliver the goods? Yes and no, on the whole he has researched and written what is mostly an excellent biography of the Netherland’s greatest scientist[4] of the Early Modern Period but it is in my opinion marred by sloppy history of science fact checking that probably won’t be noticed by the average reader but being the notorious #histSTM pedant that I am I simply can’t and won’t ignore.[5]

My regular readers will known that I describe myself as a narrative contextual historian of science and I personally believe that if we are to understand how science has evolved historical then we have to tell that story with its complete context. This being the case I’m very happy to report that Aldersey-Williams is very much a narrative contextual historian, who tells the complete story of Christiaan Huygens life within its wider context and not just offering up a list of his scientific achievements. In fact what the reader gets for his money is not just a biography of Christiaan but also a biography of his entire family with some members being given more space than other. In particular it is a full biography of Christiaan and his father Constantijn, who played a significant and central role in shaping Christiaan’s life.

The book opens by setting the scientific scene in the early seventeenth-century Netherlands. We get introduced to those scientists, who laid the scientific foundations on which Christiaan would later build. In particular we get introduced to Simon Steven, who shaped the very practice orientated science and technology of the Early Modern Netherlands. We also meet other important and influential figures such as Hans Lipperhey, Isaac Beeckman, Willebrord Snel, Cornelius Drebbel and others.

There now follows what might be termed a book within a book as Aldersey-Williams delivers up a very comprehensive biography of Constantijn Huygens diplomat, poet, composer, art lover and patron and all round lover of knowledge. Constantijn was interested in and fascinated by almost everything both scientific and technological. His interest was never superficial but was both theoretical and practical. For example he was not only interested in the newly invented instruments, the telescope and the microscope, but he also took instruction in how to grind lenses and that from the best in the business. Likewise his love for art extended beyond buying paintings and patronising artists, such as Rembrandt, but to developing his own skills in drawing and painting. Here Aldersey-Williams introduces us to the Dutch term ‘kenner’ (which is the same in German), which refers to someone such Constantijn Huygens, whose knowledge of a subject is both theoretical and practical. Constantijn Huygens married Suzanna von Baerle for love and they had five children over ten years, four sons and a daughter, Christiaan was the second oldest, and Suzanna died giving birth to their daughter, also named Suzanna.

Constantijn Huygens brought up his children himself educating them in his own polymathic diversity with the help of tutors. When older the boys spent brief periods at various universities but were largely home educated. We now follow the young Christiaan and his older brother, also Constantijn, through their formative young years. The two oldest boys remained close and much of Christiaan’s astronomical work was carried out in tandem with his older brother. We follow Christiaan’s early mathematical work and his introduction into the intellectual circles of Europe, especially France and England, through his father’s widespread network of acquaintances. From the beginning Christiaan was set up to become either a diplomat, like his father, grandfather and brothers, or a scientist and it is the latter course that he followed.

Aldersey-Williams devotes an entire chapter to Christiaan’s telescopic observations of Saturn, with a telescope that he and Constantijn the younger constructed and his reputation making discovery of Titan the largest of Saturn’s moons, and the first discovered, and his determination that the strange shapes first observed by Galileo around Saturn were in fact rings. These astronomical discoveries established him as one of Europe’s leading astronomers. The following chapter deals with Huygens’ invention of the pendulum clock and his excursions into the then comparatively new probability theory.

Saturn and the pendulum clock established the still comparatively young Huygens as a leading light in European science in the second half of the seventeenth century and Aldersey-Williams now takes us through ups and downs of the rest of Christiaan’s life. His contact with and election to the Royal Society in London, as its first foreign member. His appointment by Jean-Baptist Colbert, the French First Minister of State, as a founding member of the Académie des sciences with a fairy generous royal pension from Louis XIV. His sixteen years in Paris, until the death of Colbert, during which he was generally acknowledged as Europe’s leading natural philosopher. His initial dispute over light with the young and comparatively unknown Newton and his tutorship of the equally young and unknown Leibniz. His fall from grace following Colbert’s death and his reluctant return to the Netherlands. The last lonely decade of his life in the Netherlands and his desire for a return to the scientific bustle of London or Paris. His partial rapprochement with Newton following the publication of the Principia. Closing with the posthumous publication of his works on gravity and optics. This narrative is interwoven with episodes from the lives of Constantijn the father and Constantijn his elder brother, in particular the convoluted politics of the Netherlands and England created by William of Orange, whose secretary was Constantijn, the younger, taking the English throne together with his wife Mary Stewart. Christiaan’s other siblings also make occasional appearances in letters and in person.

Aldersey-Williams has written a monumental biography of two generations of the Huygens family, who played major roles in the culture, politics and science of seventeenth century Europe. With a light, excellent narrative style the book is a pleasure to read. It is illustrated with 37 small grey in grey prints and 35 colour plates, which I can’t comment on, as my review proof copy doesn’t contain them. There are informative footnotes scattered through out the text and the, by me hated, hanging endnotes referring to the sources of direct quotes in the text. Here I had the experience more than once of looking up what I took to be a direct quote only to discover that it was not listed. There is an extensive bibliography of both primary and secondary sources and I assume an extensive index given the number of blank pages in my proof copy. There were several times when I was reading when I had wished that the index were actually there.

On the whole I would be tempted to give this book a glowing recommendation were it not for a series of specific history of science errors that simple shouldn’t be there and some general tendencies that I will now detail.

Near the beginning Aldersey-Williams tells us that ‘Stevin’s recommendation to use decimals in arithmetical calculations in place of vulgar fractions which could have any denominator [was] surely the sand-yacht of accountancy … Thirty years later, the Scottish mathematician John Napier streamlined Stevin’s notation by introducing the familiar comma or point to separate off the fractional part…” As is all too often the case no mention is made of the fact that Chinese and Arabic mathematicians had been using decimal fractions literally centuries before Stevin came up with the concept. In my opinion we must get away from this Eurocentric presentation of the history of science. Also the Jesuit mathematician Christoph Clavius introduced the decimal point less than ten years after Stevin’s introduction of decimal fractions, well ahead of Napier, as was its use by Pitiscus in 1608, the probable source of Napier’s use.

We also get told when discussing the Dutch vocabulary that Stevin created for science that, “Chemistry becomes scheikunde, the art of separation, an acknowledgement of the beginnings of a shift towards an analytical science, and a useful alternative to chemie that severs the etymological connections with disreputable alchemy.” This displays a complete lack of knowledge of alchemy in which virtually all the analytical methods used in chemistry were developed. The art of separation is a perfectly good term from the alchemy that existed when Stevin was creating his Dutch scientific vocabulary. Throughout his book Aldersey-Williams makes disparaging remarks about both alchemy and astrology, neither of which was practiced by any of the Huygens family, which make very clear that he doesn’t actually know very much about either discipline or the role that they played in the evolution of western science, astrology right down to the time of Huygens and Newton and alchemy well into the eighteenth century. For example, the phlogiston theory one of the most productive chemical theories in the eighteenth century had deep roots in alchemy.

Aldersey-Williams account of the origins of the telescope is a bit mangled but acceptable except for the following: “By the following spring, spyglasses were on sale in Paris, from where one was taken to Galileo in Padua. He tweaked the design, claimed the invention as his own, and made dozens of prototypes, passing on his rejects so that very soon even more people were made aware of this instrument capable of bringing the distant close.”

Firstly Galileo claimed that he devised the principle of the telescope and constructed his own purely on verbal descriptions without having actually seen one but purely on his knowledge of optics. He never claimed the invention as his own and the following sentence is pure rubbish. Galileo and his instrument maker produced rather limited numbers of comparatively high quality telescopes that he then presented as gifts to prominent political and Church figures.

Next up we have Willebrord Snel’s use of triangulation. Aldersey-Williams tells us, “ This was the first practical survey of a significant area of land, and it soon inspired similar exercises in England, Italy and France.” It wasn’t. Mercator had previously surveyed the Duchy of Lorraine and Tycho Brahe his island of Hven before Snel began his surveying in the Netherlands. This is however not the worst, Aldersey-Williams tells us correctly that Snel’s survey stretched from Alkmaar to Bergen-op-Zoom “nearly 150 kilometres to the south along approximately the same meridian.” Then comes some incredible rubbish, “By comparing the apparent height of his survey poles observed at distance with their known height, he was able to estimate the size of the Earth!”

What Snel actually did, was having first accurately determined the length of a stretch of his meridian using triangulation, the purpose of his survey and not cartography, he determined astronomically the latitude of the end points. Having calculated the difference in latitudes it is then a fairly simple exercise to determine the length of one degree of latitude, although for a truly accurate determination one has to adjust for the curvature of the Earth.

Next up with have the obligatory Leonard reference. Why do pop history of science books always have a, usually erroneous, Leonardo reference? Here we are concerned with the camera obscura, Aldersey-Williams writes: “…Leonardo da Vinci gave one of the first accurate descriptions of such a design.” Ibn al-Haytham gave accurate descriptions of the camera obscura and its use as a scientific instrument about four hundred and fifty years before Leonardo was born in a book that was translated into Latin two hundred and fifty years before Leonardo’s birth. Add to this the fact that Leonardo’s description of the camera obscura was first published late in the eighteenth century and mentioning Leonardo in this context becomes a historical irrelevance. The first published European illustration of a camera obscura was Gemma Frisius in 1545.

When discussing Descartes, a friend of Constantijn senior and that principle natural philosophical influence on Christiaan we get a classic history of mathematics failure. Aldersey-Williams tells us, “His best known innovation, of what are now called Cartesian coordinates…” Whilst Descartes did indeed cofound, with Pierre Fermat, modern algebraic analytical geometry, Cartesian coordinates were first introduced by Frans van Schooten junior, who of course features strongly in the book as Christiaan’s mathematics teacher.

Along the same lines as the inaccurate camera obscura information we have the following gem, “When applied to a bisected circle (a special case of the ellipse), this yielded a new value, accurate to nine decimal places, of the mathematical constant π, which had not been improved since Archimedes” [my emphasis] There is a whole history of the improvements in the calculation of π between Archimedes and Huygens but there is one specific example that is, within the context of this book, extremely embarrassing.

Early on when dealing with Simon Stevin, Aldersey-Williams mentions that Stevin set up a school for engineering, at the request of Maurits of Nassau, at the University of Leiden in 1600. The first professor of mathematics at this institution was Ludolph van Ceulen (1540–1610), who also taught fencing, a fact that I find fascinating. Ludolph van Ceulen is famous in the history of mathematics for the fact that his greatest mathematical achievement, the Ludophine number, is inscribed on his tombstone, the accurate calculation of π to thirty-five decimal places, 3.14159265358979323846264338327950288…

Next up we have Christiaan’s correction of Descartes laws of collision. Here Aldersey-Williams writes something that is totally baffling, “The work [his new theory of collision] only appeared in a paper in the French Journal des Sçavans in 1669, a few years after Newton’s laws of motion [my emphasis]…” Newton’s laws of motion were first published in his Principia in 1687!

Having had the obligatory Leonardo reference we now have the obligatory erroneous Galileo mathematics and the laws of nature reference, “Galileo was the first to fully understand that mathematics could be used to describe certain laws of nature…” I’ve written so much on this that I’ll just say here, no he wasn’t! You can read about Robert Grosseteste’s statement of the role of mathematics in laws of nature already in the thirteenth century, here.

Writing about Christiaan’s solution of the puzzle of Saturn’s rings, Aldersey-Williams say, “Many theories had been advanced in the few years since telescopes had revealed the planet’s strange truth.” The almost five decades between Galileo’s first observation of the rings and Christiaan’s solution of the riddle is I think more than a few years.

Moving on Aldersey-Williams tells us that, “For many however, there remained powerful reasons to reject Huygens’ discovery. First of all, it challenged the accepted idea inherited from Greek philosophers that the solar system consisted exclusively of perfect spherical bodies occupying ideal circular orbits to one another.” You would have been hard put to it to find a serious astronomer ín 1660, who still ascribed to this Aristotelian cosmology.

The next historical glitch concerns, once again, Galileo. We read, “He dedicated the work [Systema Saturnium] to Prince Leopoldo de’ Medici, who was patron of the Accademia del Cimento in Florence, who had supported the work of Huygens’ most illustrious forebear, Galileo.” Ignoring the sycophantic description of Galileo, one should perhaps point out that the Accademia del Cimento was founded in 1657 that is fifteen years after Galileo’s death and so did not support his work. It was in fact founded by a group of Galileo’s disciples and was dedicated to continuing to work in his style, not quite the same thing.

Galileo crops up again, “the real power of Huygens’ interpretation was its ability to explain those times when Saturn’s ‘handles’ simply disappeared from view, as they had done in 1642, finally defeating the aged Galileo’s attempts to understand the planet…” In 1642, the year of his death, Galileo had been completely blind for four years and had actually given up his interest in astronomy several years earlier.

Moving on to Christiaan’s invention of the pendulum clock and the problem of determining longitude Aldersey-Williams tells us, “The Alkmaar surveyor Adriaan Metius, brother of the telescope pioneer Jacob, had proposed as long ago as 1614 that some sort of seagoing clock might provide the solution to this perennial problem of navigators…” I feel honour bound to point out that Adriaan Metius was slightly more than simply a surveyor, he was professor for mathematics at the University of Franeker. However the real problem here is that the clock solution to the problem of longitude was first proposed by Gemma Frisius in an appendix added in 1530, to his highly popular and widely read editions of Peter Apian’s Cosmographia. The book was the biggest selling and most widely read textbook on practical mathematics throughout the sixteenth and well into the seventeenth century so Huygens would probably have known of Frisius’ priority.

Having dealt with the factual #histSTM errors I will now turn to more general criticisms. On several occasions Aldersey-Williams, whilst acknowledging problems with using the concept in the seventeenth century, tries to present Huygens as the first ‘professional scientist’. Unfortunately, I personally can’t see that Huygens was in anyway more or less of a professional scientist than Tycho, Kepler or Galileo, for example, or quite a long list of others I could name. He also wants to sell him as the ‘first ever’ state’s scientist following his appointment to the Académie des sciences and the accompanying state pension from the king. Once again the term is equally applicable to Tycho first in Denmark and then, if you consider the Holy Roman Empire a state, again in Prague as Imperial Mathematicus, a post that Kepler inherited. Galileo was state ‘scientist’ under the de’ Medici in the Republic of Florence. One could even argue that Nicolas Kratzer was a state scientist when he was appointed to the English court under Henry VIII. There are other examples.

Aldersey-Williams’ next attempt to define Huygens’ status as a scientist left me somewhat speechless, “Yet it is surely enough that Huygens be remembered for what he was, a mere problem solver indeed: pragmatic, eclectic and synthetic and ready to settle for the most probable rather than hold out for the absolutely certain – in other words. What we expect a scientist to be today.” My ten years as a history and philosophy of science student want to scream, “Is that what we really expect?” I’m not even going to go there, as I would need a new blog post even longer than this one.

Aldersey-Williams also tries to present Huygens as some sort of new trans European savant of a type that had not previously existed. Signifying cooperation across borders, beliefs and politics. This is of course rubbish. The sort of trans European cooperation that Huygens was involved in was just as prevalent at the beginning of the seventeenth century in the era of Tycho, Kepler, Galileo, et al. Even then it was not new it was also very strong during the Renaissance with natural philosophers and mathematici corresponding, cooperating, visiting each other, and teaching at universities through out the whole of Europe. Even in the Renaissance, science in Europe knew no borders. It’s the origin of the concept, The Republic of Letters. I suspect my history of medieval science friend would say the same about their period.

In the partial rapprochement between Huygens and Newton following the Publication of the latter’s Principia leads Aldersey-Williams to claim that a new general level of reasonable discussion had entered scientific debate towards the end of the seventeenth century. Scientists, above all Newton, were still going at each other hammer and tongs in the eighteenth century, so it was all just a pipe dream.

Aldersey-Williams sees Huygens lack of public profile, as a result of being in Newton’s shadow like Hooke and others. He suggests that popular perception only allows for one scientific genius in a generation citing Galileo’s ascendance over Kepler, who he correctly sees as the more important, as another example. In this, I agree with him, however he tries too hard to put Huygens on the same level as Newton as a scientist, as if scientific achievement were a pissing contest. I think we should consider a much wider range of scientists when viewing the history of science but I also seriously think that no matter how great his contributions Huygens can’t really match up with Newton. Although his Horologium oscillatorium sive de motu pendularium was a very important contribution to the debate on force and motion, it can’t be compared to Newton’s Principia. Even if Huygens did propagate a wave theory of light his Traité de la lumière is not on a level with Newton’s Opticks. He does have his Systema saturniumbut as far as telescopes are concerned Newton’s reflector was a more important contribution than any of Huygens refractor telescopes. Most significant, Newton made massive contributions to the development of mathematics, Huygens almost nothing.

Talking of Newton, in his discussion of Huygens rather heterodox religious views Aldersey-Williams discussing unorthodox religious views of other leading scientists makes the following comment, “Newton was an antitrinitarian, for which he was considered a heretic in his lifetime, as well as being interested in occultism and alchemy.” Newton was not considered a heretic in his lifetime because he kept his antitrinitarian views to himself. Alchemy yes, but occultism, Newton?

I do have one final general criticism of Aldersey-Williams’ book. My impression was that the passages on fine art, poetry and music, all very important aspects of the life of the Huygens family, are dealt with in much greater depth and detail than the science, which I found more than somewhat peculiar in a book with the subtitle, The Making of Science in Europe. I’m not suggesting that the fine art, poetry and music coverage should be less but that the science content should have been brought up to the same level.

Despite the long list of negative comments in my review I think this is basically a very good book that could in fact have been an excellent book with some changes. Summa summarum it is a flawed masterpiece. It is an absolute must read for anybody interested in the life of Christiaan Huygens or his father Constantijn or the whole Huygens clan. It is also an important read for those interested in Dutch culture and politics in the seventeenth century and for all those interested in the history of European science in the same period. It would be desirable if more works with the wide-ranging scope and vision of Aldersey-Williams volume were written but please without the #histSTM errors.

[1] Harold J Cook, Matters of Exchange: Commerce, Medicine and Science in the Dutch Golden Age, Yale University Press, New Haven & London, 2007

[2] Cornelis Dirk Andriesse, The Man Behind the Principle, scientific biography of Christiaan Huygens, translated from Dutch by Sally Miedem, CUP, Cambridge, 2005

[3] Hugh Aldersey-Williams, Dutch Light: Christiaan Huygens and the Making of Science in Europe, Picador, London, 2020.

[4] Aldersey-Williams admits that the use of the term scientist is anachronistic but uses it for simplicity’s sake and I shall do likewise here.

[5] I have after all a reputation to uphold

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Filed under Book Reviews, History of Astronomy, History of Mathematics, History of Navigation, History of Optics, History of Physics, History of science, Newton

T’would appear so!

When you have very little income and no reserves and you run out of money, it is not easy asking other people for help, things like pride, shame and self-esteem tend to get in the way. Because of this I battled with myself for several weeks about setting up a Gofundme after it became clear that at some point I was going to have to buy a new computer. Even after I had grudgingly accepted that it was probably my best bet and wrote the text that I posted here on Saturday, I didn’t post it straight away but vacillated for more than a week, editing, rewriting and generally procrastinating, shall I, shan’t I? In the end I metaphorically closed my eyes, gritted my teeth and pushed out my text on Saturday afternoon, in my opinion probably the worst time of the week to launch an appeal, as lots of people take a sort of break from the Internet at the weekend. Because of this I was totally dumbstruck when I realised less that eighteen hours later, on the Sunday, that I had already almost doubled my original target in donations.

My immediate reaction was the following text that I posted on Twitter:

To say that I’m totally and utterly mind blown at the unbelievably kind and generous response to my appeal for help in buying a new computer would be an understatement. Will write a full response on the blog soon but till then thank you one and all!

Because so many people on Twitter had not only donated themselves but also boosted my signal on Twitter often added their own recommendation and praise for my humble scribblings, I added the following:

People moan and complain about Twitter but the #histSTM community is an incredibly rich and vibrant source of advice, information and help. Which is all offered openly, freely and with much good will. A true republic of letters.

Internet friend, seventeenth century historian and author of the excellent Killing Beauties, Pete Langman (@elegantfowl) tweeted the following:

Guess we all want you to keep on doing what you do!

To which I replied:

T’would appear so!

I currently have more than double the sum I asked for, donated by 119 wonderfully generous people and the donations haven’t stopped, yet!

I am totally overwhelmed by this unbelievable affirmation of the value of my work here on this blog and nothing I could say would adequately express my deep and heartfelt thanks that you all want me to keep on doing what I do to quote the good Dr Langman.

So I’ll just simply say:

 

thank-you-so-much-lettering_1262-7413

 

P.S. this week’s post is somewhat behind schedule but I’m working on getting it finished, so hang in there!

 

 

 

 

 

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Keep the Renaissance Mathematicus Online!

Difference_engine_plate_1853

My ancient iMac[1] is displaying increasing signs of giving up the ghost and moving on to the great electro-junk yard in the sky. My daily confrontations with the spinning beach-ball of death are increasing in frequency and the number of time where it doesn’t cease to spin and I am forced to shut down and reboot are also increasing. I assume it is only a matter of time before I will attempt to turn on my loyal workhorse and the screen will simply remain blank; this actually happened with its predecessor. This of course means that I will have to invest in a new computer, preferably before the current one decides to depart forever.

I am a pensioner with a very basic state pension, for which I am very grateful, but which doesn’t even totally cover the basics in life. I supplement this with private tutoring and some other bits and pieces. I have little or no reserves and can, quite simply, not afford a new computer at the moment. I have some potential work lined up for the autumn, but in order to do that I will need a fully functioning computer and I also don’t think that I will earn enough through that to cover the full costs of a new computer.

All of this being the case I turn to you, the readers of the Renaissance Mathematicus. I have never charged for the constant stream of history of science writing that I have delivered up over the last eleven years and I hope that the Renaissance Mathematicus will remain free for its readers in the future. I am asking you to make a onetime contribution now if you wish to go on reading the episodes of my Emergence of Modern Astronomy series, (or are waiting for the dead tree version, for which I will also need a computer), my scintillating book reviews, my accounts of obscure Renaissance scientists, mathematicians, cartographers et al and my occasional HISTSCI_HULK stomps all over bad #histSTM, then you are going to have make a small donation towards a shiny new Renaissance Mathematicus computer.

If all the readers of the Renaissance Mathematicus would each donate just €1 then I would have enough to buy two computers with enough left over for a celebratory meal. I appeal to my readers to help me in this endeavour and each to contribute, as they are able and as they are willed. Unlike book authors asking for funds to publish, I can offer no incentives or prizes for particularly generous contribution other than to promise that as long as I am able I shall continue to entertain, stimulate and educate you to the best of my ability as the Renaissance Mathematicus and of course you will have my eternal thanks.

A small special appeal to all the authors, whose books, book chapters and papers I have fact checked for their history of science content in recent years. I couldn’t have done so without a computer and will not be able to do so in the future without one.

For those who wish to donate to keep the Renaissance Mathematicus online. I have set up a Gofundme, which you can access here.

[1] Actually, in real world terms it’s not that old but in terms of computer generations it is positively stone age

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The emergence of modern astronomy – a complex mosaic: Part XLII

Why wasn’t Newton’s Principia the end of the gradual emergence and acceptance of a heliocentric astronomical model for the then known cosmos? There is not one simple answer to this question, but a serious of problems created in different areas all of which had still to be addressed if there was going to be an unquestioned acceptance of heliocentricity. Some of those problems were inherent in the Principia itself, which should best be viewed as a work in progress rather than a finished concept. In fact, as we will see, Newton carried on working on improving the Principia over two further editions, expanding and correcting the first edition. Other problems arose in the philosophical rejection of key aspects of Newton’s work by highly influential and knowledgeable detractors. Finally there were still massive unsolved empirical problems outside of the scope of the Principia itself. These sets of problems run chronologically parallel to each other some of them all the way into the nineteenth century and beyond so in dealing with them I will take each one in turn following it to its conclusion and then return to the starting point for the next problem but first I will sketch in a little bit more detail the problems listed above.

To begin with we need to look at the reception of the Principia when it was first published. On a very general level that reception can be viewed as very positive. Firstly there were only a comparatively small number of experts qualified to judge the Principia, as the work is highly technical and complex. There is a famous anecdote of two men observing Newton walking in the gardens of Trinity College and one says to the other, “there goes a man, who wrote a book that is so complex that even he doesn’t understand it.” However, those, who could and did understand it all, acknowledged that the Principia was a monumental piece of mathematic physics, which had no equal at that time. They also acknowledged that Newton belonged to the very highest levels both as a natural philosopher and mathematician. However, both the Cartesians and Leibnizians rejected the whole of Newton’s work on fundamental philosophical grounds and as we will see it was a long uphill struggle to overcome their objections.

Of course the biggest obstacle to the general acceptance of a heliocentric system was the fact that there was still absolutely no empirical evidence for movement of the Earth, either diurnal rotation or annual rotation around the Sun. This was of course no small issue and could not be dismissed out of hand no matter how convincing and coherent the model that Newton was presenting appeared to be.

The final set of problems were astronomical ones that Newton had failed to solve whilst writing the Principia, open questions that still needed to be answered. There were two major ones the succeeding history of which we will examine, comets and the orbit of the Moon. As we will see showing that the orbit of the Moon obeys the law of gravity proved to be one of the biggest astronomical problems of most of the next century. In the 1680s Newton had only managed to show that the comet of 1680/81 had rounded the Sun on a parabolic orbit and extrapolated from this one result that the orbits of all comets obeyed the law of gravity. This was an unsatisfactory situation for Newton and it was here that he first began his programme to revise the Principia.

For what might be termed project comet flight path, Newton engaged Edmond Halley, who following his efforts as copyeditor, publisher, financier and midwife of the Principia became Newton’s lieutenant and most loyal supporter and one of the few fellow savants, whom Newton apparently never fell out with. Halley willingly took on the task of trying to determine the flight path of comets other than the 1680/81 comet, already included in the 1st edition of Principia.

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Portrait of Edmond Halley painted around 1687 by Thomas Murray (Royal Society, London) Source: Wikimedia Commons

Starting around 1695 Halley began searching for and collecting observation data on all of the comets throughout history that he could find. Having acquired enough raw data to make a start he set about analysing it in order to try and determine flight paths. In the 1680s Newton had been the first astronomer to develop a technique for determining the flight path of a comet given three accurate observations at equal or nearly equal time differences. However, the method that he devised was anything but simple or practicable. Using his data he created a geometrical, semi-graphical plot of the flight path that he then iterated time and again, interpolating and extrapolating producing ever more accurate versions of the flight path. This method was both difficult and time consuming. Halley improved on this method, as he wrote to Newton, that having obtained the first three observations he had devised a purely numerical method for the determination of the flight path.

Halley started with the comet of 1683 and found a good fit for a parabolic orbit. This was followed by the comet of 1664, recognising some errors in Hevelius’ observations, and once again found a good fit for a parabolic orbit.

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The Great Comet of 1664: Johann Thomas Theyner (Frankfurt 1665) Source: Wikimedia Commons

At this point he first began to suspect that the comet of 1682,

which he had observed, was the same as the comet of 1607, observed by Thomas Harriot, William Lower and Johannes Kepler,

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David Berlitz, Von dem Cometen oder geschwentzten newen Stern, welcher sich im September dieses 1607. Source

and the comet of 1531 observed Peter Apian amongst others.

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Halley’s Comet 1531 Peter Apian Source

He also in his correspondence with Newton on the topic began to consider the problem of perturbation, that is deviation from the flight path caused by the gravitational attraction of Saturn and Jupiter, as a comet flew passed them. Neither Halley nor Newton succeeded in solving the problem of perturbation. In 1696 Halley held talks at the Royal Society in which he presented the results of his cometary research including his belief that the comets of 1607 and 1682 were one and the same comet on an elliptical orbit, which would return in 1757 or 1758.

Over a period of ten years Halley calculated the orbits of a further twenty comets presenting the results of his researches to the Royal society in 1702. Following his appointment as Savilian Professor for Astronomy at Oxford in 1705 he published the results of his work in the Philosophical Transactions of the Royal Society, Astronomiae cometicae synopsis, and also as a separate broadsheet, with the same title, from the Sheldonian Theatre in Oxford.

halley+sinopsys

An English translation, A synopsis of the astronomy of comets, was published in London in the same year. This work contained a table of results for twenty-four comets in total. Over the years Halley continued to work on comets and a final updated version of Astronomiae cometicae synopsis in 1726.

synopsisofastron00hall

In his work Halley emphasised the problem inherent in working with inaccurate historical observations. Newton used some of Halley’s results in both the second and third editions of Principia.

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Diagram of Halley’s orbit in the Solar System Popular Science Monthly Volume 76 Source: Wikimedia Commons

Halley would have been one hundred and one years old in 1757 meaning he had little chance of seeing whether he had been correct in his assumptions concerning the comet from 1682; in fact he died at the ripe old age of eight-five in 1742. A team of three French mathematicians–Alexis Clairaut (1713–1765), Joseph Lalande (1732–1807) and Nicole-Reine Lepaute (1723–1788)–recalculated the orbit of the comet making adjustments to Halley’s results.

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Alexis Claude Clairaut Source: MacTutor

Jérôme_Lalande

Jérôme Lalande after Joseph Ducreux Source: Wikimedia Commons

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Taken from Winterburn The Quite Revolution of Caroline Herschel see footnote 1

The comet returned as predicted and was first observed on Christmas Day 1758 by the German farmer and amateur astronomer Johann Georg Palitzsch (1723–1788).This was a spectacular confirmation of Newton’s theory of gravity and Halley’s work. The comet was named after Halley and is officially designated 1P/Halley. It is now know that it is the comet that appeared in 1066 and is depicted on the Bayeux tapestry

Tapisserie de Bayeux - Scène 32 : des hommes observent la comète de Halley

Bayeux Tapestry depiction of Comet Halley in 1066

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Halley comet in 1066 after emergence from the sun rays artist unknown Source: Wikimedia Commons

and it was also the comet observed by Peuerbach and Regiomontanus in 1456.

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Comet Halley 1456 artist unknown Source: Wikimedia Commons

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Comet Halley 1456 a prognostication!

It still caused a sensation in 1910

Halley's_Comet,_1910

An image of Halley’s Comet taken June 6, 1910. The Yerkes Observatory – Purchased by The New York Times for publication. Source: Wikimedia Commons

 

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Filed under History of Astronomy, History of Mathematics, Newton

Galileo was insufficiently woke?

We haven’t had a good Galileo rant here at the Renaissance Mathematicus for some time, but when you just begin to think that maybe people have stopped misusing the Tuscan natural philosopher for their own ends, up pops a new example and we’re off again.

My attention was drawn to today wonderful example by the following exchange on Twitter:

Seb Falk (@Seb_Falk): I’ve heard a lot of nonsense about Galileo, but persecuted by the Church for being insufficiently woke? That’s a new one on me.

Is there a Galileo-related law equivalent to Godwin’s Law? If not, Falk’s Law states that as a culture war continues, the probability that someone will invoke a mythologised account of the trial of Galileo in a specious defence of academic freedom approaches 1.

Dave Hitchcock (@Hitchcokian): Amazing. it shall definitely be known henceforth as Falk’s Law.

Seb Falk: I’m honoured – though I was just thinking that @rmathematicus has been calling this stuff out for so long we should call it Christie’s Law. Bloody history of science, always naming things after the wrong person

James Sumner (@JamesBSumner): Well, now, that’s perfectly consonant with Stigler’s law of eponymy

For those not aware of Stigler’s Law, it states that no scientific discovery is named after its original discoverer. Stigler’s law itself was in fact discovered by Robert K Merton and not Stephen Stigler.

So what was the piece about Galileo that provoked the creation of Falk’s Law?

Trevor Phillips (@MTREVORP) opens an article in the Times newspaper titled University bigots want to control minorities with the following:

Every scientist knows the Galileo story. When one of the greatest minds of the 17th (or any other) century concluded that, contrary to the Catholic Church’s teaching, the Earth was not the still centre of the universe but just one satellite of the sun he was for the high jump.

Subjected to six years at the hands of the Inquisition, character assassination and house arrest, he finally gave in and admitted his “wrongthink” but is reputed to have muttered under his breath “E pur si muove” – “Still, it moves”. The man whom Einstein called the father of modern science was said to be hurt most by the way his fellow philosophers abandoned him for fear of suffering the same fate.

I find it fascinating just how much a supposedly intelligent, educated, well informed writer can get wrong in just two very short paragraphs. We start with the opening sentence; experience has clearly shown that very few scientists know the actual Galileo story; most of them know one or other very mangled version of what might be termed the Galileo myth, which all have something in common, a factual, historical truth content on a par with an episode of Game of Thrones.

We then get the statutory hyperbollocks as soon as Galileo becomes the subject of discourse, “one of the greatest minds of the 17th (or any other) century.” This leads me to the thought, what if Galileo had not been hyped up to this larger than life, once in a century genius, would people be just as outraged if he had been mistreated by the Inquisition. Is it a worse crime if those in power mistreat a brilliant scientist, than if they mistreat Giuseppe, the guy who empties the trash cans? Not just here but in lots of things that I have read, I get the impression that is exactly what a very large number of people think. Are some lives really worth more than others? Their argument seems to be something along the lines of but Galileo changed the world, Giuseppe the trash can guy didn’t. What if the fact that Giuseppe was rotting in an Inquisition dungeon, instead of cleaning the streets led to an outbreak of cholera that wiped out half the population of the city? But I digress.

What follows is a significant misrepresentation of the facts that is dished every time somebody present their mythical version of the Galileo story and one that I have dealt with many times. It wasn’t just the Catholic Church’s teaching that we live in a geocentric cosmos but was the considered, majority opinion of informed astronomers based on the then available empirical evidence. Galileo was involved in a complex scientific debate on the astronomical and cosmological status of the solar system and was not this brilliant scientist taking on the ignorant, non-scientific, religious prejudices of the Catholic Church.  There are a couple of grammatical and lexigraphical anomalies in Phillips’ sentence that should have been picked up by a good sub-editor. If he is going to write Earth with a capital ‘E’ then he should also write sun with a capital ‘S’ and the earth is not a satellite of the sun it is a planet. Satellites orbit planets, planets orbit suns.

Subjected to six years at the hands of the Inquisition? Really? Galileo’s interrogation, trial and the passing of judgement by the Roman Inquisition lasted not quite four months, so I have literally no idea what Phillips is talking about here. I also have absolutely no idea what he means when he writes, “character assassination”, through out the whole affair he was treated with care and consideration and the respect due to him both because of his age and his reputation. Does one really need to repeat that Galileo was not tried for supporting the heliocentric hypothesis but for breaking an injunction from 1616 not to hold or teach the heliocentric theory as fact rather than, as a hypothesis? There was literally no question of “wrongthink”, Galileo was fully entitled to think what he liked about heliocentricity and even to express those thoughts verbally but he was not permitted to claim that heliocentricity was a proven fact. Just for the record, for the umpteenth time, it wasn’t. I find it almost funny that Phillips includes house arrest amongst the mistreatments before Galileo adjured. Having adjured he was, in fact, sentenced to imprisonment, which was immediately commuted to house arrest by the Pope, so after the fact not before.

Of course, having dished up a totally fictional account of Galileo’s dispute with the Church, Phillips doesn’t not spare us the “E pur si muove” – “Still, it moves” myth, in for a penny in for a pound. If we going to present fairy tales in place of historical accuracy then why not go the whole hog? We, natural, get that leading expert on the history of science, Albert Einstein, quoted on Galileo’s status in that history. Why ask a historian when you can ask Uncle Albert, the font of all wisdom? Another reminder, the expression ‘father of’ is a meaningless piece of crap.

Phillips’ last claim leaves me, once more, totally bewildered. “[Galileo] was said to be hurt most by the way his fellow philosophers abandoned him for fear of suffering the same fate.” There are two aspects to this claim. Firstly, the man, who is a serious candidate for the most egotistical and arrogant arsehole in the entire history of science and who spent a large part of his life actively insulting, denigrating and alienating ‘his fellow philosophers’ was hurt because they didn’t support him, really? Secondly, I have spent a life time reading about and studying Galileo and the historical context in which he lived and worked and I have never ever come across anybody claiming anything remotely like this claim made by Phillips. Put differently, Phillips is just making shit up to bolster the argument that he is going to present in his article. This is not history or journalism this is quite simply lying!

People used to refer to the Galileo Gambit, when somebody, almost always a crank, compared having his ‘fantastic ideas’ rejected to the Catholic Church’s persecution of Galileo. To this Bob Dylan delivered up the perfect retort:

He said, “They persecuted Jesus too.”

I said, “You’re not him.”

“I said you know, they refused Jesus, too. He said you’re not him.”

[Correct version of Dylan quote curtesy of Todd Timberlake]

Trevor Phillips delivers up a slightly different variation on the theme. He is using a totally mythical version of the Galileo story to beat people, who he disapproves of or disagrees with around the head. If he can’t make the points that he wishes to make without resorting to lies and deception in that he misuses an episode in the history of science then he should give up pretending to be a journalist.

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Giambattista della Porta the most polymathic of all Renaissance polymaths?

Giambattista della Porta (1535(?)–1615) is well known to historians of Renaissance science but for the general public he remains a largely unknown figure. If he is known at all,  he is often written off as an occultist, because of the title of his most well known work Magia Naturalis. In fact in the late sixteenth and early seventeenth centuries he was a highly respected and influential member of the Italian Renaissance scientific community. Although he wrote and published profusely over a wide range of scientific and related topics he made no really major discoveries and produced no major inventions and unlike his contemporaries, Kepler and Galileo, who were both well acquainted with his work, he has been largely forgotten.

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Giambattista della Porta Source: Wikimedia Commons

Giambattista Della Porta were born at Vico Equense, Near Naples, probably sometime in 1535 (he created the confusion about his birth date), the third of four sons of the nobleman Nardo Antonio dell Porta of whom three survived childhood.  His parental home resembled an intellectual salon where the boys were continually exposed to and educated by visiting philosophers, mathematicians, poets and musicians. Their education was completed by private tutors, who also taught the boys the attributes of a gentleman, dancing, riding, skilled performance in tournaments and games and how to dress well. Della Porta never attended university but enjoyed life as a well educated polymathic, gentleman of leisure. If he can be considered to have had a profession, then it is that of a dramatist, he wrote more than twenty theatrical works, but it is his extensive activities in the sciences that interest us here.

Already in 1558, at the age of 23, he published the fist version of his most well known work, the Magia Naturalis in four books, a sort of encyclopaedia of the Renaissance sciences. From the beginning it was a bestseller running to five editions in Latin within the first ten years with translations into Italian (1560), French (1565), Dutch (1566) and English (1658). A vastly expanded version in twenty books was published in 1589. This final version covers a wide range of topics:

Magiae_naturalis_sive_de_miraculis_rerum_naturalium_(Giovanni_Battista_Della_Porta,_1584)

Source: Wikimedia Commons

Book 1: Of the Causes of Wonderful Things Book 2: Of the Generation of Animals Book 3: Of the Production of New Plants Book 4: Of Increasing Household-Stuff Book 5: Of Changing Metals Book 6: Of Counterfeiting Glorious StonesBook 7: Of the Wonders of the Load-Stone Book 8: Of Physical Experiments Book 9: Of Beautifying Women Book 10: Of Distillation Book 11: Of Perfuming Book 12: Of Artificial Fires Book 13: Of Tempering Steel Book 14: Of CookeryBook 15: Of Fishing, Fowling, Hunting, etc. Book 16: Of Invisible Writing Book 17: Of Strange Glasses Book 18: Of Static Experiments Book 19: Of Pneumatic Experiment Book 20: Of the Chaos

The contents range from fairly banal parlour tricks, over engineering, experimental science, horticulture and husbandry to every day things. At the very beginning della Porta is very careful to explain what exactly he mean by the term natural magic:

There are two sorts of Magick; the one is infamous, and unhappy, because it has to do with foul Spirits and consists of incantations and wicked curiosity; and this is called Socery; an art which all learned and good men detest; neither is it able to yield an truth of reason or nature, but stands merely upon fancies and imaginations, such as vanish presently away, and leave nothing behind them; as Jamblicus writes in his book concerning the mysteries of the Egyptians. The other Magick is natural; which all excellent wise men do admit and embrace, and worship with great applause; neither is there any thing more highly esteemed, or better thought of, by men of learning. The most noble Philosophers that ever were, Pythagorus, Empedocles, Democritus, and Plato forsook their own countries, and lived abroad as exiles and banished men, rather than as strangers; and all to search out and to attain this knowledge; and when they came home again, this was the Science which they professed, and this they esteemed a profound mystery. They that have been most skillful in dark and hidden points of learning, do call this knowledge the very highest point, and the perfection’s of Natural Sciences; inasmuch that if they could find out or devise amongst all Natural Sciences, any one thing more excellent or more wonderful then another, that they would still call by the name of  Magick. Others have named it the practical part of natural Philosophy, which produces her effects by the mutual and fit application of one natural thing unto another.

The association of Magick with natural philosophy is continued in della Porta’s definition of the Magician:

This is what is required to instruct a Magician, both what he must know, and what he must observe; that being sufficiently instructed in every way, he may bring very strange and wonderful things to us. Seeing Magick, as we showed before, as a practical part of natural Philosophy, it behooves a Magician and one that aspires to the dignity of the profession, to be an exact and very perfect Philosopher.

Despite the very diverse nature of the Magia Naturalis it does contain elements of genuine experimental science. For example, it contains the first experimental disproof of the widely held medieval belief that garlic disables magnets. He also experimented with the cooling properties of dissolving nitre in water. As described here by Andrea Sella (@SellaTheChemist)

As well as the Magia Naturalis della Porta wrote and published a large number of monographs on a very wide range of topics. Cryptography was a popular topic in Renaissance Europe, the most famous book being Johannes Trithemius’ Poligraphia, della Porta published his De Furtivis Literarum Notis (1563), which contain innovative cryptographical ideas.

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In 1586 he published a work on physiognomy De humana physiognomonia libri IIII,

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From De humana physiognomonia, 1586 Source: Wikimedia Commons

which was still being referenced in the nineteenth century, two years later a book on phytonomy (the science of the origin and growth of plants), Phytognomonica, which contains the first observations on fungal spores.

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Phytognomonica, 1588 Source: Wikimedia Commons

These two books confirm della Porta’s adherence to the Renaissance doctrine of signatures. This theory claimed that it was possible to determine the nature of things based on their external appearances.

This was by no means the limit to della Porta’s publishing activities. He also wrote an agricultural encyclopaedia, separate volumes on various fruit bearing trees, books on mathematics, astronomy, meteorology, military engineering, distillation and in 1589 a book on optics, his De refractione optics. We shall return to the latter.

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This incredible literary outpouring was just part of his scientific activity, in about 1560 he founded an academic society, Accademia dei Segreti (Academia Secratorum Naturae), the Academy of the Secrets of Nature, which is considered to be the earliest scientific society. The academy met regularly in della Porta’s home and membership was open to all but to become a member one had to present a new secret of nature that one had discovered. We know what some of those new secrets were as della Porta included them in the twenty volume version of his Magia Naturalis. In 1578 della Porta was summoned to Rome and investigated by the Pope. We do not know the exact grounds for this summons but he was forced to shut down his academy on suspicion of sorcery. This is to a certain extent ironic because della Porta was very careful in all his writing to avoid controversial topics particularly religious ones.

Although it was shut down the Accademia dei Segreti, would later have a major influence on another, much more renowned, early scientific academy, Federico Cesi’s Accademia dei Lincei. Cesi was a huge admirer of della Porta and as a young man travelled to Naples to visit the older natural philosopher. On his return home he founded his own academy, whose name was inspired by a line from the preface of the Magia Naturalis:

… with lynx like eyes, examining those things which manifest themselves, so that having observed them, he may zealously use them.

In 1610 della Porta became the fifth member of the Accademia dei Lincei, one year before Galileo.

Another important aspect of Renaissance science was the establishment of private natural philosophical museums also known as Wunderkammer, or cabinets of curiosity. Della Porta had, as to be expected, a particular fine cabinet of curiosity that would influence others to create their own, the Jesuit Athanasius Kircher for example.

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Fold-out engraving from Ferrante Imperato’s Dell’Historia Naturale (Naples 1599), the earliest illustration of a natural history cabinet Source: Wikimedia Commons

Della Porta made minor contribution to the advance of science and engineering over a wide range of disciplines but I first ran into della Porta in the context of the history of optics and it his association with this history that I want to look at in somewhat more detail. The early seventeenth century saw both a significant turn in the theory of optics and independently of that the invention of the telescope, an instrument that would go one to revolutionise astronomy, della Porta played a minor roll in both of these things.

The invention of the telescope, by Hans Lipperhey, first became public in September 1608 and the role it would play in the future of astronomy became explosively obvious when Galileo published his Sidereus Nuncius in March 1610. Already in August 1609 della Porta wrote a letter to Federico Cesi claiming to have invented the telescope, he wrote:

I have seen the secret use of the eyeglass and it’s a load of balls [coglionaria] in any case it is taken from book 9 of my De Refractione.[1]

Here della Porta’s memory is faulty, he is after all over seventy years old, what he is referring to is not in the De Refractione but rather in Chapter 10 of Book 17 of Magia Naturalis (1589). Here we find the following suggestive description:

Concave Lenticulars will make one see most clearly things that are afar off.  But Convexes, things near at hand.  So you may use them as your sight requires.  With a Concave Lenticulars you shall see small things afar off very clearly.  With a Convex Lenticular, things nearer to be greater, but more obscurely.  If you know how to fit them both together, you shall see both things afar off, and things near hand, both greater and clearly.  I have much helped some of my friends, who saw things afar off, weakly, and what was near, confusedly, that they might see all things clearly.  If you will, you may.

The lens combination that della Porta describes here is indeed that of the Dutch or Galilean telescope but as van Helden say, and I agree with him, he is here describing some form of spectacles but not a telescope. Kepler, however, who owned a copy of Magia Naturalis credits him with being the inventor of the telescope in his Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger) (1610), where he wrote that a recent Dutch invention had been made public years earlier in Magia Naturalis. In 1641 Pierre Gassendi stated that the actual invention had been made by chance by Metius [Jacob Metius (after 1571–1628), who applied for a patent for a telescope two weeks later than Lipperhey] the idea for a similar one had been published years earlier by della Porta.

Later della Porta would graciously admit that his fellow Lynx, Galileo, had achieved much more with his telescope that he, della Porta, could have ever have hoped to do, whilst not abandoning his claim to having first conceived of the telescope.

Della Porta also played a small role in the history of the camera obscura, describing the improvement to the image obtained by placing convex lens into the pinhole, something probably first suggested by Gerolamo Cardano. He also suggested, this time as the first to do so, using a concave mirror to project the image onto a sheet of paper to facilitate drawing it. The popularity of the Magia Naturalis did much to spread knowledge of the camera obscura and its utility as a drawing instrument. Interestingly della Porta compared his camera obscura with the human eye but, unlike Kepler, failed to make the connection that the lens focuses the image on the retina. He continued to believe like everybody before him that the image in perceived in the lens itself.

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First published picture of camera obscura in Gemma Frisius’ 1545 book De Radio Astronomica et Geometrica Source: Wikimedia Commons

Della Porta’s role in the turn in the theory of optics is less disputed but not so widely discussed.  Ancient Greek optics was almost exclusively about theories of vision and when taken up and developed in the Islamic Middle Ages this too remained the emphasis. Ibn al-Haytham in his work on optics showed that one could combine an intromission theory of vision with the geometric optics of Euclid, Hero and Ptolemaeus, who had all propagated an extramission theory of vision. This was a major development in the history of optics. In the thirteenth century Robert Grosseteste introduced optics as a central element in both his vision of science and his theology, which led to it being established as a mathematical discipline on the medieval university. Shortly after Roger Bacon, John Peckham and Witelo introduced al-Haytham’s theories on optics into the medieval European mainstream founding what became known as the perspectivist school of optics. Strangely there were no real further developments in the theory of optics down to the end of the sixteenth century when Johannes Kepler, almost singlehandedly, turned the study of optics from one of theories of vision to one of theories of light, thereby ending the reign of the perspectivists. I say almost singlehandedly but he did have two predecessors, who made minor contributions to this turn, Francesco Maurolico (1494–1575) and della Porta.

One major flaw in the perspectivist theory was its treatment of spherical convex lenses and spherical concave mirrors, which said that the images created by them appeared at a single focus point; this is a fallacy. This flaw was in the theory from its inception in the thirteenth century and remained unchecked and uncorrected all the way down to the end of the sixteenth century. The fact that the don’t create their images at a single focal point is, of course, the cause of spherical aberration, something that would plague the construction of telescopes and microscopes well into the eighteenth century. The man who corrected this error in optical theory was della Porta.  Using a mixture of experiments and analytical light ray tracing he came very close to the correct solution an important step towards Kepler’s light ray based theory of optics.

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Della Porta’s ray tracing analysis of the reflection of a spherical concave mirror A. Mark Smith, “From Sight to Light: The Passage from Ancient to Modern Optics”, Chicago University Press, 2015 p. 349

Giambattista della Porta is an interesting example of a widespread phenomenon in the history of science. In his own times he was highly respected and regarded, throughout Europe, as a leading natural Philosopher. His books, translated into many languages, were bestsellers and that even long after his death. Johannes Kepler was a fan and Galileo disliked him because he saw him as a serious rival for the position of top dog natural philosopher, a position that Galileo very much desired for himself. However, today most people have never even heard of him and if then he is largely dismissed as a minor irrelevance or even, because of the title of his major work, as some sort of anti-science occultist. But if historians really want to understand what was going on in the scientific community of Europe in the Early Modern Period then they have to take figures like della Porta seriously and not just focus on the ‘big names’ such as Kepler and Galileo.

 

 

 

 

 

 

 

 

 

 

 

 

[1] Quoted from David Freedberg, The Eye of the Lynx: Galileo, His Friends and the Beginnings of Modern Natural History, University of Chicago Press, Chicago and London, 2002, ppb. p. 101 Albert van Helden in his The Invention of the Telescope, American Philosophical Society, Philadelphia, 1977, Reprint, 2008, translates the phrase with coglionaria as …”it’s a hoax” pp. 44-45

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Filed under History of Optics, History of science, Renaissance Science

The emergence of modern astronomy – a complex mosaic: Part XLI

 

Newton’s Principia is one of the most original and epoch making works in the history of science. There is absolutely nothing original in Newton’s Principia. These two seemingly contradictory judgements of Isaac Newton’s Philosophiæ Naturalis Principia Mathematica are slightly exaggerated versions of real judgements that have been made at various points in the past. The first was the general hagiographical view that was prevalent for much of the eighteenth, nineteenth and twentieth centuries. The second began to appear in the later part of the twentieth century as some historian of science thought that Newton, or better his reputation, needed to be cut down a bit in size. So, which, if either of them, is correct? The surprising answer is, in a way, both of them.

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Isaac Newton’s Philosophiae Naturalis Principia Mathematica manuscript volume from which the first edition was printed. Written in the hand of Humphrey Newton, Isaac Newton’s assistant. Source: Royal Society Library via Wikimedia Commons

The Principia is a work of synthesis; it synthesises all of the developments in astronomy and physics that had taken place since the beginning of the fifteenth century. All of the elements that make up Newton’s work were, so to speak, laid out for him to integrate into the book. This is what is meant when we say that there is nothing original in the Principia, however the way that Newton integrated them and what he succeeded in creating was at the time unique and totally original. The Principia was truly a case of the whole being greater than the parts. Before we take a brief look at the contents of the Principia there are a couple of anomalies in its construction that need to be addressed.

The first concerns the general methodological structure of the book. Medieval science was dominated, not exclusively, by the theories of Aristotle and Aristotelian methodology. The developments in astronomy, physics and mathematics that we have covered up to now in this series have seen a gradual but steady deconstruction of the Aristotelian structures and theories. In this situation it comes as a bit of surprise that the methodology of the Principia is classically Aristotelian. Aristotle stated that true episteme (Greek) or scientia (Latin), what we would term scientific knowledge, is achieved by setting out a set of first principles or axioms that are perceived as being true and not in need proof and then logically deducing new knowledge from them. Ironically the most famous example of this methodology is the Elements of Euclid, ironically because Aristotle regarded mathematics as not being real knowledge because it doesn’t deal with objects in the real world. This is the methodology that Newton uses in the Principia, setting out his three laws of motion as his basic principles, which we will come back to later, and not the modern methodologies of Francis Bacon or René Descartes, which were developed in the seventeenth century to replace Aristotle.

The second anomaly concerns the mathematics that Newton uses throughout the Principia. Ancient Greek mathematics in astronomy consisted of Euclidian geometry and trigonometry and this was also the mathematics used in the discipline in both the Islamic and European Middle Ages. The sixteenth and seventeenth centuries in Europe saw the development of analytical mathematics, first algebra and then infinitesimal calculus. In fact, Newton made major contributions to this development, in particular he, together with but independently of Gottfried William Leibniz, pulled together the developments in the infinitesimal calculus extended and codified them into a coherent system, although Newton unlike Leibniz had at this point not published his version of the calculus. The infinitesimal calculus was the perfect tool for doing the type of mathematics required in the Principia, which makes it all the more strange that Newton didn’t use it, using the much less suitable Euclidian geometry instead. This raises a very big question, why?

In the past numerous people have suggested, or even claimed as fact, that Newton first worked through the entire content of the Principia using the calculus and then to make it more acceptable to a traditional readership translated all of his results into the more conventional Euclidian geometry. There is only one problem with this theory. With have a vast convolute of Newton’s papers and whilst we have numerous drafts of various section of the Principia there is absolutely no evidence that he ever wrote it in any other mathematical form than the one it was published in. In reality, since developing his own work on the calculus Newton had lost faith in the philosophical underpinnings of the new analytical methods and turned back to what he saw as the preferable synthetic approach of the Greek Euclidian geometry. Interestingly, however, the mark of the great mathematician can be found in this retrograde step in that he translated some of the new analytical methods into a geometrical form for use in the Principia. Newton’s use of the seemingly archaic Euclidian geometry throughout the Principia makes it difficult to read for the modern reader educated in modern physics based on analysis.

When referencing Newton’s infamous, “If I have seen further it is by standing on the sholders [sic] of Giants”, originally written to Robert Hooke in a letter in 1676, with respect to the Principia people today tend to automatically think of Copernicus and Galileo but this is a misconception. You can often read that Newton completed the Copernican Revolution by describing the mechanism of Copernicus’ heliocentric system, however, neither Copernicus nor his system are mentioned anywhere in the Principia. Newton was a Keplerian, but that as we will see with reservations, and we should remember that in the first third of the seventeenth century the Copernican system and the Keplerian system were viewed as different, competing heliocentric models. Galileo gets just five very brief, all identical, references to the fact that he proved the parabola law of motion, otherwise he and his work doesn’t feature at all in the book. The real giants on whose shoulders the Principia was built are Kepler, obviously, Descartes, whose role we will discuss below, Huygens, who gets far to little credit in most accounts, John Flamsteed, Astronomer Royal, who supplied much of the empirical data for Book III, and possibly/probably Robert Hooke (see episode XXXIX).

We now turn to the contents of the book; I am, however, not going to give a detailed account of the contents. I Bernard Cohen’s A Guide to Newton’s Principia, which I recommend runs to 370-large-format-pages in the paperback edition and they is a whole library of literature covering aspects that Cohen doesn’t. What follows is merely an outline sketch with some comments.

As already stated the book consists of three books or volumes. In Book I Newton creates the mathematical science of dynamics that he requires for the rest of the book. Although elements of a science of dynamics existed before Newton a complete systematic treatment didn’t. This is the first of Newton’s achievement, effectively the creation of a new branch of physics. Having created his toolbox he then goes on to apply it in Book II to the motion of objects in fluids, at first glance a strange diversion in a book about astronomy, and in Book III to the cosmos. Book III is what people who have never actually read Principia assume it is about, Newton’s heliocentric model of the then known cosmos.

Mirroring The Elements of Euclid, following Edmond Halley’s dedicatory ode and Newton’s preface, Book I opens with a list of definitions of terms used. In his scholium to the definitions Newton states that he only defines those terms that are less familiar to the reader. He gives quantity of matter and quantity of motion as his first two definitions. His third and fourth definitions are rather puzzling as they are a slightly different formulation of his first law the principle of inertia. This is puzzling because his laws are dependent on the definitions. His fifth definition introduces the concept of centripetal force, a term coined by Newton in analogy to Huygens’ centrifugal force. In circular motion centrifugal is the tendency to fly outwards and centripetal in the force drawing to the centre. As examples of centripetal force Newton names magnetism and gravity. The last three definitions are the three different quantities of centripetal force: absolute, accelerative and motive. These are followed by a long scholium explicating in greater detail his definitions.

We now arrive at the Axioms, or The Laws of Motions:

1) Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed.

This is the principle of inertia that Newton had taken from Descartes, who in turn had taken it from Isaac Beeckman.

2) A change of motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.

Somewhat different from the modern formulation of F=ma, this principle has its origin in the work of Huygens although there is not a one to one correspondence.

3) To any action there is always an opposite and equal reaction, in other words, the actions of two bodies upon each other are always equal and always opposite in direction.

This law originates with Newton and its source is not absolutely clear. It seems to have been inspired by Newton’s examination of Descartes laws of inelastic collision but it might also have been inspired by a similar principle in alchemy of which Newton was an ardent disciple.

Most people are aware of the three laws of motion, the bedrock of Newton’s system, in their modern formulations and having learnt them, think that they are so simple and obvious that Newton just pulled them out of his hat, so to speak. This is far from being the case. Newton actually struggled for months to find the axioms that eventually found their way into the Principia. He tried numerous different combinations of different laws before finally distilling the three that he settled on.

Having set up his definitions and laws Newton now goes on to produce a systematic analysis of forces on and motion of objects in Book I. It is this tour de force that established Newton’s reputation as one of the greatest physicist of all time. However, what interests us is of course the law of gravity and its relationship to Kepler’s laws of planetary motion. The following is ‘plagiarised’ from my blog post on the 400th anniversary of Kepler’s third law.

In Book I of Principia, the mathematics and physics section, Newton first shows, in Proposition 11[1], that for a body revolving on an ellipse the law of the centripetal force tending towards a focus of the ellipse is inversely as the square of the distance: i.e. the law of gravity but Newton is not calling it that at this point. In Proposition 14[2] he then shows that, If several bodies revolve about a commo[3]n center and the centripetal force is inversely as the square of the distance of places from the center, I say that the principal latera recta of the orbits are as the squares of the areas which bodies describe in the same time by radii drawn to the center. And Proposition 15: Under the same supposition as in prop. 14, I say the square of the periodic times in ellipses are as the cubes of the major axes. Thus Newton shows that his law of gravity and Kepler’s third law are equivalent, although in this whole section where he deals mathematically with Kepler’s three laws of planetary motion he never once mentions Kepler by name. Newton would go one to claim the rights to laws one and two as he had, in his opinion, provided their first real proof. He acknowledges, however, Kepler’s claim to the third law.

Book II as already mentioned appears to go off a tangent in that it deals with motion in a fluid medium, as a result it tends to get ignored, although it is as much a tour de force as Book I. Why this detour? The answer can be found in the theories of René Descartes and Newton’s personal relationship to Descartes and his works in general. As a young man Newton undertook an extensive programme of self-study in mathematics and physics and there is no doubt that amongst the numerous sources that he consulted Descartes stand out as his initial primary influence. At the time Descartes was highly fashionable and Cambridge University was a centre for interest in Descartes philosophy. At some point in the future he then turned totally against Descartes in what could almost be describe as a sort of religious conversion and it is here that we can find the explanation for Book II.

Descartes was a strong supporter of the mechanical philosophy that he had learnt from Isaac Beeckman, something that he would later deny. Strangely, rather like Aristotle, objects could only be moved by some form of direct contact. Descartes also rejected the existence of a vacuum despite Torricelli’s and Pascal’s proof of its existence. In his Le Monde, written between 1629 and 1633 but only published posthumously in 1664 and later in his Principia philosophiae, published in 1644, Descartes suggested that the cosmos was filled with very, very fine particles or corpuscles and that the planets were swept around their orbits on vortexes in the corpuscles. Like any ‘religious’ convert, Newton set about demolishing Descartes theories. Firstly, the title of his volume is a play upon Descartes title, whereas Descartes work is purely philosophical speculation, Newton’s work is proved mathematically. The whole of Book II exists to show that Descartes’ vortex model, his cosmos full of corpuscles is a fluid, can’t and doesn’t work.

Book III, entitled The System of the World, is as already said that which people who haven’t actually read it think that the Principia is actually about, a description of the cosmos. In this book Newton applies the mathematical physics that he has developed in Book I to the available empirical data of the planets and satellites much of it supplied by the Astronomer Royal, John Flamsteed, who probably suffered doing this phase of the writing as Newton tended to be more than somewhat irascible when he needed something from somebody else for his work. We now get the astronomical crowning glory of Newton’ endeavours, an empirical proof of the law of gravity.

Having, in Book I, established the equivalence of the law of gravity and Kepler’s third law, in Book III of The PrincipiaThe System of the World Newton now uses the empirical proof of Kepler’s third law to establish the empirical truth of the law of gravity[4] Phenomena 1: The circumjovial planets, by radii drawn to the center of Jupiter, describe areas proportional to the times, and their periodic times—the fixed stars being et rest—are as 3/2 powers of their distances from that center. Phenomena 2: The circumsaturnian planets, by radii drawn to the center of Saturn, describe areas proportional to the times, and their periodic times—the fixed stars being et rest—are as 3/2 powers of their distances from that center. Phenomena 3: The orbits of the five primary planets—Mercury, Venus, Mars, Jupiter, and Saturn—encircle the sun. Phenomena 4: The periodic times of the five primary planets and of either the sun about the earth or the earth about the sun—the fixed stars being at rest—are as the 3/2 powers of their mean distances from the sun. “This proportion, which was found by Kepler, is accepted by everyone.”

Proposition 1: The forces by which the circumjovial planets are continually drawn away from rectilinear motions and are maintained in their respective orbits are directed to the center of Jupiter and are inversely as the squares of the distances of their places from that center. “The same is to be understood for the planets that are Saturn’s companions.” As proof he references the respective phenomena from Book I. Proposition 2: The forces by which the primary planets are continually drawn away from rectilinear motions and are maintained in their respective orbits are directed to the sun and are inversely as the squares of the distances of their places from its center. As proof he references the respective phenomenon from Book I.

In the 1st edition of Principia Newton referenced the solar system itself and the moons of Jupiter as system that could be shown empirically to Kepler’s third law and added the moons of Saturn in the 3rd edition.

Book III in the first edition closes with Newton’s study of the comet of 1680/81 and his proof that its flight path was also determined by the inverse square law of gravity showing that this law was truly a law of universal gravity.

I have gone into far more detain describing Newton’s Principia than any other work I have looked out in this series because all the various streams run together. Here we have Copernicus’s initial concept of a heliocentric cosmos, Kepler’s improved elliptical version of a heliocentric cosmos with it three laws of planetary motion and all of the physics that was developed over a period of more than one hundred and fifty years woven together in one complete synthesis. Newton had produced the driving force of the heliocentric cosmos and shown that it resulted in Kepler’s elliptical system. One might consider that the story we have been telling was now complete and that we have reached an endpoint. In fact, in many popular version of the emergence of modern astronomy, usually termed the astronomical revolution, they do just that. It starts with Copernicus’ De revolutionibus and end with Newton’s Principia but as we shall see this was not the case. There still remained many problems to solve and we will begin to look at them in the next segment of our story.

[1]  Isaac Newton, The PrincipiaMathematical Principles of Natural Philosophy, A New Translation by I: Bernard Cohen and Anne Whitman assisted by Julia Budenz, Preceded by A Guide to Newton’s Principia, by I. Bernard Cohen, University of California Press, Berkley, Los Angeles, London, 1999 p. 462

[2] Newton, Principia, 1999 p. 467

[3] Newton, Principia, 1999 p. 468

[4] Newton, Principia, 1999 pp. 797–802

 

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Filed under History of Astronomy, History of Mathematics, History of Physics, Newton

Chilli 19.02.2006–27.07.2020

The sweetest little lady in the world has left us. Somewhat more than a year ago I explained how Chilli came into my life. Yesterday she left it taking my heart with her as she went. In recent months she had begun to display the symptoms of dementia. They were unmistakable but still fairly mild, so I thought we would still have some time together.

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On Friday morning, on the way home from our early walk in the woods she had some sort of brain malfunction that seems to have blown some fuses in her head. She took off like a rocket and I had no idea where she had gone. She ran wild through the area for nearly one and a half hours, till I could finally catch her with the help of a very generous lady dog owner. She was in total panic and didn’t recognise me and attacked and bit me. She is normally the most passive and friendliest dog in the world. I managed to get her on a lead and she immediately calmed down and we walked home. Once there she fell into her bed and didn’t leave it again the whole day except when I took her briefly outside to pee.

Things did not really improve on Saturday; she was confused, disorientated and apathetic. By Sunday it was clear that the little lady, who had brought me so much joy over the last fifteen or so months was suffering without hope of recovery and that I would have to release here from her distress. On Monday afternoon the vet helped her on her way out the vale of suffering and now she is no more. My flat seems suddenly very empty.

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Chilli as a puppy taken from her vaccination pass Added 29/08/2020

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Our medieval technological inheritance.

“Positively medieval” has become a universal put down for everything considered backward, ignorant, dirty, primitive, bigoted, intolerant or just simply stupid in our times. This is based on a false historical perspective that paints the Middle Ages as all of these things and worse. This image of the Middle Ages has its roots in the Renaissance, when Renaissance scholars saw themselves as the heirs of all that was good, noble and splendid in antiquity and the period between the fall of the Roman Empire and their own times as a sort of unspeakable black pit of ignorance and iniquity. Unfortunately, this completely false picture of the Middle Ages has been extensively propagated in popular literature, film and television.

Particularly in the film and television branch, a film or series set in the Middle Ages immediately calls for unwashed peasants herding their even filthier swine through the mire in a village consisting of thatch roofed wooden hovels, in order to create the ‘correct medieval atmosphere’. Add a couple of overweight, ignorant, debauching clerics and a pox marked whore and you have your genuine medieval ambient. You can’t expect to see anything vaguely related to science or technology in such presentations.

Academic medieval historians and historians of science and technology have been fighting an uphill battle against these popular images for many decades now but their efforts rarely reach the general lay public against the flow of the latest bestselling medieval bodice rippers or TV medieval murder mystery. What is needed, is as many semi-popular books on the various aspects of medieval history as possible. Whereby with semi-popular I mean, written for the general lay reader but with its historical facts correct. One such new volume is John Farrell’s The Clock and the Camshaft: And Other Medieval Inventions We Still Can’t Live Without.[1]

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Farrell’s book is a stimulating excursion through the history of technological developments and innovation in the High Middle Ages that played a significant role in shaping the modern world.  Some of those technologies are genuine medieval discoveries and developments, whilst others are ones that either survived or where reintroduced from antiquity. Some even coming from outside of Europe. In each case Farrell describes in careful detail the origins of the technology in question and if known the process of transition into European medieval culture.

The book opens with agricultural innovations, the deep plough, the horse collar and horse shoes, which made it possible to use horses as draught animals instead of or along side oxen, and new crop rotation systems. Farrell explains why they became necessary and how they increased food production leading indirectly to population growth.

Next up we have that most important of commodities power and the transition from the hand milling of grain to the introduction of first watermills and then windmills into medieval culture. Here Farrell points out that our current knowledge would suggest that the more complex vertical water mill preceded the simpler horizontal water mill putting a lie to the common precept that simple technology always precedes more complex technology. At various points Farrell also addresses the question as to whether technological change drives social and culture change or the latter the former.

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Having introduced the power generators, we now have the technological innovations necessary to adapt the raw power to various industrial tasks, the crank and the camshaft. This is fascinating history and the range of uses to which mills were then adapted using these two ingenious but comparatively simple power take offs was very extensive and enriching for medieval society. One of those, in this case an innovation from outside of Europe, was the paper mill for the production of that no longer to imagine our society without, paper. This would of course in turn lead to that truly society-changing technology, the printed book at the end of the Middle Ages.

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Along side paper perhaps the greatest medieval innovation was the mechanical clock. At first just a thing of wonder in the towers of some of Europe’s most striking clerical buildings the mechanical clock with its ability to regulate the hours of the day in a way that no other time keeper had up till then gradually came to change the basic rhythms of human society.

Talking of spectacular clerical buildings the Middle Ages are of course the age of the great European cathedrals. Roman architecture was block buildings with thick, massive stonewalls, very few windows and domed roofs. The art of building in stone was one of the things that virtually disappeared in the Early Middle Ages in Europe. It came back initially in an extended phase of castle building. Inspired by the return of the stonemason, medieval, European, Christian society began the era of building their massive monuments to their God, the medieval cathedrals. Introducing architectural innovation like the pointed arch, the flying buttress and the rib vaulted roof they build large, open buildings flooded with light that soared up to the heavens in honour of their God. Buildings that are still a source of wonder today.

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In this context it is important to note that Farrell clearly explicates the role played by the Catholic Church in the medieval technological innovations, both the good and the bad. Viewed with hindsight the cathedrals can be definitely booked for the good but the bad? During the period when the watermills were introduced into Europe and they replaced the small hand mills that the people had previously used to produce their flour, local Church authorities gained control of the mills, a community could only afford one mill, and forced the people to bring their grain to the Church’s mill at a price of course. Then even went to the extent of banning the use of hand mills.

People often talk of the Renaissance and mean a period of time from the middle of the fifteenth century to about the beginning of the seventeenth century. However, for historians of science there was a much earlier Renaissance when scholars travelled to the boundaries between Christian Europe and the Islamic Empire in the twelfth and thirteenth centuries in order to reclaim the knowledge that the Muslims had translated, embellished and extended in the eight and ninth centuries from Greek sources. This knowledge enriched medieval science and technology in many areas, a fact that justifies its acquisition here in a book on technology.

Another great medieval invention that still plays a major role in our society, alongside the introduction of paper and the mechanical clock are spectacles and any account of medieval technological invention must include their emergence in the late thirteenth century. Spectacles are something that initially emerged from Christian culture, from the scriptoria of the monasteries but spread fairly rapidly throughout medieval society. The invention of eyeglasses would eventually lead to the invention of the telescope and microscope in the early seventeenth century.

Another abstract change, like the translation movement during that first scientific Renaissance, was the creation of the legal concept of the corporation. This innovation led to the emergence of the medieval universities, corporations of students and/or their teachers. There is a direct line connecting the universities that the Church set up in some of the European town in the High Middle Ages to the modern universities throughout the world. This was a medieval innovation that truly helped to shape our modern world.

Farrell’s final chapter in titled The Inventions of Discovery and deals both with the medieval innovations in shipbuilding and the technology of the scientific instruments, such as astrolabe and magnetic compass that made it possible for Europeans to venture out onto the world’s oceans as the Middle Ages came to a close. For many people Columbus’ voyage to the Americas in 1492 represents the beginning of the modern era but as Farrell reminds us all of the technology that made his voyage possible was medieval.

All of the above is a mere sketch of the topics covered by Farrell in his excellent book, which manages to pack an incredible amount of fascinating information into what is a fairly slim volume. Farrell has a light touch and leads his reader on a voyage of discovery through the captivating world of medieval technology. The book is beautifully illustrated by especially commissioned black and white line drawing by Ryan Birmingham. There are endnotes simply listing the sources of the material in main text and an extensive bibliography of those sources. The book also has, what I hope, is a comprehensive index.[2]

Farrell’s book is a good, readable guide to the world of medieval technology aimed at the lay reader but could also be read with profit by scholars of the histories of science and technology and as an ebook or a paperback is easily affordable for those with a small book buying budget.

So remember, next time you settle down with the latest medieval pot boiler with its cast of filthy peasants, debauched clerics and pox marked whores that the paper that it’s printed on and the reading glasses you are wearing both emerged in Europe in the Middle Ages.

[1] John W. Farrell, The Clock and the Camshaft: And Other Medieval Inventions We Still Can’t Live Without, Prometheus Books, 2020.

[2] Disclosure: I was heavily involved in the production of this book, as a research assistant, although I had nothing to do with either the conception or the actual writing of the book that is all entirely John Farrell’s own work. However, I did compile the index and I truly hope it will prove useful to the readers.

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Filed under Book Reviews, History of science, History of Technology, Mediaeval Science