Category Archives: Newton

Astrology in the age of Newton

My Annus Mythologicus blog post was recently retweeted on Twitter in response to an inane tweet from Richard Dawkins and somebody questioned the reference in it that Newton was inspired to take up mathematics upon reading a book on astrology. This was not a nasty attack but a genuine statement on interest from somebody who had difficulty believing a man, who has been called the greatest mathematician ever, should have had anything to do with an astrology book. There is a sort of naïve belief that it is impossible for the people in the age of Newton, which is touted as the birth of the age of modern science and rationalism, could have had anything to do with the so-called occult sciences. This belief led many people, who should have known better, to try and sweep Newton’s very active engagement with alchemy under the carpet. During Newton’s lifetime astrology lost its status as a university discipline but was still all pervasive and permeated all aspects and levels of society. In what follows I will sketch some of the details of the role of astrology in the age of Newton.

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Newton – 1677 Source: Wikimedia Commons

The Renaissance/Early Modern Period could with justification be called the golden age of astrology in Europe. This period was actually coming to an end during Newton’s lifetime, but astrology had by no means totally disappeared. That golden age began roughly with the beginning of the fifteenth century. During the first half of the century the humanist universities of Northern Italy and Poland created the first regular, dedicated chairs for mathematics and astronomy, which were in fact chairs for astrology, created to teach astrology to medical students. Teaching astrology to medical students was one of the principle obligations of the professors for mathematics at these universities and continued to be so well down into the seventeenth century. This trend continued with the creation of the first such chair in Germany, at the University of Ingolstadt, in the early 1470s. Astrological medicine, or iatromathematics to it is formal name was just one branch of astrology that flourished in this period.

Medical astrology was along with astrological meteorology considered to be a form of natural astrology and even those, who rejected natal astrology, for example, accepted the validity of natural astrology. Opposed to natural astrology was judicial astrology collective term for a group of other forms of astrology. Natal astrology, or genethliacal astrology, is the classic birth horoscope astrology that everybody thinks of, when they first hear the term astrology.  Other forms of judicial horoscope astrology are mundane astrology concerns the fate of nations etc., horary astrology answers question by casting a horoscope when the question is presented, and electional astrology, which is used to determine the most appropriate or auspicious time to carry out a planned action.

All these forms of astrology were widespread and considered valid by the vast majority during the fifteenth and sixteenth centuries. Astrology was firmly established in the fabric of European society and almost all of the active astronomers were also active astrologers right down to those astronomers, who were responsible for the so-called astronomical revolution. Georg Peuerbach, Regiomontanus, Tycho Brahe, Johannes Kepler and Galileo Galilei were all practicing astrologers and in fact owed much of the patronage that they received to their role as astrologer rather to that of astronomer, although the terms were interchangeable in this period. The terms Astrologus, Astronomus and Mathematicus were all synonym and all had astrologer in the modern sense as their principle meaning. Following the invention of moving type printing in about 1450, by far and away, the largest number of printed articles were astrological ephemera, almanacs, prognostica, and writing and single sheet wall calendars. A trend that continued all the way down to the eighteenth century.

During the fifteenth and sixteenth century efforts to give astrology a solid empirical footing were central to the activities of the astronomer-astrologers. Starting with Regiomontanus several astronomers believed that the inaccuracies in astrological forecasting were due to inaccuracies in the astronomy on which it was based. The reform of astronomy, for exactly this reason, was a principle motivation for the research programmes of Regiomontanus, Tycho Brahe and Wilhelm IV, Landgrave of Hessen-Kassel. Another approach was through astro-meteorology, with astronomer keeping weather diaries in which they noted the horoscope for the day and the actual weather on that day. They were looking for correlations, which they failed to find, but the practice led to the beginnings of modern weather forecasting. Notable weather diarists were Tycho Brahe and Johannes Werner. There were also attempts to find genuine correlations between birth charts and biographies of prominent people. Such biographical horoscope collections existed in manuscript before the invention of movable type printing. One of the largest, still extant, such manuscript collections is that of Erasmus Reinhold, a professor of mathematics at Wittenberg. The first such printed collection was that of Gerolamo Cardano, Libelli duo: De Supplemento Almanach; De Restitutione temporum et motuum coelestium; Item Geniturae LXVII insignes casibus et fortuna, cum expositione, printed and published by Johannes Petreius, specialist for astrological literature, in Nürnberg in 1543; the same year as he published Copernicus’ De revolutionibus.

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During the first half of the seventeenth century the failures to find empirical evidence for astrology, a change in the philosophy underpinning science, astrology was justified with Aristotelian metaphysics, and changes in the ruling methodologies of mainstream medicine led to a decline in the academic status of astrology. Although a few universities continued teaching astrology for medical students into the eighteenth century, astrology as a university discipline largely ceased to exist by 1660. However, astrology was still very much woven into the fabric of European society.

Newton was born in 1642, which meant he grew up during the Civil War and the Interregnum. Astrology was used by both sides as propaganda during Civil War. Most famously William Lilly (1602–1681) publishing powerful pamphlets on behalf of the parliamentary side.

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Portrait of Lilly, aged 45, now housed in the Ashmolean Museum at Oxford Source: Wikimedia Commons

This caused him major problem following the restitution. Lilly’s Christian Astrology (1647) was a highly influential book in the genre. Lilly was friends with many important figures of the age including Elias Ashmole (1617–1692) an antiquary who gave his name to the Ashmolean Museum of Art and Archaeology in Oxford, which was founded on his collection of books, manuscripts many objects. Ashmole was a passionate astrologer and a founding member of the London Society of Astrologers, which included many prominent intellectuals and existed from 1649 to 1658 and was briefly revived in 1682 by the astronomer, astrologer, printer and globemaker Joseph Moxon (1627–1691).

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Joseph Moxon. Line engraving by F. H. van Hove, 1692. Source: Wikimedia Commons

Moxon successfully sold Ptolemaic globes in the last quarter of the seventeenth century, which were intended for astrologers not astronomers. Moxon’s Ptolemaic globes reflect an actual fashion in astrological praxis that could be described as back to the roots. In the middle of the seventeenth century many astrologers decide that astrology wasn’t working, as it should, because the methodology used had drifted to far from that described by Ptolemaeus in his Tetrabiblos. This movement was led by the Italian P. Placido de Titis (1603 – 1668) whose Physiomathematica sive coelestis philosophia published in 1650 with an improved 2nd edition, 1675.

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Alongside Moxon another English supporter of this back to the roots movement was John Partridge (1644–c. 1714), who published the first ever English translation of Ptolemaeus’ Tetrabiblos in 1704. Partridge was one of the most well-known astrologers of the age until he got skewered by Jonathan Swift in his infamous Isaac Bickerstaff letters beginning in 1708.

V0004503ER John Partridge. Line engraving by R. White, 1682, after hims

John Partridge. Line engraving by R. White, 1682 Credit: Wellcome Library, London. Wellcome Images Source: Wikimedia Commons http://wellcomeimages.org John Partridge. Line engraving by R. White, 1682, after himself. 1682 By: Robert WhitePublished: – Copyrighted work available under Creative Commons Attribution only licence CC BY 4.0 http://creativecommons.org/licenses/by/4.0/

We always talk about the big names in the histories of astronomy and mathematics, but it is often more insignificant practitioners, who teach the next generation. In this Newton’s education in astronomy followed the norm and he learnt his astronomy from the books of Vincent Wing (1619–1668) Astronomia Britannica (1669)

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Author portrait of Vincent Wing engraved by T. Cross (Frontispiece to the “Astronomia Britannica” of 1669) Source: Wikimedia Commons

and Thomas Streete (1621–1689) Astronomia Carolina, a new theorie of Coelestial Motions (1661).

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They were the two leading astronomers in England during Newton’s youth and were both practicing astrologers. The two men were rivals and wrote polemics criticising the errors in the others work. Streete was friends with several other astronomers such as Flamsteed, who also used the Astronomia Carolina as his textbook, or Halley together with whom Streete made observation. Streete was Keplerian and it’s Kepler’s astronomy that he presents in his Astronomia Carolina , although he rejected Kepler’s second law and presented the theories of Boulliau and Ward instead. It is very probable that reading Streete was Newton’s introduction to Kepler’s theories.

Flamsteed, as already said, like Newton, a student of Steete, actually cast an electional horoscope for the laying of the foundation stone of the Royal Observatory in 1675 although he didn’t actually believe in astrology but was maintaining a well-established tradition.

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Another example of this sort of half belief can be found in the attitude of Newton and Halley to comets. The two of them did far more than anybody else to establish comets as real celestial bodies affected by the same physical laws as all other celestial bodies and not some sort of message from the heavens. However, whilst neither of them believed in the truth of astrology both retained a belief that comets were indeed harbingers of doom.

As I said at the beginning Newton grew up and lived all of his life in a culture permeated with a belief in astrology. At the end of the seventeenth century astrological ephemera–almanacs, prognostica, etc.–were still a mass market phenomenon.

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Zodiac man in EPB/61971/A: Goldsmith, 1679. An almanack for the year of our Lord God, 1679 (London: Printed by Mary Clark, for the Company of Stationers, 1679), leaf B2 recto. Image credit: Elma Brenner. Source:

A large annual fair such as Sturbridge in 1663, the largest annual fair in Europe, would have had a large selection of astrological literature on offer for the visitors; a public many of whose yearly almanac was the only printed book that they bought and read.

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It is perfectly reasonable that a twenty-one year old Newton, just entering his second year at Cambridge university, stumbled across an astrological publication that awakened his mathematical curiosity as reported separately by both John Conduitt and Abraham DeMoirvre, in their memoirs based on conversations with Newton.

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Filed under History of Astrology, History of Astronomy, Newton, Renaissance Science

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

Whilst the European community mathematicians and physicist, i.e. those who could comprehend and understand it, were more than prepared to acknowledge Newton’s Principia as a mathematical masterpiece, many of them could not accept some of the very basic premises on which it was built. Following its publication the Baconians, the Cartesians and Leibniz were not slow in expressing their fundamental rejection of various philosophical aspects of Newton’s magnum opus.  

Francis Bacon had proposed a new scientific methodology earlier in the seventeenth century to replace the Aristotelian methodology.

Sir Francis Bacon, c. 1618

You will come across claims that Newton’s work was applied Baconianism but nothing could be further from the truth. Bacon rejected the concept of generating theories to explain a group of phenomena. In his opinion the natural philosopher should collect facts or empirical data and when they had acquired a large enough collections then the explanatory theories would crystallise out of the data. Bacon was also not a fan of the use of mathematics in natural philosophy. Because of this he actually rejected both the theories of Copernicus and Gilbert.

Newton, of course did the opposite he set up a hypothesis to explain a given set of seemingly related phenomena, deduced logical consequences of the hypothesis, tested the deduced conclusions against empirical facts and if the conclusions survive the testing the hypothesis becomes a theory. This difference in methodologies was bound to lead to a clash and it did. The initial clash took place between Newton and Flamsteed, who was a convinced Baconian. Flamsteed regarded Newton’s demands for his lunar data to test his lunar theory as a misuse of his data collecting. 

Source: Wikimedia Commons

The conflict took place on a wider level within the Royal Society, which was set up as a Baconian institution and rejected Newton’s type of mathematical theorising. When Newton became President of the Royal Society in 1704 there was a conflict between himself and his supporters on the one side and the Baconians on the other, under the leadership of Hans Sloane the Society’s secretary. At that time the real power in Royal Society lay with the secretary and not the president. It was first in 1712 when Sloane resigned as secretary that the Royal Society became truly Newtonian. This situation did not last long, when Newton died, Sloane became president and the Royal Society became fundamentally Baconian till well into the nineteenth century. 

Hans Sloane by Stephen Slaughter Source: Wikimedia Commons

This situation certainly contributed to the circumstances that whereas on the continent the mathematicians and physicists developed the theories of Newton, Leibnitz and Huygens in the eighteenth century creating out of them the physics that we now know as Newtonian, in England these developments were neglected and very little advance was made on the work that Newton had created. By the nineteenth century the UK lagged well behind the continent in both mathematics and physics.

The problem between Newton and the Cartesians was of a completely different nature. Most people don’t notice that Newton never actually defines what force is. If you ask somebody, what is force, they will probably answer mass time acceleration but this just tells you how to determine the strength of a given force not what it is. Newton tells the readers how force works and how to determine the strength of a force but not what a force actually is; this is OK because nobody else does either. The problems start with the force of gravity. 

Frans Hals – Portrait of René Descartes Source: Wikimedia Commons

The Cartesians like Aristotle assume that for a force to act or work there must be actual physical contact. They of course solve Aristotle’s problem of projectile motion, if I remove the throwing hand or bowstring, why does the rock or arrow keep moving the physical contact having ceased? The solution is the principle of inertia, Newton’s first law of motion. This basically says that it is the motion that is natural and it requires a force to stop it air resistance, friction or crashing into a stationary object. In order to explain planetary motion Descartes rejected the existence of a vacuum and hypothesised a dense, fine particle medium, which fills space and his planets are carried around their orbits on vortices in this medium, so physical contact. Newton demolished this theory in Book II of his Principia and replaces it with his force of gravity, which unfortunately operates on the principle of action at a distance; this was anathema for both the Cartesians and for Leibniz. 

What is this thing called gravity that can exercise force on objects without physical contact? Newton, in fact, disliked the concept of action at a distance just as much as his opponents, so he dodged the question. His tactic is already enshrined in the title of his masterpiece, the Mathematical Principles of Natural Philosophy. In the draft preface to the Principia Newton stated that natural philosophy must “begin from phenomena and admit no principles of things, no causes, no explanations, except those which are established through phenomena.” The aim of the Principia is “to deal only with those things which relate to natural philosophy”, which should not “be founded…on metaphysical opinions.” What Newton is telling his readers here is that he will present a mathematical description of the phenomena but he won’t make any metaphysical speculations as to their causes. His work is an operative or instrumentalist account of the phenomena and not a philosophical one like Descartes’.  

The Cartesians simply couldn’t accept Newton’s action at a distance gravity. Christiaan Huygens, the most significant living Cartesian natural philosopher, who was an enthusiastic fan of the Principia said quite openly that he simply could not accept a force that operated without physical contact and he was by no means alone in his rejection of this aspect of Newton’s theory. The general accusation was that he had introduced occult forces into natural philosophy, where occult means hidden.

Christiaan Huygens. Cut from the engraving following the painting of Caspar Netscher by G. Edelinck between 1684 and 1687. Source: Wikimedia Commons

Answering his critics in the General Scholium added to the second edition of the Principia in 1713 and modified in the third edition of 1726, Newton wrote:

Thus far I have explained the phenomena of the heavens and of our sea by the force of gravity, but I have not assigned a cause to gravity.

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I have not been able to deduce from phenomena the reasons for these properties of gravity, and I do not feign hypotheses; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this experimental philosophy, propositions are deduced from the phenomena and are made general by induction. The impenetrability, mobility, and impetus of bodies, and the laws of motion and the law of gravity have been found by this method. And it is enough that gravity really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the heavenly bodies and of our sea.

Newton never did explain the cause of gravity but having introduced the concept of a pervasive aethereal medium in the Queries in Book III of his Opticks he asks if the attraction of the aether particles could be the cause of gravity. The Queries are presented as speculation for future research.

Both the Baconian objections to Newton’s methodology and the Cartesian objections to action at a distance were never disposed of by Newton but with time and the successes of Newton’s theory, for example the return of Comet Halley, the objections faded into the background and the Principia became the accepted dominant theory of the cosmos.

Leibniz shared the Cartesian objection to action at a distance but also had objections of his own.

Engraving of Gottfried Wilhelm Leibniz Source: Wikimedia Commons

In 1715 Leibniz wrote a letter to Caroline of Ansbach the wife of George Prince of Wales, the future George III, in which he criticised Newtonian physics as detrimental to natural theology. The letter was answered on Newton’s behalf by Samuel Clarke (1675–1729) a leading Anglican cleric and a Newtonian, who had translated the Opticks into Latin. There developed a correspondence between the two men about Newton’s work, which ended with Leibniz’s death in 1716. The content of the correspondence was predominantly theological but Leibniz raised and challenged one very serious point in the Principia, Newton’s concept of absolute time and space.

In the Scholium to the definitions at the beginning of Book I of Principia Newton wrote: 

1. Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration. 

Relative, apparent, and common time […] is commonly used instead of true time.

2. Absolute space, of its own nature without reference to anything external, always remains homogeneous and immovable. Relative space is any moveable or dimension of the absolute space…

Newton is saying that space and time have a separate existence and all objects exists within them.

In his correspondence with Clarke, Leibniz rejected Newton’s use of absolute time and space, proposing instead a relational time and space; that is space and time are a system of relations that exists between objects. 

 In his third letter to Clarke he wrote:

As for my own opinion, I have said more than once, that I hold space to be something merely relative, as time is, that I hold it to be an order of coexistences, as time is an order of successions.

Leibniz died before any real conclusion was reached in this debate and it was generally thought at the time that Newton had the better arguments in his side but as we now know it was actually Leibniz who was closer to how we view time and space than Newton. 

Newton effectively saw off his philosophical critics and the Principia became the accepted, at least mathematical, model of the then known cosmos. However, there was still the not insubstantial empirical problem that no proof of any form of terrestrial motion had been found up to the beginning of the seventeenth century.

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

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

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.

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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.

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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.

clairaut

Alexis Claude Clairaut Source: MacTutor

Jérôme_Lalande

Jérôme Lalande after Joseph Ducreux Source: Wikimedia Commons

lepaute001

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.

PSM_V76_D015_Halley_comet_in_1456

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

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

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

The event that would eventually lead to Isaac Newton writing and publishing his magnum opus, the Philosophiæ Naturalis Principia Mathematica (the Mathematical Principles of Natural Philosophy), took place in a London coffee house.

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Title page of ‘Principia’, first edition (1687). Source: Wikimedia Commons

This is not quite as strange as it might at first appear, shortly after their first appearance in England around 1650 coffee houses became the favourite meeting places of the English scientific intelligentsia, the astronomers, mathematicians and natural philosophers. Here, these savants would meet up to exchange ideas, discuss the latest scientific theories and pose challenges to each other. These institutions also earned the appellation Penny Universities, as some of those savants, such as William Whiston, Francis Hauksbee and Abraham de Moivre, bettered their incomes by holding lectures or demonstrating experiments to willing audiences, who paid the price of a cup of coffee, a penny, for their intellectual entertainment. Later, after he had become Europe’s most famous living natural philosopher, Isaac Newton would come to hold court in a coffee shop, surrounded by his acolytes, the original Newtonians, distributing words of wisdom and handing round his unpublished manuscripts for scrutiny. However, all that still lay in the future.

One day in January 1684 Christopher Wren, Robert Hooke and Edmond Halley were discussing the actual astronomical theories over a cup of coffee. Wren, today better known as one of England most famous architects, was a leading mathematician and astronomers, who had served both as Gresham and Savilian professor of astronomy. Newton would name him along with John Wallis and William Oughtred as one of the three leading English mathematicians of the seventeenth century.

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Wren, portrait c.1690 by John Closterman Source: Wikimedia Commons

Hooke was at the time considered to be the country’s leading experimental natural philosopher and Halley enjoyed an excellent reputation as a mathematician and astronomer.

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Portrait by Richard Phillips, before 1722 Source: Wikimedia Commons

The topic of discussion was Kepler’s elliptical, heliocentric astronomy and an inverse, squared law of gravity. All three men had arrived separately and independently at an inverse, squared law of gravity probably derived from Huygens’ formula for centrifugal force. Wren posed the question to the other two, whether they could demonstrate that such a law would lead to Kepler’s elliptical planetary orbits.

Hooke asserted that he already had such a demonstration but he would first reveal it to the others after they had admitted that they couldn’t solve the problem. Wren was sceptical of Hooke’s claim and offered a prize of a book worth forty shillings to the first to produce such a demonstration.  Hooke maintained his claim but didn’t deliver. It is worth noting that Hooke never did deliver such a demonstration. Halley, as already said no mean mathematician, tried and failed to solve the problem.

In August 1684 Halley was visiting Cambridge and went to see Newton in his chambers in Trinity College, who, as we know, he had met in 1682.

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Trinity College Cambridge, David Loggan’s print of 1690 Source: Wikimedia Commons

According the Newton’s account as told to Abraham DeMoivre, Halley asked Newton, “what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of the distance from it. Sir Isaac replied immediately that it would be an Ellipse…” Here was Newton claiming to know the answer to Wren’s question. Halley asked Newton how he knew it and he replied, “I have calculated it…” Newton acted out the charade of looking for the supposed solution but couldn’t find it. However he promised Halley that he would send him the solution.

In November Edward Paget, a fellow of Trinity College, brought Halley a nine page thesis entitled De motu corporum in gyrum (On the Motion of Bodies in an Orbit).

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Page of the De motu corporum in gyrum

When Halley read Newton’s little booklet he was immediately aware that he held something truly epoch making in the history of astronomy and physics in his hand. Newton had delivered up a mathematical proof that an elliptical orbit would be produced by an inverse square force situated at one of the foci of the ellipse, thus combining the inverse square law of gravity with Kepler’s first law. He went on to also derive Kepler’s second and third laws as well as laying down the beginnings of a mathematical theory of dynamics. Halley reported details of this extraordinary work to the Royal Society on 10 December 1684:

Mr Halley gave an account, that he had lately seen Mr. Newton at Cambridge, who had shewed him a curious treatise, De motu: which, upon Mr. Halley’s desire, was he said promised to be sent to the Society to be entered upon their register.

Mr. Halley was desired to put Mr. Newton in mind of his promise for securing his invention to himself till such time as he could be at leisure to publish it. Mr. Paget was desired to join with Mr. Halley.

The interest in and the demand to read Newton’s new production was very high but the author decided to improve and rewrite his first offering, triggering one of the most extraordinary episodes in his life.

Although he was Lucasian Professor and would turn forty-two on 25 December 1684, Newton remained a largely unknown figure in the intellectual world of the late seventeenth century. Following the minor debacle that resulted from the publication of his work in optics in the 1670s he had withdrawn into his shell, living in isolation within the walls of Cambridge University. He carried out his duties as Lucasian Professor but had almost no students to speak of and definitely no disciples. Thanks to the word of mouth propaganda of people like his predecessor as Lucasian Professor, Isaac Barrow, and above all the assiduous mathematics groupie, John Collins, it was rumoured that a mathematical monster slumbered in his chambers in Trinity College but he had done nothing to justify this bruited reputation. His chambers were littered with numerous unfinished scientific manuscripts, mostly mathematical but also natural philosophical and an even larger number of alchemical and theological manuscripts but none of them was in a fit state to publish and Newton showed no indication of putting them into a suitable state. Things now changed, Newton had found his vocation and his muse and the next two and a half years of his life were dedicated to creating the work that would make him into a history of science legend, the reworking of De motu into his Principia.

Over those two and a half years Newton turned his nine-page booklet into a major three-volume work of science. The modern English translation by I B Cohen runs to just over 560 large format pages, although this contains all the additions and alterations made in the second and third editions, so the original would have been somewhat shorter. Halley took over the editorship of the work, copyediting it and seeing it through the press. In 1685 the Royal Society had voted to take over the costs of printing and publishing Newton’s masterpiece, so everything seemed to be going smoothly and then disaster struck twice, firstly in the form of Robert Hooke and secondly in the form of a financial problem.

Hooke never slow to claim his priority in any matter of scientific discovery or invention stated that he alone had first discovered the inverse square law of gravity and that this fact should, indeed must, be acknowledged in full in the preface to Newton’s book. Halley, realising at once the potential danger of the situation, was the first to write to Newton outlining Hooke’s claim to priority, stating it, of course, as diplomatically as possible. Halley’s diplomacy did not work, Newton went ballistic. At first his reaction was comparatively mild, merely pointing out that he had had the inverse square law well before his exchanges with Hook in 1679 and had, in fact, discussed the matter with Wren in 1677, go ask him, Newton said. Then with more time to think about the matter and building up a head of steam, Newton wrote a new letter to Halley tearing into Hooke and his claim like a rabid dog. All of this ended with Newton declaring that he would no longer write volume three of his work. Halley didn’t know this at the time but this was in fact, as we shall see, the most important part of the entire work in which Newton presented his mathematical model of a Keplerian cosmos held together by the law of gravity. Halley remained calm and used all of his diplomatic skills to coax, flatter, persuade and cajole the prickly mathematician into delivering the book as finished. In the end Newton acquiesced and delivered but acknowledgements to Hooke were keep to a minimum and offered at the lowest level of civility.

The financial problem was of a completely different nature. In 1685 the Royal Society had taken over the cost of printing and publishing the deceased Francis Willughby’s Historia piscium as edited by John Ray.

This was an expensive project due to the large number plates that the book contained and the book was, at the time, a flop. This meant when it came time to print and publish Newton’s work the Royal Society was effectively bankrupt. One should note here that the popular ridicule poured out over Willughby’s volume, it having almost prevented Newton’s masterpiece appearing, is not justified. Historia piscium is an important volume in the history of zoology. Halley once again jumped into the breach and took over the costs of printing the volumes; on the 5 July 1687 Halley could write to Newton to inform him that the printing of his Philosophiæ Naturalis Principia Mathematica had been completed.

 

 

 

 

 

 

 

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

Annus mythologicus

Almost inevitably Newton’s so-called Annus mirabilis has become a social media meme during the current pandemic and the resulting quarantine. Not surprisingly Neil deGrasse Tyson has once again led the charge with the following on Twitter:

When Isaac Newton stayed at home to avoid the 1665 plague, he discovered the laws of gravity, optics, and he invented calculus.

Unfortunately for NdGT and all the others, who have followed his lead in posting variants, both positive and negative, the Annus mirabilis is actually a myth. So let us briefly examine what actually took place and what Isaac actually achieved in the 1660s.

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

We will start with the calculus, which he didn’t actually invent at all, neither in the 1660s nor at any other time. Calculus has a more than two thousand year history stretching back to fourth century BCE. The development of calculus accelerated in the seventeenth century beginning with Kepler and Cavalieri and, previous to Newton, reaching a high point in the work of John Wallis. What Newton, like Leibniz, did was to collate, order and expand the work that others had already produced. Let us take a closer look at what Newton actually achieved in the 1660s.

But before we start, one point that various people have made on the Internet is that during this time Newton was a completely free agent with no commitments, obligations or burdens, a bachelor without children. In college his chambers were cleaned by servants and his meals were prepared by others. At home in Woolsthorpe all of his needs were also met by servants. He could and did devote himself to studying without any interruptions.

Newton, who entered Trinity College Cambridge in June 1661, was an indifferent student apparently bored by the traditional curriculum he was supposed to learn. In April 1664 he was due to take a scholarship exam, which would make him financially independent. The general opinion was not positive, however he did pass as he also passed his BA in the following year, when the prognosis was equally negative. Westfall suggests that he had a patron, who recommended that Cambridge retain him.

Freed by the scholarship, Newton now discovered his love and aptitude for the modern mathematics and set off on a two-year intensive study of the subject, almost to the exclusion of everything else, using the books of the leading mathematicians of the period, Descartes (but in the expanded, improved Latin edition of van Schooten), Viète and Wallis. In October 1666 Newton’s total immersion in mathematics stopped as suddenly as it had begun when he wrote a manuscript summarising all that he had internalised. He had thoroughly learnt all of the work available on the modern analytical mathematics, extended it and systematised it. This was an extraordinary achievement by any standards and, although nobody knew about it at the time, established Newton as one of the leading mathematicians in Europe. Although quite amazing, the manuscript from 1666 is still a long way from being the calculus that we know today or even the calculus that was known, say in 1700.

It should be noted that this intense burst of mathematical activity by the young Newton had absolutely nothing to do with the plague or his being quarantined/isolated because of it. It is an amusing fact that Newton was stimulated to investigate and learn mathematics, according to his own account, because he bought a book on astrology at Sturbridge Fair and couldn’t understand it. Unlike many of his contemporaries, Newton does not appear to have believed in astrology but he learnt his astronomy from the books of Vincent Wing (1619–1668) and Thomas Street (1621–1689) both of whom were practicing astrologers.

I said above that Newton devoted himself to mathematics almost to the exclusion of everything else in this period. However, at the beginning he started a notebook in which he listed topics in natural philosophy that he would be interested in investigating further in the future. Having abandoned mathematics he now turned to one of those topics, motion and space. Once again he was guided in his studies by the leaders in the field, once again Descartes, then Christiaan Huygens and also Galileo in the English translation by Thomas Salusbury, which appeared in 1665. Newton’s early work in this field was largely based on the principle of inertia that he took from Descartes and Descartes’ theories of impact. Once again Newton made very good progress, correcting Descartes errors and demonstrating that Galileo’s value for ‘g’ the force of acceleration due to gravity was seriously wrong. He also made his first attempt to show that the force that causes an object to fall to the ground, possibly the legendary apple, and the force that prevents the Moon from shooting off at a tangent, as the principle of inertia says it should, were one and the same. This attempt sort of failed because the data available to Newton at the time was not accurate enough. Newton abandoned this line of thinking and only returned to it almost twenty years later.

Once again, the progress that the young Newton made in this area were quite impressive but his efforts were very distant from his proof of the law of gravity and its consequences that he would deliver in the Principia, twenty year later. For the record Newton didn’t discover the law of gravity he proved it, there is an important difference between the two. Of note in this early work on mechanics is that Newton’s concepts of mass and motions were both defective. Also of note is that to carry out his gravity comparison Newton used Kepler’s third law of planetary motion to determine the force holding the Moon in its orbit and not the law of gravity. The key result presented in Principia is Newton’s brilliant proof that Kepler’s third law and the law of gravity are in fact mathematically equivalent.

The third area to which Newton invested significant time and effort in the 1660s was optics. I must confess that I have absolutely no idea what Neil deGrasse Tyson means when he writes that Newton discovered the laws of optics. By the time Newton entered the field, the science of optics was already two thousand years old and various researchers including Euclid, Ptolemaeus, Ibn al-Haytham, Kepler, Snel, and Descartes had all contributed substantially to its laws. In the 1660s Newton entered a highly developed field of scientific investigation. He stated quite correctly that he investigated the phenomenon of colour. Once again his starting point was the work of others, who were the leaders in the field, most notably Descartes and Hooke. It should be clear by now that in his early development Newton’s debt to the works of Descartes was immense, something he tried to deny in later life. What we have here is the programme of experiments into light that Newton carried out and which formed the basis of his very first scientific paper published in 1672. This paper famously established that white light is made up of coloured light. Also of significance Newton was the first to discover chromatic aberration, the fact that spherical lenses don’t sharply focus light to a single point but break it up into a spectrum, which means the images have coloured fringes. This discovery led Newton to develop his reflecting telescope, which avoids the problem of chromatic aberration.

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Newton’s sketch of his crucial experiment. Source: Royal Society

Here trying to establish a time line of when and where he carried out these experiments is very difficult, not alone because Newton’s own statements on the subject are contradictory and some of them are provably false. For example he talks about acquiring a second prism from Sturbridge Fair in a year when one didn’t take place. Also Newton’s source of light was sunlight let into a darkened room through small hole in the shutters. This was only possible at certain times of year and certain times of day when the sun is in the right position respective the window. Newton claims experiments made at times where these conditions weren’t met. That not all the experiments were made in Woolsthorpe Manor is clear, as many of them required two operators, which means that they were made when Newton was back in his chambers in Trinity College. The best guestimate is that this programme of experiments took place over the period 1660 to 1670, so once again not in Newton’s year of quarantine.

Another thing that keeps getting mentioned in connection with this story is that during his experiments on light Newton, shock-horror, stuck a pin in his eye! He didn’t. What he did was to insert a bodkin, a flat, blunt, threading needle, into his eye-socket between his skull and his eyeball in order to apply pressure to the back of his eyeball. Nasty enough, but somewhat different to sticking a pin in his eye.

All in all the developments that the young Newton achieved in mathematics and physics in the 1660s were actually spread out over a period of six years. They were also not as extensive or revolutionary as implied in Neil deGrasse Tyson brief tweeted claim. In fact a period of six intensive years of study would be quite normal for a talented student to acquire the basics of mathematics and physics. And I think we can all agree that Newton was very talented. His achievements were remarkable but not sensational.

It is justified to ask where then does the myth of the Annus Mirabilis actually come from? The answer is Newton himself. In later life he claimed that he had done all these things in that one-year, the fictional ones rather than the real achievements. So why did he claim this? One reason, a charitable interpretation, is that of an old man just telescoping the memories of his youth. However, there is a less charitable but probably more truthful explanation. Newton became in his life embroiled in several priority disputes with other natural philosophers over his discoveries, with Leibniz over the calculus, with Hooke over gravity and with Hook and Huygens over optics. By pushing back into the distant past some of his major discoveries he can, at least to his own satisfaction, firmly establish his priority.

The whole thing is best summarised by Westfall in his Newton biography Never at Rest at the end of his chapter on the topic, interestingly entitled Anni mirabiles, amazing years, not Annus mirabilis the amazing year, on which the brief summary above is largely based. It is worth quoting Westfall’s summary in full:

On close examination, the anni mirabiles turn out to be less miraculous than the annus mirabilis of Newtonian myth. When 1660 closed, Newton was not in command of the results that have made his reputation deathless, not in mathematics, not in mechanics, not in optics. What he had done in all three was to lay foundations, some more extensive than others, on which he could build with assurance, but nothing was complete at the end of 1666, and most were not even close to complete. Far from diminishing Newton’s stature, such a judgement enhances it by treating his achievements as a human drama of toil and struggle rather than a tale of divine revelation. “I keep the subject constantly before me, “ he said, “and wait ‘till the first dawnings open slowly, by little and little, into full and clear light.” In 1666 by dint of keeping subjects constantly before him, he saw the first dawnings open slowly. Years of thinking on them continuously had yet to pass before he gazed on a full and clear light.[1]

Neil deGrasse Tyson has form when it comes to making grand false statements about #histSTM, this is by no means the first time that he has spread the myth of Newton’s Annus mirabilis. What is perhaps even worse is that when historians point out, with evidence, that he is spouting crap he doesn’t accept that he is wrong but invents new crap to justify his original crap. Once he tweeted the classic piece of fake history that people in the Middle Ages believed the world was flat. As a whole series of historians pointed out to him that European culture had known since antiquity that that the world was a sphere, he invented a completely new piece of fake history and said, yes the people in antiquity had known it but it had been forgotten in the Middle Ages. He is simply never prepared to admit that he is wrong. I could bring other examples such as my exchange with him on the superstition of wishing on a star that you can read here but this post is long enough already.

Bizarrely Neil deGrasse Tyson has the correct answer to his behaviour when it comes to #histSTM, of which he is so ignorant. He offers an online course on the scientific method, always ready and willing to turn his notoriety into a chance to make a quick buck, and has an advertising video on Youtube for it that begins thus:

One of the great challenges in this world is knowing enough about a subject to think you’re right but not enough about the subject to know you’re wrong.

This perfectly encapsulates Neil deGrasse Tyson position on #histSTM!

If you want a shorter, better written, more succinct version of the same story then Tom Levenson has one for you in The New Yorker 

[1] Ricard S. Westfall, Never at Rest: A Biography of Isaac Newton, CUP; Cambridge, ppb. 1983, p. 174.

 

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War, politics, religion and scientia

There is a strong tendency to view the history of science and the people who produced it in a sort of vacuum, outside of everyday society–Copernicus published this, Kepler published that, Newton synthesised it all… In fact the so-called scientific revolution took place in one of the most troubled times in European history, the age of the religious wars, the main one of which the Thirty Years War is thought to have been responsible directly and indirectly for the death of between one third and two thirds of the entire population of middle Europe. Far from being isolated from this turbulence the figures, who created modern science, were right in the middle of it and oft deeply involved and affected by it.

The idea for this blog post sort of crept into my brain as I was writing my review, two weeks ago, of two books about female spies during the English Revolution and Interregnum that is the 1640s to the 1660s. Isaac Newton was born during this period and grew up during it and, as I will now sketch, was personally involved in the political turbulence that followed on from it.

Born on Christmas Day in 1642 (os) shortly after the outbreak of the first of the three wars between the King and Parliament, Britain’s religious wars, he was just nine years old when Charles I was executed at the end of the second war.

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

Newton was too young to be personally involved in the wars but others whose work would be important to his own later developments were. The Keplerian astronomer William Gascoigne (1612-1644), who invented the telescope micrometer, an important development in the history of the telescope, died serving in the royalist forces at the battle of Marston Moor. The mathematician John Wallis (1616–1703), whose Arithmetica Infinitorum (1656) strongly influenced Newton’s own work on infinite series and calculus, worked as a code breaker for Cromwelland later for Charles II after the restoration.

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John Wallis by Sir Godfrey Kneller

Newton first went up to university after the restoration but others of an earlier generation suffered loss of university position for being on the wrong side at the wrong time. John Wilkins (1614–1672), a parliamentarian and Cromwell’s brother-in-law, was appointed Master of Trinity College Cambridge, Newton’s college, in 1659 and removed from this position at the restoration. Wilkins’ Mathematical Magick (1648) had been a favourite of Newton’s in his youth.

Greenhill, John, c.1649-1676; John Wilkins (1614-1672), Warden (1648-1659)

Greenhill, John; John Wilkins (1614-1672), Warden (1648-1659); Wadham College, University of Oxford;

Newton’s political career began in 1689 following the so-called Glorious Revolution, when James II was chased out of Britain by William of Orange, his son-in-law, invited in by the parliament out of fear that James could reintroduce Catholicism into Britain. Newton sat in the House of Commons as MP for the University of Cambridge in the parliament of 1689, which passed the Bill of Rights, effectively a new constitution for England. Newton was not very active politically but he identified as a Whig, the party of his student Charles Montagu (1661–1715), who would go on to become one of the most powerful politicians of the age. It was Montagu, who had Newton appointed to lead the Royal Mint and it was also Montagu, who had Newton knighted in 1705in an attempt to get him re-elected to parliament.

In the standard version of story Newton represents the end of the scientific revolution and Copernicus (1473–1543) the beginning. Religion, politics and war all played a significant role in Copernicus’ life.

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Copernicus, the “Torun portrait” (anonymous, c. 1580), kept in Toruń town hall, Poland.

Copernicus spent the majority of his life living in the autonomous prince-bishopric of Warmia, where as a canon of the cathedral he was effectively a member of the government. Warmia was a Catholic enclave under the protection of the Catholic Crown of Poland but as the same time was geographically part of Royal Prussia ruled over by Duke Albrecht of Prussia (1490–1568), who had converted to Lutheran Protestantism in 1552. Ironically he was converted by Andreas Osiander (1498–1552), who would go on the author the controversial ad lectorum in Copernicus’ De revolutionibus. Relations between Poland and Royal Prussia were strained at best and sometimes spilled over into armed conflict. Between 1519 and 1521 there was a war between Poland and Royal Prussia, which took place mostly in Warmia. The Prussians besieged Frombork burning down the town, but not the cathedral, forcing Copernicus to move to Allenstein (Olsztyn), where he was put in charge of organising the defences during a siege from January to February 1521.  Military commander in a religious war in not a role usually associated with Copernicus. It is an interesting historical conundrum that, during this time of religious strife, De revolutionibus, the book of a Catholic cathedral canon, was published by a Protestant printer in a strongly Protestant city-state, Nürnberg.

The leading figure of the scientific revolution most affected by the religious wars of the age must be Johannes Kepler. A Lutheran Protestant he studied and graduated at Tübingen, one of the leading Protestant universities. However, he was despatched by the university authorities to become the mathematics teacher at the Protestant school in Graz in Styria, a deeply Catholic area in Austria in 1594. He was also appointed district mathematicus.

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Johannes Kepler Source: Wikimedia Commons

In 1598, Archduke Ferdinand, who became ruler of Styria in 1596, expelled all Protestant teachers and pastors from the province. Kepler was initially granted an exception because he had proved his worth as district mathematicus but in a second wave of expulsion, he too had to go. After failing to find employment elsewhere, he landed in Prague as an assistant to Tycho Brahe, the Imperial Mathematicus.

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Tycho Brahe Source: Wikimedia Commons

Once again he, like Tycho, was a Protestant in a Catholic city serving a Catholic Emperor, Rudolf II. Here he soon inherited Tycho’s position as Imperial Mathematicus. However, Rudolf was tolerant, more interested in Kepler’s abilities as an astrologer than in his religious beliefs. Apart from a substantial problem in getting paid in the permanently broke imperial court, Kepler now enjoyed a fairly quiet live for the next twelve years, then everything turned pear shaped once more.

In 1612, Rudolf’s younger brother Archduke Matthias deposed him and although Kepler was allowed to keep his title of Imperial Mathematicus, and theoretically at least, his salary but he was forced to leave Prague and become district mathematicus in Linz. In Linz Kepler, who openly propagated ecumenical ideas towards other Protestant communities, most notably the Calvinists, ran into conflict with the local Lutheran pastor. The pastor demanded that Kepler sign the Formula of Concord, basically a commitment to Lutheran theology and a rejection of all other theologies. Kepler refused and was barred from Holy Communion, a severe blow for the deeply religious astronomer. He appealed to the authorities in Tübingen but they up held the ban.

In 1618 the Thirty Years War broke out and in 1620 Linz was occupied by the Catholic army of Duke Maximilian of Bavaria, which caused problems for Kepler as a Lutheran. At the same time he was fighting for the freedom of his mother, Katharina, who had been accused of witchcraft. Although he won the court case against his mother, she died shortly after regaining her freedom. In 1625, the Counterreformation reach Linz and the Protestants living there were once again persecuted. Once more Kepler was granted an exception because of his status as Imperial Mathematicus but his library was confiscated making it almost impossible for him to work, so he left Linz.

Strangely, after two years of homeless wandering Kepler moved to Sagen in Silesia in 1628, the home of Albrecht von Wallenstein the commander of the Catholic forces in the war and for whom Kepler had interpreted a horoscope much earlier in life. Kepler never found peace or stability again in his life and died in Ulm in 1630. Given the turbulence in his life and the various forced moves, which took years rather than weeks, it is fairly amazing that he managed to publish eighty-three books and pamphlets between 1596 and his death in 1630.

A younger colleague of Kepler’s who also suffered during the Thirty Years’ War was Wilhelm Schickard, who Kepler had got to know during his time in Württemberg defending his mother. Schickard would go on to produce the illustrations both Kepler’s Epitome Astronomiae Copernicanae and his Harmonice Mundi, as well as inventing a calculating machine to help Kepler with his astronomical calculations. In 1632 Württemberg was invaded by the Catholic army, who brought the plague with them, by 1635 Schickard, his wife and his four living children, his sister and her three daughters had all died of the plague.

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Wilhelm Schickard, artist unknown Source: Wikimedia Commons

As I have pointed out on numerous occasions Galileo’s initial problems in 1615-16 had less to do with his scientific views than with his attempts to tell the theologians how to interpret the Bible, not an intelligent move at the height of the Counterreformation. Also in 1632 his problems were very definitely compounded by the fact that he was perceived to be on the Spanish side in the conflict between the Spanish and French Catholic authorities to influence, control the Pope, Urban VIII.

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Galileo Portrait by Ottavio Leoni Source: Wikimedia Commons

I will just mention in passing that René Descartes served as a soldier in the first two years of the Thirty Year’s War, at first in the Protestant Dutch States Army under Maurice of Nassau and then under the Catholic Duke of Bavaria, Maximilian. In 1620 he took part in the Battle of the White Mountain near Prague, which marked the end of Elector Palatine Frederick V’s reign as King of Bohemia. During his time in the Netherlands Descartes trained as a military engineer, which was his introduction to the works of Simon Stevin and Isaac Beeckman.

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René Descartes Portrait after Frans Hals Source: Wikimedia Commons

We have now gone full circle and are almost back to Isaac Newton. One interesting aspect of these troubled times is that although the problems caused by the wars, the religious disputes and the associated politics caused major problems in the lives of the astronomers and mathematicians, who were forced to live through them, and certainly affected their ability to carry on with their work, I can’t somehow imagine Copernicus working on De revolutionibus during the siege of Allenstein, the scholars themselves communicated quite happily across the religious divide.

Rheticus was treated as an honoured guest in Catholic Warmia although he was a professor at the University of Wittenberg, home to both Luther and Melanchthon. Copernicus himself was personal physician to both the Catholic Bishop of Frombork and the Protestant Duke of Royal Prussia. As we have seen, Kepler spent a large part of his life, although a devoted Protestant, serving high-ranking Catholic employers. The Jesuits, who knew Kepler from Prague, even invited him to take the chair for mathematics at the Catholic University of Bologna following the death of Giovanni Antonio Magini in 1617, assuring him that he did not need to convert. Although it was a very prestigious university Kepler, I think wisely, declined the invitation. The leading mathematicians of the time all communicated with each other, either directly or through intermediaries, irrespective of their religious beliefs. Athanasius Kircher, professor for mathematics and astronomy at the Jesuit Collegio Romano, collected astronomical data from Jesuits all over the world, which he then distributed to astronomers all over Europe, Catholic and Protestant, including for example the Lutheran Leibniz. Christiaan Huygens, a Dutch Calvinist, spent much of his life working as an honoured guest in Catholic Paris, where he met and influenced the Lutheran Leibniz.

When we consider the lives of scientists we should always bear in mind that they are first and foremost human beings, who live and work, like all other human beings, in the real world with all of its social, political and religious problems and that their lives are just as affected by those problems as everybody else.

 

 

 

 

 

 

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Christmas Trilogy 2018 Part 1: The Harmonic Isaac

Isaac Newton is often referred to, as the ‘father’ of modern science but then again so is Galileo Galilei. In reality modern science has many fathers and some mothers as well. Those who use this accolade tend to want to sweep his theological studies and his alchemy under the carpet and pretend it doesn’t really count. Another weird aspect of Newton’s intellectual universe was his belief in prisca theology. This was the belief that in the period following the creation humankind had perfect knowledge of the natural world that got somehow lost over the centuries. This meant for Isaac that in his own scientific work he wasn’t making discoveries but rediscovering once lost knowledge. Amongst, what we would now regard as his occult beliefs, Isaac also subscribed to the Pythagorean belief in Harmonia (harmony), as a unifying concept in the cosmos.

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Robert Fludd’s Pythagorean Monocord

Although he was anything but a fan of music, he was a dedicated student of Harmonia, the mathematical theory of proportions that was part of the quadrivium. According to the legend Pythagoras was the first to discover that musical interval can be expressed as simple ratios of whole numbers related to a taut string: 1:1 (unison), 2:1 (octave), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third). Unfortunately, anybody who has studied the theory of music knows these ratios don’t quite work. If you start on a given tone and move up in steps of a perfect fifth you don’t actually arrive back at the original tone seven octaves higher after twelve fifths but slightly off. This difference is known as the Pythagorean comma. This disharmony was well known and in the sixteenth and seventeenth centuries a major debate developed on how to ‘correctly’ divide up musical scale to avoid this problem. The original adversaries were Gioseffo Zarlino (1570–1590) and Vincenzo Galilei (1520–1591) (Galileo’s father) and Kepler made a contribution in his Harmonice Mundi; perhaps the most important contribution being made by Marin Mersenne (1588–1648) in his Harmonie universelle, contenant la théorie et la pratique de la musique.

Marin_Mersenne_-_Harmonie_universelle_1636_(page_de_titre)

Harmonie Universelle title page

Here he elucidated Mersenne’s Laws:

Frequency is:

  1. Inversely proportional to the length of the string (this was known to the ancients; it is usually credited toPythagoras)
  2. Proportional to the square root of the stretching force, and
  3. Inversely proportional to the square root of the mass per unit length.

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Source: Gouk p. 115

As a student Newton took up the challenge in one of his notebooks and we don’t need to go into his contribution to that debate here, however it is the first indication of his interest in this mathematics, which he would go on to apply to his two major scientific works, his optics and his theory of gravity.

After he graduated at Cambridge Newton’s first serious original research was into various aspects of optics. This led to his first published paper:

A Letter of Mr. Isaac Newton, Professor of the Mathematicks in the University of Cambridge; Containing His New Theory about Light and Colors: Sent by the Author to the Publishee from Cambridge, Febr. 6. 1671/72; In Order to be Communicated to the R. Society

In which he described his experiments with a prism that showed that white light consists of blended coloured light and that the spectrum that one produces with a prism is the splitting up of the white light into its coloured components. Previous theories had claimed that the spectrum was produced by the dimming or dirtying of the white light by the prism. Newton wrote an extensive paper expanding on his optical research, An hypothesis explaining the properties of light, but due to the harsh criticism his first paper received he withheld it from publication. This expanded work only appeared in 1704 in his book, Opticks: A Treatise of the Reflections, Refractions, Inflections & Colours of Light. Here we can read:

In the Experiments of the fourth Proposition of the first Part of this first Book, when I had separated the heterogeneous Rays from one another, the Spectrum ptformed by the separated Rays, did in the Progress from its End p, on which the most refrangible Rays fell, unto its other End t, on which the most refrangible Rays fell, appear tinged with this Series of Colours, violet, indigo, blue, green, yellow, orange, red, together with all their intermediate Degrees in a continual Succession perpetually varying . So that there appeared as many Degrees of Colours, as there were sorts of Rays differing in Refrangibility.

This is of course the list of seven colours that we associate with the rainbow today. Before Newton researchers writing about the spectrum listed only three, four or at most five colours, so why did he raise the number to seven by dividing the blue end of the spectrum into violet, indigo and blue? He did so in order to align the number of colours of the spectrum with the notes on the musical scales. In the Queries that were added at the end of the Opticks over the years and the different editions we find the following:

Qu. 13. Do not several sorts of Rays make Vibrations of several bigness, which according to their bignesses excite Sensations of several Colours, much after the manner that the Vibrations of the Air, according to their several bignesses excite Sensations of several Sounds? And particularly do not Vibrations for making a Sensation of deep violet, the least refrangible the largest for making a Sensation of deep red, and several intermediate sorts of Rays, Vibrations of several intermediate bignesses to make Sensations of the several intermediate Colours?

Qu. 14. May not the harmony and discord of Colours arise from the proportions of the Vibrations propagated through the Fibres of the optick Nerves into the Brain, as the harmony and discord of Sounds arise from the proportions of the Vibrations of the Air? And some Colours, if they be view’d together, are agreeable to one another, as those of Gold and Indigo and other disagree.

In the An Hypothesis, Newton published a diagram illustrated the connection he believed to exist between the colours of the spectrum and the notes of the scale.

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Source: Gouk p. 118

Interestingly Voltaire presented Newton’s theory in his Elemens de la philosophie de Newton (1738), again as a diagram.

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Source: Gouk p. 119

Turning now to Newton’s magnum opus we find the even more extraordinary association between his theory of gravity and the Pythagorean theory of harmony. Newton’s Law of Gravity is probably the last place one would expect to meet with Pythagorean harmony but against all expectations one does. In unpublished scholia on Proposition VIII of Book III of the Principia(the law of gravity) Newton claimed that Pythagoras had known the inverse square law. He argued that Pythagoras had discovered the inverse-square relationship in the vibration of strings (see Mersenne above) and had applied the same principle to the heavens.

…consequently by comparing those weights with the weights of the planets , and the lengths of the strings with the distances of the planets, he understood by means of the harmony of the heavens that the weights of the planets towards the Sun were reciprocally as the squares of their distances from the Sun.[1]

Although Newton never published this theory David Gregory (1661–1708) did. David Gregory was a nephew of the physicist James Gregory who in 1684 became professor of mathematics at the University of Edinburgh, where he became “the first to openly teach the doctrines of the Principia, in a public seminary…in those days this was a daring innovation.”[2]

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Davis Gregory bust Source: Wikimedia Commons

In 1691, with Newton’s assistance, he was appointed Savilian Professor of Astronomy at Oxford going on to become an important mathematician, physicist and astronomer. He worked together with Newton on the planned second edition of the Principia, although he did not edit it, dying in 1708; the second edition appearing first in 1713 edited by Richard Bentley. In his Astronomiae physicae et geometricae elementa, a semi-popular presentation of Newton’s theories first published in Latin in 1702

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Gregory wrote the following:

The Elements of Astronomy, Physical and Geometrical By David Gregory M.D. SavilianProfessor of Astronomy at Oxfordand Fellow of the Royal Society (1615)

The Author’sPreface

As it is manifest that the Ancients were apprized of, and had discover’d the Gravity of all Bodies towards one another, so also they were not unacquainted with the Law and Proportion which the action of Gravity observ’d according to the different Masses and Distances. For that Gravity is proportional to the Quantity of Matter in the heavy Body, Lucretiusdoes sufficiently declare, as also that what we call light Bodies, don’t ascend of their own accord, but by action of a force underneath them, impelling them upwards, just as a piece of Wood is in Water; and further, that all Bodies, as well the heavy as the light, do descend in vacuo, with an equal celerity. It will be plain likewise, from what I shall presently observe, that the famous Theorem about the proportion whereby Gravity decreases in receding from the Sun, was not unknown at least to Pythagoras. This indeed seems to be that which he and his followers would signify to us by the Harmony of the Spheres: That is, they feign’d Apolloplaying on a Harp of seven Strings, by which Symbol, as it is abundantly evident from Pliny, Macrobiusand Censorinus, they meant the Sun in Conjunction with the seven planets, for they made him the leader of that Septenary Chorus, and Moderator of Nature; and thought that by his Attractive force he acted upon the Planets (and called it Jupiter’s Prison, because it is by this Force that he retains and keeps them in their Orbits, from flying off in Right Lines) in the Harmonical ration of their Distances. For the forces, whereby equal Tensions act upon Strings of different lengths (being equal in other respects) are reciprocally as the Squares of the lengths of the Strings.

I first came across this theory, as elucidated by Gregory, years ago in a book, which book I have in the meantime forgotten, where it was summarised as follows:

Gravity is the strings upon which the celestial harmony is played.

 

 

 

 

 

 

 

 

[1]Quoted from Penelope Gouk, The harmonic roots of Newtonian science, in John Fauvel, Raymond Flood, Michael Shortland & Robin Wilson eds., Let Newton Be: A new perspective on his life and works, OUP, Oxford, New York, Tokyo, ppb. 1989 The inspiration and principle source for this blog post.

[2]Quoted from Significant Scots: David Gregory

https://www.electricscotland.com/history/other/gregory_david.htm

 

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