Category Archives: History of Astronomy

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a coffee shop, surrounded by his acolytes, the original Newtonians, distributing words of wisdom and handing round his unpublished manuscripts for scrutiny.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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The emergence of modern astronomy – a complex mosaic: Part XXXIX

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

One of the most often repeated false statements in the history of science is that Isaac Newton discovered gravity. Of course he didn’t discovery it, it’s all around us. You can observe gravity every time you drop something. Making the claim more precise, by saying Newton discovered the law of gravity, doesn’t really improve the situation much. What Newton did do was he proved the law of gravity and made the fairly rational assumption based on the available evidence that this law applies universally to all bodies in the cosmos. An assumption that is not written in stone and has been questioned in the present time for the general theory of relativity, the theory that replaced the Newtonian theory of universal gravity and of which the Newtonian theory of gravity is a very good approximation for local cases. However we don’t want to take the path to modern theories of cosmology and dark matter but want to stay firmly in the seventeenth century with Newton.

We can start with a brief survey of theories of gravity before Newton. Originally gravity was the Latin term applied to Aristotle’s explanation of why, when dropped, things fall to the ground. Aristotle thought that objects did so through a form of vital attraction, returning to their natural home, consisting predominantly of the elements earth and water. Fire and air rise up. This only applied to the Earth, as things beyond the Moon were made of a fifth element, aether, the quintessence, for which the natural form of motion was uniform circular motion.

This neat model wouldn’t work, however for Copernicus’ heliocentric model, which disrupted the division between the sublunar and supralunar worlds. To get around this problem Copernicus suggested that each planet had its own gravity, like the Earth. So we have terrestrial gravity, Saturnian gravity, Venusian gravity etc. This led Alexander von Humboldt, in the 19th century, to claim that Copernicus should be honoured as the true originator of the universal theory of gravity, although it is by no means clear that Copernicus thought that he planetary gravities were all one and the same phenomenon.

The whole concept became even more questionable when the early telescopic astronomers, above all Galileo, showed that the Moon was definitely Earth like and by analogy probably the other planets too. At the end of a long line of natural philosophers stretching back to John Philoponus in the sixth century CE, Galileo also showed that gravity, whatever it might actually be, was apparently not a vitalist attraction but a force subject to mathematical laws, even if he did get the value for the acceleration due to gravity ‘g’ wrong and although he didn’t possess a clear concept of force.. Throughout the seventeenth century other natural philosophers, took up the trail and experimented with pendulums and dropped objects. A pendulum is of course an object, whose fall is controlled. Most notable were the Jesuit, natural philosopher Giovanni Battista Riccioli (1598–1671) and the Dutch natural philosopher Christiaan Huygens (1629–1695). Riccioli conducted a whole series of experiments, dropping objects inside a high tower, making a direct confirmation of the laws of fall. Both Riccioli and Huygens, who independently of each other corrected Galileo’s false value for ‘g’, experimented extensively with pendulums in particular determining the length of the one-second pendulum, i.e. a pendulum whose swing in exactly one second. As we will see later, the second pendulum played a central roll in an indirect proof of diurnal rotation. Huygens, of course, built the first functioning pendulum clock.

Turning to England, it was not Isaac Newton, who in the 1670s and 80s turned his attention to gravity but Robert Hooke (1635–1703), who was Curator of Experiments for the newly founded Royal Society. Like Riccioli and Huygens Hooke experimented extensively with dropping objects and pendulums to try and determine the nature of gravity. However his experiments were not really as successful as his continental colleagues. However, he did develop the idea that it was the force of gravity that controlled the orbits of the planets and, having accepted that comets were real solid objects and not optical phenomena, also the flight paths of comets. Although largely speculative at this point Hooke presented a theory of universal gravity, whilst Newton was still largely confused on the subject. Hooke turned to Newton in a letter with his theory in order to ask his opinion, an act that was to lead to a very heated priority dispute.

Before we handle that correspondence we need to go back to the beginnings of the 1670s and an earlier bitter dispute between the two.  In 1672 Newton announced his arrival on the European natural philosophy scene with his first publication, a letter in the Philosophical Transactions of the Royal Society (1671/72), A New Theory of Light and Colours, which described the experimental programme that he had carried out to demonstrate that white light actually consisted of the colours of the spectrum.

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Newton’s original letter. Source: Royal Society

This brilliant piece of experimental optics did not receive the universal praise that, reading it today, we might have expected, in fact it was heavily criticised and attacked. Some critics were unable to reproduce Newton’s experimental results, probably because their prisms were of too poor quality. However, others, Hooke to the fore, criticised the content. Hooke and Huygens, the two current leaders in the field of optics both criticised Newton for interpreting his results within the framework of a particle theory of light, because they both propagated a wave theory of light. Newton actually wrote a paper that showed that his conclusions were just as valid under a wave theory of light, which, however, he didn’t publish. The harshest criticism came from Hooke alone, who dismissed the whole paper stating that he had already discovered anything of worth that it might contain . This did not make Newton very happy, who following this barrage of criticism announced his intention to resign from the Royal Society, to which he had only recently been elected.  Henry Oldenburg (c. 1619–1677), secretary of the Royal Society, offered to waive Newton’s membership fees if he would stay. Newton stayed but had little or nothing more to do with the society till after Hooke’s death in 1703. Newton did, however, write a very extensive paper on all of his optical work, which remained unpublished until 1704, when it formed a major part of his Opticks.

By  1679 tempers had cooled and Robert Hooke, now secretary of the Royal Society, wrote to Isaac Newton to enquire if he would be interested in reopening his dialogue with the Royal Society. In the same letter he asked Newton’s opinion on his own hypothesis that planetary motions are compounded of a tangential motion and “an attractive motion towards the centrall body…” Hooke is here referencing his Attempt to Prove the Motion of the Earth from Observations (1674, republished 1679),

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which contains the following fascinating paragraph:

This depends on three Suppositions. First, That all Coelestial Bodies whatsoever, have an attractive or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them from flying from the, as we observe the earth to do, [here Hooke is obviously channelling Copernicus] but that they do also attract all other Coelestial Bodies that are within the sphere of their activity … The second supposition is this, That all bodies whatsoever that are put into a direct and simple motion, will so continue to move forward in a streight line, till they are by some other effectual power deflected and bent into a Motion, describing a Circle, Ellipsis, or some other more compounded Curve Line. [the principle of inertia, as propounded by Descartes] The third supposition is, That these attractive powers are so much the more powerful in operating, by how much nearer the body wrought upon is to there own Centers. Now what these several degrees are I have not yet experimentally verified…

Whether or not this is truly a universal theory of gravity is a much-debated topic, but if not, it comes very close and was moving much more in that direction than anything Newton had produced at the time. As we shall see later this was to cause not a little trouble between the two rather prickly men.

Newton declined the offer of a regular exchange of ideas, claiming that he was moving away from (natural) philosophy to other areas of study. He also denied having read Hooke’s paper but referred to something else in it in a later letter to Flamsteed. However, in his reply he suggested an experiment to determine the existence of diurnal rotation involving the usually dropping of objects from high towers. Unfortunately for Newton, he made a fairly serious error in his descripting of the flight path of the falling object, which Hooke picked up on and pointed out to him, if unusually politely, in his reply. Newton of course took umbrage and ended the exchange but he did not forget it.

In our next episode we will deal with the events leading up to the writing and publication of Newton’s great masterpiece, Philosophiæ Naturalis Principia Mathematica (1687), which include the repercussions of this brief exchange between Hooke and its author.

 

 

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

The ongoing astronomical/cosmological discussion on the nature of comets in the Early Modern Period has weaved its way continuously through our narrative. Starting with Toscanelli’s attempts to track the paths of comets, as if they were celestial objects in the mid fifteenth century, through the Europe wide discussion, amongst the leading astronomers of the period in the 1530s, leading up to the great comet of 1577 (usually called Tycho’s comet) and on to the great comet of 1618. The discussion was rekindled by two great comets in the 1660s, the great comets of 1664 (modern designation C/1644 W1)

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

and 1665 (modern designation C/1665 F1).

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The Great Comet 1665 Sigismund Trew Source: Wikimedia Commons

It would not be an exaggeration to say that there was an outbreak of comet fever amongst European astronomers.

There are surviving observational reports on the appearance and path of these comets not just from Europe but also from China, Japan and North America. The earliest reported siting for C/1664 W1 was from Spain on 17 November. Samuel Pepys, who observed it together with Robert Hooke, mentions it in his famous diary and Daniel Defoe (1660–1731) included it in his fictional account of the bubonic plague in London, A Journal of the Plague Year (1722). This comet was, of course, regarded as the harbinger of both the plague and the Great Fire of London.

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The Great Comet of 1664 from an anonymous pamphlet Source: Wikimedia Commons

Christiaan Huygens observed it in Leiden beginning on 2 December and his observations were included in a dissertation by the French astronomer, mathematician, physicist and instrument maker Pierre Petit (1594–1677). Giovanni Domenico Cassini (1625–1712), Geminiano Montanari (1633–1687) and Giovanni Borelli (1608-1679) all observed both comets in Italy, and Pierre Petit and Adrien Auzout (1622–1691) in Paris. Johannes Hevelius observed the comets in Danzig and published a report of his 1664 observations, Prodromus cometicus in 1665,

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HEVELIUS, Joannes. Prodromus Cometicus, quo Historia Cometae anno 1664. Danzig: Simon Reiniger for the author, 1665. SourceSource

and then later a book on his observations of both comets, Cometographia (1668).

The Polish theologian, historian and astronomer, Stanisław Lubieniecki (1623–1675) observed both comets from his house in Hamburg.

He corresponded with Ismäel Boulliau (1605–1694) in Paris and Henry Oldenburg (1618–1677), secretary of the Royal Society in London about the 1664 comet. In 1668 he published a three-part work on both comets, his Theatrum cometicum. Part one contained his correspondence on the topic with other European astronomers including Oldenburg, Hevelius and Athanasius Kircher (1602–1680), professor for mathematics and astronomy on the Jesuit University in Rome, including their observations. The first part also contained an impressive collection of copper plate prints of many historical comets.

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Hevelius’ drawings go the Comet tails 1665 Source

The second part consisted of criticism by other scholars of his cometary theories and his answers to his critics, whilst the third part contained his astrological interpretations, including his opinion that the Great Fire of London was a punishment from God announced by the 1664 comet.

The French Jesuit, François-Joseph Le Mercier (1604–1690), reported observing the comet of 1664 for the first time in Québec on 29 November and continued observing it until 15 January 1665. He also observed the 1665 comet from 29 March until 17 April. In New England the Puritan minister and amateur astronomer Samuel Danforth (1626–1674) observed both comets. The author of three almanacs for the years 1647, 1648 and 1649, he wrote and published a book on the comets, which is considered one of the earliest printed astronomy publication in America.

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Samuel Danforth Source

By the 1660s there was no doubt amongst astronomers that comets were supralunar bodies and that they were real solid objects and not some sort of optical phenomena. This being the case the debate that raged throughout Europe concerned the flight path that comets were thought to take. One reference work consulted by most of the participants in this discussion was Johannes Kepler’s De cometis libelli tres I. astronomicus, theoremata continens de motu cometarum … II. physicus, continens physiologiam cometarum novam … III. astrologicus, de significationibus cometarum annorum 1607 et 1618 / autore Iohanne Keplero … (1609), which was regarded as an authoritative work on the subject. Of interest is that Kepler expressed the opinion that the flight paths of comets were rectilinear and explained than any apparent curvature observed in the flight path was due to the movement of the Earth, the observation platform. Others argued that the fight paths were curved and began to reference Kepler’s laws of planetary motion to support this position.  Sir William Lower (1570–1615), friend and student of Thomas Harriot, had already suggested in a letter 1610, having read Kepler’s Astronomia Nova (1609) and based on his and Harriot’s observation of Comet Halley in 1607 that the flight path was elliptical.

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Comet Halley 1607: David Herlitz, Von dem Cometen oder geschwentzten newen Stern, welcher sich im September dieses 1607. Pub. Johann Witten, Lubeck,1607 Source

The discussion about the flight paths of comets in the 1660s can be regarded as a defining moment, together with Nikolaus Mercator’s reformulation of Kepler’s second law in 1664, for the acceptance of Kepler’s elliptical heliocentric model of the cosmos over its rival the Tychonic geo-heliocentric model. This of course didn’t happen overnight but 1664 can be regarded as the turning point in the battle of the systems.

In the 1660s opinions varied. Some, such as Christopher Wren (1632–1723) Savillian Professor of astronomy at Oxford, and John Wallis (1616–1703) Savillian Professor of geometry at Oxford, stuck to the traditional rectilinear flight paths, whilst others suggested various curved flight paths ranging from circles over parabolas to ellipses. Cassini had already, in a work about comets from the 1650s, following the Tychonic theory, committed to circular orbits a view he maintained based on his observations of the 1664 comet. Auzout in Paris voted for ellipses, as did Hevelius. Borelli criticised both Cassini and Auzout and suggested that the flight paths were parabolas.

Danforth’s account is interesting because it comes very close to being the current accepted view of comets. In his An Astronomical Description of the Late Comet or Blazing Star; As it appeared in New-England in the 9th, 10th, 11th, and in the beginning of the 12th Moneth, 1664. Together with a Brief Theological Application thereof (1665) he states that comets are supralunar bodies, that the bright tail was sunlight reflected off exhalations from the head of the comet and the tail always points away from the sun. He thought that its flight path was possibly an ellipse but in this case he was wrong. Modern calculations suggest that both the 1664 and 1665 are either extremely long period elliptical comets or had parabolic flight paths and were thus not periodic. Although the proof that some comets were, in fact, periodical still lay in the future some astronomers already speculated in the 1660s that this was the case. Robert Hooke, for example, thought the 1664 comet was a return of the 1618 great comet, whilst Cassini speculated that the comets of 1577, 1665 and 1680 were periodical.

In 1664, Isaac Newton (1642–1726 os) was still an undergraduate student at Cambridge University. Up till then an indifferent student in 1664 he had embarked on a six-year period of study in mathematics and natural philosophy that would lay the foundations for his life’s work. To record the results of his reading in natural philosophy he started a notebook that he had titled, Questiones quaedam Philosophicae. On 29 December 1664 and on the following day he made and entered observations of a comet. On 31 August 1726, in a conversation with John Conduitt (1688-1737) he mentioned his extended observations of this comet. Another Cambridge student, Nicholas Wickins, who shared chambers with Newton at that time, told Conduitt, “He sate up so often long in the year 1664 to observe a comet that appeared then.” This is probably Newton’s first activity as an astronomer. As we shall see, comets and their orbits would come to play an important roll in Newton’s future theory of universal gravitation and in his magnum opus, the Principia.

 

 

 

 

 

 

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Galileo sources: a starter kit

Following my last post, numerous people have asked me for book recommendations on Galileo and his opponents. What follows is a list of books that I have and have consulted to create my Galileo. I should add that over the years I have also read a cartload of academic papers on Galileo and related topics. What I list here is only a small fraction of the available literature on the topic. My friend Pierre, the editor of the Simon Marius book, who is a real Galileo expert, I’m not, has currently 1514 items listed in his Galileo bibliography and even that is only a small fraction.

L. Heilbron, Galileo, OUP, 2010

David Wootton, Galileo: Watcher of the Skies, Yale University Press, 2010

Mario Biagioli, Galileo Courtier: The Practice of Science in The Culture of Absolutism, University of Chicago Press, 1993

Mario Biagioli, Galileo’s Instruments of Credit: Telescopes, Images, Secrecy, University of Chicago Press, 2006

William R. Shea & Mariano Artigas, Galileo in Rome: The Rise and Fall of a Troublesome Genius, OUP, 2003

Maurice A. Finocchiaro, On Trial for Reason: Science, Religion, and Culture in the Galileo Affair, OUP, 2019

 

Galileo Galilei, trans. Albert van Helden, Sidereus Nuncius or The Sidereal Messenger, University of Chicago Press, 1989

Galileo Galilei, trans. Stillman Drake, Dialogue Concerning the Two Chief World Systems, University of California Press, 1967

Galileo Galilei, trans. Henry Crew & Alfonso de Salvio, Dialogues Concerning Two New Science, Dover, 1954

Discoveries and Opinions of Galileo, translated with an Introduction and Notes by Stillman Drake, Anchor Books, 1957. (Starry Messenger, Letter to the Grand Duchess Christina, plus excerpts from Letters on Sunspots & The Assayer)

The Essential Galileo, Edited and Translated by Maurice A. Finocchiaro, Hackett Publishing Company, 2008

Galileo on the World Systems: A New Abridged Translation and Guide, Maurice A. Finocchiaro, University of California Press, 1997

Galileo Galilei & Christoph Scheiner, On Sunspots, Translated and Introduced by Eileen Reeves & Albert van Helden, University of Chicago Press, 2010

Eileen Reeves, Galileo’s Glassworks: The Telescope and the Mirror, Harvard University Press, 2008

Massimo Bucciantini, Michele Canmerota, Franco Giudice, Galileo’s Telescope’s: A European Story, Harvard University Press, 2015

James M Lattis, Between Copernicus and Galileo: Christoph Clavius and the Collapse of Ptolemaic Cosmology, University of Chicago Press, 1994

Franz Daxecker, Der Physiker und Astronom Christoph Scheiner, Universitätsverlag Wagner, 2006 (I don’t know of anything good on Scheiner in English)

Christopher M Graney, Setting Aside All Authority: Giovanni Battista Riccioli and the Science against Copernicanism in the Age of Galileo, University of Notre Dame Press, 2015

Mordechai Feingold, Jesuit Science and the Republic of Letters, MIT Press, 2002

Hans Gaab & Pierre Leich eds., Simon Marius and His Research, Springer, 2018

 

 

 

 

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How to create your own Galileo

Writing this book review caused me a great deal of of stress, even leading to sleepless night when I made the mistake of reading the offending piece of literature as bedtime reading. The review itself has become horrendously long and I must at times fight my instinct to add even more explanations, as to why this or that was wrong. It is in the words of that excellent history of science author, Matthew Cobb, ‘baggy and rambling’ and should actually be radically edited but I just can’t be arsed to do it, so I’m simply posting the whole monstrosity. For those, who don’t want to read the whole thing, and I wouldn’t blame you, the first three and the last five paragraphs offer a sort of synopsis of the whole thing.

Since I began writing book reviews on a more regular basis I have tried only to review books that I personally find good and which I think might be of interest to those who come here to read my weekly scribblings. I decided that on the whole it isn’t worth wasting time and energy writing about uninteresting, mediocre or simply bad books. However, occasionally a book come along that I feel duty bound, given my reputation as a #histSTM grouch, to debunk as a favour to my readers so that they don’t waste their time and energy reading it; today’s review is one such.

Some time back I wrote a post about the Alexandrian mathematician and philosopher Hypatia, which started with the fact that she has been used as a sort of blank slate onto which numerous people down the centuries have projected their images of what they would have wanted her to be. In the case of Hypatia this is fairly easy, as the rest of my post pointed out we know next to nothing about the lady. Another figure, who has been used extensively over the years as a silhouette, which people fill out according to their own wishes is Galileo Galilei; in his case this is more difficult as we actually know an awful lot about the Tuscan mathematician’s life and work. However, this has not prevented numerous authors from creating their own Galileos.

The latest author, who has decided to present the world with his Galileo, is the astrophysicist and very successful author of popular books on mathematics and science, Mario Livio with his Galileo and the Science Deniers.[1] I might not have bothered with this book but Livio is a very successful pop science book author, as is made very clear by the fact that the hardback and paperback were both issued simultaneously and at very low prices; the publishers expect it to sell well, so it will unfortunately have a big impact on uninformed peoples perceptions of Galileo. I say unfortunately, which, of course, gives readers of this review a very strong clue as to what I think of this book. Quite simply don’t bother, it brings nothing new to our knowledge of Galileo and in fact is full of, at times, quite serious historical errors, serious that is if you’re a historian, who takes getting the facts right seriously.

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The opening sentences starts with a couple of wonderful errors and also lays out Livio’s version of Galileo:

Being an astrophysicist myself, I have always been fascinated by Galileo. He was, after all, not only the founder of modern astronomy and astrophysics–the person who turned an ancient profession into the universe’s deepest secrets and awe-inspiring wonders–but also a symbol of the fight for intellectual freedom.

I think Copernicus, Tycho Brahe and Johannes Kepler might want a word with Livio about, who exactly is the founder of modern astronomy. Also, excuse the language, but what the fuck did Galileo ever do for astrophysics? The final half sentence tells us into which silhouette Livio has decided to pour his Galileo; Livio’s Galileo is the white knight of freedom of speech and freedom of thought, who has mounted his charger and taking up his lance sets off to kill the anti-science dragon of the Holy Roman Catholic Church. This is, of course not a new Galileo but a well-known old model, which historians of science have spent a lot of time and effort dismantling over the last fifty plus years.

Central to the problems with Livio’s book is that he completely ignores the historical context in which the Galileo story took place. His is totally a presentist view in which he applies the social rules and moral judgements of the twentieth-first century to the various occurrences he sketches in the early seventeenth century. This is quite simply very bad historiography. He compounds this error by trying to draw parallels between Galileo’s conflict with the Catholic Church and the current problems with science denialists in our times, hence the title of his book. To do this he simply denies Galileo’s critics any scientific basis for their criticism whatsoever, Galileo is science, his critics are anti-science. A rather simplistic and historically highly inaccurate presentation of the known facts.

Just to make clear what exactly the historical context was, there existed no freedom of speech or freedom of thought under any civil or religious authority anywhere in Europe at the beginning of the seventeenth century; such social concepts still lay in the future. There is a slight irony in the fact that the current wave of science denialists, against whom Livio’s book is directed, are in fact exercising their, protected by law, rights of freedom of thought and speech. More importantly the Holy Roman Catholic Church was not just a religion and a church but also a powerful political and judicial body with judicial rights over all within its dominion and this in an age of absolutism with the Pope as the most absolute of all absolute rulers. All authorities both civil and religious reserved for itself the right to determine what its subject were permitted to express in public, the Catholic Church was in no way unique in claiming and exercising this right.

Still in the preface to Livio’s book we find his first distortion of the historical scientific facts, he writes that Galileo’s telescopic discoveries, “All but destroyed the stability of the Earth-centered Ptolemaic universe.” Here Livio, and not only here, fails to differentiate between Aristotelian cosmology and Ptolemaic astronomy. All of the telescopic discoveries, with the exception of the phases of Venus, demolished aspects of Aristotelian cosmology but had no significance for Ptolemaic geocentric astronomy. The discovery of the phases of Venus, of course, refuted a pure geocentric system but was perfectly compatible with a Tychonic geo-heliocentric system, which then became the default alternative to a heliocentric system. With two notable exceptions that I will deal with later Livio makes no clear mention of the fact that the telescopic discoveries were made within the same approximately three year period not only by Galileo but simultaneous by others, so if Galileo had never used a telescope it would have made very little difference to the subsequent history of astronomy. This makes rather a mockery of Livio’s next dubious claim, “his [Galileo’s] ideas became the basis on which modern science has been erected.” This is much less true than Livio and other Galileo groupies would have us believe. Galileo made a contribution but others in the seventeenth century actually contributed significantly more.

One last comment from the preface, Livio writes:

He insisted on publishing many of his scientific findings in Italian [actually Tuscan not Italian] (rather than Latin), for the benefit of every educated rather than for a limited elite.

In the early seventeenth century almost every educated person would per definition have been able to read and write Latin; Latin was the default language of education.

Reading the opening chapter of Livio’s book, Rebel with a Cause, I constantly had the feeling that I had been transported back to the 1960s and 70s, when I first began to read books about the history of science in general and Galileo in particular. It as if the last fifty plus years of history of science research had never taken place, he even relies on Einstein and Bertrand Russell as his historical authorities, at times I shuddered. He goes so far as to tell us that the Renaissance happened because people discovered that they were individuals! I can’t remember when I last read this particular piece of inanity and I would be curious who actually put it into the world. The final page of this chapter contains all of the classic Galileo clichés.

Perhaps most important, Galileo was the pioneer and star of advancing the new art of experimental science. He realised that he could test or suggest theories by artificially manipulating various terrestrial phenomena. He as also the first scientist whose vision and scientific outlook incorporated methods and results that were applicable to all branches of science.

There is a long historical list of people who would disagree–Archimedes, Ptolemaeus, al-Haytham, Grosseteste, Roger Bacon, William Gilbert and a whole host of alchemists starting with Abū Mūsā Jābir ibn Hayyān (for Livio opinion on alchemy see below)–just to name the most prominent. Modern research has also conclusively shown that artisanal practice in the fifteenth and sixteenth centuries played a significant role in the development of empirical, experimental science. Livio’s last sentence here is also rather dubious, apart from some rather trivial aspects, there are no methods and results that are applicable to all branches of science.

…in four areas he revolutionised the field: astronomy and astrophysics; the laws of motion and mechanics; the astonishing relationship between mathematics and physical reality […]; and experimental science.

Despite everything, Galileo’s contributions to astronomy were rather minimal and he certainly didn’t revolutionise the field, others such as Kepler, whom he ignored, did. I am still trying to work out what his contributions to astrophysics could possibly be? His real major contribution was indeed to motion and mechanics but he was no means alone in this others such as Simon Stevin and Isaac Beeckman made substantial contributions to the new developments in these areas. The mathematics thing, to which Livio keeps returning, is baloney and I shall deal with it separately later. Galileo made contributions to the development of experimental science but he was by no means alone in this and to say he revolutionised it is hyperbole.

The only defense remaining to those obstinately refusing to accept the conclusions implied by the accumulating weight of empirical facts and scientific reasoning was to reject the results almost solely on the basis of religious or political ideology

Here Livio betrays his own tactic, put crudely, throughout the book he twists the historical facts in order to try and make out that there no legitimate scientific objections to Galileo’s claims, however there were.

The next chapter is the usual enthusiastic fan boy description of Galileo’s talents as an all round humanist and contains nothing particularly objectionable but does contain a strong indication of the superficiality of Livio’s historical knowledge. He writes, “First, at age twenty-two, Galileo, already had the chutzpah to challenge the great Aristotle on topics related to motion…” People had been consistently challenging the great Aristotle on topics related to motion since the sixth century CE and Galileo was merely joining a long tradition of such work. Livio also casually calls Aristotle’s theory of motion impetus! Impetus was, of course, a theory initially developed by John Philoponus in the sixth century CE when seriously challenging Aristotle’s theory of motion. On a side note Livio says that the tools to treat such variables such as velocity and acceleration, i.e. calculus, were first developed by Newton and Leibniz. Other seventeenth century mathematicians who contributed substantially to the development of the calculus such as Cavalieri, de Saint-Vincent, Fermat, Pascal, Descarte, John Wallis and Isaac Barrow would be very surprised to hear this. On the same page he repeats the myth that Christoph Clavius was “the senior mathematician on the commission that instituted the Gregorian calendar, he wasn’t, Ignazio Danti was.

Clavius turns up as one of the leading mathematicians, who the young Galileo turned to for mentorship when he was trying to establish a reputation as a mathematician and get support to find an appointment as professor of mathematics. Interestingly Galileo’s other mentor Guidobaldo del Monte (1545–1607) appears nowhere in Livio’s book. This is strange as it was del Monte, who acquired the professorship in Pisa for Galileo through his brother Cardinal Francesco Maria del Monte (1549–1627), who was the de ‘Medici cardinal and recommended Galileo to the Grand Duke. It was also del Monte, who devised the experiment that led Galileo to the parabola law, which Livio calls one of Galileo’s crowning achievements.

In the next chapter on Galileo’s work on the theory of fall Livio can’t help taking a sideswipe at alchemy and astrology:

It is certainly true that, at their inception, the sciences were not immune to false beliefs, since they are sometimes connected to fictitious fields such as alchemy and astrology. This was partly the reason why Galileo decided later to rely on mathematics, which appeared to provide a more secure foundation.

This off hand rejection ignores completely that astrology was the main driving force behind astronomy since its beginnings in antiquity down to the seventeenth century and that all the leading Renaissance astronomers, including Galileo, were practicing astrologers. The practice of astrology/astronomy, of course, requires a high level of mathematical ability. Alchemy developed virtually all of the experimental methods and the necessary equipment to carry out those experiments on which chemistry was built.

Now in Padua, where Galileo was also professor of mathematics, a position that he once again acquired with the assistance of del Monte, we get the story of Galileo’s three lectures on the nova of 1604. Livio informs us that “Christoph Clavius confirmed the null parallax determination–that is, no shift had been observed–but refused to accept its implications as compelling.”

This is once again Livio’s tactic of trying to discredit the Jesuits. The implications that he is talking about are that the heavens are not unchanging as claimed by Aristotle. Clavius observed the nova of 1572 and already in 1581 published a digression on the subject fully accepting that the nova was supralunar and that the heavens were not unchanging. He included this in his Sphaera in 1585, the most widely read astronomy textbook in the late sixteenth and early seventeenth centuries and he probably thus had the most influence in persuading others that change had occurred in the heavens. He also included the same results for the novae of 1600 and 1604, so what is Livio talking about? Clavius was unable to explain what these novae were but then again nobody else in the seventeenth century could either.

We now move on to Galileo, telescopic astronomy and the Sidereus Nuncius. Although he actually talks about other telescopic astronomers–Scheiner, Marius, Harriot, Fabricius–they are only offered bit parts in Livio’s screenplay, which follows the usual path of giving Galileo credit for everything. He attributes the discovery of Earthshine, the Moon illuminated by sunlight reflected by the Earth, to Galileo, whereas it was previously discovered by Leonardo, who didn’t publish, and Michael Mästlin, who did. He attributes the discovery of stars that can’t be seen without a telescope to Galileo, whereas this was already noted in the printed account of the first telescope demonstration in Den Hague, the source of Sarpi’s and thus Galileo’s first knowledge of the telescope. We then get one of the most bizarre claims made by Livio in the book:

Even more consequential for the future of astrophysics was Galileo’s discovery that stars varied enormously in brightness, with some being a few hundred times brighter than others.

Coming from a professional astrophysicist I find this statement mind boggling. The difference in brightness between celestial objects is obvious to anybody with reasonable eyesight, who simply looks up at the night sky in an area without light pollution. Astronomers even use a six-point scale to designate the different levels of brightness, which is termed magnitude; this was first introduced by Ptolemaeus around 150 CE!

We then get a very brief account of the star size argument as originated by Tycho, which Livio falsely claims Galileo dismissed by saying that the observed star discs are merely artefacts. They are in fact merely artefacts but Galileo didn’t say this. He accepts their existence and uses a completely different argument to try and dismiss the star size argument.

We now arrive at the Moons of Jupiter and Simon Marius. Livio mentions Marius several times in his book but insists on calling him Simon Mayr, his birth name, why? Marius issued all of his publications under the Latinised version of his name and so historian refer to him as Simon Marius. Livio doesn’t call Copernicus, Kopernik or Tycho, Tyge their birth names, so why does he call Marius, Mayr? What he writes about Marius and the Moons of Jupiter left me, as a Marius expert, totally flabbergasted:

What would have undoubtedly annoyed Galileo no end is that the Galilean satellites are known today by the names assigned to them by the German astronomer Simon Mayr rather than as the “Medici stars.” Mayr may have independently discovered the satellites before Galileo, but he failed to understand that the moons were orbiting the planet. [my emphasis]

First off, the names were suggested by Kepler not Marius, who however first published them specifically mentioning the fact that they were suggested by Kepler. Secondly Marius discovered the moons, famously, one day later than Galileo, any confusion about who discovered what when being produced by use of different calendars, Gregorian and Julian. Thirdly, the clause that I have emphasised above is pure and utter bullshit. Marius knew very well that the moons orbited Jupiter and he calculated the orbits, calculations that he published before Galileo. Marius’ calculations are also more accurate than those of Galileo. Should Livio doubt any of this I can send him scans of the relevant pages of Mundus Jovialis in the original Latin or in German and/or English translation. Livio now brings the story of Galileo hating Marius because he accused him of being behind Baldessar Capra’s plagiarism of Galileo’s proportional compass pamphlet in 1606. Marius had been Capra’s mathematics teacher earlier in Padua. Livio fails to mention that the accusations are provably false. Galileo in 1607 had himself cleared Marius of any involvement in the case and the whole episode took place a year after Marius had left Padua.

We now move on to the peculiar shape of Saturn and the discovery of the phases of Venus. In the later case we get absolutely no mention that the phases of Venus were discovered independently by Harriot, Marius, and the astronomers of the Collegio Romano, the latter almost certainly before Galileo. Livio notes correctly that the discovery of the phases definitively refutes the possibility of a pure geocentric system. However, it does not refute a geo-heliocentric Tychonic system. Livio admits this very grudgingly:

…but could not definitely dispose of Brahe’s geocentric-heliocentric compromise […]. This left a potential escape route for those Jesuit astronomers who were still determined to avoid Copernicanism.

Throughout his book Livio tries to imply that there is no real justification for supporting the Tychonic system, whereas it was not only the Jesuits, who did so but many other astronomers as well because the empirical evidence supported it more that a heliocentric one, of which more later. However, Livio consistently ignores this fact because it doesn’t fit his fairy-tale narrative.

Livio deals fairly conventionally with the telescopic discovery of sunspots and the discussion on their nature between Galileo and Christoph Scheiner and although he ends his account by noting the publication of Scheiner’s Rosa Ursina sive Sol (1626–1630) he makes no mention of the fact that the book is a masterpiece of astronomy, far better than anything Galileo published in the discipline. As should always be noted, due to the haste in which he wrote and published it, Sidereus Nuncius was closer to a press report than a scientific publication. He does however mention, what he calls “some further comments he made later in the book The Assayer, which the Jesuit astronomer took to be directed at him personally, did turn him into an unappeasable enemy.” Galileo actual vehemently and totally falsely accused Scheiner of plagiarism in The Assayer, which he later compounded by plagiarising Scheiner’s work in his own Dialogo. Scheiner’s antagonism is understandable. We now get the real reason why Livio keeps badmouthing the Jesuits; he sees them as behind Galileo’s trial in 1633. He writes, “This marked just the beginning of a conflict with the Jesuits, which would culminate in the punitive actions against Galileo in 1633.” This is an old myth and quite simply not true, the Jesuits did not come to Galileo defence but they were also not responsible for his trial.

We now come to objections to the telescopic discoveries:

How could anyone be sure that what Galileo was seeing was a genuine phenomenon and not a spurious artifact produced by the telescope itself?

Not only wasn’t there a convincing theory of optics a that could demonstrate that the telescope doesn’t deceive, they contended but also the validity of such a theory in itself based on mathematics, was questionable. [my emphasis]

 

Livio tries to imply that both objections are just anti-science nit picking but they are in fact very solid, very necessary scientific question that had to be asked and to be answered if people were going to accept the validity of the telescopic discovery. To the first general objection, although Galileo, an excellent observer, made none himself, there were numerous cases of published discoveries that turned out to be merely optical artefacts in the early years of telescopic astronomy. Not really surprising given the really poor quality of the instruments being used, Galileo’s included.

That an optical theory of the telescope didn’t exist was a very serious problem, as it would be with any new scientific instrument. If you can’t explain how the instrument works how do you expect people to accept the results? Kepler solved the problem with his Dioptrice published in 1611, which explained fully and scientifically how lenses and lens combinations function, describing various different types of telescope. Galileo dismissed and mocked, what is now regarded as a milestone in the history of geometrical optics. The last clause is, once again, Livio spouting total crap. Theories of optics had been geometrical, i.e. mathematical, since at least, in the fourth century BCE and even Aristotle classified optics as one of the mixed sciences, i.e. those such as astronomy that are dependent on mathematics for their proofs. Kepler’s book was accepted by all those qualified to pass judgement on the matter, with the notable exception of Galileo, who didn’t want to share the limelight with anybody, and together with Kepler’s earlier Pars Optica (1604) formed the foundations of modern scientific optics.

The reference to mathematics here is Livio’s attempt to create or propagate a myth that before Galileo, nobody conceived of a mathematics-based science. It is time to tackle that myth. Livio argues that Aristotle rejected mathematics in science and that Aristotelians regarded anything proof based on mathematics as not valid. He, of course, finds an obscure Aristotelian contemporary of Galileo’s to quote to prove this but does not quote any evidence to the contrary or even appear to think that some might exist. He is very wrong in this. Because, in Aristotle’s opinion, mathematics does no deal with the real world the results of mathematic are not episteme or scientia or as we would say knowledge. He however makes allowances for the so-called mixed sciences, astronomy, optics and statics. Livio acknowledges this status for astronomy but argues with the medieval Aristotelians that astronomical mathematical models are mere calculating devices and not models of reality; describing cosmological reality was the domain of the philosophers and not the mathematical astronomers. He also claims that this was still the situation in the second decade of the seventeenth century, it wasn’t. Beginning with Copernicus astronomers began to claim that their mathematical models were models of reality and by the time of Galileo’s first dispute with the Catholic Church this had become the generally accepted state of the discipline. The debate was which mathematical model describes the real cosmos?

It is a standard cliché in the history of science that one of the major factors that drove the so-called scientific revolution was the mathematization of science. Like many clichés there is more that a modicum of truth in this claim. Livio believes it is absolutely central and one of the major themes of his book is that Galileo was the first to mathematize science in his experiments on motion and the laws of fall. This is quite simply not true and Livio can only maintain his claim by steadfastly ignoring the history of mathematics in science prior to Galileo or did he even bother to look if there was any?

Starting with Galileo’s researches into motion and fall there is a three hundred year history of experimental and mathematical investigation into exactly this area starting with the Oxford Calculatores, who derived the mean speed theorem, which lies at the heart of the laws of fall and going down to Giambattista Benedetti (1530–1590), who produced all of the arguments and thought experiments on the subject for which Galileo is famous. There is much more, which I have already dealt with in an earlier post and won’t repeat here.Galileo knew of all of this work. The Archimedean renaissance in mathematics and the sciences, replacing the authority of Aristotle with that of Archimedes, in which Galileo is a major figure, does not start with Galileo but goes back at least to Regiomontanus (1436–1476).  The works of Archimedes were edited by Thomas Venatorius (1488–1551) and printed and published in a bilingual Greek and Latin edition in Basel in 1544. In general the sixteenth century saw a massive increase in the application of mathematics to a wide range of subjects, a development that was already well underway in the fifteenth century, including linear perspective in art, cartography, surveying, navigation, physics and astronomy. Galileo in no way started the mathematization but represents, together with several of his contemporaries such as Johannes Kepler, Simon Stevin, Christoph Clavius and Isaac Beeckman, a temporary high point in these developments. All four of those contemporaries were actually better mathematicians than Galileo.

On the question of the epistemological status of mathematical proofs, which Livio clearly states was still doubted in Galileo’s time, Christoph Clavius, who many people don’t realise was an excellent epistemologist, had already changed perceptions on this when Galileo was still a child. Clavius a Jesuit and thus by definition a Thomist Aristotelian used Aristotle’s own arguments to demonstrate that mathematical proofs have the same epistemological status as philosophical proofs. He even went to the extent of translating parts of the Elements of Euclid into Aristotelian syllogisms to show that mathematical proofs transport truth in the same way as philosophical, logical ones. Clavius’ influence was massive, he fought to get mathematics accepted as part of the educational reform programme of the Jesuits and then got the mathematical sciences established as a central part of the curriculum in Catholic schools, colleges and university also training the necessary teachers to carry out his programme. There is a reason why the young Galileo turned to Clavius, when seeking a mentor for his mathematical ambitions.

Taking all of this together the roll of mathematics and status of mathematical proofs in the sciences was very different in the early seventeenth century than the picture that Livio serves up. Far from being ground breaking Galileo’s (in)famous quote from The Assayer  “the book of nature is written in the language of mathematics” (which Livio offers up several times in his book) was actually stating a truth that had been generally accepted by many natural philosophers and mathematicians for many decades before Galileo put pen to paper.

Returning to Galileo’s telescope discoveries, Livio tells us that Kepler published his letter praising Galileo’s telescopic discoveries under the title Dissertio cum Nuncio Sidero (1610) then goes on to write: “Galileo was clearly pleased with its content, the letter was reprinted in Florence later in the year.” What Livio neglects to mention is that Galileo was responsible for that edition in Florence, which was a pirate edition published without Kepler’s knowledge and without his permission or consent. Livio makes it appear that the Jesuit astronomers of the Collegio Romano only reluctantly started to try and confirm Galileo’s discoveries and then only when ordered to do so. This is a complete distortion of what actually happened.

The astronomers in the Collegio Romano had their own telescopes and had been making astronomical telescopic observations well before Galileo published the Sidereus Nuncius. They immediately leapt on the pamphlet and set out to try and confirm or refute his observations. They had some difficulties constructing telescopes good enough to make the necessary observations and Christoph Grienberger (1561–1636), who was acting head of the school of mathematics due to Clavius’ advanced age, corresponded with Galileo, who provided copious advice and tips on observing and telescope construction. This was a work of friendly cooperation under fellow mathematicians. After some difficulties they succeeded in providing the necessary confirmation, which they made public and celebrated by throwing a banquet for Galileo when he visited Rome in 1611. As already stated above the Jesuit astronomers probably observed the phases of Venus before Galileo.

Livio then goes on to draw parallels with the fact that, “The current debate on global warming had to go […] through a similar painful [my emphasis] type of confirmation process.” I find this statement, quite frankly, bizarre coming from a scientist. All scientific discoveries have to be independently confirmed by other scientists, it is a central and highly important part of the whole scientific process. What the astronomers of the Collegio Romano did for Galileo was in no way “painful” but a necessary part of that scientific process for which Galileo was very thankful. I find it particularly bizarre given the very lively current debate on the significant number of scientific papers that have to be retracted because of failing confirmation. Reading Livio in the worst possible light, and not just here but at numerous other points in his narrative, he seems to be saying, if Galileo says it is so, then it must be true and anybody, who dares to criticise him, is in the wrong.

Of course, Livio cannot avoid the myth that, “First Copernicus and Galileo removed the Earth from its central position in the solar system.” Having previously quoted the “Copernicus principle”: the realisation that the Earth, and we human beings, are nothing special…” Also: “ What’s more the Copernican system was bound to be at odds with a worldview that had placed humans at the very center of creation, not only physically but also as a purpose and focus of for the universe’s existence.” Although geometrically central, the philosophers and astronomers in the Renaissance did not regard the Earth’s position as central in any special way. It was far more the bottom, the dregs of the universe. Trying to move the Earth into the heavens was moving it into an exalted place. At least Livio is honest enough to admit that Galileo remained blind to Kepler’s work, although Livio reduces it to just the discovery of elliptical orbits, whereas Kepler actually contributed more to modern astronomy than Copernicus and Galileo together.

Livio now moves on to Galileo’s entry into theology and his Letter to Castelli. As with all Galileo apologists, whist admitting that Galileo was trespassing in the territory of the theologians, he thinks that Galileo was right to do so and what he wrote was eminently sensible and should have been acknowledged and accepted. What Galileo did struck at the vey heart of the Reformation/Counter Reformation dispute that had been raging in Europe for one hundred years and just three years later would trigger the Thirty Years War, which devastated central Europe and resulted in the death of somewhere between one and two thirds of the entire population. The Catholic Church had always claimed that they and only they were permitted to interpret Holy Scripture. Luther claimed in opposition to this that every man should be allowed to interpret it for themselves. This led to schism and the Reformation. The Catholic Church confirmed, with emphasis, at the Council of Trent that only the Church’s own theologians were permitted to interpret the Bible. Now along comes a mere mathematicus, the lowest rang in the academic hierarchy, and cheerfully tells the theologians how to interpret the Holy Writ. The amazing thing is that they didn’t simply throw him into a foul dungeon and throw away the key.  I mentioned earlier that the Church was a judicial organ and the decisions of the Council of Trent were binding laws on all Catholics. Galileo knowingly and very provocatively broke that law and got mildly and unofficially admonished for doing so. Whatever a modern observer may think about the quality of Galileo’s theological arguments is completely irrelevant, it’s the fact that he made them at all that was the offence. However, in doing so he together with Foscarini provoked the Church into taking the heliocentric hypothesis under the microscope. He had been warned, as early as 1613, by various friends including Cardinal Maffeo Barberini, the future Pope Urban VIII not to do so.

Livio thinks that because he finds Galileo’s arguments in the Letter to Castelli reasonable and ‘because of science’ that the Catholic Church should have cut Galileo some slack and let him reinterpret the Bible. The Catholic Church should abandon their exclusive right to interpret Holy Writ, one of the fundaments of their entire religion, so that a nobody, and despite his celebrity status, in the grand scheme of things Galileo was a nobody, could promote an unproven astronomical hypothesis! This is the same exclusive right for which the same Church was prepared to engage in one of the most devastating wars in European history, just three years later. In his pseudo-historical narrative Livio has here completely lost touch with the historical context.  In fact Livio is not writing history at all but making presentist moral judgements with hindsight.

There is another bizarre statement by Livio where he writes:

All this notwithstanding, however, the Church might have still accommodated (albeit with difficulty) a hypotheticalsystem that would have made it easier for mathematicians to calculate orbits, positions, and appearances of planets and stars as long as such a system could be dismissed as not representing a true physical reality. The Copernican system could be accepted as a mere mathematical framework: a model invented so as to “save the appearances” of astronomical observations–that is, to fit the observed motion of the planets.

I am frankly baffled by this paragraph because that is exactly what the Church did in fact do. They fully accepted heliocentricity as a hypothesis, whilst rejecting it as a real physical description of the cosmos. This is shown very clearly by their treatment of Copernicus’ De revolutionibus, which unlike Kepler’s books, for example, was not placed on the Index of forbidden books but was only placed on it until corrected. This correction was carried out by 1620 and consisted only of changing or removing the comparatively few statement in the book claiming that heliocentricity was a real physical description of the cosmos. From 1621 Catholics were free to read the now purely hypothetical De revolutionibus. Livio relates all of this fairly accurately and then drops another clangour. He writes:

In reality, the modifications introduced by Cardinal Luigi Caetani and later by Cardinal Francesco Ingoli were indeed relatively minor and the publication of the revised version was approved in 1620. However, the new edition never reached the press, and so Copernicus’s book remained on the Index of Prohibited Books until 1835!

This is once again complete rubbish. The Catholic Church never intended to publish a new or revised edition of De revolutionibus. What they did was to issue the list of corrections deemed necessary and every Catholic owner of the book was expected to carry out the corrections in the own copies themselves. Quite a few obviously did and we have a number of surviving copies, including Galileo’s own private copy, with the corrections carried out according to the issued instructions. Interestingly almost all of the thus censored copies are in Italy or of Italian provenance, it seems that Catholics outside of Italy didn’t take much notice of the Vatican’s censorship order. De revolutionibuswas of course removed from the Index in 1620 having been corrected. Also, I know of no case of anyone being prosecuted for reading or owning an uncensored copy of the book.

Livio tries to counter the argument that I have presented above that Galileo was admonished because he meddled in theology by claiming that the motivation was one of anti-science. Livio. “[They] were trying only to convince Galileo not to meddle in theology, as a few modern scholars have concluded.” To counter this he brings statements from Grienberger and Bellarmino saying that elements of Copernicus theory contradict passages of Holy Writ. He writes:”[they] were quite intent on crushing the Copernican challenge as a representation of reality because, from their perspective, they were vindicating the authority of Scripture in determining truth.” Dear Dr Livio that is theology! As Bellarmino wrote in his letter to Foscarini, if a contradiction exists between Holy Writ and a proven scientific fact, the heliocentric hypothesis was of course at this point in time no where near being a proven scientific fact, then the theologians have to very carefully considered how to reinterpret Holy Writ; that is what theologians do!

This brings us to Roberto Bellarmino famous letter to Paolo Antonio Foscarini. Foscarini, a monk, had written a book defending heliocentricity and reinterpreting the Bible in a similar way to Galileo. Criticised, he sent his book to Roberto Bellarmino for his judgement; he hoped it would be favourable. The title contains the word Pythagorean, so Livio explains that the Pythagoreans thought Earth etc. orbited a central fire, therefore the comparison with Copernicus’ theory. Livio then writes, “Greek philosopher Heraclides of Pontus added, also in the fourth century BCE that the Earth rotated on its axis too…” As far as can be determined Heraclides proposed diurnal rotation in a geocentric system and not in a heliocentric or Pythagorean one.

Livio goes into a lot of detail about Foscarini’s text and Bellarmino’s letter but I will only mention two points. Livio quotes the paragraph that I have already paraphrased above, “…if there were a true demonstration that the sun is at the center of the world and the earth in the third heaven, and that the sun does not circle the earth but the earth circles the sun, then one would have to proceed with great care in explaining the Scriptures that appear contrary, and say rather that we do not understand them, than what is demonstrated is false.” Livio adds, “But I will not believe that there is such a demonstration, until it is shown me. Nor is it the same to demonstrate that by supposing the sun to be at the center and the earth in heaven one can save the appearances, and to demonstrate that in truth the sun is at the center and the earth in the heaven; for I believe the first demonstration may be available, but I have very great doubts about the second, and in case of doubt one must not abandon the Holy Scripture as interpreted by the Holy Fathers.”

This is of course eminently sensible and rational. If you want me to accept you scientific theory then show me the proof! Livio doesn’t accept this and goes of into a long diatribe, which demonstrates his own prejudices rather more than any faults in Bellarmino’s logic. He then comes with a totally spurious argument:

If two theories explain all the observed facts equally well, scientists would prefer to adopt, even if tentatively, the simpler one. Following Galileo’s discoveries, such a process would have definitely favoured the Copernican system over the Ptolemaic one, which was what Galileo had been championing all along. The requirement of simplicity would have also given an advantage to Copernicanism over Tycho Brahe’s hybrid geocentric-heliocentric model.

Ignoring the fact that the Ptolemaic system was dead in the water after the discovery of the phases of Venus and so the comparison is a waste of time, any alert reader will immediately spot the massive error in this argument. The two theories, Copernicus and Brahe, do not explain all the observed facts equally well. The Copernican system requires something very central that the Tychonic system does not, terrestrial motion. Livio adds this in a very off hand way, “Of course the ultimate test would have been to find direct proof for the Earth’s motion…” There was in fact absolutely no empirical proof of the Earth’s motion and wouldn’t be until Bradley discovered stellar aberration in 1725! To give the “advantage to Copernicanism over Tycho Brahe’s hybrid geocentric-heliocentric model” would be under the circumstances actually unscientific.

A little bit further on Livio delivers another highly spurious comment, he writes, “…but Bellarmino’s position was extremely rigid. He did not believe that a proof of Copernicanism could ever be found.” Livio is here putting words into Bellarmino’s mouth, who never said anything of the sort, rather he expressed doubt that that such a proof existed.  Livio finishes off his series of spurious attacks on Bellarmino by claiming to prove him theologically wrong. I find it slightly amusing that a twenty-first century astrophysicists claims that Bellarmino, who was universally regarded as the greatest living Catholic theologian and whose reputation as a theologian was such that at the end of his life he was both head of the Index and head of the Inquisition, was theologically wrong.

Things developed as they must and we now have Galileo rushing off to Rome to try and rescue the situation with his infamous theory of the tides. Livio explains the theory and its possible origins then he drops the following jewel:

Albeit wrong, Galileo’s commitment to mechanical easy-to-understand causation made his theory of tides at least plausible.

There is only one possible answer to this claim, bullshit! A theory that states there is only one high tide and one low tide at the same time every day, when there are in fact two of each of which the times travel around the clock over the lunar month (a strong indication of the correct theory of the tides) is anything but a plausible theory. It is as I said bullshit.

We now turn to the committee of consultors set up to examine the theological implications of heliocentricity. Livio of course has much to say against this. His first objection:

Ironically, the same office that had objected vehemently to scientists intruding into theology was now asking the theologians to judge on two purely scientific questions–two of the central tenets of he Copernican model.

Once again Livio appears to have no idea what theology is. The discipline of theology covers all forms of human activity in their entirety. There is absolutely nothing in human existence that doesn’t fall under the remit of theology. Secondly the function of the consultors in this case were being asked to examine the two central tenets of heliocentricity in relation to Catholic religious belief, not a scientific question at all.

Next up, Livio objects to the consultors themselves: “Not one was a professional astronomer or even an accomplished scientist in any discipline.” All of the consultors were highly educated, learned men, who would have had a solid instruction to Ptolemaic astronomy during there education and were more than capable of asking an expert for his advice if necessary.

Consultor: Is there any empirical evidence that the Earth moves and the Sun stands still?

Astronomer: No

Consultor: Is there any empirical evidence that the Sun and not the Earth is at the centre of the cosmos?

Astronomer: No

Simple wasn’t it.

 

The decisions of the consultors are well know:

On February 24 the Qualifiers delivered their unanimous report: the proposition that the Sun is stationary at the centre of the universe is “foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture”; the proposition that the Earth moves and is not at the centre of the universe “receives the same judgement in philosophy; and … in regard to theological truth it is at least erroneous in faith. (Wikipedia)

Foolish and absurd in philosophy is the scientific judgement and sounds somewhat harsh but can be simply translated as, is not supported by the available empirical evidence. Livio would disagree with both the judgement and my interpretation of it but it is historically fundamentally accurate. The second part of each judgement is of course the theological one. As is also well known the Pope commissioned Cardinal Bellarmino to inform Galileo of the decision and to instruct him not to hold or teach the heliocentric theory. Books, such as those of Kepler, claiming the physical reality of heliocentricity, were placed on the Index and De revolutionibus, as detailed above until corrected, which it was.

Bewilderingly Livio accuses Bellarmino and the Jesuits of failing to support Galileo against the Pope, which displays an incredible ignorance of the Catholic Church, the Pope and the Jesuit Order in the seventeenth century. As stated at the beginning the Catholic Church was a religious, political and judicial power in an age of absolutism and the Pope was an absolutist ruler. The Society of Jesus (Jesuits), and Bellarmino was also a Jesuit, is a religious order dedicated to and directly under the authority of the Pope. Livio’s accusations are totally insane.  He, of course, can’t resist making ahistorical and inaccurate comments about the decision, he writes:

The ruling made by officers of the Church for whom retaining authoritative power over areas totally outside their expertise took priority over open-minded critical thinking informed by scientific evidence.

Livio here continues to ignore/deny the simple fact that the scientific evidence in the early seventeenth century simply did not support an interpretation of heliocentricity as a physical reality and whilst it appears somewhat draconian the Church decision doesn’t actually say anything else.

Livio also launches the presentist moral outrage attack, “[some] argue that some of the responsibility for the prohibition of Copernicanism lies with Galileo himself, because he wouldn’t keep his mouth shut. Such claims are outrages.” Firstly the heliocentric hypothesis was never prohibited only the heliocentric theory, which given its scientific status at the time was in fact, although unnecessarily harsh, justifiable and secondly if Galileo had displayed somewhat more tact, instead of behaving like the proverbial bull in a china shop, things would never have taken the turn that they did.

We move on to the dispute over the nature of comets between the Jesuit astronomer Orazio Grassi and Galileo. Here Livio again displays his ignorance of the history of astronomy. He writes:

Grassi’s theory of comets deviated courageously from the Aristotelian view, which placed comets at about the distance of the Moon. Instead following Tycho Brahe, Grassi proposed that the comets were further out between the Moon and the Sun.

[…]

As to the actual nature of comets, many astronomers at the time were sill adopting Aristotle’s theory, which stated that these represented exhalations of the Earth that became visible above a certain height due to combustion, disappearing from view as soon as that inflammable material was exhausted. Grassi, however, again followed Brahe in suggesting that comets were some sort of “imitation planets.”

 

The modern debate on the nature of comets and whether they were sub- or supralunar began in the fifteenth century with Toscanelli (1397–1482), who tried to track the path of Comet Halley in 1456, as if it were a supralunar object. The debate continued in the work of Georg von Peuerbach (1423–1461), Toscanelli’s one time student, and Peuerbach’s student, Regiomontanus (1436–1476), who wrote a work on how to detect parallax in a moving comet. The debate continued in the 1530’s with many leading European astronomers taking part, including, Johannes Schöner (1477–1547), who published Regiomontanus’ work on comets, Peter Apian (1495–1552), after whom the law concerning comets’ tails in named, Copernicus (1473–1543), Gerolamo Cardano (1501–1576) and Jean Pena (1528–1558). The latter two both proposed a theory that comets were translucent, supralunar, bodies that focused the Sun’s rays like a lens creating the comets tail. Tycho’s comet, the great comet of 1577 was observed by astronomers all over Europe and Tycho, Michael Mästlin (1550-1631) and Thaddaeus Hagecius ab Hayek (1525–1600), three leading astronomers, all determined that comets were supralunar. Clavius accepted these results and included the fact that comets were supralunar in his Sphaera. This meant that the official view of the Catholic Church in general and the Jesuits in particular was that comets were supralunar. This view was confirmed again by astronomers throughout Europe observing Comet Halley in 1607. The was nothing courageous about Grassi’s theory of comets and in fact you would be hard put to it to find a serious European astronomer, apart from Galileo, who still adhered to Aristotelian cometary theory in 1618. In the same year Grassi’s Jesuit colleague Johann Baptist Cysat (c. 1587–1657), a student of Christoph Scheiner, became the first astronomer to observe a comet with a telescope giving the first ever description of a comet’s nucleus in his Mathemata astronomica de loco, motu, magnitudine et causis cometae qui sub finem anni 1618 et initium anni 1619 in coelo fulsit. Ingolstadt Ex Typographeo Ederiano 1619 (Ingolstadt, 1619). He followed Tycho Brahe in believing that comets orbited the sun. He also demonstrated the orbit was parabolic not circular.

Galileo, who due to ill health had not observed the comets of 1618, launched a vicious and insulting, unprovoked attack on Grassi’s publication, presenting a view of comets that was totally out of date, ignoring all of the accumulated scientific evidence from the last two centuries on the nature of comets just to put one over on the Jesuits and the supporters of Tycho’s theories. Livio does his best to defend Galileo’s disgusting behaviour but even he admits that Grassi was principally in the right and Galileo simply wrong. Livio goes as far as to claim that because comets has an elongated elliptical orbit (actually only some do) that Galileo’s claim that they travel in straight lines was more correct than Grassi’s claim that they orbit the Sun. In all other instances Livio goes out of his way to emphasise that hindsight shows that Galileo was right and his critics wrong so why the opposite tack here? Comets do orbit the Sun. Livio scrabbles around in the cesspit that is Galileo’s paper on comets looking for crumbs for which he can give Galileo credit.

Livio now criticises Grassi’s answer to Galileo’s attack because it contained sarcastic attacks on Galileo. Talk about pot calling the kettle black. He even brings up the obtuse suggestion that it was actually written by Christoph Scheiner because of his antagonism towards Galileo. This theory has a small problem; Scheiner only became antagonistic towards Galileo after Galileo had viciously insulted him in The Assayer, a publication that still lay in the future. Livio’s whole account of the affair is biased in Galileo’s favour so that it serves as a lead up to The Assayer, for the time being the last document in the dispute, because, as already mentioned, Livio sees it as the document in which Galileo established the place of mathematics in science. Livio’s account of The Assayer and its significance is more than somewhat outlandish.

With very little evidence to base this opinion upon, Galileo thought in 1623 that he knew the answer: the universe “is written in the language of mathematics.” It was this dedication to mathematics that raised Galileo above Grassi and the other scientist of his day, even when his specific arguments fell short of convincing–and even though he assigned to geometry a more important role than it seemed to deserve at the time. His opponents, he wrote, “failed to notice that to go against geometry is to deny truth in broad daylight.”

This whole paragraph contains so much that is wrong that it is difficult to know where to start.  I have already explained above that by the time Galileo wrote this infamous piece of purple prose it was widely accepted by both mathematician and natural philosophers that the future of science lay in an intensive mathematization. A process that was well under way when Galileo wrote something that was not new and sensational but a common place. A lot of contemporary scientists were dedicated to mathematics, such as Johannes Kepler, Simon Steven and Isaac Beeckman. In fact the last two both contributed at least as much to the development of mathematical physics in the seventeenth century as Galileo if not more. Unfortunately their achievements tend to get blended out on the popular level by the Galileo myth machine of which, Livio is just the latest in a long line of operators.

To raise Galileo above Grassi because of his dedication to mathematics is more than a joke; it’s grotesque. Earlier in his account of the dispute between Grassi and Galileo, Livio acknowledged that Grassi was an excellent optical physicist and an equally excellent architect both disciplines are fundamentally mathematical disciplines. He also points out that Grassi succeeded Grienberger as professor for mathematics at the Collegio Romano, who had succeeded Clavius. The chair for mathematics at the Collegio Romano was unique in European universities. Clavius had set up what we would now call an institute for advanced mathematics, a roll that both Grienberger and Grassi kept alive. This institute was dedicated to exemplifying, establishing and developing the roll of mathematics in the sciences. The Collegio Romano was quite simply the most advanced school for mathematics and its application anywhere in Europe. As far as geometry goes the standard textbook for geometry throughout most of the seventeenth century was Christoph Clavius’ Euclides Elementorum Libri XV, Rom 1574, note the date. This was not simply a new translation of Euclid’s classic but a modernised, simplified, streamlined textbook that was used extensively by both Catholic and Protestant educational establishments; the last edition was printed in 1717.

Shortly after the above passage on Galileo’s supposed revolutionary thoughts on mathematics we get the following throwaway line:

Galileo introduced the revolutionary departure from the medieval, ludicrous notion that everything worth knowing was already known.

When I read this I didn’t know whether to laugh, cry, rip my hair out (if I had any), or simply go out and throw myself off a high cliff in the face of such imbecilic drivel. I strongly suspect that any of my history of medieval science friends and colleagues will react similarly should they happen to read the above sentence. Starting at the very latest with the translation movement in the twelfth century medieval science was an evolving developing field with advances in a wide range of disciplines. The medieval scholars laid the foundations upon which Galileo built his own achievements. I would be quite happy to give Dr Livio a very long reading list of good books on medieval science to help him find a way out of his ignorance.

At the end of his chapter on The Assayer Livio warms up the old discovery of Pierto Redondi that Galileo was denounced to the Inquisition for the bits of primitive atomism contained in The Assayer. This was indeed true but the accusation was dismissed and nothing came of it, as Livio admits. Livio, however, now writes a whole paragraph about how important atomism, he actually means particle physics, is in modern physics, mentioning quarks, leptons, gage bosons etc., etc. I wonder how Livio would react if he knew that the principle source of atomism in the seventeenth century is now considered to be the German alchemist Daniel Sennert (1572–1637) reviving the theories of the thirteenth century alchemist Paul of Taranto. You remember alchemy one of those fictitious fields together with astrology that scientists sometime connected to.

Next up the Dialogo: Livio acknowledges that there were external political and social factors that affected the situation within the Vatican in the years leading up to the publication of the Dialogo. He starts with the astrological scandal. In 1630 an astrological prognostication predicting the Pope’s death was made and circulated by, to quote Livio, the abbot of Saint Praxedes in Rome. Livio then tells us, “some of Galileo’s adversaries tried to pin the blame on Galileo…” What Livio neglects to mention is that although Galileo was in this case innocent there were plausible ground for suspecting him, it was a case of guilt by association. Firstly, Galileo was known to be a practicing astrologer. Secondly, the abbot of Saint Praxedes, Orazio Morandi had been a good friend of Galileo’s since at least 1613. Thirdly, following an audience with the Pope concerning the forthcoming Dialogo in 1630, Galileo took part in a supper with Moriandi in Saint Praxedes together with Rafaello Visconti (Master of the Sacred Palace), another friend of Galileo’s, who read the manuscript of the Dialogo for Niccolò Ricardi the censor, who never actually read it, and an appraiser of the Inquisition. When Morandi was arrested for his horoscope and thrown into the Vatican’s dungeon, Visconti was also implicated and banished from the Vatican. That Galileo came under suspicion by association is hardly surprising. This was not a plot against Galileo as Livio claims.

We then have a wonderfully mangled piece of history from Livio, who write:

Unfortunately, this was not the end of the trials and tribulations Galileo had to endure for the publication of the Dialogo. Most significant of these was the sudden death on August 1, 1630, of Federico Cesi, the founder and sole source of funding for the Accademia dei Lincei. As a result the printing had to be done in Florence, outside of Riccardi’s jurisdiction. After some negotiations, it was agreed that Father Jacinto Stefani, a consultor of the Inquisition in Florence, would be in charge, but only after Riccardi approved the introduction and conclusion.

Although Cesi’s death was a serious blow to Galileo’s plans because he Cesi was supposed to finance the publication of the Dialogo, but this was not the reason why it was published in Florence and not in Rome. What actually happened is that after Galileo had returned to Florence from Rome with his manuscript the plague broke out in Florence. Restrictions on travel imposed by the authorities meant that Galileo could not return to Rome to oversee the printing and publication of his book. He requested permission from Riccardi to get the book published in Florence instead, but as already mentioned Riccardi hadn’t actually read the book intending to review the pages as they came of the printing press instead, having accepted Visconti’s recommendation. Riccardi was now in a pickle and wanted Galileo to send him a copy of the manuscript but due to the immense cost of producing such a copy, Galileo was very reluctant to do so.  Riccardi agreed to Galileo just sending the introduction and conclusion to Rome to be controlled and the rest being controlled in Florence by Stefani. Galileo and his circle of supporters now manipulated and even oppressed the two censors and played them against each other. The result was that the imprimatur was granted by Stefani under the impression that Ricarrdi had already cleared the manuscript for publication in Rome, he hadn’t, without actually controlling the text himself. Galileo had an imprimatur that had been obtained under false pretences, which meant that he didn’t actually have an imprimatur at all. All of this came out during the investigations following publication, which contributed to Galileo’s being prosecuted but did not play a role in the actual trial.

All of this, which Livio doesn’t mention at all, is important because when dealing with the trial Livio several times emphasises that the Church had given Galileo to publish the book as it was because he had not one but two imprimaturs, whereas in fact formally he didn’t have one at all.

Livio now tells us:

There is a certain sleight of hand in the title. [Dialogue Concerning the Two Chief Systems of the World, Ptolemaic and Copernican, Propounding Inconclusively in the Philosophical Reasons as Much for the One Side as for the Other] Even if one were to ignore the fact that the Aristotelian and the Ptolemaic systems were not identical, there was at least one other world system that in terms of agreement with observations was superior to the Ptolemaic: Tycho Brahe’s Hybrid system in which the planets revolved around the Sun, but the Sun itself revolved around the Earth. Galileo always regarded that system as unnecessarily complex and contrived, and he also thought that he’d found proof for the Earth’s motion through the phenomenon of the tides, so in striving to hand Copernicanism a clear victory (although formally the book was inconclusive) he probably didn’t want to confuse the issue with superfluous qualifications.

Once again so much to unpick. Livio obviously doesn’t understand that the system propagated by the Catholic Church before Copernicus was an uneasy mixture of Ptolemaic astronomy and Aristotelian cosmology, not Aristotelian astronomy, which is a whole different kettle of fish that had been revived by some in the sixteenth century and against which Clavius had fought tooth and nail. In fact he devotes much more space to refuting the Aristotelian homocentric astronomy in his Sphaera than he devotes to refuting Copernicus. The developments in astronomy since Copernicus published De revolutionibus had left Aristotelian cosmology in shreds and Clavius had been quite happy to also jettison that, so for Clavius, speak the Catholic Church, the world system was simply the Ptolemaic.

In fact Galileo’s whole title and thus his whole book is a complete sham By 1630 the two chief systems of the world were the Tychonic system and Johannes Kepler’s elliptical heliocentric system, which was regarded as separate from and as a competitor to Copernicus’ system. The Ptolemaic system had been killed off by the discovery of the phases of Venus and the plausible assumption that Mercury would also orbit the Sun as its general behaviour was identical to that of Venus; the phases of Mercury were first observed in 1639. Galileo just used Ptolemy as a fall guy for his sham Copernican victory. Copernicus’ heliocentric system had been rendered totally obsolete by Kepler’s discovery of the three laws of planetary motion, empirically based mathematical laws I would point out, which Galileo just completely ignored clinging to Copernicus’ ‘unnecessarily complex and contrived’ system of deferents and epicycles. Livio’s dismissal of the Tychonic system as ‘superfluous qualifications’ is put quite simply a joke, especially given that the Tychonic system was at the time the leading contender as the world system because of the failing evidence of terrestrial motion.

Livio without realising it now points out the central problem with the Dialogo:

The Dialogo is one of the most engaging science texts ever written. There are conflicts and drama, yes, but also philosophy, humor, cynicism, and poetic usage of language, so that the sum is much more than its parts.

All of the above is true except that as a piece of astronomy the sum is much less than its parts, which I will explain shortly. There is no doubt whatsoever that for all of his undeniably polymathic talents, Galileo’s greatest gift was as a polemicist. A friend of mine, who is a Galileo expert, calls him the first science publicist and this is a function that he carried out brilliantly. Yes, the Dialogo is a brilliant piece of literature, which is probably unequalled by any other scientific publication in the entire history of science. However, its literary brilliance appears to have blinded many of its readers to the fact that as a piece of astronomy it’s total crap.

As already mention, Galileo struts on to the stage to discuss what he calls the two chief world systems but actually delivers up is a sham battle between two obsolete and refuted systems. He clung stubbornly to his completely false theory that comets are mere optical illusions originating on the Earth against a mass of solid, empirical, scientific evidence that comets were in fact supralunar celestial objects that orbited the Sun. Something that Galileo was no prepared to accept because it was first proposed by Tycho, who saw it as supporting evidence for his system. He clung to Copernicus’ deferents and epicycles rather than acknowledge Kepler’s much simpler, empirically proven elliptical orbits. In fact, Galileo completely ignores Kepler’s three laws of planetary motion, by far and away, the best scientific supporting evidence for a heliocentric system because if he did acknowledge them he would have to hand the laurels for proving the superiority of the heliocentric system to Kepler instead of winning them for himself, his one and only aim in the whole story. Last but by no means least he structures his whole book and his argument around his totally ludicrous theory of the tides. One of the greatest mysteries in Galileo’s life is why he, an undeniably brilliant scientist, clung so tenaciously to such an obviously bankrupt theory.

Galileo’s masterwork sailed majestically past the actually astronomy debate in the 1630s and played little or no role in the ensuing astronomical discussion of the seventeenth century in which it was largely ignored being of no real relevance. It only became crowned as a classic in the late eighteenth and early nineteenth centuries when Galileo was declared to be a scientific martyr

Livio, like so many others, blinded by the radiance of Galileo’s rhetoric sees the matter somewhat differently. In a surprisingly short presentation of the book he praises Galileo’s achievements. There are a couple of minor points that I would like to pick up on, Livio delivers up once again the myth of heliocentricity removing the Earth from its central place in the cosmos:

More important, the act of removing humans from their central place in the cosmos was too brutal to be remedied by some philosophical pleasantries at the end of a debate from a very different tone.

The whole central place in the cosmos myth is one created in the late eighteenth century and I know of no seventeenth century use of it to criticise the heliocentric hypothesis. In a bit of waffle towards the end of this chapter Livio says the “He [Galileo] did his best…” If Galileo had truly done his best he would not have ignored the most compelling evidence for the heliocentric hypothesis, Kepler’s laws of planetary motion. He goes on to say that, “History has indeed proved that Galileo was right,” it hasn’t Galileo was wrong and Kepler was right.

Livio gives a fairly short and largely accurate account of Galileo’s trial by the Inquisition and the events leading up to following the publication of the book. The only major error being, as mentioned above, his insistence that the book had two imprimaturs. Livio acknowledges that the judgement of the three clerics, commissioned to read the book and determine whether Galileo taught or defended in anyway the heliocentric theory, that he had in fact done just that and thus broken the order from 1616 was correct. Although he can’t avoid a dig at Melchior Inchofer, the Jesuit under the three. This was the charge that was brought against Galileo and of which he was found guilty. He also can’t avoid turning up the emotional rhetoric, “What happened on the following day remains one of the most shameful events in our intellectual history.” Galileo deliberately and wilfully broke the law and received the standard punishment for having done so, which included abjuring. There is an old saying under criminals, if you can’t do the time don’t do the crime. Galileo was arrogant enough to think that he could put one over on the Catholic Church and get away scot-free, it turned out that he couldn’t.

We get a short, once again, rather gushing account of the Discorsi, Galileo real claim to fame but Livio rather spoils it by once again trying to claim that Galileo created modern science.

Through an ingenious combination of experimentation (for example, with inclined planes), abstraction (discovering mathematical laws), and rational generalisation (understanding that the same laws apply to all accelerated motions), Galileo established what has since become the modern approach to the study of all natural phenomena.

Although in the case of the studies presented by Galileo in the Discorsi he proved himself to be an excellent experimental scientist, all of these things had been done by others before Galileo and independently by others contemporaneously to Galileo. He was only one amongst other who helped to establish this methodology. Galileo was part of the evolution of a new scientific methodology that had started long before he was born and which he did not initiate. Like many others before him Livio also falsely attributes Newton’s first law, the principle of inertia, to Galileo. Whilst Galileo did indeed produce a version of the principle of inertia, Newton took his first law from the works of René Descartes, who in turn had taken it from Isaac Beeckman, who had formulated it independently of Galileo.

The next chapter of Livio’s book is an obtuse story of an account of the Galileo affair commissioned by the Vatican in the 1940s and then not published but then published under the name of a different author in the 1960s. The sole aim of this chapter is simply to take another gratuitous swing at the Catholic Church. The book closes with a fairly long digression on Einstein’s views on science and religion, which brings us to a major problem with the book, apart from the historical inaccuracies, it tries to be too many things at once.

One thing that I have mentioned in passing is Livio’s attempts to draw parallels between what happened to Galileo and the current crop of science deniers. The analogies simply don’t work because no matter how hard Livio tries to claim the opposite, Galileo’s critics in astronomy, especially the Jesuits, were not science deniers but just as much scientists as Galileo, who argued for an equally valid, in fact empirically more valid, system of astronomy, the Tychonic one, as Galileo’s heliocentric system. All the way through the book Livio keeps trying to disqualify the Tychonic system as unscientific but in the first half of the seventeenth century it was just as scientific as the heliocentric hypothesis. The only person practicing science denial here is Livio. He also wants to present the book as a discussion of the general relationship between science and religion but the whole time he argues from a presentist standpoint and refuses to view the relationship in Galileo’s time in its correct historical context. Lastly he actually wants to sell the book as a new biography of Galileo presented with the insights of a working astrophysicist, his own claim at the beginning of the book. Unfortunately it is here that he fails most.

He enters his story with a preconceived image of Galileo as a white knight on his mighty charger fighting for freedom of speech and freedom of thought in the sciences and as the originator and creator of modern experimental and mathematical science. With this image firmly in mind, from the start of his narrative, he fills out the picture with a classic case of confirmation bias. He completely ignores any real facts from the history of science that might force him to rethink his preconceived image of his hero. There is no mistaking the fact that is a strong element of hero worship in Livio’s vision of Galileo. Instead of describing the real state of science in the early seventeenth century, he present the reader with a comic book version of Aristotelian philosophy from the thirteenth century making it easier for him to present Galileo as some sort of superman, who dragged natural philosophy kicking and screaming into the modern world, whilst singlehandedly creating modern science. Edward Grant the eminent historian of medieval science (a discipline that Livio probably thinks doesn’t exist, because he seems to think that there was no medieval science), once very perceptively wrote that Aristotelian philosophy was not Aristotle’s philosophy and went on to point out that it is very difficult to define Aristotelian philosophy, as it kept on evolving and changing down the centuries. The Thomist philosophy of the Jesuits in the first third of the seventeenth century was a very different beast to the Aristotelian philosophy that Thomas Aquinas propagated in the thirteenth century. The historical distortions that Livio presents would be funny if they weren’t so grotesque.

On the question of Galileo being ‘a symbol of the fight for intellectual freedom, a lifetime of studying and thinking about Early Modern science has brought me to the conclusion that he wasn’t. In my opinion Galileo didn’t really care about such abstractions as freedom of thought, freedom of speech or intellectual freedom, all he cared about was his own vainglory. As Mario Biagioli clearly shows in his Galileo Courtier,[2] Galileo was a social climber. He was a relatively unknown, middle aged, professor of mathematics, who overnight became the most celebrated astronomer in Europe because of his telescopic discoveries. Alone the way he presented those discoveries shows his principle aim was to see what he could gain socially from them. Galileo loved his celebrity status and revelled in it. His engagement for heliocentricity was all motivated by the thought that if he could prove it true, then he would become even more famous and even more feted. To achieve this aim he lied, cheated and plagiarised. He attacked and viciously stomped on all those he regarded as competitors in his strivings for fame and adulations. He also deliberately ignored any evidence for heliocentricity presented by others (see Kepler’s laws of planetary motion) that might mean that they get the laurels and not he. Galileo might have been a great scientist but he was also a vain egoist. I think all of this might go someway to explaining his extraordinary blindness to the enormous inadequacies of his theory of the tides.

Reading this book made me very angry. The only positive thing I can say about it is that Livio is an excellent writer and the book is very well written and easy to read, but in the end even this must be viewed negatively. Mario Livio is a prominent scientist and the very successful author of popular books on mathematics and science. Because of his reputation non-specialist journals will have glowing reviews of his book, mostly written by people, who are neither Galileo experts and nor historians of science. If it follows the normal pattern for such books, specialist journals and professional historians of science will decline to review it, because it’s a pop book. The book will almost certainly become a genre bestseller and another generation of readers will acquire a mythical image of Galileo Galilei and a totally false impression of Renaissance science, something I have battled against in the eleven years that I have been writing this blog.

[1] Mario Livio, Galileo and the Science Deniers, Simon & Schuster paperbacks, New York, London, Toronto, Sydney, New Delhi, 2020

[2] Mario Biagioli, Galileo Courtier: The Practice of Science in the Culture of Absolutism, University of Chicago Press, Chicago & London, ppb. 1994

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May 27, 2020 · 8:35 am

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

 

From about 1630 onwards there were only two serious contenders under European astronomers, as the correct scientific description of the cosmos, on the one hand a Tychonic geo-heliocentric model, mostly with diurnal rotation and on the other Johannes Kepler’s elliptical heliocentric system; both systems had their positive points at that stage in the debate.

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A 17th century illustration of the Hypothesis Tychonica from Hevelius’ Selenographia, 1647 page 163, whereby the Sun, Moon, and sphere of stars orbit the Earth, while the five known planets (Mercury, Venus, Mars, Jupiter, and Saturn) orbit the Sun. Source: Wikimedia Commons

A lot of the empirical evidence, or better said the lack of that empirical evidence spoke for a Tychonic geo-heliocentric model. The first factor, strangely enough spoke against diurnal rotation. If the Earth was truly rotating on its axis, then it was turning at about 1600 kilometres an hour at the equator, so why couldn’t one feel/detect it? If one sat on a galloping horse one had to hang on very tightly not to get blown off by the headwind and that at only 40 kilometres an hour or so. Copernicus had already seen this objection and had actually suggested the correct solution. He argued that the Earth carried its atmosphere with it in an all-enclosing envelope. Although this is, as already mentioned, the correct solution, proving or explaining it is a lot more difficult than hypothesising it. Parts of the physics that was first developed in the seventeenth century were necessary. We have already seen the first part, Pascal’s proof that air is a material that has weight or better said mass. Weight is the effect of gravity on mass and gravity is the other part of the solution and the discovery of gravity, in the modern sense of the word, still lay in the future. Copernicus’ atmospheric envelope is held in place by gravity, we literally rotate in a bubble.

In his Almagestum Novum (1651), Giovanni Battista Riccioli (1598–1671) brought a list of 126 arguments pro and contra a heliocentric system (49 pro, 77 contra) in which religious argument play a minor role and carefully argued scientific grounds a major one.

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Frontispiece of Riccioli’s 1651 New Almagest. Mythological figures observe the heavens with a telescope and weigh the heliocentric theory of Copernicus in a balance against his modified version of Tycho Brahe’s geo-heliocentric system Source: Wikimedia Commons

Apart from the big star argument (see below) of particular interest is the argument against diurnal rotation based on what is now know as the Coriolis Effect, named after the French mathematician and engineer, Gaspard-Gustave de Coriolis (1792–1843), who described it in detail in his Sur les équations du mouvement relatif des systèmes de corps (On the equations of relative motion of a system of bodies) (1835). Put very simply the Coriolis Effect states that in a frame of reference that rotates with respect to an inertial frame projectile objects will be deflected. An Earth with diurnal rotation is such a rotating frame of reference.

Riccioli argued that if the Earth rotated on its axis then a canon ball fired from a canon, either northwards or southwards would be deflected by that rotation. Because such a deflection had never been observed Riccioli argued that diurnal rotation doesn’t exist. Once again with have a problem with dimensions because the Coriolis Effect is so small it is almost impossible to detect or observe in the case of a small projectile; it can however be clearly observed in the large scale movement of the atmosphere or the oceans, systems that Riccioli couldn’t observe. The most obvious example of the effect is the rotation of cyclones.

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Illustration from Riccioli’s 1651 New Almagest showing the effect a rotating Earth should have on projectiles.[36] When the cannon is fired at eastern target B, cannon and target both travel east at the same speed while the ball is in flight. The ball strikes the target just as it would if the Earth were immobile. When the cannon is fired at northern target E, the target moves more slowly to the east than the cannon and the airborne ball, because the ground moves more slowly at more northern latitudes (the ground hardly moves at all near the pole). Thus the ball follows a curved path over the ground, not a diagonal, and strikes to the east, or right, of the target at G. Source: WIkimedia Commons

Riccioli was not alone in using the apparent absence of the Coriolis Effect to argue against diurnal rotation. The French Jesuit mathematician Claude François Milliet Deschales (1621–1678) in his Cursus seu Mundus Mathematicus (1674) brought a very similar argument against diurnal rotation.

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Source: WIkimedia Commons

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Image from Cursus seu Mundus Mathematicus (1674) of C.F.M. Dechales, showing how a cannonball should deflect to the right of its target on a rotating Earth, because the rightward motion of the ball is faster than that of the tower. Source: Wikimedia Commons

It was first 1749 that Euler derived the mathematical formula for Coriolis acceleration showing it to be two small to be detected in small projectiles.

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A nearby star’s apparent movement against the background of more distant stars as the Earth revolves around the Sun is referred to as stellar parallax. Source:

The second empirical factor was the failure to detect stellar parallax. If the Earth is really orbiting the Sun then the position of prominent stars against the stellar background should appear to shift when viewed from opposite sides of the Earth’s orbit, six months apart so to speak. In the seventeenth century they didn’t. Once again supporters of heliocentricity had an ad hoc answer to the failure to detect stellar parallax, the stars are too far away so the apparent shift is too small to measure. This is, of course the correct answer and it would be another two hundred years before the available astronomical telescopes had evolved far enough to detect that apparent shift. In the seventeenth century, however, this ad hoc explanation meant that the stars were quite literally an unimaginable and thus unacceptable distance away. The average seventeenth century imagination was not capable of conceiving of a cosmos with such dimensions.

The distances that the fixed stars required in a heliocentric system produced a third serious empirical problem that has been largely forgotten today, star size.  This problem was first described by Tycho Brahe before the invention of the telescope. Tycho ascribed a size to the stars that he observed and calculating on the minimum distance that the fixed stars must have in order not to display parallax in a heliocentric system came to the result that stars must have a minimum size equal to Saturn’s orbit around the Sun in such a system. In a geo-heliocentric system, as proposed by Tycho, the stars would be much nearly to the Earth and respectively smaller.  This appeared to Tycho to be simply ridiculous and an argument against a heliocentric system. The problem was not improved by the invention of the telescope. Using the primitive telescopes of the time the stars appeared as a well-defined disc, as recorded by both Galileo and Simon Marius, thus confirming Tycho’s star size argument. Marius used this as an argument in favour of a geo-heliocentric theory; Galileo dodged the issue. In fact, we now know, that the star discs that the early telescope users observed were not real but an optical artefact, now known as an Airy disc. This solution was first hypothesised by Edmond Halley, at the end of the century and until then the star size problem occupied a central place in the astronomical system discussion.

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With the eccentricity of the orbits exaggerated: Source

The arguments in favour of Kepler’s elliptical, heliocentric system were of a very different nature. The principle argument was the existence of the Rudolphine Tables. These planetary tables were calculated by Kepler using Tycho’s vast collection of observational data. The Rudolphine Tables possessed an, up till that time, unknown level of accuracy; this was an important aspect in the acceptance of Kepler’s system. Since antiquity, the principle function of astronomy had been to provide planetary tables and ephemerides for use by astrologers, cartographers, navigators etc. This function is illustrated, for example, by the fact that the tables from Ptolemaeus’ Mathēmatikē Syntaxis were issued separately as his so-called Handy Tables. Also the first astronomical texts translated from Arabic into Latin in the High Middle Ages were the zījes, astronomical tables.

The accuracy of the Rudolphine Tables were perceived by the users to be the result of Kepler using his elliptical, heliocentric model to calculate them, something that was not quite true, but Kepler didn’t disillusion them. This perception increased the acceptance of Kepler’s system. In the Middle Ages before Copernicus’ De revolutionibus, the astronomers’ mathematical models of the cosmos were judge on their utility for producing accurate data but their status was largely an instrumentalist one; they were not viewed as saying anything about the real nature of the cosmos. Determining the real nature of the cosmos was left to the philosophers. However, Copernicus regarded his system as being a description of the real cosmos, as indeed had Ptolemaeus his system before him, and by the middle of the seventeenth century astronomers had very much taken over this role from the philosophers, so the recognition of the utility of Kepler’s system for producing data was a major plus point in its acceptance as the real description of the cosmos.

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The other major point in favour of Kepler’s system, as opposed to a Tychonic one was Kepler’s three laws of planetary motion. Their reception was, however, a complex and mixed one. Accepting the first law, that the planetary orbits were ellipses with the Sun at one focus of the ellipse, was for most people fairly easy to accept. An ellipse wasn’t the circle of the so-called Platonic axioms but it was a very similar regular geometrical figure. After Cassini, using a meridian line in the San Petronio Basilica in Bologna, had demonstrated that either the Earth’s orbit around the Sun or the Sun’s around the Earth, the experiment couldn’t differentiate, Kepler’s first law was pretty much universally accepted. Kepler’s third law being strictly empirical should have been immediately accepted and should have settled the discussion once and for all because it only works in a heliocentric system. However, although there was no real debate with people trying to refute it, it was Isaac Newton who first really recognised its true significance as the major game changer.

Strangely, the problem law turned out to be Kepler’s second law: A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This seemingly obtuse relationship was not much liked by the early readers of Kepler’s Astronomia Nova. They preferred, what they saw, as the purity of the Platonic axiom, planetary motion is uniform circular motion and this despite all the ad hoc mechanism and tricks that had been used to make the anything but uniform circulation motion of the planets conform to the axiom. There was also the problem of Kepler’s proof of his second law. He divided the ellipse of a given orbit into triangles with the Sun at the apex and then determined the area covered in the time between two observations by using a form of proto-integration. The problem was, that because he had no concept of a limit, he was effectively adding areas of triangles that no longer existed having been reduced to straight lines. Even Kepler realised that his proof was mathematically more than dubious.

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Ismaël Boulliau portrait by Pieter van Schuppen Source: Wikimedia Commons

The French astronomer and mathematician Ismaël Boulliau (1605–1694) was a convinced Keplerian in that he accepted and propagated Kepler’s elliptical orbits but he rejected Kepler’s mathematical model replacing it with his own Conical Hypothesis in his Astronomica philolaica published in 1645.

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He criticised in particular Kepler’s area rule and replaced it in his work with a much simpler model.

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Boulliau’s Conical Hypothesis [RA Hatch] Source: Wikimedia Commons

The Savilian Professor of astronomy at Oxford University, Seth Ward (1617–1689)

Greenhill, John, c.1649-1676; Seth Ward (1617-1689), Savilian Professor of Astronomy, Oxford (1649-1660), Bishop of Exeter and Salisbury

Bishop Seth Ward, portrait by John Greenhill Source: Wikimedia Commons

attacked Boulliau’s presentation in his In Ismaelis Bullialdi astro-nomiae philolaicae fundamenta inquisitio brevis (1653), pointing out mathematical errors in the work and proposing a different alternative to the area law.

L0040222 Title Page of 'Astronomiae Philolacae Fundamenta'

Source: Wikimedia Commons

Boulliau responded to Ward’s criticisms in 1657, acknowledging the errors and correcting but in turn criticising Ward’s model.

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Source: Wikimeda Commons

Ward in turn had already presented a fully version of his Keplerian system in his Astronomia geometrica (1656).

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The whole episode is known as the Boulliau-Ward debate and although it reached no satisfactory conclusion, the fact that two high profile European astronomers were disputing publically over the Keplerian system very much raised the profile of that system. It is probable the Newton was first made aware of Kepler’s work through the Boulliau-Ward debate and he is known to have praised the Astronomica philolaica, which as Newton was later to acknowledge contained the first presentation of the inverse square law of gravity, which Boulliau personally rejected, although he was the one who proposed it.

The Boulliau-Ward debate was effectively brought to a conclusion and superseded by the work of the German mathematician Nikolaus Mercator (c. 1620–1687), whose birth name was Kauffman. His birthplace is not certain but he studied at the universities of Rostock and Leiden and was a lecturer for mathematics in Rostock (1642–1648) and then Copenhagen (1648–1654). From there he moved to Paris for two years before emigrating to England in 1657. In England unable to find a permanent position as lecturer he became a private tutor for mathematics. From 1659 to 1660 he corresponded with Boulliau on a range of astronomical topics. In 1664 he published his Hypothesis astronomica, a new presentation of the Keplerian elliptical system that finally put the area law on a sound mathematical footing. In 1676 he published a much-expanded version of his Keplerian astronomy in his two-volume Institutionum astronomicarum.

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Mercator’s new mathematical formulation of Kepler’s second law ended the debate on the subject and was a major step in the eventual victory of Kepler’s system over its Tychonic rival.

Addendum: Section on Coriolis Effect added 21 May 2020

 

 

 

 

 

 

 

 

 

 

 

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Filed under Early Scientific Publishing, History of Astronomy, Renaissance Science

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

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The seventeenth century is commonly called the scientific revolution principally for the emergence of two branches of science, although much more was actually going on. Firstly, the subject of this series, astronomy, and secondly the branch of science we now know as physics. The name physics had a significantly different meaning in the medieval Aristotelian philosophy. As we know astronomy and physics are intimately connected, in fact, intertwined with each other and this connection came into being during the seventeenth century. We have already seen in an earlier episode how the modern concepts of motion began to emerge from Aristotelian philosophy in the sixth century reaching a temporary high point in the early seventeenth century in the works of Galileo and Beeckman.

Galileo is often regarded as the initiator, founder of these developments and lauded with titles such as the father of physics, which is just so much irrelevant verbiage. In fact as we saw in the case of the laws of fall he was just following developments that had long preceded him. On a more general level the situation is no different. Kepler was apparently the first to use the concept of a physical force rather than a vitalist anima. Simon Stevin (1548–1620) resolved the forces acting on an object on an inclined plane, effectively using the parallelogram of forces to do so. In hydrostatics he also discovered the so-called hydrostatic paradox i.e. that the pressure in a liquid is independent of the shape of the vessel and the area of the base, but depends solely on its depth. Thomas Harriot (c. 1560–1621) actually developed a more advanced mechanics than Galileo but as usually didn’t publish, so his work had no impact. However, it clearly shows that Galileo was by no means the only person considering the problems. All of these early discoveries, including Galileo’s, suffered from a problem of vagueness. Nobody really knew what force was and the definitions of almost all the basic concepts–speed, velocity, acceleration etc.–were defective or simply wrong. The century saw the gradual development of a vocabulary of correctly defined terms for the emerging new physics and a series of important discoveries in different areas, mechanics, statics, hydrostatics, optics etc.

I’m not going to give a blow-by-blow history of physics in the seventeenth century, I would need a whole book for that, but I would like to sketch an aspect that in popular accounts often gets overlooked. The popular accounts tend to go Galileo–Descartes–Newton, as if they were a three-man relay team passing the baton of knowledge down the century. In reality there were a much larger community of European mathematicians and proto-physicists, who were involved, exchanging ideas, challenging discovery claims, refining definitions and contributing bits and pieces to big pictures. Each of them building on the work of others and educating the next generation. What emerged was a pan European multidimensional cooperative effort that laid the foundations of what has become known as classical or Newtonian physics, although we won’t be dealing with Newton yet. Once again I won’t be able to give all the nodes in the network but I hope I can at least evoke something of the nature of the cooperative effort involved.

I will start of with Simon Stevin, a man, who few people think of when doing a quick survey of seventeenth century physics but who had a massive influence on developments in the Netherlands and thus, through connections, in France and further afield. Basically an engineer, who also produced mathematics and physics, Stevin motivated Maurits of Nassau, Stadholder of the young Dutch Republic to establish engineering and the mathematical sciences on the new Dutch universities. Stevin’s work influenced both the Snels, Rudolph (1546–1613) and his son Willebrord (1580–1626), the latter translated Stevin’s work into French and Latin from the Dutch, making it available to a much wider audience.

Simon-stevin

Source: Wikimedia Commons

Stevin set up a school for engineering at the University of Leiden with Ludolph van Ceulen as the first professor of mathematics teaching from textbooks written by Stevin. Van Ceulen (1540–1610), who was Willebrord Snel’s teacher, was succeeded by his pupil Frans van Schooten the elder (1581–1646), whose pupils included his own son, Frans van Schooten the younger (1615–1660), Jan de Witt (1625–1672), Johann Hudde (1628–1704), Hendrick van Heuraet (1633–1660?), René-François de Sluse ((1622–1685) and Christiaan Huygens (1629–1695), all of whom would continue their mathematical development under van Schooten junior and go on to make important contributions to the mathematical sciences. An outlier in the Netherlands was Isaac Beeckman (1588–1637), a largely self taught natural philosopher, who made a point of seeking out and studying Stevin’s work. This group would actively interact with the French mathematicians in the middle of the century.

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Portrait of Frans van Schooten the younger by Rembrandt Source: Wikimedia Commons

On the French side with have a much more mixed bunch coming from varying backgrounds although Descartes and Mersenne were both educated by the Jesuits at the College of La Flèche. Nicolas-Claude Fabri de Peiresc (1580–1637), the already mentioned René Descartes (1596–1650) and Marin Mersenne (1588–1648), Pierre de Fermat (1607–1665), Pierre Gassendi (1592–1655), Ismaël Boulliau (1605–1694) and Blaise Pascal (1623–1662) are just some of the more prominent members of the seventeenth century French mathematical community.

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Pierre de Fermat artist unknown Source: Wikimedia Commons

René Descartes made several journeys to the Netherlands, the first as a soldier in 1618 when he studied the military engineering of Simon Stevin. He also got to know Isaac Beeckman, with whom he studied a wide range of areas in physics and from who he got both the all important law of inertia and the mechanical philosophy, borrowings that he would later deny, claiming that he had discovered them independently. Descarte and Beeckman believed firmly on the necessity to combine mathematics and physics. Beeckman also met and corresponded with both Gassendi and Mersenne stimulating their own thoughts on both mathematics and physics.

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René Descartes at work Source: Wikimedia Commons

On a later journey to the Netherlands Descartes met with Frans van Schooten the younger, who read the then still unpublished La Géometrié. This led van Schooten to travel to Paris where he studied the new mathematics of both living, Pierre Fermat, and dead, François Viète (1540–1603), French mathematicians before returning to the Netherlands to take over his father’s professorship and his group of star pupils. Descartes was also a close friend of Constantijn Huygens (1596–1687), Christiaan’s father.

GeometryDescartes

Source: Wikimedia Commons

Peiresc and Mersenne were both scholars now referred to as post offices. They both corresponded extensively with mathematicians, astronomers and physicists all over Europe passing on the information they got from one scholar to the others in their networks; basically they fulfilled the function now serviced by academic journals. Both had contacts to Galileo in Italy and Mersenne in particular expended a lot of effort trying to persuade people to read Galileo’s works on mechanics, even translating them into Latin from Galileo’s Tuscan to make them available to others. Mersenne’s endeavours would suggest that Galileo’s work was not as widely known or appreciated as is often claimed.

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Nicolas-Claude Fabri de Peiresc by Louis Finson Source: Wikimedia Commons

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Marin Mersenne Source: Wikimedia Commons

Galileo was, of course, by no means the only mathematician/physicist active in seventeenth century Italy. The main activist can be roughly divided in two groups the disciples of Galileo and the Jesuits, whereby the Jesuits, as we will see, by no means rejected Galileo’s physics. The disciples of Galileo include Bonaventura Francesco Cavalieri (1598–1647) a pupil of Benedetto Castelli (1578­–1643) a direct pupil of Galileo, Evangelista Torricelli (1608–­1647) another direct pupil of Galileo and Giovanni Alfonso Borelli (1608-1679) like Cavalieri a pupil of Castelli.

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Benedetto Castelli artist unknown Source: Wikimedia Commons

On the Jesuit side we have Giuseppe Biancani (1565–1624) his pupil Giovanni Battista Riccioli (1598–1671) and his one time pupil and later partner Francesco Maria Grimaldi (1618–1663) and their star pupil Giovanni Domenico Cassini (1625–1712), who as we have already seen was one of the most important telescopic astronomers in the seventeenth century. Also of interest is Athanasius Kircher (1602–1680), professor at the Jesuit University, the Collegio Romano, who like Peiresc and Mersenne was an intellectual post office, collecting scientific communications from Jesuit researchers all over the world and redistributing them to scholars throughout Europe.

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Athanasius Kircher Source: Wikimedia Commons

Looking first at the Jesuits, Riccioli carried out extensive empirical research into falling bodies and pendulums. He confirmed Galileo’s laws of fall, actually using falling balls rather than inclined planes, and determined an accurate figure for the acceleration due to gravity; Galileo’s figure had been way off. He was also the first to develop a second pendulum, a device that would later prove essential in determining variation in the Earth’s gravity and thus the globes shape.

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Riccioli as portrayed in the 1742 Atlas Coelestis (plate 3) of Johann Gabriel Doppelmayer. Source: Wikimedia Commons

Grimaldi was the first to investigate diffraction in optics even giving the phenomenon its name. Many of the people I have listed also did significant work in optics beginning with Kepler and the discovery of more and more mathematical laws in optics helped to convince the researchers that the search for mathematical laws of nature was the right route to take.

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Francesco Maria Grimaldi Source: Wikimedia Commons

As we saw earlier Borelli followed Kepler’s lead in trying to determine the forces governing the planetary orbits but he also created the field of biomechanics, applying the newly developed approaches to studies of muscles and bones.

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Giovanni Alfonso Borelli Source: Wikimedia Commons

Torricelli is, of course, famous for having invented the barometer, a device for measuring air pressure, of which more in a moment, he was trying to answer the question why a simple air pump cannot pump water to more than a height of approximately ten metres. However, most importantly his experiments suggested that in the space above the mercury column in his barometer there existed a vacuum. This was a major contradiction to traditional Aristotelian physics, which claimed that a vacuum could not exist.

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Evangelista Torricelli by Lorenzo Lippi (c. 1647) Source: Wikimedia Commons

Torricelli’s invention of the barometer was put to good use in France by Blaise Pascal, who sent his brother in law, Périer, up the Puy de Dôme, a volcano in the Massif Central, carrying a primitive barometer. This experiment demonstrated that the level of the barometer’s column of mercury varied according to the altitude thus ‘proving’ that the atmosphere had weight that lessened the higher one climbed above the earth’s surface. This was the first empirical proof that air is a material substance that has weight. One person, who was upset by Torricelli’s and Pascal’s claims that the barometer demonstrates the existence of a vacuum, was René Descartes to whom we now turn.

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Painting of Blaise Pascal made by François II Quesnel for Gérard Edelinck in 1691 Source: Wikimedia Commons

Descartes, who is usually credited with being one of, if not the, founders of modern science and philosophy, was surprisingly Aristotelian in his approach to physics. Adopting Beeckman’s mechanical philosophy he thought that things could only move if acted upon by another object by direct contact; action at a distance was definitely not acceptable. Aristotle’s problem of projectile motion, what keeps the projectile moving when the contact with the projector breaks was solved by the principle of inertia, which reverses the problem. It is not longer the question of what keeps the projectile moving but rather what stops it moving. He also, like Aristotle, adamantly rejected the possibility of a vacuum. His solution here was to assume that all space was filled by very fine particles of matter. Where this theory of all invasive particles, usually called corpusculariansim, comes from would takes us too far afield but it became widely accepted in the second half of the seventeenth century, although not all of its adherents rejected the possibility of a vacuum.

Descartes set up laws of motion that are actually laws of collision or more formally impact. He starts with three laws of nature; the first two are basically the principle of inertia and the third is a general principle of collision. From these three laws of nature Descartes deduces seven rules of impact of perfectly elastic (i.e. solid) bodies. Imagine the rules for what happens when you play snooker or billiards.  The details of Descartes rules of impact needn’t bother us here; in fact his rules were all wrong; more important is that he set up a formal physical system of motion and impact. Studying and correcting Descartes rules of impact was Newton’s introduction to mechanics.

Turning to another Frenchman, we have Ismaël Boulliau, who was a convinced Keplerian. Kepler had hypothesised that there was a force emanating from the Sun that swept the planets around their orbits, which diminished inversely with increasing distance from the Sun. Boulliau didn’t think that such a force existed but if it did then it would be an inversed square force in analogy to Kepler’s law for the propagation of light; a candidate for the first modern mathematical law of physics. The foundations of the new physics were slowly coming together.

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Ismaël Boulliau portrait by Pieter van Schuppen Source: Wikimedia Commons

Our last link between the Dutch and French mathematicians is Christiaan Huygens. Huygens initially took up correspondence with Mersenne around 1648; a correspondence that covered a wide range of mathematics and physics. In 1655 he visited Paris and was introduced to Boulliau and a year later began correspondence with Pierre Fermat. Frans van Schooten the younger continued to act as his mathematical mentor.

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Christiaan Huygens by Caspar Netscher, 1671, Museum Boerhaave, Leiden Source: Wikimedia Commons

Huygens absorbed the work of all the leading European mathematician and physicists and as an avowed Cartesian became acknowledged as Europe’s leading natural philosopher. He realised that Descartes rules of impacts were wrong and corrected them. Huygens was also the first to derive and state what is now know as Newton’s second law of motion and derived the law of centripetal force, important steps on the route to a clear understanding of forces and how they operate. Huygens also created the first functioning pendulum clock in the process of which he derived the correct formula for the period of an ideal mathematical pendulum. It is very easy to underestimate Huygens contributions to the development of modern physics; he tends to get squeezed out between Descartes and Newton.

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Spring-driven pendulum clock, designed by Huygens, built by instrument maker Salomon Coster (1657), and a copy of the Horologium Oscillatorium. Museum Boerhaave, Leiden Source: Wikimedia Commons

All the way through I have talked about the men, who developed the new physics as mathematicians and this is highly relevant. The so-called scientific revolution has been referred to as the mathematization of science, an accurate description of what was taking place. The seventeenth century is also known as the golden age of mathematics because the men who created the new physics were also at the same time creating the new mathematical tools needed to create that physics. An algebra based analytical mathematics came to replace the geometric synthetic mathematics inherited from the Greeks.

Algebra first entered Europe in the twelfth century with Robert of Chester’s translation of Muḥammad ibn Mūsā al-Khwārizmī’s ninth century Al-kitāb al-mukhtaṣar fī ḥisāb al-ğabr wa’l-muqābala (The Compendious Book on Calculation by Completion and Balancing), the word algebra coming from the Arabic al-ğabr, meaning completion or setting together (in Spanish an algebraist is a bone setter). This introduction had little impact. It was reintroduced in the thirteenth century by Leonardo of Pisa, this time as commercial arithmetic, where it, especially with the introduction of double entry bookkeeping, had a major impact but still remained outside of academia.

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Leonardo of Pisa Liber Abaci

It was first in the sixteenth century that algebra found its way into academia through the work of Scipione del Ferro (1465–1526), Niccolò Fontana known as Tartaglia (c.1499–1557)and above all Gerolamo Cardano (1501–1576), whose Artis Magnæ, Sive de Regulis Algebraicis Liber Unus (Book number one about The Great Art, or The Rules of Algebra) published by Johannes Petreius (c. 1496–1550) in Nürnberg in 1545 is regarded as the first modern algebra textbook or even the beginning of modern mathematics (which, as should be obvious to regular readers, is a view that I don’t share).

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Source: Wikimedia Commons

Modern readers would find it extremely strange as all of the formulas and theorems are written in words or abbreviations of words and there are no symbols in sight. The status of algebra was further established by the work of the Italian mathematician Rafael Bombelli (1526–1572),

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Source: Wikimedia Commons

(1572)

Another school of algebra was the German Cos school represented by the work of the

German mathematician Michael Stifel (1487–1567), Arithmetica integra (1544),

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Source: Wikimedia Commons

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Michael Stifel’s Arithmetica Integra (1544)

Simon Stevin in the Netherlands L’arithmétique (1585)

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and Robert Recorde (c. 1512–1558) in Britain with his The Whetstone of Witte (1557).

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The passage in The Whetstone of Witte introducing the equals sign Source: Wikimedia Commons

Algebra took a new direction with the French mathematician François Viète (1540–1603),

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François Viète Source: Wikimedia Commons

who wrote an algebra text based on the work of Cardano and the late classical work of Diophantus of Alexandria (2nd century CE) In artem analyticam isagoge (1591) replacing many of the words and abbreviations with symbols.

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Algebra was very much on the advance. Of interest here is that Galileo, who is always presented as the innovator, rejected the analytical mathematics, whereas the leading Jesuit mathematician Christoph Clavius (1538–1612), the last of the staunch defenders of Ptolemaic astronomy, wrote a textbook on Viète’s algebra for the Jesuit schools and colleges.  Two further important publications on symbolic algebra in the seventeenth century were the English mathematician, William Oughtred’s Clavis Mathematicae (1631),

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which went through several editions and was read all over Europe and Thomas Harriot’s unnamed (1631), the only one of his scientific works ever published and that only posthumously.

The development of the then new analytical mathematics reach a high point with the independent invention by Pierre Fermat and René Descartes of analytical geometry, which enabled the geometrical presentation of algebraic functions or the algebraic presentation of geometrical forms; a very powerful tool in the armoury of the mathematical physicists in the seventeenth century. Fermat’s pioneering work in analytical geometry (Methodus ad disquirendam maximam et minimam et de tangentibus linearum curvarum) was circulated in manuscript form in 1636 (based on results achieved in 1629) This manuscript was published posthumously in 1679 in Varia opera mathematica, as Ad Locos Planos et Solidos Isagoge (Introduction to Plane and Solid Loci).

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Descartes more famous work was published as La Géometrié, originally as an appendix to his Discours de la méthode (1637). However, much more important for the dissemination of Descartes version of the analytical geometry was the expanded Latin translation produced by Frans van Schooten the younger with much additional material from van Schooten himself, published in 1649 and the second edition, with extra material from his group of special students mentioned above, in two volumes 1659 and 1661. Van Schooten was the first to introduce the nowadays, ubiquitous orthogonal Cartesian coordinates and to extend the system to three dimensions in his Exercises (1657).

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The other branch of analytical mathematics that was developed in the seventeenth century was what we now know as infinitesimal calculus, the mathematics that is necessary to deal with rates of change, for example for analysing motion. There is a prehistory, particularly of integral calculus but it doesn’t need to interest us here. Kepler used a form of proto-integration to prove his second law of planetary motion and a more sophisticated version to calculate the volume of barrels in a fascinating but often neglected pamphlet. The Galilean mathematician Cavalieri developed a better system of integration, his indivisibles, which he published in his Geometria indivisibilibus continuorum nova quadam ratione promota, (Geometry, developed by a new method through the indivisibles of the continua) (1635) but actually written in 1627, demonstrated on the area of a parabola. This work was developed further by Torricelli, who extended it to other functions.

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The other branch of calculus the calculating of tangents and thus derivatives was worked on by a wide range of mathematicians. Significant contributions were made by Blaise Pascal, Pierre de Fermat, René Descarte, Gregoire de Saint-Vincent, John Wallis and Isaac Barrow. Fermat’s work was the most advanced and included contributions to both integral and deferential calculus, including a general method for determining tangents that is still taught in schools. The Scottish mathematician, James Gregory (1638–1675), inspired by Fermat’s work developed the second fundamental theory of calculus, which states that the integral of a function f over some interval can be computed by using any one, say F, of its infinitely many anti-derivatives. Isaac Barrow (1630–1677) was the first to provide a full proof of the fundamental theorem of calculus, which is a theorem that links the concept of differentiating a function with the concept of integrating a function. Fermat’s work and John Wallis’ Arithmetica Infinitorum (1656) would be an important jumping off point for both Leibniz and Newton in the future.

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Source: Wikimedia Commons

By about 1670, the mathematicians of Europe, who knew of and built on each other’s work had made major advances in the development of both modern mathematics and physics laying the foundations for the next major development in the emergence of modern astronomy. However, before we reach that development there will be a couple of other factors that we have to consider first.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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May 6, 2020 · 8:33 am

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

Without any doubt the biggest impact on the discussion of astronomy and cosmology at the beginning of the seventeenth century was made by the invention of the telescope in 1608 and the subsequent discoveries that were made by astronomers with the new revolutionary instrument. That the Moon was not smooth and perfect as claimed by Aristotle but had geological features like the Earth, that the Milky Way and some nebula resolved into separate stars when viewed through the telescope, that the Sun had spots, that Jupiter had four Moons orbiting it and lastly that Venus displayed phases showing that it must orbit the Sun and not the Earth. All of these, for the times, amazing discoveries were made between the end of 1609 and 1613 then the stream of new discoveries dried up as suddenly as it had begun, why? The problem was a technological one.

All of these initial discoveries had been made using so-called Dutch or Galilean telescopes that consisted of a simple tube with two lenses a convex objective at the front and a concave eyepiece at the back.

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Optical diagram of Galilean telescope y – Distant object ; y′ – Real image from objective ; y″ – Magnified virtual image from eyepiece ; D – Entrance pupil diameter ; d – Virtual exit pupil diameter ; L1 – Objective lens ; L2 – Eyepiece lens e – Virtual exit pupil – Telescope equals Source: Wikimedia Commons

A simple instrument with a serious drawback, by adjusting the focal lengths of the lenses one can increase the magnifying power of the instrument but the greater the magnifying power the smaller the field of vision. Most of the discoveries were made using telescopes with a magnifying power of between twenty and thirty. With such telescopes, for example, Galileo could only view about one quarter of the Moon at a time. With magnifying powers above thirty the Dutch telescope becomes effectively useless as an astronomical instrument. The discoveries that had been made by 1613 marked the limit of discoveries that could be made with the simple Dutch telescope, another instrument had to be found if new discoveries were to be made.

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Galileo’s sketches of the Moon from Sidereus Nuncius. Source: Wikimedia Commons

The solution to the problem had already been presented by Johannes Kepler in his Dioptrice published in 1611.

In this important contribution to the science of optics Kepler not only explained, for the first time, how the Dutch telescope functioned but also what became known as the Keplerian or astronomical telescope with a convex objective and a convex eyepiece. He also described the function of the so-called terrestrial telescope with three convex lenses. The astronomical telescope had a much bigger field of view than the Dutch telescope and could thus be constructed with a much higher magnification.

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Source: Wikimedia Commons

It, however, suffered from the problem that whereas the image in the Dutch telescope was upright, in the astronomical telescope it was inverted. Thus the terrestrial telescope the third lens functioning as an inverter, righting the image.

Christoph Scheiner constructed astronomical telescopes for his work observing the Sun.

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Scheiner’s astronomical telescope for recording sunspots Source: Wikimedia Commons

However, Scheiner remained an exception, if a prominent one, and in general it took three decades before other astronomers turned from the Dutch telescope to telescopes with convex lenses. This of course raises the question, why? The inverted image in the simple two lens astronomical telescope was one problem, however not for Scheiner, who projected the Sun’s image onto a sheet of paper and could thus simply invert his drawn image when finished. There is, however another reason for the very protracted move away from the Dutch telescope to the astronomical telescope and that reason bears the name Galileo Galilei.

Since the publication of his Sidereus Nuncius in 1610, Galileo had become the authority for all things connected with telescopic astronomy.

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Title page of Sidereus nuncius, 1610, by Galileo Galilei (1564-1642). *IC6.G1333.610s, Houghton Library, Harvard University Source: Wikimedia Commons

Galileo was also arrogant enough to reject anything that he didn’t discover or originate. He made rude noises about the astronomical telescope praising the advantages of the Dutch telescope against the astronomical telescope, even though they didn’t exist. He was also very rude about and dismissive of Kepler’s Dioptrice claiming that it was unreadable. His authority was sufficient to hinder the adoption of the astronomical telescope.

One of the first to go against the authority of Galileo and construct and observe with an astronomical telescope was the Italian astronomer Francesco Fontana (c. 1558–1656), who as we saw earlier made the telescope with which Zupi first observed the phases of Mercury.

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Fontana drew a new more accurate map of the Moon, discovered the bands visible on Jupiter. He made the first drawings of Mars and discovered its rotation also inferring the rotation of both Jupiter and Saturn. He published a book of all of his discoveries Novae coelestium terrestriumque rerum observationes, et fortasse hactenus non vulgatae  in 1646.

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Italian astronomer Francesco Fontana created woodcuts showing the Moon and the planets as he saw them through a self-constructed telescope. In 1646, he published most of them in the book Novae Coelestium, Terrestriumque Rerum Observationes, et Fortasse Hactenus Non Vulgatae. Source

This turned out to be a major problem as the book also contained discoveries that Fontana claimed to have made, for example new moons of Jupiter Saturn and Venues, which simply didn’t exist. The charitable explanation is that these were optical artefacts produced by his telescope. This highlights another major problem of early telescopic astronomy, the quality of the early telescopes ranged from bad to abysmal.

The quality of the glass used to make the lenses was usually fairly poor. Often discoloured and equally often containing inclusions, bubbles created during the cooling of the glass, which interfered with the optical quality of the glass. All the early lenses were spherical, i.e. their curvature was segment of the surface of a sphere. This was the only shape that could be ground and polished with the technology available at the time. Even so, the further one got from the centre of a lens the more it tended to deviate from the correct form. This meant that the image formed by such lenses tended to be fairly severely distorted. The current theory is that the invention of the telescope occurred not when somebody succeeded in grinding and polishing lenses, spectacle makers had been doing that for three hundred years before the telescope emerged, or when somebody came up with the right combination of lenses, there is evidence that the magnifying property of the combination of a convex and a concave lens was known sometime before the breakthrough, but when somebody (Hans Lipperhey?) first came up with the idea of masking the outer edges of the objective lens reducing the available area to the truly spherical centre and thus creating a sharp image at the cost of a loss of light. Another problem was so-called spherical aberration. A spherical lens doesn’t actually focus light to a single point but the image is spread out over a small area causing it to blur. This was already known to Ibn al-Haytham (c. 965–c. 1040), who also knew the solution, lenses shaped according to the surfaces of ellipsoids or hyperboloids but lens makers in the seventeenth century were incapable of grinding such shapes. A much bigger problem was chromatic aberration. This is caused by the fact that simple lenses focus different wavelengths and thus different colours of light at slightly different points, causing coloured fringes on the images.  However, the discovery of chromatic aberration by Isaac Newton still lay in the future and its solution even further in the future. Over time the telescope makers discovered that making objective lenses with very long focal lengths reduced the problem of spherical and chromatic aberration and so throughout the seventeenth century the telescopes got longer and longer. Given all of these optical problems it is not surprising that astronomers made discoveries that were illusions; it is to a certain extent a wonder that they discovered anything at all.

The major breakthrough in the use of the astronomical telescope came with the invention of the multiple lens eyepiece by Anton Maria Schyrleus de Rheita, born Johann Burkhard Schyri  (1604–1660), an Capuchin monk, who had studied optics and astronomy at the University of Ingolstadt, the university of Christoph Scheiner and Johann Baptist Cysat, which, although they were no longer present when he studied there, still maintained a high standard in these disciplines. Schyri built his own telescopes and made astronomical observations. In 1643 he published his observations in his Novem stellae, which was full of new discoveries but like those of Fontana they mostly weren’t. Much more important was the publication in 1645 of his Oculus Enoch et Eliae in which he describe, without illustrations, a terrestrial telescope with a three lens eyepiece, as well a description of a pair of binoculars.

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Beginning in 1643 he had already begun to manufacture his new telescope together with the Augsburger instrument maker and optician Johann Wiesel (1583–1662), Germany’s first commercial telescope maker.

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Johann Wiesel with one of his telescopes. Copper engraving by Bartholomäus Kilian, 1660 Source: Wikimedia Commons

The Wiesel/ Schyri terrestrial telescope, which had an upright image, a wide field of vision and high-level magnification, was a huge success throughout Europe. Not only did they sell well but they were soon copied and used not just on land but also as astronomical instruments. In his book Schyri also coined the terms ocular and objective for telescopes.

The Wiesel/ Schyri telescope broke the dam and opened the market for convex lens, astronomical telescopes. In Italy Eustachio Divini (1610–1685) a clockmaker began to manufacture optical instruments becoming by 1646 the leading optician in Italy selling astronomical telescopes throughout Europe.

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Portrait of Eustachio Divini in Carlo Antonio Manzini’s “Dioptrica Pratica” Bologna 1660 Source: Wikimedia Commons

In 1649 he published his first book of observations centred round a spectacular selenography.

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Eustachio Divini Selenography

He would later go on to make detailed observations of Jupiter, the changing shape of the belts, the big red spot and the shadows cast by the satellites. His observation confirmed the axial rotation of the planet.

Divini’s reputation as Europe’s leading telescope maker/astronomer was usurped in 1656 by the still young Dutch polymath Christiaan Huygens (1629–1695), who designed his own astronomical telescope, which he constructed with his brother Constantijn (1628–1697) and with which he discovered Titan the largest of Saturn’s moons.

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Christiaan Huygens by Caspar Netscher, 1671, Museum Boerhaave, Leiden Source: Wikimedia Commons

The year before he had already staked his territory by explaining that the strange observations made by various astronomers of Saturn were in fact differing views of rings surrounding the planet. He explained this in his Systema Saturnium in 1659, which also contained the first telescopic sketches of the Orion Nebula. His explanation of the rings led to a major dispute with Divini, who was convinced that they were a belt of satellites.

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Huygens’ explanation for the aspects of Saturn, Systema Saturnium, 1659 Source: Wikimedia Commons

In the same year he made the first observations of a surface feature of another planet, Syrtis Major, a volcanic plain on Mars, using it to determine the length of the Martian day.

Divini lost his status as Italy’s prime telescope maker to the Campani brothers Matteo (1620–after 1678) and Giuseppe (1635–1715) in a series of contests staged the Accademia del Cimento to test the quality of their telescopes in 1664, which the Campani brothers won, although largely through skulduggery. Of interest is that the quality of the telescopes were compared by reading printed letters though them, a forerunner of the letter charts in the practice of every ophthalmic optician.

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Giuseppe Campani (1635-1715) Telescope with four tubes, Rome, 1666 Florence, Istituto e Museo di Storia della Scienza, inv. 2556

Although Giuseppe Campani was an active astronomer, who made his own observations and discoveries it is their most famous customer, who made the biggest impact, Giovanni Domenico Cassini (1625–1712), who became Jean-Dominique when he moved to France in 1669.

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Giovanni Cassini artist unknown Source: Wikimedia Commons

Employed as an astronomer at the observatory in Panzano by the Marquis Cornelio Malvasia (1603–1664) from 1648, Cassini was able to study under Giovanni Battista Riccioli (1598–1671) and Francesco Maria Grimaldi (1618–1663), themselves important telescopic astronomers, who produced an important lunar map, at the University of Bologna.

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Riccioli/Grimaldi Lunar Map Source: Wikimedia Commons

In 1650 he was appointed professor for astronomy at the university. During his time in Bologna Cassini was able, with the assistance of Riccioli and Grimaldi, using a meridian line in the San Petronio Basilica to prove that that either the Sun’s orbit around the Earth or the Earth’s orbit around the Sun was an ellipse thus confirming a part of Kepler’s astronomical system. The experiment was unable to determine if the system was geo-heliocentric or heliocentric.

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San Petronio Basilica The winter solstice end of the meridian line Source: Wikimedia Commons

As Europe’s leading telescopic astronomer Cassini discovered and published surface markings on Mars, determined the rotation periods of Mars and Jupiter, discovered four satellites of Saturn–Iapetus and Rhea in 1671 and 1672 followed by Tethys and Dione in 1684–he is also credited with the co-discovery with Robert Hooke of the big red spot on Jupiter. He was able to determine the orbits of the moons of Jupiter with enough accuracy that they could be used as a clock to determine longitude, as originally suggested by Galileo. A spin off of this research was the determination of the speed of light by Cassini’s assistant, Ole Rømer (1644–1710). He also showed that both the moons of Jupiter and Saturn obeyed Kepler’s third law, a fact used later by Newton in his Principia Mathematica.

The problem of aberration and the semi-solution of having objectives with ever-longer focal lengths led to the development of the aerial telescope. These are extremely long focal length telescopes that have an objective lens and an eyepiece but no tube, instead having some mechanism to keep the two lens units aligned. Christiaan Huygens constructed one with a cord between the objective and the ocular.

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An engraving of Huygens’s 210-foot aerial telescope showing the eyepiece and objective mounts and connecting string. Source: Wikimedia Commons

The most famous aerial telescope, however, was that of Johannes Hevelius (1611–1687), a wealthy beer brewer and amateur astronomer who lived in Danzig.

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Johannes Hevelius and his wife Elizabeth observing together Source: Wikimedia Commons

Hevelius constructed a telescope with a focal length of 150 feet, which became a tourist attraction.

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1673 engraved illustration of Johannes Hevelius’s 8 inch telescope with an open work wood and wire “tube” that had a focal length of 150 feet to limit chromatic aberration. Source: Wikimedia Commons

He also built a fully equipped observatory on the roof of his brewery and undertook extensive astronomical observations. He, like other, produced a very detailed map of the Moon, discovered four comets and hypothesised that comets obit the Sun on parabolic orbits, created an extensive star atlas in which he described and named ten new constellations, seven of which are still included in official star maps.

With the exception of the discovery of the five largest moons of Saturn, this second wave of seventeenth century telescopic astronomy, starting in about 1640 and continuing till the end of the century, was not as spectacular as the first one. However by the end of the century the small discoveries had accumulated to create a completely different picture of the heavens to the one that existed at the beginning. Planets were no longer Aristotle’s perfectly smooth, spherical bodies but had satellites and surface features, rotated on their axes and had determinable day lengths. The Moon had been accurately mapped by several independent astronomers and there was absolutely no doubt in the minds of the observers that it was fundamentally earth like. The position of many more stars had been accurately mapped and the orbits of the newly discovered satellites had been accurately determined. The celestial spheres of Aristotle and Ptolemaeus had been totally banished. During this second wave of telescopic observation and discovery telescopic astronomy came of age and became a recognised scientific discipline.

In 1669 Cassini was appointed the first director of the Paris Observatory, which had been founded in 1667 by the French minister of finance, Jean-Baptiste Colbert (1619–1683).

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An engraving of The Paris Observatory in the beginning of the 18th century with the wooden “Marly Tower” on the right, erected by Cassini to support both tubed and aerial very long telescopes Source: Wikimedia Commons

The founding of the Paris observatory was followed in 1675 with the founding in England of the Royal Observatory in Greenwich by Charles II, with John Flamsteed appointed in the same year as the first Astronomer Royal.

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Royal Observatory Greenwich Source: Wikimedia Commons

Berlin came somewhat later in 1700 with the appointment of Gottfried Kirch (1639–1710) but who never lived to see his observatory, which first opened in 1711. What we see here is a radical change in the status of astronomy. Whereas for most of the seventeenth century astronomy had been the province of either private citizens or university professors it now became the province of governments with astronomers appointed as civil servants required to deliver astronomical data for cartographical and navigational purposes.

 

 

 

 

 

 

 

 

 

 

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Filed under History of Astronomy, History of Optics, History of science

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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Filed under History of Astronomy, History of Mathematics, History of Optics, Myths of Science, Newton

April 12th

The HISTSCI_HULK had just been settling down to the beautiful sunny morning and deciding, which of his Easter eggs he wanted to eat first (chocolate for breakfast on Easter is OK, isn’t it?), when he let out an ear shattering bellow of rage that signalled that he was about to go on the rampage. What could have so upset the valiant defender of truth and accuracy in the history of science? He had been casually perusing the website Today in Science History, a useful calendar of birth, deaths and events in #histSTM, when his eyes were drawn to the following brief statement:

 

“In 1633, Galileo Galilei’s second trial before the Inquisition began. At its conclusion his belief that the Earth was not the centre of the Universe was pronounced heretical”

What could possible have so enraged the HISTSCI monster in this apparently innocuous historical claim? Well, almost everything. The date and the name are correct but both substantive claims are simply false. Of course, there is the possibility that we have slipped into a parallel universe and are dealing with another Galileo Galilei about whom the stated facts are correct but Ockham’s razor would suggest that the simplest solution is that the facts are wrong.

We start with, “Galileo Galilei’s second trial before the Inquisition began,” Galileo only ever had one trial before the Inquisition so this could not have been the second. This is a wide spread misconception that occurs here not for this first time and it is worth explaining why it’s false. Galileo had to do with the Inquisition three times in his life. Three times, I hear you ask, when or what was the third time. Most people aren’t aware of Galileo’s first run in with the Inquisition, which took place when he was still a relatively unknown professor for mathematics in Padua in 1604.

Galileo was denounced to the Venetian Inquisition by a former amanuensis, Silvestro Pagnoni from Pesaro for practicing deterministic astrology. Yes, Galileo was a practicing astrologer and no, he didn’t just do it for the money. Greek astrology was deterministic, which meant that ones entire life was determined at the point of birth. This conflicted with the Christian belief in free will and was thus considered heretical. Quite why the Medieval Church didn’t just dump astrology is somewhat puzzling but in the thirteenth century Albertus Magnus and Thomas Aquinas redefined astrology, so that it was non-deterministic for human thought. You can read exactly how they did so in Darrel Rutkin’s excellent book, Sapientia Astrologica. Although the Church accepted astrology in the seventeenth century, deterministic astrology was definitely not acceptable. The Venetian Inquisition duly investigated the accusation and, having cleared Galileo of all suspicion, did not pursue the case any further. Galileo’s next brush with the Inquisition was the much more famous one in 1615/16 and it is this one that people mistakenly think was a trial with Galileo as the accused.

What actually happened was that the Church provoked by Galileo’s Letter to Benedetto Castelli and Paolo Antonio Foscarini’s Epistle concerning the Pythagorean and Copernican opinion of the Mobility of the Earth and the stability of the sun and of the new system or constitution of the World set up a commission to investigate and pass judgement on the heliocentric cosmological theory. The conclusion of the commission is generally well known.

The proposition that the Sun is stationary at the centre of the universe is “foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture”; the proposition that the Earth moves and is not at the centre of the universe “receives the same judgement in philosophy; and … in regard to theological truth it is at least erroneous in faith.”

Absurd in philosophy can be translated as scientifically false, a correct judgement based on the knowledge of the time, as the available empirical evidence solidly supported a helio-geocentric system and not a heliocentric one.

As Galileo was the leading proponent of a heliocentric world view the Pope, Paul V, instructed Roberto Bellarmino, the Church’s leading theologian to inform Galileo of the commission’s findings and to instruct him that he could no longer hold or teach the heliocentric theory. Bellarmino did as instructed but at no point was Galileo on trail.

The astute reader will have already noticed that it was not at the end of his trial in 1633 that the “belief that the Earth was not the centre of the Universe was pronounced heretical” but already by the commission of investigation in 1616. In fact we now stumble upon a conundrum, the heliocentric theory was never actually officially pronounced heretical. The commission found that the proposition that the Sun is stationary at the centre of the universe is “foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture” but only a Pope can formally declare something heretical and no pope ever did.

I’m not going to address the trial itself and the factors leading up to it, as I fairly recently wrote a whole blog post on the topic, which you can read here.

This anniversary provoked an at times heated exchange on Twitter, yesterday and this morning, in which various people attacked the Catholic Church and/or the Inquisition, their attacks based largely on false or inaccurate information and I, as all too often, ended up trying my best to correct their mistaken utterances. I will now repeat some of the core insights from that exchange.

Galileo was during his interrogation and trial by the Roman Inquisition never imprisoned nor tortured and not even shown the instruments of torture, all of which claims are too often believed to represent the truth. He was, in fact, treated with care and respect as an honoured guest throughout his interrogation. He was housed in a luxury apartment with servants to see to his needs and during the breaks between the separate interrogations was even allowed to return to the apartment in Rome where he was staying before the interrogations began. Following the trial where he was found guilty of grave suspicion of heresy, and not heresy as if often falsely claimed, he was sentenced to life imprisonment, which was immediately commuted to house arrest. He spent the first weeks of his house arrest as the honoured guest of Archbishop Piccolomini in his palace in Sienna until it proved too much of a good thing and Urban ordered that he go home. He spent the rest of his house arrest in his own villa in Arceti near Florence, where he was cared for by servants. He was allowed visitors and now too old and too frail to travel anyway he devoted himself to writing the Discorsi, his most important scientific work, which despite a ban was published without the Church undertaking any action against it. The average European peasant in the period certainly lived a much worse life.

One topic that came up several times was that even if not tortured or threatened with torture, Galileo would have been scared of the Inquisition because of its reputation and especially because of what they did to Bruno. If there were a false facts about the Church and Galileo bingo game evoking Bruno would certainly occupy the centre square. These comment stimulated the following speculations on my part:

Actually, I don’t think Galileo was particularly concerned about the Inquisition; his self-opinionated arrogance protected him from such thoughts. He wasn’t a religious nutcase like Bruno, he was the greatest scientist in Europe, he was a Medicean courtier, he was a much admired and feted member of Roman high society, he counted princes and powerful cardinals amongst his best friends and supporters, Maffeo Barberini had been one of his best friends since 1612. When he became Pope Urban VIII, Barberini granted him several private audiences and praised his latest book, Il Saggiatore, it was Barberini who, as Pope, had commissioned him to write his book comparing the geocentric and heliocentric systems, what could he possibly have to fear?

This is of course, as I say, purely speculative but the way Galileo is known to have behaved during his interrogations would seem to support such a view.

 

 

 

 

 

 

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Filed under History of Astronomy, Myths of Science, Renaissance Science