Category Archives: History of science

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

Without a doubt the most well-known, in fact notorious, episode in the transition from a geocentric to a heliocentric cosmology/astronomy in the seventeenth century was the publication of Galileo Galilei’s Dialogo sopra i due massimi sistemi del mondo (Dialogue Concerning the Two Chief World Systems) in 1632 and his subsequent trial and conviction by the Supreme Sacred Congregation of the Roman and Universal Inquisition or simply Roman Inquisition; an episode that has been blown up out of all proportions over the centuries. It would require a whole book of its own to really do this subject justice but I shall deal with it here in two sketches. The first to outline how and why the publication of this book led to Galileo’s trial and the second to assess the impact of the book on the seventeenth century astronomical/cosmological debate, which was much less than is often claimed.


Frontispiece and title page of the Dialogo, 1632 Source: Wikimedia Commons

The first salient point is Galileo’s social status in the early seventeenth century. Nowadays we place ‘great scientists’ on a pedestal and accord them a very high social status but this was not always the case. In the Renaissance, within society in general, natural philosophers and mathematicians had a comparatively low status and within the ruling political and religious hierarchies Galileo was effectively a nobody. Yes, he was famous for his telescopic discoveries but this did not change the fact that he was a mere mathematicus. As court mathematicus and philosophicus to the Medici in Florence he was little more than a high-level court jester, he should reflect positively on his masters. His role was to entertain the grand duke and his guests at banquets and other social occasions with his sparkling wit, either in the form of a discourse or if a suitable opponent was at hand, in a staged dispute. Points were awarded not for truth content but for verbal brilliance. Galileo was a master at such games. However, his real status as a courtier was very low and should he bring negative attention to the court, they would drop him without a thought, as they did when the Inquisition moved against him.


Galileo Portrait by Ottavio Leoni Source: Wikimedia Commons

As a cardinal, Maffeo Barberini (1568–1644) had befriended Galileo when his first came to prominence in 1611 and he was also an admirer of the Accademia dei Lincei. When he was elected Pope in 1623 the Accademia celebrated his election and amongst other things presented him with a copy of Galileo’s Il Saggiatore, which he read and apparently very much enjoyed. As a result he granted Galileo several private audiences, a great honour. Through his actions Barberini had raised Galileo to the status of papal favourite, a situation not without its dangers.


C. 1598 painting of Maffeo Barberini at age 30 by Caravaggio Source: Wikimedia Commons

Mario Biagioli presents the, I think correct, hypothesis that having raised Galileo up as a court favourite Barberini then destroyed him. Such behaviour was quite common under absolutist rulers, as a power demonstration to intimidate potential rebels. Galileo was a perfect victim for such a demonstration highly prominent and popular but with no real political or religious significance. Would Barberini have staged such a demonstration at the time? There is evidence that he was growing more and more paranoid during this period. Barberini, who believed deeply in astrology, heard rumours that an astrologer had foreseen his death in the stars. His death was to coincide with a solar eclipse in 1630. Barberini with the help of his court astrologer, Tommaso Campanella (1568–1639) took extreme evasive action and survived the cosmic threat but he had Orazio Morandi (c. 1570–1630), a close friend and supporter of Galileo’s, arrested and thrown in the papal dungeons, where he died, for having cast the offending horoscope.

Turning to the Dialogo, the official bone of contention, Galileo succeeded in his egotism in alienating Barberini with its publication. Apparently during the phase when he was very much in Barberini’s good books, Galileo had told the Pope that the Protestants were laughing at the Catholics because they didn’t understand the heliocentric hypothesis. Of course, during the Thirty Years War any such mockery was totally unacceptable. Barberini gave Galileo permission to write a book presenting and contrasting the heliocentric and geocentric systems but with certain conditions. Both systems were to be presented as equals with no attempts to prove the superiority or truth of either and Galileo was to include the philosophical and theological opinion of the Pope that whatever the empirical evidence might suggest, God in his infinite wisdom could create the cosmos in what ever way he chose.

The book that Galileo wrote in no way fulfilled the condition stated by Barberini. Presented as a discussion over four days between on the one side a Copernican, Salviati named after Filippo Salviati (1682–1614) a close friend of Galileo’s and Sagredo, supposedly neutral but leaning strongly to heliocentricity, named after Giovanni Francesco Sagredo (1571–1620) another close friend of Galileo’s. Opposing these learned gentlemen is Simplicio, an Aristotelian, named after Simplicius of Cilicia a sixth-century commentator on Aristotle. This name is with relative certainty a play on the Italian word “semplice”, which means simple as in simple minded. Galileo stacked the deck from the beginning.

The first three days of discussion are a rehash of the previous decades of discoveries and developments in astronomy and cosmology with the arguments for heliocentricity, or rather against geocentricity in its Ptolemaic/Aristotelian form, presented in their best light and the counter arguments presented decidedly less well. Galileo was leaving nothing to chance, he knew who was going to win this discussion. The whole thing is crowned with Galileo’s theory of the tides on day four, which he falsely believed, despite its very obvious flaws, to be a solid empirical proof of the Earth’s movements in a heliocentric model. This was in no way an unbiased presentation of two equal systems but an obvious propaganda text for heliocentricity. Worse than this, he placed the Pope’s words on the subject in the mouth of Simplicio, the simpleton, not a smart move. When it was published the shit hit the fan.

However, before considering the events leading up to the trial and the trial itself there are a couple of other factors that prejudiced the case against Galileo. In order to get published at all, the book, as with every other book, had to be given publication permission by the censor. To repeat something that people tend to forget, censorship was practiced by all secular and all religious authorities throughout the whole of Europe and was not peculiar to the Catholic Church. Freedom of speech and freedom of thought were alien concepts in the world of seventeenth century religion and politics. Galileo wanted initially to title the book, Dialogue on the Ebb and Flow of the Seas, referring of course to his theory of the tides, and include a preface to this effect. He was told to remove both by the censor, as they, of course, implied a proof of heliocentricity. Because of an outbreak of the plague, Galileo retired to Florence to write his book and preceded to play the censor in Florence and the censor in Rome off against each other, which meant that the book was published without being properly controlled by a censor. This, of course, all came out after publication and did not help Galileo’s case at all; he had been far too clever for his own good.

Another major problem had specifically nothing to do with Galileo in the first instance but rebounded on him at the worst time.  On 8 March 1632 Cardinal Borgia castigated the Pope for not supporting King Philipp IV of Spain against the German Protestants. The situation almost degenerated into a punch up with the Swiss Guard being called in to separate the adversaries. As a result Barberini decided to purge the Vatican of pro-Spanish elements. One of the most prominent men to be banished was Giovanni Ciampoli (1589–1643) Barberini’s chamberlain. Ciampoli was an old friend and supporter of Galileo and a member of the Accademia dei Lincei. He was highly active in helping Galileo trick the censors and had read the manuscript of the Dialogo, telling Barberini that it fulfilled his conditions. His banishment was a major disaster for Galileo.


Giovanni Ciampoli Source: Wikimedia Commons

One should of course also not forget that Galileo had effectively destroyed any hope of support from the Jesuits, the leading astronomers and mathematicians of the age, who had very actively supported him in 1611, with his unwarranted and libellous attacks on Grazi and Scheiner in his Il Saggiatore. He repeated the attacks on Scheiner in the Dialogo, whilst at the same time plagiarising him, claiming some of Scheiner’s sunspot discoveries as his own. There is even some evidence that the Jesuits worked behind the scenes urging the Pope to put Galileo on trial.

When the Dialogo was published it immediately caused a major stir. Barberini appointed officials to read and assess it. Their judgement was conclusive, the Dialogo obviously breached the judgement of 1616 forbidding the teaching of heliocentricity as a factual theory. Anybody reading the Dialogo today would confirm that judgement. The consequence was that Galileo was summoned to Rome to answer to the Inquisition. Galileo stalled claiming bad health but was informed either he comes or he would be fetched. The Medici’s refused to support him; they did no consider him worth going into confrontation with the Pope for.


Ferdinando II de’ Medici Grand Duke of Tuscany in Coronation Robes (school of Justus Sustermans). Source: Wikimedia Commons

We don’t need to go into details of the trial. Like all authoritarian courts the Inquisition didn’t wish to try their accused but preferred them to confess, this was the case with Galileo. During his interviews with the Inquisition Galileo was treated with care and consideration because of his age and bad health. He was provided with an apartment in the Inquisition building with servants to care for him. At first he denied the charges but when he realised that this wouldn’t work he said that he had got carried away whilst writing and he offered to rewrite the book. This also didn’t work, the book was already on the market and was a comparative best seller, there was no going back. Galileo thought he possessed a get out of jail free card. In 1616, after he had been interviewed by Bellarmino, rumours circulated that he had been formally censured by the Inquisition. Galileo wrote to Bellarmino complaining and the Cardinal provided him with a letter stating categorically that this was not the case. Galileo now produced this letter thinking it would absolve him of the charges. The Inquisition now produced the written version of the statement that had been read to Galileo by an official of the Inquisition immediately following his interview with Bellarmino expressly forbidding the teaching of the heliocentric theory as fact. This document still exists and there have been discussions as to its genuineness but the general consensus is that it is genuine and not a forgery. Galileo was finished, guilty as charged. Some opponents of the Church make a lot of noise about Galileo being shown the instruments of torture but this was a mere formality in a heresy trial and at no point was Galileo threatened with torture.

The rest is history. Galileo confessed and formally adjured to the charge of grave suspicion of heresy, compared to heresy a comparatively minor charge. He was sentenced to prison, which was immediately commuted to house arrest. He spent the first months of his house arrest as the guest of Ascanio II Piccolomini (1590–1671), Archbishop of Siena,


Ascanio II Piccolomini Source: Wikimedia Commons

until Barberini intervened and sent him home to his villa in Arcetri. Here he lived out his last decade in comparative comfort, cared for by loyal servants, receiving visitor and writing his most important book, Discorsi e dimostrazioni matematiche intorno a due nuove scienze (Discourses and Mathematical Demonstrations Relating to Two New Sciences).

Galileo’s real crime was hubris, trying to play an absolutist ruler, the Pope, for a fool. Others were executed for less in the seventeenth century and not just by the Catholic Church. Galileo got off comparatively lightly.

What role did the Dialogo actually play in the ongoing cosmological/astronomical debate in the seventeenth century? The real answer is, given its reputation, surprisingly little. In reality Galileo was totally out of step with the actual debate that was taking place around 1630. Driven by his egotistical desire to be the man, who proved the truth of heliocentricity, he deliberately turned a blind eye to the most important developments and so side lined himself.

We saw earlier that around 1613 there were more that a half a dozen systems vying for a place in the debate, however by 1630 nearly all of the systems had been eliminated leaving just two in serious consideration. Galileo called his book Dialogue Concerning the Two Chief World Systems, but the two systems that he chose to discuss, the Ptolemaic/Aristotelian geocentric system and the Copernican heliocentric system, were ones that had already been rejected by almost all participants in the debate by 1630 . The choice of the pure geocentric system of Ptolemaeus was particularly disingenuous, as Galileo had helped to show that it was no longer viable twenty years earlier. The first system actually under discussion when Galileo published his book was a Tychonic geo-heliocentric system with diurnal rotation, Christen Longomontanus (1562–1647), Tycho’s chief assistant, had published an updated version based on Tycho’s data in his Astronomia Danica in 1622. This was the system that had been formally adopted by the Jesuits.


The second was the elliptical heliocentric system of Johannes Kepler, of which I dealt with the relevant publications in the last post.

Galileo completely ignores Tycho, whose system could explain all of the available evidence for heliocentricity, because he didn’t want to admit that this was the case, arguing instead that the evidence must imply a heliocentric system. He also, against all the available empirical evidence, maintained his belief that comets were sublunar meteorological phenomena, because the supporters of a Tychonic system used their perceived solar orbit as an argument for their system.  He is even intensely disrespectful to Tycho in the Dialogo, for which Kepler severely castigated him. He also completely ignores Kepler, which is even more crass, as the best available arguments for heliocentricity were to be found clearly in Kepler published works. Galileo could not adopt Kepler’s system because it would mean that Kepler and not he would be the man, who proved the truth of the heliocentric system.

Although the first three days of the Dialogo provide a good polemic presentation for all of the evidence up till that point for a refutation of the Ptolemaic/Aristotelian system, with the very notable exception of the comets, Galileo’s book was out dated when it was written and had very little impact on the subsequent astronomical/cosmological debate in the seventeenth century. I will indulge in a little bit of hypothetical historical speculation here. If Galileo had actually written a balanced and neutral account of the positive and negative points of the Tychonic geo-heliocentric system with diurnal rotation and Kepler’s elliptical heliocentric system, it might have had the following consequences. Firstly, given his preeminent skills as a science communicator, his book would have been a valuable contribution to the ongoing debate and secondly he probably wouldn’t have been persecuted by the Catholic Church. However, one can’t turn back the clock and undo what has already been done.

I will close this overlong post with a few brief comments on the impact of the Church’s ban on the heliocentric theory, the heliocentric hypothesis was still permitted, and the trial and sentencing of Galileo, after all he was the most famous astronomer in Europe. Basically the impact was much more minimal than is usually implied in all the popular presentations of the subject. Outside of Italy these actions of the Church had almost no impact whatsoever, even in other Catholic countries. In fact a Latin edition of the Dialogo was published openly in Lyon in 1641, by the bookseller Jean-Antoine Huguetan (1567–1650), and dedicated to the French diplomat Balthasar de Monconys (1611–1665), who was educated by the Jesuits.


Within Italy well-behaved Catholics censored their copies of Copernicus’ De revolutionibus according to the Church’s instructions but continued to read and use them. Censored copies of the book are virtually unknown outside of Italy. Also within Italy, astronomers would begin their discussions of heliocentricity by stating in the preface that the Holy Mother Church in its wisdom had declared this system to be false, but it is an interesting mathematical hypothesis and then go on in their books to discuss it fully. On the whole the Inquisition left them in peace.


***A brief footnote to the above: this is a historical sketch of what took place around 1630 in Northern Italy written from the viewpoint of the politics, laws and customs that ruled there at that time. It is not a moral judgement on the behaviour of either the Catholic Church or Galileo Galilei and I would be grateful if any commentators on this post would confine themselves to the contextual historical facts and not go off on wild moral polemics based on hindsight. Comments on and criticism of the historical context and/or content are, as always, welcome.











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

Christmas Trilogy Part 3: The emergence of modern astronomy – a complex mosaic: Part XXVI


In popular presentations of the so-called scientific or astronomical revolutions Galileo Galilei is almost always presented as the great champion of heliocentricity in the first third of the seventeenth century. In fact, as we shall see, his contribution was considerably smaller than is usually claimed and mostly had a negative rather than a positive influence. The real champion of heliocentricity in this period was Johannes Kepler, who in the decade between 1617 and 1627 published four major works that laid the foundations for the eventual triumph of heliocentricity over its rivals. I have already dealt with one of these in the previous post in this series, the 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 …, which was published in 1619 and as I’ve already said became the most important reference text on comets in the 1680’s during a period of high comet activity that we will deal with in a later post.


Source: ETH Library Zurich

Chronologically the first of Kepler’s influential books from this decade was Volume I (books I–III) of his Epitome Astronomiae Copernicanae published in 1617, Volume II (book IV) followed in 1620 and Volume III (books V–VII) in 1621. This was a text book on heliocentric astronomy written in question and answer dialogue form between a teacher and a student spelling out the whole of heliocentric astronomy and cosmology in comparatively straight forward and simple terms, the first such textbook. There was a second edition containing all three volumes in 1635.


Second edition 1635 Source

This book was highly influential in the decades following its publication and although it claims to be a digest of Copernican astronomy, it in fact presents Kepler’s own elliptical astronomy. For the first time his, now legendary, three laws of planetary motion are presented as such together. As we saw earlier the first two laws–I. The orbit of a planet is an ellipse and the Sun is at one of the focal points of that ellipse II: A line connecting the Sun and the planet sweeps out equal areas in equal times–were published in his Astronomia Nova in 1609. The third law was new first appearing in, what he considered to be his opus magnum, Ioannis Keppleri Harmonices mundi libri V (The Five Books of Johannes Kepler’s The Harmony of the World) published in 1619 and to which we now turn our attention.


Source: Wikimedia Commons

Kepler’s first book was his Mysterium Cosmographicum published in 1597 with its, to our way of thinking, somewhat bizarre hypothesis that there are only six planets because the spaces between their orbits are defined by the five regular Platonic solids.


Kepler’s Platonic solid model of the Solar System from Mysterium Cosmographicum Source: Wikimedia Commons

Although his calculation in 1597 showed a fairly good geometrical fit for his theory, it was to Kepler’s mind not good enough and this was his motivation for acquiring Tycho Brahe’s newly won more accurate data for the planetary orbits. He believed he could quite literally fine tune his model using the Pythagorean theory of the harmony of the spheres, that is that the ratio of the planetary orbits build a musical scale that is only discernable to the enlightened Pythagorean astronomer. The Harmonices Mundi was that fine tuning.

The first two books of the Harmonices Mundi layout Kepler’s geometrical theory of music, which geometrical constructions produced harmonious musical intervals and which disharmonious ones, based on which are constructible with straight edge and compass, harmonious, and which are not, disharmonious. The third book is Kepler’s contribution to the contemporary debate on the correct division of the intervals of the musical scale, in which Vincenzo Galilei (1520–1591), Galileo’s father, had played a leading role. The fourth book is the application of the whole to astrology and the fifth its application to astronomy and it is here that we find the third law.

In the fifth Kepler compare all possible ratios of planetary speeds and distances constructing musical scales for planets and musical intervals for the relationship between planets. It is here that he, one could say, stumbles upon his third law, which is known as the harmony law. Kepler was very much aware of the importance of his discovery as he tells us in his own words:

“After I had discovered true intervals of the orbits by ceaseless labour over a very long time and with the help of Brahe’s observations, finally the true proportion of the orbits showed itself to me. On the 8th of March of this year 1618, if exact information about the time is desired, it appeared in my head. But I was unlucky when I inserted it into the calculation, and rejected it as false. Finally, on May 15, it came again and with a new onset conquered the darkness of my mind, whereat there followed such an excellent agreement between my seventeen years of work at the Tychonic observations and my present deliberation that I at first believed that I had dreamed and assumed the sought for in the supporting proofs. But it is entirely certain and exact that the proportion between the periodic times of any two planets is precisely one and a half times the proportion of the mean distances.”

Translated into modern notation the third law is P12/P22=R13/R23, where P is the period of a planet and R is the mean radius of its orbit. It can be argues that this was Kepler’s greatest contribution to the history of the emergence of heliocentricity but rather strangely nobody really noticed its true significance until Newton came along at the end of the seventeenth century.

However they should have done because the third law gives us is a direct mathematical relationship between the size of the orbits of the planets and their duration, which only works in a heliocentric system. There is nothing comparable for either a full geocentric system or for a geo-heliocentric Tychonic or semi-Tychonic system. It should have hit the early seventeenth-century astronomical community like a bomb but it didn’t, which raises the question why it didn’t. The answer is because it is buried in an enormous pile of irrelevance in the Harmonices Mundi and when Kepler repeated it in the Epitome he gave it no real emphasis, so it remained relatively ignored.

On a side note, it is often thought that Kepler had abandoned his comparatively baroque Platonic solids concepts from the Mysterium Cosmographicum but now that he had, in his opinion, ratified it in the Harmonices Mundi he published a second edition of the book in 1621.


Second Edition 1621 Source

Ironically the book of Kepler’s that really carried the day for heliocentricity against the geocentric and geo-heliocentric systems was his book of planetary tables based on Tycho Brahe’s data the Tabulae Rudolphinae (Rudolphine Tables) published in 1627, twenty-eight years after he first began working on them. Kepler had in fact been appointed directly by Rudolph II in Prague to produce these tables at the suggestion of Tycho in 1601. Turning Tycho’s vast collection of data into accurately calculated tables was a horrendous and tedious task and over the years Kepler complained often and bitterly about this burden.


Tabulae Rudolphinae The frontispiece presents in graphic form a potted history of Western astronomy Source

However, he persevered and towards the end of the 1620s he was so far. Because he was the Imperial Mathematicus and had prepared the tables under the orders of the Emperor he tried to get the funds to cover the printing costs from the imperial treasury. This proved to be very difficult and after major struggles he managed to acquire 2000 florins of the more than 6000 that the Emperor owed him, enough to pay for the paper. He began printing in Linz but in the turmoil of the Thirty Years War the printing workshop got burnt down and he lost the already printed pages. Kepler decamped to Ulm, where with more difficulties he succeeded in finishing the first edition of 1000 copies. Although these were theoretically the property of the Emperor, Kepler took them to the Frankfurt book fair where he sold the entire edition to recoup his costs.

The Tabulae Rudolphinae were pretty much an instant hit. The principle function of astronomy since its beginnings in Babylon had always been to produce accurate tables and ephemerides for use initially by astrologers and then with time also cartographers, navigators etc. Astronomical systems and the astronomers, who created them, were judged on the quality and accuracy of their tables. Kepler’s Tabulae Rudolphinae based on Tycho’s data were of a level of accuracy previous unknown and thus immediately won many supporters. Those who used the tables assumed that their accuracies was due to Kepler’s elliptical planetary models leading to a gradually increasing acceptance of heliocentricity but this was Kepler’s system and not Copernicus’. Supported by the Epitome with the three laws of planetary motion Kepler’s version of heliocentricity became the dominant astronomical/cosmological system over the next decades but it would be another thirty to forty years, long after Kepler’s death, before it became the fully accepted system amongst astronomers.









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

Christmas Trilogy 2019 Part 2: Babbage, Airy and financing the Difference Engine.

Charles Babbage first announced his concept for his first computer, the Difference Engine, in a Royal Astronomical Society paper, Note on the application of machinery to the computation of astronomical and mathematical tables in 1822.


Engraving of Charles Babbage dated 1833 Source: Wikimedia Commons

He managed to convince the British Government that a mechanical calculator would be useful for producing numerical tables faster, cheaper and more accurately and in 1823 they advance Babbage £1700 to begin construction of a full scale machine. It took Babbage and his engineer, Joseph Clements, nine years to produce a small working model but costs had spiralled out of control and the government suspended payment at around £17,000, in those days a small fortune, in 1833.


A portion of the difference engine. Woodcut after a drawing by Benjamin Herschel Babbage Source: Wikimedia Commons

Babbage and Clement had parted in dispute by this time. The next nine years saw Babbage negotiating with various government officials to try and get payment reinstated. Enter George Biddel Airy (1801–1892).


George Biddell Airy caricatured by Ape in Vanity Fair Nov 1875 Source: Wikimedia Commons

Airy entered Trinity College Cambridge in 1819, graduating Senior Wrangler and Smith Prize man in 1823. He was elected a fellow of Trinity in 1824 and Lucasian Professor of mathematics beating Babbage for the position in 1826. In 1828 he was elected Plumian Professor of astronomy and director of the new Cambridge Observatory. Babbage succeeded him as Lucasian Professor. Airy proved very competent and very efficient as the director of the observatory, which led to him being appointed Astronomer Royal at the Greenwich Observatory in 1835 and thus the leading state scientist and effectively the government scientific advisor. It was in this capacity that the paths of the two Cambridge mathematicians crossed once again[1].

In 1842 Henry Goulburn (1784–1856), Chancellor of the Exchequer in the cabinet of Sir Robert Peel (1788–1850) was asked by Peel to gather information on Babbage’s Difference Engine project, which he would have liked to ditch, preferable yesterday rather than tomorrow. Goulburn turned to Airy as the countries leading scientific civil servant and also because the Royal Observatory was responsible for producing many of the mathematical tables, the productions of which the Difference Engine was supposed to facilitate. Could Airy offer an opinion on the utility of the proposed mechanical calculator? Airy could and it was anything but positive:

Mr Babbage made the approval of the machine a personal question. In consequence of this, I, and I believe other persons, have carefully abstained for several years from alluding to it in his presence. I think he lives in a sort of dream as to its utility.

An absurd notion has been spread abroad, that the machine was intended for all calculations of every kind. This is quite wrong. The machine is intended solely for calculations which can be made by addition and subtraction in a particular way. This excludes all ordinary calculation.

Scarcely a figure of the Nautical Almanac could be computed by it. Not a single figure of the Geenwich Observations or the great human Computations now going on could be computed by it. Indeed it was proposed only for the computation of new Tables (as Tables of Logarithms and the like), and even for these, the difficult part must be done by human computers. The necessity for such new tables does not occur, as I really believe, once in fifty years. I can therefore state without the least hesitation that I believe the machine to be useless, and that the sooner it is abandoned, the better it will be for all parties[2].

Airy’s opinion was devastating Peel acting on Goulburn’s advice abandoned the financing of the Difference Engine once and for all. Even the personal appeals of Babbage directly to Peel were unable to change this decision. Airy’s judgement was actually based on common sense and solid economic arguments. The tables computed by human computers were comparatively free of errors and nothing could be gained here by replacing their labour with a machine that would probably prove more expensive. Also setting up the machine to compute any particular set of tables would first require human computers to determine the initially values for the algorithms and to determine that the approximations delivered by the difference series remained within an acceptable tolerance range. Airy could really see no advantages in employing Babbage’s machine rather than his highly trained human computers. Also any human computers employed to work with the Difference Engine would, by necessity, also need first to be trained for the task.

Airy’s views on the utility or rather lack thereof of mechanical calculators was shared by the Swedish astronomer Nils Seelander (1804–1870) also used the same arguments against the use of mechanical calculators in 1844 as did Urbain Le Verrier (1811–1877) at the Paris Observatory.

Babbage was never one to take criticism or defeat lying down and in 1851 when the working model of the Difference Engine No. 1 was on display at the Great Exhibition he launched a vicious attack on Airy in his book The Exposition of 1851: Views of The Industry, The Science and The Government of England.


Babbage was not a happy man. By 1851 Airy was firmly established as a leading European scientist and an exemplary public servant and could and did publically ignore Babbage’s diatribe. Privately he wrote a parody of the rhyme This is the House that Jack Built mocking Babbage’s efforts to realise his Difference Engine. Verse seven of This is the Engine that Charles Built reads as follows:

There are Treasury lords, slightly furnished with sense,

Who the wealth of the nation unfairly dispense:

They know but one man, in the Queen’s vast dominion,

Who in things scientific can give an opinion:

And when Babbage for funds for the Engine applied,

The called upon Airy, no doubt, to decide:

And doubtless adopted, in apathy slavish,

The hostile suggestions of enmity knavish:

The powers of official position abused,

And flatly all further advances refused.

For completing the Engine that Charles built.[3]

Today Charles Babbage is seen as a visionary in the history of computers and computing, George Airy very clearly did not share that vision but he was no Luddite opposing the progress of technology out of principle. His opposition to the financing of Babbage’s Difference Engine was based on sound mathematical and financial principles and delivered with well-considered arguments.

[1] The following account is based almost entirely on Doran D. Swade’s excellent paper, George Biddell Airy, Greenwich and the Utility of Calculating Engines in Mathematics at the Meridian: The History of Mathematics at Greenwich, de. Raymond Flood, Tony Mann & Mary Croarken, CRC Press, Boca Raton, London New York, 2019 pp. 63–81. A review of the entire, excellent volume will follow some time next year.

[2] All three quotes are from Airy’s letter to Goulburn 16 September 1842 RGO6–427, f. 65. Emphasis original. Quoted by Swade p. 69.

[3] Swade p. 74 The whole poem can be read in Appendix I of Doran David Swade, Calculation and Tabulation in the Nineteenth Century: Airy versus Babbage, Thesis submitted for the degree of PhD, University College London, 2003, which of course deals with the whole story in great depth and detail and is available here on the Internet.

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Filed under History of Astronomy, History of Computing, History of Mathematics, History of science

The Renaissance Mathematicus Christmas Trilogies explained for newcomers


Being new to the Renaissance Mathematicus one might be excused if one assumed that the blogging activities were wound down over the Christmas period. However, exactly the opposite is true with the Renaissance Mathematicus going into hyper-drive posting its annual Christmas Trilogy, three blog posts in three days. Three of my favourite scientific figures have their birthday over Christmas–Isaac Newton 25thDecember, Charles Babbage 26thDecember and Johannes Kepler 27thDecember–and I write a blog post for each of them on their respective birthdays. Before somebody quibbles I am aware that the birthdays of Newton and Kepler are both old style, i.e. on the Julian Calendar, and Babbage new style, i.e. on the Gregorian Calendar but to be honest, in this case I don’t give a shit. So if you are looking for some #histSTM entertainment or possibly enlightenment over the holiday period the Renaissance Mathematicus is your number one address. In case the new trilogy is not enough for you:

The Trilogies of Christmas Past

Christmas Trilogy 2009 Post 1

Christmas Trilogy 2009 Post 2

Christmas Trilogy 2009 Post 3

Christmas Trilogy 2010 Post 1

Christmas Trilogy 2010 Post 2

Christmas Trilogy 2010 Post 3

Christmas Trilogy 2011 Post 1

Christmas Trilogy 2011 Post 2

Christmas Trilogy 2011 Post 3

Christmas Trilogy 2012 Post 1

Christmas Trilogy 2012 Post 2

Christmas Trilogy 2012 Post 3

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Filed under History of Astronomy, History of Mathematics, History of Physics, History of science, History of Technology, Uncategorized

Both sides of history: Some thoughts on a history of science cliché

Earlier in the yeary, University of Edinburgh historian of mathematics, Michael Barany, used the expression “the wrong side of history” whilst live tweeting the university’s conference on Charles Piazzi Smyth the nineteenth century English astronomer and pyramidologist. This oft repeated cliché somehow struck a chord and I asked on Twitter what people actually thought it meant. I received quite a lot of answers spread over a fairly wide spectrum. Some though of it as a moral judgement, others on a similar wavelength viewed it as purely political, listing the well-known villain of history, Hitler, Stalin et al. But the view that really interested me, and the reason Michael Barany had used it, was its use in the history of science to designate people, who had strongly defended a theory or hypothesis that was later proved to be false. I think its use in this way is largely inappropriate, as it paints a much too black and white picture, whereas the history of science is, in my opinion, mostly various shades of grey. I would like to illustrate what I mean with some historical examples; this is not a systematic study but some musings provoked by my initial reaction to the phrase.

Copernicus is something of an icon in the history of astronomy, as the first Early Modern European astronomer to suggest that the cosmos was heliocentric and not, as had generally been believed, geocentric, so that puts him very much on the right side of history. However, although we actually know very little about his motivation, we do know that his main concern was to remove Ptolemeaus’ equant point in order to make astronomy conform with the so-called Platonic axioms i.e. all celestial motion takes place in uniform circular motion around a common centre. This desire of his to maintain the Platonic axioms places him firmly on the wrong side of history.

Tycho Brahe rejected heliocentricity both on astronomical and on religious grounds landing him on the wrong side of history but revolutionised observational astronomy delivering vast quantities of new astronomical data of an unheard of accuracy; you guessed it, right side of history.

Johannes Kepler, however, not only strongly propagated heliocentricity but using Tycho’s new data abandoned the Platonic axioms completely, replacing them with his three laws of planetary motion, still valid today, right side of history with a vengeance. Unfortunately the extremely devote Christian believed in a closed, finite cosmos with God as the sun, Jesus as the fixed stars and the Holy Ghost as the space in between; you can’t really get further on the wrong side of history than that.

In the popular imagination Galileo Galilei is considered to be one-hundred pre cent on the right side of history but was he really? The book, that most people know is his Dialogue Concerning the Two Chief World Systems, which is a polemic for heliocentricity and because we actually live in a heliocentric system it is assumed that what Galileo has to say is correct; unfortunately this assumption is far from the truth. Firstly the two systems he discusses Copernican heliocentricity and Ptolemaic geocentricity were both out dated when he wrote the book, Copernicus displaced by Kepler’s elliptical system and Ptolemy refuted by the discovery of the phases of Venus. Galileo simply ignores the true contemporary contenders, Kepler and some form of geo-heliocentric system. So he is very much on the wrong side of history. Even worse his supposedly crowning argument, his theory of the tides, presented on the fourth and final day of his dialogue, was already contradicted by the available empirical evidence. He even goes so far as to rubbish Kepler’s correct assumption that tides are somehow caused by the moon. Galileo did many things that were in fact on the right side of history but his sally into the astronomical/cosmological debate of the period was anything but.

For modern scientists astronomy is an honourable and ancient science, whereas astrology is merely occult mumbo jumbo. However, all three of our early modern astronomers, Tycho, Kepler and Galileo, were practicing astrologers, who genuinely believed in it. Distinctly wrong side of history there.

Moving to the other end of the seventeenth century we meet Isaac Newton. Like Galileo, Newton is venerated as a scholar firmly on the right side of history. However, beyond his achievements in mathematics, astronomy and physics, as every Newton aficionado well knows, he held views on religion and alchemy that make life very difficult for his rational fans. They like to argue that his science has nothing to do with his non-scientific activities but any analysis of his work shows that the various fields of his thought scientific and non-scientific were thoroughly integrated with one another. So which side of history do we place him on?

I briefly mentioned astrology above, which today is without doubt regarded, as being on the wrong side of history but astrology was one of the major driving forces behind the evolution of European astronomy from its beginnings in the Fertile Crescent sometime in the third millennium BCE all the way down to the end of the seventeenth century. Although, he was not a believer even Newton learnt his astronomy from books written by astrologers.

An eighteenth century theory that gets mocked by believers in right and wrong sides of history, as truly beyond the pale is the phlogiston theory in chemistry. It is of course viewed with hindsight stupendously and wonderfully wrong. However, what those, who mock it ignore is that scholars such as Joseph Black, Daniel Rutherford, Carl Wilhelm Scheele, Joseph Priestley and Henry Cavendish working within the framework of the phlogiston theory discovered, isolated and identified the properties of carbon dioxide, nitrogen, oxygen, hydrogen and the structure of water amongst other things; these researchers laid the foundations of modern chemistry. All on the wrong side of history, really? Some go so far as to attribute the discovery of oxygen to Lavoisier and not to Scheele and Priestley because unlike Priestley he didn’t believe it to be dephlogisticated air and was thus on the right side of history. But was he? Lavoisier named the gas oxygen from the Greek for sharp or acid believing it to be the element that makes all acids acidic, a belief that was just as false as Priestley’s dephlogisticated air.

Like Galileo and Newton in the seventeenth century, Albert Einstein is an icon of twentieth century science. Einstein is criticised and said to be on the wrong side of history because although he, together with Max Planck, founded the quantum theory, for which they both won Nobel Prizes, he refused to accept the indeterminate model of quantum mechanics created by Niels Bohr, based on the theories of Schrödinger, Heisenberg et al. Einstein was a determinist and was in this case shown to be wrong in the long run but Bohr himself said that Einstein contribute as much as anybody else to the development of quantum mechanics through his astute criticism.

I hope I have brought enough clear examples to show that categorising scientist or developments in science, as either on the right or wrong side of history is actually complete rubbish. Every scientific scholar, who has ever lived, has got some things right, some wrong and quite a lot, sort of half right. Science advances by others correcting the wrong and the half right bits. Also theories that in the end proved to be totally wrong, such as astrology, the phlogiston theory or alchemy, can, and in fact did, generate important results that furthered the evolution of science. The evolution of science is not categorised by clear black and white situations but as I said above consists of multifarious shades of grey. The right/wrong side of history concept is actually nothing more than a veiled version of presentism i.e. only acknowledging those aspects of the history of science that we consider to be right from our current standpoint.

I firmly believe that the concept of right or wrong side of history together with presentism and the expressions ‘father of’, ‘greatest’, and ‘first’ belongs in the rubbish bin and should never ever be applied in anything that purports to be serious history of science.








Filed under History of science, Myths of Science

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

When contemplating the advent of the heliocentric hypothesis in the Early Modern Period, one of the first things that occurs to many people is the conflict between the emerging new astronomy and Christianity, in particular the Holy Roman Catholic Church. What took place in those early years was actually very different to what most people think occurred and to a large extent has over the years been blown up out of all proportions.

To a certain extent some sort of conflict was pre-programmed, as the Bible, which the majority in this period believed to be basically true , clearly presented a geocentric world, even to a small extent a flat earth given the Old Testament’s fundamentally Babylonian origins and the new astronomy was attempting to establish a heliocentric one. This situation called for a lot of diplomatic skill on the part of those proposing the new heliocentric cosmological system, a skill that some of those proponents, most notably Galileo Galilei failed to display.

Between the publication of Copernicus’ De revolutionibus, which was actively supported by several leading figures within the Catholic Church, and the sensational telescopic discoveries of 1610-1613 there was surprising little backlash against heliocentrism from any of the European Christian communities. I have dealt with this in detail in an earlier post and don’t intend to repeat myself here. The real problems first began in around 1615 and were provoked by Galileo Galilei and the Carmelite theologian Paolo Antonio Foscarini (c. 1565–1616).


Source: Wikimedia Commons

Again I have already dealt with this in great detail in two earlier posts, here and here, so I will only outline the real bone of contention now, which surprisingly has little to do with the science and a lot to do with who gets to interpret the Holy Word of God e.g. The Bible.

From its foundation the Catholic Church had claimed the exclusive right to interpret the Bible for its followers, i.e. all true Christians. With time that interpretation was anchored in the writings of the early church fathers, what they had written was holy gospel and to openly contradict it was considered to be heresy. The Church was not only a powerful religious institution but also a powerful political one and over the centuries the adage that power corrupts and absolute power corrupts absolutely certainly proved true within the Catholic Church. This led to several attempts to reform the Church and bring it back to the ‘true path’ as outlined in the gospels.

Before what we now know as The Reformation, notable attempts on varying levels were made by, amongst other, John Wycliffe (c. 1320s–1384) in England, Jan Hus (c. 1372–1415) in Bohemia and Desiderus Erasmus (1466–1536), although Erasmus’ reform efforts were very moderate when compared to the other two and those that came after. In the sixteenth century that which we call the Protestant Reformation broke out in several parts of Europe instigated by Martin Luther (1483–1546), Philipp Melanchthon (1497–1560), Thomas Müntzer (1489–1525), Huldrych Zwingli (1484–1531), Jean Calvin (1509–1564) and a host of other minor figure, such as Andreas Osiander (1496 or 1498–1552), who wrote the infamous Ad lectorum in De revolutionibus. The major characteristic of the Reformation was that those calling for reform demanded the right for each individual to be allowed to interpret The Bible for themselves, thus removing the Church’s monopoly on biblical interpretations. This was of course unacceptable for the Catholic Church, which in turn launched its Counter Reformation, with the Council of Trent (1545–1563), to try and stem the tide of dissent. This was the situation in 1615 just three years before the outbreak of the Thirty Years War, one of the bloodiest conflicts in the history of Europe triggered by just this religious dispute, when Galileo made the move that turned the Catholic Church against heliocentrism and began Galileo’s own downfall.

Before we examen what Galileo actually did to so annoy the Catholic Church, it pays to look at the historical context in which this all took place. Too often people try to judge what happened from a presentist point of view, thereby distorting the historical facts. As usual when I write on this subject I am not trying to apologise for the Catholic Church’s actions or to excuse them, merely to present them within the practices and beliefs at the beginning of the seventeenth century. Firstly, this was a historical period in which all social, cultural and political institutions were hierarchical and fairly rigidly structured. It was an age of absolutism in which most rulers, including or above all the Pope, had and exercised absolute power. Secondly, there was no such thing as freedom of speech or freedom of thought in either religious or secular society. Those at the top largely prescribed what could or could not be said or thought out loud. Anybody who pushed against those prescriptions could expect to be punished for having done so.


Galileo Portrait by Ottavio Leoni Source: Wikimedia Commons

In 1615 both Foscarini and Galileo tried to tell the Church how to reinterpret those passages in the Bible that presupposed a geocentric cosmos in order to make a heliocentric cosmos theologically acceptable. This was simply not on. In my comments I will restrict myself to the case of Galileo. Modern commentators think that what Galileo said in his Letter to Castelli and in the extended version, his Letter to Christina, is eminently sensible and applaud him for his theological analysis but in doing so they miss several important points. In the Renaissance intellectual hierarchy theologians were at the top and mathematici, and Galileo was a mere mathematicus, were very much at the bottom. In fact the social status of the mathematicus was so low that Galileo telling the theologians how to do their job was roughly equivalent to the weekly cleaning lady telling the owner of a luxury villa how to run his household. This was definitely a massive failure on Galileo’s part, one that he should have been well aware of. The very low social and intellectual status of mathematici was the reason why he insisted on being appointed court philosophicus and not just mathematicus to the Medicean court. Philosophers ranked just below theologians in the hierarchy. Also given the fact that the Reformation/Counter Reformation conflict was rapidly approaching its high point in the Thirty Years War, this was not the time to tell the Catholic Church how to interpret the Bible.

As formal complaints began to be made about his Letter to Castelli, Galileo realised that he had gone too far and claimed that the copies in circulation had been changed by his enemies to make him look bad and presented the Church with a modified version to show what “he had actually written.” I fact we now know that the unmodified version was his original letter.

The writings of Foscarini and Galileo on the subject now led the Church to formally examine the relationship between Catholic doctrine and the heliocentric hypothesis, for the first time, and the result was not good for Galileo and the heliocentric hypothesis. A commission of eleven theologians, known as Qualifiers, undertook this examination and came to the conclusion that the idea that the Sun is stationary is “foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture…”; while the Earth’s movement “receives the same judgement in philosophy and … in regard to theological truth it is at least erroneous in faith.” The first part is obvious the Bible states clearly that it is the Sun that moves and not the Earth and as the heliocentric hypothesis directly contradicts Holy Scripture it is formally heretical. The second part is more interesting because it that the hypothesis is philosophically, read scientifically, absurd and foolish. Although the language used here in the judgement is rather extreme it was a fact in 1615 that there existed no empirical proof for the heliocentric hypothesis, actually most of the then available empirical evidence supported a geocentric cosmos. If there had been empirical support for heliocentrism then the Church’s judgement might well have been different, as Roberto Bellarmino (1542–1621) wrote in his infamous letter to Foscarini:

Third, I say that, if there were a real proof that the Sun is in the centre of the universe, that the Earth is in the third sphere, and that the Sun does not go round the Earth but the Earth round the Sun, then we should have to proceed with great circumspection in explaining passages of Scripture which appear to teach the contrary, and we should rather have to say that we did not understand them than declare an opinion to be false which is proved to be true.


Roberto Bellarmino Source: Wikimedia Commons

In other words, if you provide proof of your hypothesis, then we will be prepared to reinterpret the Bible.

This was the point where Galileo, realising that he was potentially in serious trouble, first rushed to Rome to peddle his theory of the tides, which he appeared to believe delivered the necessary empirical proof for the heliocentric hypothesis.


Source: Wikimedia Commons

This theory had been developed together with Paolo Sarpi (1552–1623) in the 1590’s and basically claimed that the tides were caused by the movements of the Earth, in the same way that water sloshes around in a moving bowl. The theory has however a fatal empirical flaw; it only allows for one high tide in twenty-four hours whereas there are actually two. Galileo tried to deal with this discrepancy with a lot of hand waving but couldn’t really provide a suitable explanation. This was, however, irrelevant in 1615, as Galileo having through his actions poked the proverbial bear with a sharp stick, nobody was prepared to listen to his latest offerings and his efforts fell on deaf ears.

The inevitable happened, the Church formally banned heliocentricity in 1616, although it was never actually declared heretical, something that only the Pope could do and no Pope ever did, and books explicating the heliocentric hypothesis were placed on the Index of forbidden books. Interestingly Copernicus’ De revolutionibus was only placed on the Index until corrected and rather surprisingly this was carried out fairly quickly, the corrected version becoming available to Catholic scholars already by 1621. The Church had realised that this was an important book that should not be banned completely. The corrections consisted or removing or correcting the surprisingly few places in the text where the heliocentric hypothesis was stated as being scientifically true. This meant that Catholics were permitted to write about and discuss heliocentricity as a hypothesis but not to claim that it was empirically true.

Galileo who together with Foscarini had provoked this whole mess got off relatively lightly. At the Pope’s request he was personally informed by Cardinal Roberto Bellarmino that he could no longer hold or teach the heliocentric theory and given a document confirming this in writing. He was not punished in anyway and continued to be popular amongst leading figures in the Church including Maffeo Barberini, the future Pope Urban VIII.

Many modern commentators say why couldn’t the Church accept the eminently sensible suggestion made by Galileo and Foscarini and thus avoid the whole sorry mess. The answer is quite simple. If they had done so they would have surrendered their absolute right to interpret Holy Scripture, which, as pointed out above, lay at the centre of the Reformation/Counter Reformation conflict; a right that the Catholic Church has not surrendered up to the present day.





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

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

The first period of telescopic, astronomical discoveries came to an end in 1613, which was seventy years after the publication of Copernicus’ De revolutionibus. This makes it a good point to stop and take stock of the developments that had taken place since the appearance of that epoch defining magnum opus. First we need to remind ourselves of the situation that had existed before Copernicus heliocentric hypothesis entered the world and triggered a whole new cosmology and astronomy debate. The mainstream standpoint was an uneasy combination of Aristotelian cosmology and Ptolemaic astronomy. Uneasy because, as some saw it, the Ptolemaic deferent and epicycle model of planetary motion contradicted Aristotle’s homocentric principle, which led to a revival of homocentric astronomy. Others saw the principle of uniform circular motion contradicted by Ptolemaeus’ use of the equant point. In fact, we know that the removal of the equant point, for exactly this reason, was the starting point of Copernicus’ own reform efforts. Another minority view that was extensively discussed was a geocentric system with diurnal rotation, as originated in antiquity by Heraclides of Pontus, regarded by some as more rational or acceptable than that the sphere of the fixed stars rotated once in twenty-four hours. Also still up for debate was the Capellan system with Mercury and Venus orbiting the Sun in a geocentric system. Then came Copernicus and added a new radical alternative to the debate.

By 1613 most of the Aristotelian cosmology had been disposed of bit for bit. Aristotle’s sublunar meteorological comets had definitely become supralunar astronomical objects, although what exactly they were was still largely a mystery. As we shall see Galileo later embarrassed himself by maintaining a position on comets very close to that of Aristotle. The comets becoming supralunar had also disposed of Aristotle’s crystalline spheres, although Copernicus seems to have still believed in them. The telescopic discovery of the geographical features on the Moon and the spots on the Sun had put an end to Aristotle’s perfection of the celestial spheres. They together with the comets and the supernovas of 1573 and 1604, both of which had clearly been shown to be supralunar, also contradicted his immutability of the heavens. The discovery of the four largest moons of Jupiter ended the homocentric concept and the discovery of the phases of Venus, originating in a solar orbit, ruled a pure geocentric system but not a geo-heliocentric one. As a result of all these changes cosmology was up for grabs.

In astronomy the biggest single change was that nearly all astronomers, following Copernicus, now believed in the reality of their models and no longer viewed them as purely mathematical constructions designed to save the phenomena. This was a major shift as previously the discussion of the reality of the heavens was regarded as a discussion for philosophers and definitely not astronomers. So which models were up for discussion? Had in the intervening seventy years the debate simplified, reduced to a choice between two competing models, Ptolemaic geocentrism and Copernican heliocentrism, as Galileo would have us believe twenty years later? Actually no, if anything the situation had got considerably more confused with a whole raft full of astronomical models jostling for a place at the table. What were these competing models?

Given the telescopic observations of the phases of Venus and the assumption of similar phases for Mercury, a pure Ptolemaic geocentric model should have been abandoned but there was still a hard core that refused to simply give up this ancient model. Christoph Clavius (1538–1612) in the last edition of his Sphaera, the standard Jesuit textbook on astronomy, acknowledged problems with the geocentric model but urged his readers to find solutions to the problems within the model. As late as 1651 Giovanni Battista Riccioli (1598–1671), in the famous frontispiece to his Almagestum novum, shows Ptolemaeus lying defeated on the ground, whilst the heliocentric and geo-heliocentric systems are weighed against each other, but he is saying, I will rise again.


Frontispiece of Riccioli’s 1651 New Almagest. Source: Wikimedia Commons

Due to William Gilbert’s revival of the Heraclidian diurnal rotation, we now have two geocentric models, with and without diurnal rotation. The Copernican heliocentric system is, of course, still very much in the running but with much less support than one might expect after all the developments of the intervening seventy years.

Despite the phases of Venus all the various geo-heliocentric models are still in contention and because of the lack of empirical evidence for movement of the Earth these are actually more popular at this point in time than heliocentric ones. However, despite the lack of empirical evidence diurnal rotation enjoys a surprising level of popularity. We have a Capellan system, Venus and Mercury orbit the Sun, which orbits the Earth, both with and without diurnal rotation. Very much in consideration is the full Tychonic system; the five planets orbit the Sun, which together with the Moon orbits the Earth. Once again both with and without diurnal rotation. Riccioli favoured another variation with Venus, Mercury and Mars orbiting the Sun but with Jupiter and Saturn orbiting the Earth along with the Sun and Moon.

Perhaps the most interesting development was Kepler’s heliocentric system. Whilst Kepler regarded his system as Copernican, others regarded his elliptical system as a rival to not only to the geocentric and geo-heliocentric system but also to the Copernican heliocentric system with its deferent and epicycle orbital models. The most prominent example of this being Galileo, who promoted the Copernican system, whilst deliberately ignoring Kepler’s more advanced developments.

We can find solid evidence for this multiplicity of systems in various sources. The earliest in a card game devised by Johann Praetorius (1573–1616), professor for astronomy at the University of Altdorf near Nürnberg, which only exists in manuscript.


Source: Wikimedia Commons











Source: All playing card images Wikimedia Commons

Another much read source is the extraordinary Anatomy of Melancholy by the Oxford scholar Robert Burton (1577–1640). First published in 1621, it was republished five times over the next seventeen years, each edition being massively modified and expanded.


The Anatomy of Melancholy frontispiece 1638 ed. Source: Wikimedia Commons

In a section entitled Melancholy of the Air Burton discusses the various astronomical models, favouring the system of David Origanus (1558–1629), professor for Geek Greek and mathematics at the University of Frankfurt an der Oder, a Tychonic system with diurnal rotation.


Source: Wikimedia Commons

Burton, as well as being one of the most erudite scholars of the seventeenth century, was also a practicing astrologer, who is said to have hung himself in his Oxford chambers to fulfil his own prediction of his death.

Already mentioned above is Giovanni Battista Riccioli, whose Almagestum novum (1551) contains descriptions of a wide range of different systems.


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

The book also contains a list of 126 arguments pro and contra heliocentricity, 49 for and 77 against, in which religios arguments play only a very minor role.

Another Jesuit was Athanasius Kircher (1602–1680), who sat at the centre of a world spanning astronomy correspondence network, receiving astronomical data from Jesuits all of the world, collating it and re-distributing it to astronomers throughout Europe.


Source: Wikimedia Commons

He described six different systems as late as 1656 in his Itinerarium extaticum, with a revised edition from 1671.


Diagrams of the different world systems, Ptolemaic, Platonic, Egyptian, Copernican, Tychonic and semi-Tychonic from Iter Exstaticum (1671 ed.) p. 37 Source:

Contrary to a widespread view the question of the correct astronomical system was still very much an open question throughout most of the seventeenth century, largely because there existed no conclusive empirical evidence available to settle the question.





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