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

At the end of the last section Isaac Newton was still a student, who had embarked on a six-year period of intensive study teaching himself the modern analytical mathematics, the basics of mechanics and optics.In 1666 during the phase when he was learning mechanics, principally from the works of Descartes and where like Huygens he corrected Descartes theories of elastic collision and Galileo’s false value for g, the acceleration due to gravity, he had his legendary flash on inspiration, possibly inspired by the equally legendary falling apple, in which he asked himself if the force that causes an object to fall to the ground is the same as the force that prevents the Moon from flying off at a tangent, as the law of inertia, acquired from Descartes, said it should. Newton made a back of an envelope calculation, which gave an interesting correlation but was somewhat inaccurate due to inaccurate input data. Newton dropped the line of enquiry and didn’t take it up again for almost twenty years. However, one aspect of his calculation was very important for the future. In order to calculate the force holding the Moon he plugged Kepler’s third law into Huygens’ formula for centripetal force, which led to the inverse square law of gravity.

In 1669, on the recommendation of Isaac Barrow the retiring incumbent, Newton was appointed Lucasian Professor of Mathematics at Cambridge University.The appointment was not as impressive as it appears today and Newton remained still largely under the radar, although the mathematics fan John Collins (1625–1683) had circulated some of his mathematical manuscripts awaking the world to his immense mathematical talent. This changed in the early 1670s when he presented the world with his reflecting telescope, the first functioning one, and published his first paper on the nature of white light. A new leading natural philosopher had arrived on the European stage.

In 1680 and 1681 two new great comets lit up the skies and once again the astronomers all turned their attentions into trying to determine their flight paths. The 1680 comet was discovered by the German astronomer Gottfried Kirch (1639–1710) from Coburg, who lived from writing and publishing almanacs, on 4 November.


The Comet C/1680 V1 as seen over Nürnberg just south of Coburg with Georg Christoph Eimart’s observatory in the foreground Source

It was the first ever comet to be discovered by telescope, that is before it became visible to the naked eye. It remained visible until 7 December when it disappeared. The comet of 1681 first appeared on 20 December. One astronomer, John Flamsteed (1646–1719), who had been appointed Astronomer Royal for the new Royal Observatory at Greenwich in 1675, had the bright idea that these were not two separate comets but one single comet on its way to and from the sun (modern designation C/1680 V1). Unsure of his assumption Flamsteed turned to Isaac Newton to ask his opinion. Flamsteed did not know Newton personally so the contact, by letter, was initially through a mutual acquaintance at Cambridge.


Historical picture of the first comet ever discovered using telescope,  the Great Comet of 1680 (C/1680 V1), as painted by Lieve Verschuier: Source

Flamsteed’s hypothesis was that the comet turned in front of the Sun upon reaching it; he, echoing Johannes Kepler, suggested that the comet was attracted to the Sun magnetically and then through a change in polarity as it neared the Sun repulsed. In two letters in February 1881 Newton dismantled Flamsteed’s hypothesis, concentrating on his magnetic argument but also not accepting that the two comets were actually just one. Newton had applied the inverse square law of gravity to a theoretical system consisting of a single planet and the Sun, a year earlier, but did not apparently consider applying it to the comet at this point in time. However, in a draft of his second letter to Flamsteed, which he never sent, he did sketch a dynamic system of the comet circling behind the Sun but in terms of magnetic attraction.


John Flamsteed by Godfrey Kneller, 1702 Source. Wikimedia Commons

Later in the year Newton received new observational data on the comet from an old school acquaintance, Arthur Storer (c. 1648–1686) an amateur astronomer, who had emigrated to Maryland in 1679. He also later sent Newton data on the 1682 comet (Comet Halley), which he was amongst the first to observe in North America and which was named after him there for some time. Edmond Halley (1656–1741), an excellent astronomer and mathematician, who observed the comet of 1680/81, whilst travelling in France, also believed, like Flamsteed, that the two comets were one. In 1682 he came to Cambridge to visit Newton and the two of them discussed the comets.


Source: Wikimedia Commons

Newton observed the comet of 1682 and at some point after 1680 he systematically collected together data on all recorded comets and decided that comets did indeed obey the inverse square law of gravity just like planets, their paths being oval if they returned and hyperbola if not. This was possibly the point where Newton’s thoughts on gravity became a universal theory of gravity. Comets and their flight paths would go on to play a significant role in the Principia. Newton apparently didn’t think to inform Flamsteed of his change of mind and acknowledge that Flamsteed had been right, at least in principle, until 1685.


The orbit of the comet of 1680, fit to a parabola, as shown in Isaac Newton’s Principia Source: Wikimedia Commons

Newton and Flamsteed were not the only people to reconsider the flight paths of comets in the early 1680s and Newton was not the only person to think that the inverse square law of gravity applied to them, Newton’s rival Robert Hooke also did so. Robert Hooke had been investigating the effects of gravity for many years and had discovered the inverse square law for himself and became convinced of a universal gravity. He thought that the flight paths of comets, like planets, were determined by gravity and that the inverse square law also applied to them. However, unlike Newton he didn’t do the mathematics. This mutual independent discovery of universal gravity would lead to renewed conflict between the two natural philosophers, who had already crossed swords over the nature of light.




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Eleven is a number word in English that derives from the Old English ęndleofon, which is first attested in Bede’s Ecclesiastical History of the English People. There are cognates in all the Germanic languages, all of which have the same meaning of ‘one is left’. Left that is having counted up to ten. This is of course, a clear linguistic indication that we use, and have long used, a ten based, or decimal, number system contingent on the fact that through evolutionary chance we possess ten fingers or digits. Just to round up the picture twelve and its equivalents in other Germanic languages originally meant ‘two are left’ before we move onto thirteen, fourteen etc., which are simply three plus ten, four plus ten and so on and so fourth.


Coming back to eleven, on this day one year ago we celebrated, in our own inimitable way, the glorious tenth anniversary of the Renaissance Mathematicus that we are still here 366 days later, don’t forget that 2020 is a leap year, means that your favourite malcontent, #histSTM blogger has managed to fill yet another year with his incoherent scribblings. Counting up to ten we have one left. Ignoring such trivial matters, as the current world pandemic not much has changed in the world of the Renaissance Mathematicus. I have somehow managed, against my usually tendency to wander off and start something else, to complete another twenty-five slices of my, in the meantime, monumental series on the emergence of modern astronomy, bringing the word count up to a guesstimated fifty to sixty thousand. An end is actually in sight even if we haven’t quite reached it yet. This will be when the real work starts if I really want to turn it into a book. I need to go back to the beginning and basically rewrite the entire thing!

Turning to other matters, today is purely by chance the religious festival Corpus Christi or to give it it’s official title Dies Sanctissimi Corporis et Sanguinis Domini Iesu Christi (Day of the Most Holy Body and Blood of Jesus Christ the Lord), a Christian liturgical solemnity celebrating the Real Presence of the Body and Blood, Soul and Divinity of Jesus Christ in the elements of the Eucharist, to quote Wikipedia.


Corpus Christi procession. Oil on canvas by Carl Emil Doepler Source: Wikimedia Commons

Now you might think that this particular piece of Catholic mumbo-jumbo (you might remember that one of the things that divided Catholics and Protestants during the Reformation, is that Protestants stopped believing that the bread and wine actually changed into the body and blood of Christ) has little or nothing to do with the history of science, you would be wrong.

To start with we need to address the chance bit. Corpus Christi, which is anchored to Easter, is one of those movable feasts in the Church calendar the irregular occurrences of which are determined by the Gregorian calendar, the introduction of which involved some very intricate astronomy and mathematics, which have the been the subject of a couple of blog posts here.

The actually Church feast was suggested by and campaigned for, thirty years long by Juliana of Liège (c. 1192–1258) prioress of the double canonry of Liège and her wish was granted by Pope Urban IV, who commissioned his chief theologian Thomas Aquinas (1225–1274) to compose an office for the Feast of Corpus Christi to be celebrated on the Thursday after Pentecost, which is itself celebrated fifty days after Easter Sunday. Thomas Aquinas plays a very central role in the history of European science, as it was he together with his teacher Albertus Magnus (before 1200–1280), who made Aristotelian natural philosophy acceptable for the Catholic Church, thus establishing it as the predominant scientific corpus in the European High Middle Ages.

The next #histSTM connection with the feast of Corpus Christi actually occurred in the life of Galileo. In his Il Saggiatore Galileo speculated a little bit with the ancient Greek theory of atomism. Because of this he was denounced anonymously to the Inquisition. The denunciation claimed that atomism contradicted the Church’s teaching on transubstantiation, which was based on the medieval Aristotelian theory of matter.  This distinguished between substantial and accidental properties of matter. In this theory the appearance of a piece of matter is accidental but its true nature is substantial. According to the transubstantiation theory the bread and the wine change in their substance into the body and blood of Christ whilst retaining the accidental appearance of bread and wine. If, however, the Aristotelian theory of matter were to be replaced with atomism this theory would no longer function. The Inquisition never proceeded against Galileo in this matter but it is of note that in England Thomas Harriot and Sir Walter Raleigh were held and questioned on a similar charge somewhat earlier.

Returning to personal matters, as is usually my wont in my birthday posts, I recently had an acrimonious exchange with one of my readers, whose comments were from the beginning aggressive, insulting and historically false. I tried to reason with him and he just got more abusive in his tone. In the end I blocked him and erased his comments but I found his parting shot insult, and it was clearly meant as an insult, fascinating; he stated that I was not a historian but a storyteller.

This is interesting because, as is very clear to see history and story share the same etymological root, the Latin historia, “narrative of past events, account, tale, story,” from Greek historia “a learning or knowing by inquiry; an account of one’s inquiries; knowledge, account, historical account, record, narrative.” It is not until the late 15thcentury that the two differentiated meanings for history and story began to slowly appear. In German the same word, Die Geschichte means both story and history, the different meanings depending on context.

Book of ideas

If I get asked in a formal or semi-formal context how I describe what I do, my answer is that I’m a narrative historian of the contextual history of science. That quite a mouthful and might sound, to some, rather pretentious. If I get asked what that means, my answer is I’m a storyteller. I don’t regard being called a storyteller as an insult; I regard it as a compliment.




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Another Negative Review

For those, who don’t always read the comments, Renaissance Mathematicus friend and sometime guest blogger, Chris Graney, who is also a leading expert on the arguments pro and contra heliocentricity in the early 17th century, has written another negative review of Galileo and the Science Deniers. More moderate in tone, than your favourite HIST_SCI HULK, but not in content, he also takes Mario Livio to the cleaners.

We will combat science denial by showing how vigorous scientific debate over a universally accepted set of facts was present at the very birth of modern science, as it often is in science today. Galileo and the Science Deniers does not do this, despite its author being a scientist. It retells a tale that is central to the genre of conspiracy and science denial, and so it will in all likelihood contribute to the very science denial problem it purports to help solve.

It is well worth a read, so pop on over and boost Professor Graney’s reader figures.


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My name is Bond, Jamie Bond.

Today we have a first at the Renaissance Mathematicus, a book review of two interrelated books that have nothing, or at least very little, to do with the histories of science and mathematics. They, however, both deal with England during the Revolution (Civil War) and Interregnum in the middle of the seventeenth century, so very much home territory for this blog.

The word spy is one that for most people instantly evokes a male figure, for someone of my generation, a man in a dinner jacket with a martini glass in one hand and a Beretta pistol in the other. Very few people would immediately associate the word spy with a woman, although there have been some notable female spies throughout history. Dutch historian of early modern English literature Nadine Akkerman, Reader at Leiden University, stumbled across a female spy during her research into the correspondence of Elizabeth Stuart, Queen of Bohemia (1596–1662), who lived out the last forty years of her life in The Hague. Inspired by this discovery Akkerman, who believed that female spies were perhaps not so rare as one might suspect, began to systematically search archives for traces of other women involved in espionage in the seventeenth century. The result of her researches appeared in a book two years ago, Invisible Agents: Women and Espionage in Seventeenth-Century Britain. [1] The paperback, that I’ve been reading, was published just this month.

Invisible Agents001

Akkerman’s book is a truly excellent piece of historical scholarship. Her, apparently tireless, excavations of the archives have turned up a large amount of evidence for the existence and activities of female spies, or as she prefers to call them she-intelligencers, as they were then commonly known, in the three decades of the seventeenth century, 1640s to1660s, in Britain. She has sorted, analysed and interpreted this flood of data to produce a coherent narrative about her she-intelligencers. From the start she explains that there is both too much data and too much of it fragmentary to produce a complete picture of the women involved in espionage in this period so instead she presents the reader with a series of case studies.

The first chapter deals with the mostly aristocratic women who worked as she-intelligencers for Charles I during his imprisonment by the parliamentary forces acting as couriers in the various plots to free the king. These women, on the whole, engaged in these activities out of loyalty to king and country. This is contrasted in the second chapter with accounts of the largely working class women, who sold information to Thurloe the parliamentary spymaster. Here we should note in particular, for later, her account of Diana Stewart, who appears to have supplied information to both sides, a double agent perhaps, or was she simply some sort of early modern con artist?

The third chapter is dedicated to the story of Susan Hyde, the sister of Sir Edward Hyde, a prominent royalist politician, who became 1st Earl of Clarendon and Lord Chancellor under Charles II. Susan Hyde was an active royalist she-intelligencer but has till now remained under the radar and Akkerman is the first to entangle and tell her story, giving it the attention it deserves. The next two chapters deal with Elizabeth Murray, who unlike Susan Hyde is a well-documented historical figure. Here Akkerman displays her analytical talents to the full. In the first chapter she deconstructs the accepted historical narrative about Murray and shows why it is at best dubious and at worst false. In the second chapter she reconstructs Murray’s story using the sources that she has excavated in her research.

Following Murray we have another Elizabeth, Elizabeth Carey, Lady Mordaunt. A she-intelligencer, who together with her husband was involved in espionage during the late phases of the Interregnum. Of particular interest here is Akkerman’s analysis of Carey through her correspondence with the gardener and diarist John Evelyn. Next up, is Anne, Lady Halkett and another deconstruction by Akkerman. This time she deconstructs the interpretations by other literary historians of Halkett’s own extensive written account of her espionage activities. The final figure in the book is probably the most well known female English author of the seventeenth century Aphra Behn, who was also a she-spy, or was she? Another deconstruction job by Akkerman.

Each subject in the book is presented in the full political and social context of her times. Her activities are described in as much detail as the sources allow and we, the readers, are introduced to the full array of early modern espionage activities. The post offices and the post routes the coded letters, the cyphers used, the secret societies, the counter espionage activities of the other side and the fate of those, who were trapped by those counter espionage activities. After having read Akkerman’s book one comes away with a rich knowledge of the activities of the seventeenth century English she-intelligencers.

Akkerman’s book is a masterpiece in the assimilation, ordering and interpretation of archival sources within a given historical area and can be held up as an example of how to do and present historical research. The book bristles with extensive footnotes, no endnotes, and has an equally extensive bibliography of both primary and secondary sources. The index is first class and is followed by an Index Occultus, a key to all the code names used in the original source documents for the historical characters in the book.

At the beginning I said this was a review of two interrelated book, the second is the novel Killing Beauties by Pete Langman[2].

Invisible Agents002

As far as I know this is Langman’s first novel but it is not, by a long chalk, his first artistic endeavour. A one time rock guitarist and then music teacher, he has worked as a music journalist, is a cricketer and along the way acquired a doctorate in early modern literature with a thesis about Francis Bacon. On a side note he gently and politely corrects me when I say something stupid about the Viscount St. Alban. Pete Langman also suffers from early-onset Parkinson’s disease and is the author of the highly acclaimed Slender Threads: A young person’s guide to Parkinson’s Disease.[3]

Pete Langman is also Nadine Akkerman’s partner and has borrowed two of the central figures from Invisible Agents, Diana Stewart and Susan Hyde, to weave a semi-fictional tale of espionage in the Interregnum, imaginatively filling out the gaps in Akkerman’s research.

Langman takes his readers on a fascinating journey through the streets, alleyways, drinking holes, apothecaries and seats of espionage of Interregnum London, evoking an authentic picture of life in the capital city in Cromwell’s time. A wide cast of fascinating and captivating characters lead the readers through the twists and turns of a risky espionage coup and the counter espionage moves to prevent that coup from being put into effect. None of the characters is entirely good or entirely bad but each of them is a real human being with all the normal faults and virtues, meaning that one doesn’t end up rooting for one side or the other, or at least I didn’t. There are enough twists and turns in the narrative to delight Agatha Christie fans and things don’t necessarily turn out, as you might have expected during the earlier chapters.

Langman’s voice is the authoritative voice of the seventeenth century historian but is is the voice of the story teller and not the lecturer, the artist and not the teacher. He recreates a visceral and authentic picture of a period of English history when the populous was torn between two philosophies of life and politics and some paid for their beliefs in one or other of those systems with their honour and even their lives.

His book is both an excellent historical novel and an excellent espionage novel that should delight fans of both genres and is also a wonderful companion to Akkerman’s historical presentation of the material. I would recommend both books to anybody interested in seventeenth century Britain, the history of espionage or simply just good writing. According to taste a potential reader can choose one or the other, but if you should choose to read both then I would recommend first reading Langman’s novel and then Akkerman’s historical presentation as the back story.

Disclosure: As should be obvious from various comments in this review, Pete Langman is an Internet friend, known as @elegantfowl on Twitter, with whom I share a mutual interest in the guitar playing of Gary Lucas and the history of seventeenth century science, amongst other things. Unbound is a crowd funding book publisher and when Pete announced on Twitter that he was trying to publish a novel on Unbound I became a subscriber, which is why I came to read Killing Beauties. Having read it, I was intrigued enough to acquire Invisible Agents when it appeared in paperback. Some might therefore not regard me as a neutral reviewer but as I have said in the past in similar circumstances if I didn’t like the book then I wouldn’t have reviewed it.

[1] Nadine Akkerman, Invisible Agents: Women and Espionage in Seventeenth-Century Britain, OUP, Oxford, 2018, ppb. 2020

[2] Pete Langman, Killing Beauties, Unbound, London, 2020.

[3] Pete Langman, Slender Threads: A young person’s guide to Parkinson’s Disease, Self Published, 2013. On a personal note, Pete said some very sensible and comforting things when I discussed my own problems with coming to terms with my brother’s Parkinson’s with him.


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Christmas Trilogy 2019 Part I: Would the real Mr Newton please stand up?

Probably the more wide spread and popular image of Isaac Newton is of him discovering the law of gravity after being hit on the head by a falling apple.


For many generations of school kids throughout the world the name Newton is associated with his laws of motion and that law of gravity, often with unpleasant thoughts of having to solve physics home work problem involving them. For many Newton is the ‘father of modern science’ or the ‘father of physics’ or in some way synonymous with the scientific revolution. Also for those worldwide, generations of school kids he was the inventor/discoverer of the bane of mathematics the calculus. In reality, as well as his most well known achievements in mathematics, astronomy and physics, Newton took a lively interest in a surprising range of topics and, never a dabbler, he invested the full power of his vast intellect in whatever he undertook to investigate.


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

Born in Woolsthorpe Manor on 25 December 1642, the son of a yeoman farmer, who died before he was born, Newton grew up in a strongly puritan environment and remained deeply religious throughout his entire, very long life. He devoted an immense amount of time and energy to studying the Bible that tradition claims he could recite off by heart. He would learn both Greek and Hebrew in order to further his theological studies. His religious views were anything but orthodox and he was in fact probably an Arian i.e. he denied the concept of the Trinity believing in a Unitarian concept of God instead. He would have normally been required to take holy orders in order to become a professor at Cambridge and even considered leaving the university because he was not prepared to do so. Through the assistance of Isaac Barrow he was granted a special dispensation and was thus able to accept the Lucasian Chair without having to take holy orders. Although he wrote many papers on his religious beliefs, including his belief that the Catholic Church had corrupted the text of the Bible in order to justify their belief in the Holy Trinity, he largely kept his heterodox religious views to himself, sharing them only with selected sympathetic correspondents.

His religious views played a central role in his scientific endeavours as he believed that he was uncovering God’s plan of the universe. He went further than this in that he believed that he, and he alone, had been chosen by God to reveal that plan. He was also a prisca theologian, who believed that Adam and the early generations of humanity had had perfect knowledge of God’s creation and that this knowledge had been lost down through the succeeding generations. He was not discovering the plans of God’s creation but rediscovering them.

Newton was also, like many others in the High Middle Ages and the Early Modern Period, a millennialist that is he believed in a second coming and the end of the world. This led to the second of his great intellectual passions, history. Newton was a Bible chronologist, who thought that if he could accurately determine the date of creation and thus the current age of the Earth then he could also determine the time of the second coming. In order to do this he devoted a lot to the study of history in order to establish the time and durations of the great civilisations based, of course, around an analysis of the Old Testament as a historical source. He also tried, as an astronomer, to tie historical descriptions of astronomical phenomena, eclipses etc., to mathematically determined dates of those phenomena. This led other chronologists to eagerly await access to Newton’s chronological writings after his death hoping that the great astronomer mathematician would provide solid scientific evidence for his historical dating scheme. On the whole those hopes were disappointed when Newton’s chronological manuscripts did finally see the light of day.

Newton’s prisca theological beliefs also led to another of his better-known intellectual activities his alchemical investigations. He believed that alchemy was the oldest of all the sciences and that if he could unravel the secrets of this arcane discipline then it would bring him closer to knowledge of God’s creation plan. You will often see the highly incorrect assertion that the scientist Newton only turned to the occult alchemy in his dotage, after his scientific creativity had been drained; this is far from the truth. Newton began his alchemical studies in about 1666 at the height of his intellectual powers. He built a hut in the gardens of Trinity College, which served as his laboratory and devoted the winter months of the next thirty years to the serious study of alchemy. He read and annotated hundreds of alchemical manuscripts, carried out numerous experiments and wrote his own thoughts on the subject none of which he ever published. On interesting side note to this intensive engagement is that he used the knowledge of chemical processes that he had won to develop new and better methods of assaying when he was running the Royal Mint later in life.

The years that Newton devoted to the study of alchemy were also the years that he devoted to the study of mathematics, physics and astronomy. Those people who reached a high enough level in mathematics in their own education usually know than Newton is credited with being the co-creator, together with Leibniz, of the calculus. What most people don’t realise is just how vast Newton’s output of creative mathematics was. The edited edition of his collected mathematical papers runs to eight very thick, large format volumes covering a very wide range of mathematical topics. His scientific crowning glory is, of course, his Principia Mathematica (1687) combining, as it does a definitive, uniform presentation of the physical mechanics that had been developed piecemeal over the preceding two centuries adding much that was new in the process, as well as a complete consistent heliocentric model of the solar system. With this one book he established himself as Europe’s number one physicist and number one astronomer. He second masterpiece was his Opticks, created and written largely before the mathematics, mechanics and astronomy but first published, due to negative reactions to his first papers on the subject, in 1704. It was of course in this period that Newton was also Lucasian Professor of mathematics at Cambridge University. This however was not that much of a burden, as Newton famously had virtually no students attending his lectures. Mathematics was not particularly popular at English universities during the seventeenth century.

In 1696 Newton left the world of academia, and to some extent his scientific investigations, to start a completely new career as a government servant, first as warden then later as comptroller of the Royal Mint in London. He obtained this appointment through the services of one of his former students, Charles Montagu, later 1st Earl of Halifax, one of the most powerful Whig politicians and for a time Chancellor of the Exchequer. Newton’s association with Montagu illustrates another aspect of his life that of politician. Newton was a member of the Whig Party, who sat as an MP for Cambridge University, the universities were their own parliamentary constituencies, at the convention to settle the revolution of 1689. This was however one activity where Newton remained very passive and did nothing to distinguish himself. In 1705 Montagu persuaded him to stand again and even arranged for him to be knightedto increase his chances of election but he lost the election and thus ended his active political career.

The job at the Royal Mint, which Newton desired because he thought being a mere university professor did not fit his status as a leading European intellectual, was actually normally considered a political sinecure, i.e. the office holder was not actually expected to do anything, just hold the title and collect the pay. Others would actually do the work. Newton was not a man for sinecures. He plunged right in taking over the day-to-day running of the mint. He personally supervised the recoining of the nation, a monstrous task, which Montague had introduced as a measure to combat the debasement of the English currency. Newton applied his scientific mind to modernising the Mint, introducing as indicated above, new methods of chemically assaying metals. One of the responsibilities of the Warden of the Mint was to track down and bring to trial coiners, i.e. those who forged coin of the realm, and clippers, i.e. those who clipped are shaved metal of the edges of coins. The milling of the edges of coins was introduced in Newton’s times to make life more difficult for clippers. Normally a Warden would employ others to track down these criminals, Newton took on the job himself working as a sort of seventeenth century gumshoe[1]. He was very much a hands on boss and remained so until late in his life, when he began to hand over the reigns to John Conduit, the husband of his niece and housekeeper, Catherine Barton.

From 1704 onwards until his death, he was also President of the Royal Society, which he ruled in a very autocratic manner. Once again he was not prepared to be merely some sort of figurehead but was deeply engaged in shaping the society’s profile and business. In this role he also became a tourist attraction, foreign visitors to London attending meetings of the Royal Society in order to witness Sir Isaac Newton Europe’s greatest, living natural philosopher.

Although the term natural philosopher signifies what we would now call a scientist, Newton was also a philosopher in the true sense. Although, unlike Leibniz, he didn’t publish separate philosophical texts, his major works, the Principia Mathematica and the Opticks, both contain a lot of serious thoughts on the philosophy and methodology of science. He was also very much pulling the strings, as the puppet master, in the philosophical debate about Newton’s natural philosophy between Leibniz and Samuel Clarke, who acted as Newton’s mouth piece. Newton’s philosophical approach to science influenced, not necessarily positively, John Locke, David Hume and Immanuel Kant amongst others.

Last but perhaps by no means least there is an aspect to Newton that often gets overlooked, Newton the family man. This might seem like a contradiction in terms given that Newton lost his father before he was born and was abandoned as a small child by his mother, to be looked after by relatives, when she remarried. Newton, also, never married and had no children. However, he inherited the family’s not insubstantial holdings in Lincolnshire, they generated a yearly income of six hundred pounds at a time when the annual salary of the Astronomer Royal was one hundred pounds per annum. Newton brought his niece Catherine Barton to London to be his housekeeper and by no means treated her as a servant but as the lady of the house, who enjoyed the status of a lady in London’s high society. Newton also managed the family holdings personally and took good care of those members of his extended family living in Lincolnshire. Newton has acquired a historical reputation for being cantankerous and unfriendly but towards his extended family but also towards his scientific acolytes, the first so-called Newtonians, he could be and often was warm and generous.

Although the above is at best an inadequate sketch I hope I have made it clear that the real Isaac Newton was much more than a caricature of a scientist with an apple falling on his head. He was a theologian, historian, Bible chronologist, alchemist, mathematician, physicist, astronomer, public servant, detective, politician, society president, philosopher, farm manager and family man quite a lot for any individual.

[1] For an excellent account of this activity read Thomas Levenson’s Newton and the Counterfeiter, Houghton Mifflin Harcourt, 2009



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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

Christmas Trilogy 2013 Post 1

Christmas Trilogy 2013 Post 2

Christmas Trilogy 2013 Post 3

Christmas Trilogy 2014 Post 1

Christmas Trilogy 2014 Post 2

Christmas Trilogy 2014 Post 3

Christmas Trilogy 2015 Post 1

Christmas Trilogy 2015 Post 2

Christmas Trilogy 2015 Post 3

Christmas Trilogy 2016 Post 1

Christmas Trilogy 2016 Post 2

Christmas Trilogy 2016 Post 3

Christmas Trilogy 2017 Post 1

Christmas Trilogy 2017 Post 2

Christmas Trilogy 2017 Post 3

Christmas Trilogy 2018 Post 1

Christmas Trilogy 2018 Post 2

Christmas Trilogy 2018 Post 3






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

On Becoming German

Ten days ago I got my Personalausweis (identity card), which kind of make me feel like a real German citizen for the first time, although my certificate of naturalisation was issued on the 15 October and I officially became a German citizen when it was handed to me 21 October. It’s a rather strange feeling to become a citizen of another country, although as a EU citizen I retain my British citizenship and am thus a dual national.

It is a move I have been considering making for several years now, but as a ADDer with dysgraphia I hate, fear and loathe all bureaucracy, so my innerer Schweinehund (translates roughly as internal lazy hound) kept me from making it. The result of the Brexit referendum finally pushed me to get off my fat arse and do something but even then my inertia held me back. Last autumn I paid two hundred plus euro and took my German language and German citizenship exams. The first shouldn’t have been necessary, as I took and passed the much harder university German Language exam three decades ago but couldn’t prove it, the records have got lost, so I spent a whole day proving that I could master the German language. The citizenship exam was a joke. You have to answer 33 multiple-choice questions, 28 of which are taken from a catalogue of 3000 questions that you can read and learn on the Internet (I didn’t bother) and 5 specific to the German State in which you live, in my case Bavaria. To pass you have to get at least 17 right. You have 60 minutes for the exam; I took 4 minutes and I wasn’t the fastest. I got 31 right and am annoyed because I know one that I got wrong but have no idea what the other one was!

Having taken this step I still kept putting off having to actually deal with the bureaucracy. Eventually on 27 March just four days before the final Brexit deadline (remember that?!) I finally pulled myself together and submitted my application for German citizenship; with all the forms, documents and whatever that I had to submit, the pile was literally three centimetres thick; the Germans are very thorough. And then you sit and wait! I was actually fairly convinced that my application would be rejected because of lack of financial support. Having led a rather fucked up life, I live on a basic state pension, which is a pittance and have no financial resources whatsoever. I got more and more nervous as the next Brexit deadline approached fearing, I would become an undesirable alien in my country of residence. I breathed a deep sigh of relief when I received the letter telling me to come and collect my certificate of naturalisation.

Having changed my nationality or rather acquired a second one as I am now a dual national, as I said above, I suppose I should feel something but I don’t and don’t really know what I’m supposed to feel.

I’m a white, middle class male born of British parents in Clacton-on-Sea of all places, so I suppose I couldn’t really be more British. However, as I pointed out in an earlier post my mother, although British, was born in Burma and grew up in British India first coming to Europe at the age of thirty-one. I’ve never really identified as British. It’s a word I fill in, in the appropriate section on official forms that ask for my nationality and it’s what is on the front of my passport. I enjoy watching sport but have never been particularly or even mildly fanatical about any team. Except for in rugby, which I played and enjoyed at school, and the Olympics there are no British sports teams but separate ones for England, Scotland, Wales and Northern Ireland. I take an Englishman’s perverse pleasure, I think the term is schadenfreude, in watching the inevitable English bating collapse in test matches or another golden generation of English soccer players crashing out of yet another European/World Cup. But that’s about it. I’ve never understood sentiments like “my country right or wrong” or dying for “king and country.” I’m a lifelong pacifist, who would adopt Bertrand Russell’s policy if those that I love and care for were threatened by fascism or anything similar and do what ever was necessary to oppose.

I vaguely identify as a West European; I have lived in England, Wales, Belgium, Sweden and the largest part of my life in Germany, Middle Franconia to be precise. Beyond that, I have travelled and holidayed in Denmark, Holland, France, Spain, Italy, Luxembourg, Andorra and Lichtenstein. However, my family background and my upbringing have led me to regard all culture and peoples to be fundamentally the same and to abhor discrimination of any sort.

I identify Middle Franconia in general and the area in and around Erlangen in particular, as being my Wahlheimat, Heimat is the German for home, home town, home country but has connotations of belonging that can’t really be translated into English and Wahlheimat is Heimat of choice. It’s where I feel at home, comfortable and everything else considered where I would like to live out the rest of my life. All of this was true before I applied for German citizenship and being granted it hasn’t really changed anything.

Going through the process of acquiring a new nationality has shown me that the word nationality really doesn’t have any deep meaning for me at all. I probably shouldn’t but I worry slightly about this realisation.


Filed under Autobiographical, Uncategorized

Finding your way on the Seven Seas in the Early Modern Period

I spend a lot of my time trying to unravel and understand the complex bundle that is Renaissance or Early Modern mathematics and the people who practiced it. Regular readers of this blog should by now be well aware that the Renaissance mathematici, or mathematical practitioners as they are generally known in English, did not work on mathematics as we would understand it today but on practical mathematics that we might be inclined, somewhat mistakenly, to label applied mathematics. One group of disciplines that we often find treated together by one and the same practitioner consists of astronomy, cartography, navigation and the design and construction of tables and instruments to aid the study of these. This being the case I was delighted to receive a review copy of Margaret E. Schotte’s Sailing School: Navigating Science and Skill, 1550–1800[1], which deals with exactly this group of practical mathematical skills as applied to the real world of deep-sea sailing.

Sailing School001.jpg

Schotte’s book takes the reader on a journey both through time and around the major sea going nations of Europe, explaining, as she goes, how each of these nations dealt with the problem of educating, or maybe that should rather be training, seamen to become navigators for their navel and merchant fleets, as the Europeans began to span the world in their sailing ships both for exploration and trade.

Having set the course for the reader in a detailed introduction, Schotte sets sail from the Iberian peninsular in the sixteenth century. It was from there that the first Europeans set out on deep-sea voyages and it was here that it was first realised that navigators for such voyages could and probably should be trained. Next we travel up the coast of the Atlantic to Holland in the seventeenth century, where the Dutch set out to conquer the oceans and establish themselves as the world’s leading maritime nation with a wide range of training possibilities for deep-sea navigators, extending the foundations laid by the Spanish and Portuguese. Towards the end of the century we seek harbour in France to see how the French are training their navigators. Next port of call is England, a land that would famously go on, in their own estimation, to rule the seven seas. In the eighteenth century we cross the Channel back to Holland and the advances made over the last hundred years. The final chapter takes us to the end of the eighteenth century and the extraordinary story of the English seaman Lieutenant Riou, whose ship the HMS Guardian hit an iceberg in the Southern Atlantic. Lacking enough boats to evacuate all of his crew and passengers, Riou made temporary repairs to his vessel and motivating his men to continuously pump out the waters leaking into the rump of his ship, he then by a process of masterful navigation, on a level with his contemporaries Cook and Bligh, brought the badly damaged frigate to safety in South Africa.

Sailing School004

In each of our ports of call Schotte outlines and explains the training conceived by the authorities for training navigators and examines how it was or was not put into practice. Methods of determining latitude and longitude, sailing speeds and distances covered are described and explained. The differences in approach to this training developed in each of the sea going European nations are carefully presented and contrasted. Of special interest is the breach in understanding of what is necessary for a trainee navigator between the mathematical practitioners, who were appointed to teach those trainees, and the seamen, who were being trained, a large yawning gap between theory and practice. When discussing the Dutch approach to training Schotte clearly describes why experienced coastal navigators do not, without retraining, make good deep-sea navigators. The methodologies of these two areas of the art of navigation are substantially different.

The reader gets introduced to the methodologies used by deep-sea navigators, the mathematics developed, the tables considered necessary and the instruments and charts that were put to use. Of particular interest are the rules of thumb utilised to make course corrections before accurate methods of determining longitude were developed. There are also detailed discussions about how one or other aspect of the art of navigation was emphasised in the training in one country but considered less important in another. One conclusion the Schotte draws is that there is not really a discernable gradient of progress in the methods taught and the methods of teaching them over the two hundred and fifty years covered by the book.

Sailing School003.jpg

As well as everything you wanted to know about navigating sailing ships but were too afraid to ask, Schotte also delivers interesting knowledge of other areas. Theories of education come to the fore but an aspect that I found particularly fascinating were her comments on the book trade. Throughout the period covered, the teachers of navigation wrote and marketed books on the art of navigation. These books were fairly diverse and written for differing readers. Some were conceived as textbooks for the apprentice navigators whilst others were obviously written for interested, educated laymen, who would never navigate a ship. Later, as written exams began to play a greater role in the education of the aspirant navigators, authors and publishers began to market books of specimen exam questions as preparation for the exams. These books also went through an interesting evolution. Schotte deals with this topic in quite a lot of detail discussing the authors, publishers and booksellers, who were engaged in this market of navigational literature. This is detailed enough to be of interest to book historians, who might not really be interested in the history of navigation per se.

Schotte is excellent writer and the book is truly a pleasure to read. On a physical level the book is beautifully presented with lots of fascinating and highly informative illustrations. The apparatus starts with a very useful glossary of technical terms. There is a very extensive bibliography and an equally extensive and useful index. My only complaint concerns the notes, which are endnotes and not footnotes. These are in fact very extensive and highly informative containing lots of additional information not contained in the main text. I found myself continually leafing back and forth between main text and endnotes, making continuous reading almost impossible. In the end I developed a method of reading so many pages of main text followed by reading the endnotes for that section of the main text, mentally noting the number of particular endnotes that I wished to especially consult. Not ideal by any means.

This book is an essential read for anybody directly or indirectly interested in the history of navigation and also the history of practical mathematics. If however you are generally interested in good, well researched, well written history then you will almost certainly get a great deal of pleasure from reading this book.

[1] Margaret E. Schotte, Sailing School: Navigating Science and Skill, 1550–1800, Johns Hopkins University Press, Baltimore, 2019.


Filed under Book Reviews, History of Astronomy, History of Cartography, History of Mathematics, History of Navigation, Renaissance Science, Uncategorized

The role of celestial influence in the complex structure of medieval knowledge.

My entire life has followed a rather strange and at time confusing path that bears no relationship to the normal career path of a typical, well educated, middle class Englishman. It has taken many twists and turns over the years but without doubt one of the most bizarre was how I got to know historian of astrology Darrel Rutkin. We met on a bus, when he a total stranger commented that he knew the author of the book that I was reading, Monica Azzolini’s excellent, The Duke and the Stars: Astrology and Politics in Renaissance Milan. You can read the story in full here. At the time Darrel was a fellow at the International Consortium for Research in the Humanities: Fate, Freedom and Prognostication. Strategies for Coping with the Future in East Asia and Europe in Erlangen, where he was working on his book on the history of European astrology. Darrel and I became friends, talking about Early Modern science and related topics over cups of coffee and he twice took part in my History of Astronomy tour of Nürnberg. Before he left Erlangen he asked me if I would be interested in reading and reviewing his book when he finished writing it. I, of course, said yes. Some weeks ago I received my review copy of H. Darrel Rutkin, Sapientia Astrologica: Astrology, Magic and Natural Knowledge, ca. 1250–1800: I.Medieval Structures (1250–1500): Conceptual, Institutional, Socio-Political, Theologico-Religious and Cultural and this is my review.


As should be obvious from the impressive title this is not in anyway a popular or even semi-popular presentation but a very solid piece of hard-core academic research. What I have, and will discuss here, is just volume one of three, which weighs in at over six hundred pages. In his work Rutkin present two theses the first of which he explicates in Volume I of his epos and the second of which forms the backbone of the two future volumes. The central thesis of Volume I is summed up in the slightly intimidating twelve-word term “astrologizing Aristotelian natural philosophy with its geometrical-optical model of celestial influences.” A large part of the book is devoted to constructing this object and I will now attempt to produce a simplified description of what it means and how it operated in medieval Europe.

It is common in the history of astrology to treat it as a separate object, as if it had little or nothing to do with the rest of the contemporary knowledge complex. It is also very common to lump astrology together with magic and the other so-called occult sciences. For the High Middle Ages, the period that his book covers, Rutkin rejects both of these approaches and instead proposes that astrology was an integral and important part of the accepted scientific knowledge of the period. His book is divided into five sections each of which I will now outline.

The first section is an eighty-nine-page introduction, which contains a detailed road map of the author’s intentions including a brief summary of what he sees as the current situation in various aspects of the study of the subject under investigation. This also includes an excursion: Astrological Basics: Horoscopes and Practical Astrology. This section is not based on the author’s own work but on that of Roger Bacon, one of the central figures of the book, so if you want to know how a leading medieval astrologer set up and worked with a horoscope then this is the right place to come.

The first section of the book proper deals with the relationship between astrology and natural philosophy in the thirteenth century and it is this section that defines and explains our intimidating twelve-word term from above. Rutkin’s analysis is based on four primary sources; these are an anonymous astrological text the Speculum Astronomiae, written around 1260 and often attributed to Albertus Magnus, an attribution that Rutkin disputes, the writings of Albertus Magnus (before 1200–1280), those of Thomas Aquinas (1225–1274) and those of Roger Bacon (ca. 1220­–1292), as well as numerous other sources from antiquity, and both the Islamic and Christian Middle Ages. In this first section he first presents those writings of Aristotle that contain his thoughts on celestial influence, which form the philosophical foundations for the acceptance of astrology as a science. He then demonstrates how the Speculum Astronomiae, Bacon and Albertus expanded Aristotle’s thoughts to include the whole of horoscope astrology and imbedded it into medieval Aristotelian natural philosophy, this is our “astrologizing Aristotelian natural philosophy.” He also shows how Thomas, whilst not so strongly astrological, as the others, also accepts this model. The technical astrology that is considered here is a highly mathematical, read geometrical, one based on the radiation theories of the Arabic scholar al-Kindi in his De radiis stellarum, as originally introduced into European thought by Robert Grosseteste (1175–1253) in his optical theories and adopted by Bacon. This explains how every geographical point on the earth at every point in time has a unique horoscope/astrological celestial influence: the “geometrical-optical” part of our intimidating twelve-word term. This also ties in with Aristotle’s geographical theories of the influence of place on growth and change. What comes out of this analysis is an astrological-geographical-mathematical-natural philosophical model of knowledge based on Aristotle’s natural philosophy, Ptolemaeus’ astronomy and astrology, and al-Kindi’s radiation theory at the centre of thirteenth century thought.

Rutkin does not simple state an interpretation of Albertus’, Bacon’s or Aquinas’ views but analyses their actual writings in fine detail. First he outlines one step in a given thought process then he quotes a paragraph from their writings in English translation, with the original in the footnotes, including original terms in brackets in the translation if they could possible be considered ambiguous. This is followed by a detailed analysis of the paragraph showing how it fits into the overall argument being discussed. He proceeds in this manner paragraph for paragraph cementing his argument through out the book. This makes hard work for the reader but guarantees that Rutkin’s arguments are as watertight as possible.

The second section of the book proper deals with the subject of theology, a very important aspect of the medieval knowledge complex. Rutkin shows that both Albertus and Thomas accepted astrology within their theology but were careful to show that celestial influence did not control human fate, providence or free will these being the dominion of their Christian God. This is of course absolutely central for the acceptance of astrology by Christian theologians. Bacon’s attitude to astrology and theology is completely different; he builds a complete history of the world’s principle religions based on the occurrence of planetary conjunctions, explaining why, as a result, Christianity is the best religion and addressed to the Pope, for whom he is writing, how one needs to combat the religion of the Anti-Christ.

The third section of the book proper now turns to the vexed question of the relationship between astrology and magic. Rutkin shows that both the Speculum Astronomiae and Albertus in his writing accept that astrology can be used to create magical images or talisman for simple tasks such as killing snakes. However, this is the limit of the connection between the two areas, other aspects of magic being worked by evil spirits or demons. Thomas, not surprisingly rejects even this very circumscribed form of astrological magic regarding all of magic to have its roots in evil. Bacon is much more open to a wider range of connections between the areas of astrology and magic.

Having set up the place of astrology in the medieval knowledge complex of the thirteenth century, the fourth and final section of the book proper takes brief looks at the evidence for its use in various fields within Europe in the period up to 1500. Fields sketched rather than covered in great detail included mathematics, medicine, teaching in the various faculties at the universities, annual prognostications at the universities and to close astrology in society, politics and culture.

Does Rutkin succeed in proving his central thesis for this his first volume? History is not like mathematics and does not deliver conclusive proofs but Rutkin’s thesis is argued in great detail with an impressive array of very convincing evidence. His work is rock solid and anybody wishing to refute his thesis is going to have their work cut out for them. That is not to say that with time, new research and new evidence his thesis will not undergo modification, refinement and improvement but I think its foundations will stand the test of time.

His second main thesis, which will be presented in the two future volumes of his work, is to explain how and why the medieval, mathematics based (read mathematical astrology), Aristotelian natural philosophy that had been created in the High Middle Ages came to replaced by a very different mathematics based, system of natural philosophy in the seventeenth and eighteenth centuries. Having ploughed my way through Volume I, I very much look forward to reading both future volumes.

It goes without saying that the book has an impressively long bibliography of both primary and secondary sources that the author has consulted. I consider myself reasonably well read on the history of European astrology but if I were to sit down and read all of the new, interesting titles I discovered here, I would be very busy for a number of years to come. There is also a first class index and I’m very happy to report that the book also has excellent footnotes, many of which I consulted whilst reading, rather than the unfortunately ubiquitous endnotes that plague modern publishing.

Before I move to a conclusion I wish to point out a second way to read this book. As it stands this is not a book that I would necessarily dump on an undergraduate or a historian, whose interest in the fine detail of Rutkin’s argument was peripheral but that is not necessary or at least not in its totality. I have already mentioned that the introduction contains a detailed road map to the whole volume and as well as this, each of the four sections has an introduction outlining what the section sets out to show and a conclusion neatly summarising what has been demonstrated in the section. By reading main introduction and the introductions and conclusions to the sections a reader could absorb the essence of Rutkin’s thesis without having to work through all of the documentary proof that he produces.

In general I think that Rutkin has set standards in the historiography of medieval astrology and that his book will become a standard work on the topic, remaining one for a long time. I also think that anybody who wishes to seriously study medieval European astrology and/or medieval concepts of knowledge will have to read and digest this fundamental and important work.

I’m posting this today, having pulled it up from the back of a list of planned blog posts because today Darrel’s book is being formally presented at the University of Venice, where he is currently working in a research project, this afternoon with Monica Azzolini as one of those discussing the book and so a circle closes. I shall be there with them in spirit.





Filed under Book Reviews, History of Astrology, Uncategorized

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

Although highly anticipated the expectation placed upon De revolutionibus and the reactions to it were highly diverse and covered a very wide spectrum from complete acceptance to total rejection with many variation in between. It would be impossible in a blog post series such as this one to deal with the multitude of single reactions that would require a fairly substantial book; in fact I have two such books sitting next to my computer at the moment–Pietro Daniel Omodeo, Copernicus in the Cultural Debates of the Renaissance: Reception, Legacy, Transformation (Brill, 2014) & Jerzy Dobrzycki ed., The Reception of Copernicus’ Heliocentric Theory (D Reidel, 1972)–which I recommend to anybody who wants an in depth, blow by blow account. What I intend to do here is sketch the basic trends of that reception.

Famously Robert Westman once claimed that only ten people in the whole world accepted Copernicus’ heliocentric hypothesis, including his cosmology, completely between its publication in 1553 and the year 1600. His list actually misses a couple of total accepters such as Gemma Frisius, who acknowledged his acceptance in his foreword to Johannes Stadius’ ephemerides, and the Englishman John Feild who made the same acknowledgement in his ephemerides. However, it does include three others who either dropped or appeared to drop their acceptance. Christoph Rothmann (born between 1550 & 1560 died probably after 1600) one of Wilhelm IV’s astronomers (of which more later), who had an extensive dispute with Tycho Brahe, who of course didn’t accept Copernicus’ cosmology, on the subject and in the end, and according to Tycho was converted to his point of view.  Diego de Zúñiga (1536–1597), a Spanish Augustinian hermit and academic, who wrote a defence of the heliocentric hypothesis in his In Job commentaria (1584) but later in life rejected Copernicus’ hypothesis as incompatible with Aristotelian philosophy, probably under religious pressure from his superiors. The most peculiar renegade was Copernicus’ first and initially strongest supporter, Rheticus. Having gone quiet on Copernicus and his hypothesis for some time after he moved to Kraków, in a correspondence with Pierre de la Ramée (1515-1572) he announced that he had erected a large gnomon in Kraków and was now practicing the true astronomy of the Egyptians, whatever that might be. Summa summarum, one can say without much contradiction that there were never more than about fifteen, and probably less, true Copernican in the world before 1600 or even before 1609/10 when the publications of Kepler and the invention of the telescope became game changers.

There were a few astronomers, who simply rejected Copernicus’ hypothesis without comment and some, who simply ignored it but they won’t interest us here because the evidence shows that the vast majority did react to it in some way or another. As already mentioned earlier Owen Gingerich carried out a survey of all known surviving copies of the 1st(Nürnberg 1543) and 2nd(Basel 1566) editions of De revolutionibus[1]and his analysis of the annotation and marginalia of the readers clearly shows that the majority took very little notice of the first cosmological part of the book but concentrated their reading instead on the technical parts of the book, the mathematical models and the data.

This rejection of the heliocentric aspect of Copernicus’ work was a simple and direct consequence of the fact that he could not provide any empirical evidence to support his claims that the Earth revolved on its own axis and that it orbited a stationary Sun. Both claims very clearly contradicted the evidence of one’s own senses, we still say the Sun rises and sets, and suggested consequences that Copernicus was unable to answer. If the Earth is rotating at approximately 1600 kilometres an hour at the equator, why doesn’t everything on the surface get blown off by the headwind? And if the Earth is orbiting the Sun, why can’t we detect stellar parallax? These are just two of the possible objections to which Copernicus could not provide scientific answers.

The answers, based on assumptions, which he did propose would prove with time and new developments in science to be fundamentally correct but at the time there were merely unsubstantiated assumptions. In answer to the first he suggested that everything on the Earth’s surface would be carried along with it in some sort of envelope. This turned out to be correct but Copernicus lacked the physics necessary to explain how this would function. In fact the history of physics of the seventeenth century, as we shall see, consisted to a large extent of developing the knowledge to provide this explanation. As far as stellar parallax was concerned, or rather the lack of it, Copernicus simply and correctly assumed that the stars were simply too far away for the parallax to be detected with the naked-eye. However, Copernicus and almost all of his contemporaries still believed in the sphere of the fixed stars and if this sphere was so far away that stellar parallax was undetectable then the distance between the orbit of Saturn and the sphere of the fixed stars would have to be inconceivably vast and thus not very acceptable. Simply put, why all of that empty space out there?

The ambivalence towards Copernicus magnum opus is nicely illustrated by the Welsh mathematicus Robert Recorde (c. 1512–1558) in his The Castle of Knowledge (1556) the first English text to refer to the Copernican hypothesis. On the subject of the possible motion of the Earth he wrote:

             But as for the quietness of the earth, I need not to spend any time in proving of it, since that opinion is so firmly fixed in most men’s heads, that they accompt it mere madness to bring the question in doubt. And therefore it is as much folly to travail to prove that which no man denieth, as it were with great study to dissuade that thing which no man doth covet, neither any man allow: or to blame that which no man praiseth, neither any man liketh.

Scholar: Yet sometimes it chanceth, that the opinion most generally received, is not most true

Master: And so do some man judge of this matter, for not only Eraclides [Heraclides] Ponticus, a great Philosopher, and two great clerks of Pythagoas school, Philolaus and Ecphantus, were of the contrary opinion, but also Nicias [Hicetas] Syracusius, and Aristarchus Samius, seem with strong arguments to approve it: but the reasons are too difficult for this first Introduction, and therefore I will omit them till another time. And so I will do the reasons that Ptolemy, Theon and others do allege, to prove the earth to be without motion: and the rather, because those reasons do not proceed so demonstrably, but they may be answered fully, of him that holds the contrary. I mean, concerning circular motion: marry, direct motion out of the centre of the world seemeth more easy to be confuted, and that by the same reasons, which were before alleged for proving the earth to be in the middle and centre of the world.

Scholar: I perceive it well: for as if the earth were always out of the centre of the world, those former absurdities would at all times appear: so if at any time the earth should move out of his place, those inconveniences would then appear.

Master: That is truly to be gathered: how be it, Copernicus, a man of great learning, of much experience, and of wonderful diligence in observation, hath renewed the opinion of Aristarchus Samius, and affirmeth that the earth not only moveth circularly about its centre, but also may be, yea and is, continually out of the precise centre of the world 38 hundred thousand miles: but because the understanding of that controversy dependeth of profounder knowledge than in this Introduction may be uttered conveniently, I will let it pass till some other time.

Scholar: Nay sir in good faith, I desire not to hear such vain fantasies, so far against common reason, and repugnant to the consent of all the multitude of Writers, and therefore let it pass for ever, and a day longer.

Master: You are too young to be a good judge in so great a matter: it passeth for your learning, and theirs also that are much better learned than you to improve [i.e. disprove] his supposition by good arguments, and therefore you were best to condemn nothing that you do not well understand but another time, as I said, I will so declare his supposition, that you shall not only wonder to hear it, but also peradventure be as earnest then to credit it, as you are now to condemn it.


In this exchange Recorde appears to both reject and praise Copernicus’ hypothesis. Unfortunately we will never know his true opinion as he died before he could write the advanced text that he promises his readers here. What, however, is very clear is that Recorde is very well informed about the history of both diurnal rotation and the heliocentric hypothesis.

Some of the readers, who only considered the mathematical parts of the book, simply took Copernicus’ models for the various planets and applied them to a geocentric system, hoping thereby to produce a better predictive model for the position of the planets. Other took this remodelling a step further and using Copernicus’ mathematical models revived the Capellan model, well-known and much loved in the Middle Ages; a geocentric system in which Mercury and Venus orbit the Sun, which in turn orbits the Earth.


Naboth’s representation of Martianus Capella’s geo-heliocentric astronomical model (1573) Source: Wikimedia Commons

Others took this thought one step further and developed, what is now known the Tychonic system, named after Tycho Brahe (1546–1601), although he was by no means the first or the only astronomer to publish this system in the second half of the sixteenth century, all claiming to have developed it independently. In this helio-geocentric system all of the planets except the Moon, orbit the Sun, which together with the Moon orbits the stationary Earth. Heliocentric, geocentric and helio-centric model based on Copernicus’ parameters and mathematical model can and have been shown to be mathematically equivalent with nothing to recommend one over the other, without further information.


The Tychonic System Source: Wikimedia Commons

One interesting but slightly confusing development was that some geocentric and helio-geocentric astronomers accepted the arguments for the Earth spinning on its own axis, diurnal rotation, whilst still rejecting the Earth orbiting the Sun. As I wrote here in an earlier blog post, this idea goes back at least to Heraclides Ponticus (c.390 BCE–c.310 BCE) and was adopted or discussed and rejected many times over the centuries down to Copernicus’ times. The argument in its favour is a purely physical one. It is much simpler for the comparatively small Earth to rotate than for the vastly larger and heavier sphere of the fixed stars. This acceptance of diurnal rotation would prove to be an important steeping stone to the complete acceptance of the heliocentric model in the seventeenth century.

On major group, who showed great interest in Copernicus’ mathematics and above all in the planetary tables and ephemerides that they delivered were the astrologers. This basically means all professional and half professional astronomers, as they were almost all practicing astrologers. As stated above Robert Westman once claimed that there were only ten Copernicans in the whole world between 1543 and 1600, a historian of astrology correctly pointed out that all ten were practicing astrologers. Like Regiomontanus in the previous century (see Part II of this series) they all thought that more accurate astronomical data would improve the quality of their astronomical prognoses. Not only did they avidly consult the ephemerides of Stadius and Feild but several of them such as the Italian mathematicus Giovanni Antonio Magini (1555–1617) unsatisfied with Stadius’ and Feild’s accuracy also calculated their own new ephemerides. In the end, however, the astrologers recognised that although the errors in Copernican tables were different to those in Ptolemaic ones they were not much more accurate as we will see in the next instalment.

[1]Owen Gingerich, An Annotated Census of Copernicus’ De Revolutionibus(Nuremberg, 1543 and Basel, 1566), Brill, Leiden, Boston, Köln, 2002


Filed under History of Astronomy, Renaissance Science, Uncategorized