Some first class history of science reading for the holiday weekend: Giants’ Shoulders #70: The Sir Hans Sloane Birthday Collection

At a lose end on Good Friday or Easter Monday? Read up on the best history of science bloggage from the last thirty days gathered from the far reaches of cyberspace for your pleasure.

Lisa Smith (@historybeagle) has put together a wonderful edition of the histories of science, medicine and technology blog carnival Giants’ Shoulders to celebrate the birthday of Augustan physician, scientific official, and collector, Sir Hans Sloane, just in time for the holiday weekend.

The next edition of Giants Shoulders #71 will be presented here at the Renaissance Mathematicus on 16 May 2014. Submission as ever to me here at RM or on Twitter by 15 May at the latest.

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People appear to love list. The Internet is full of lists. The 10 most popular dog breeds, the 10 biggest waves ever ridden by a surfer, the 10… you get the idea. The lists very often have ten entries, it’s a shame that we all have the same number of fingers otherwise we could a bit more variation, the 7 biggest… or the 11 smartest… Science and its history are far from immune from this cyber cancer, lists of all sorts being produced and posted with gay abandon. We recently even had the Top 10 scientists of the 13th century! Apart from the fact that the use of the word scientist here is highly anachronistic any such selection is of course subjective and disputable. However the subject of this post is not medieval scholars, tempting though it is, but a list of “17 Equations That Changed the World”

17 Equations that Changed the World

17 Equations that Changed the World

Although it claims to be by Ian Stewart I have no idea of the original source of this list but I have stumbled across it several times in the last few months. Now when I was a young mathematical acolyte and budding historian of maths I devoured Ian Stewart’s books at the same rate as those of Martin Gardner and Isaac Asimov. Put another way Ian Stewart was a major influence on my development. As I got older, but probably not wiser, I came to realise that Stewart, a mathematician and populariser, wasn’t very accurate in his historical attributions, in fact he is down right sloppy. This list is no exception.

Don’t worry I’m not going to go through all seventeen entries but the first time I read it I immediately noticed that the first five all have significant problems and I thought it would make an interesting exercise to explain why.

We start off with what is possibly the most well known theorem in the whole of mathematics Proposition 47 from Book I of Euclid’s Elements. The correct attribution of this theorem is actually an exercise in history of mathematics 101.

In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.

Now Euclid is thought to have written his Elements around 300 BCE and he doesn’t attribute this theorem to anybody. The first to putatively attach Pythagoras’ name to Euclid’s Proposition 47 was Proclus in his commentary on the Elements written in the fifth century CE. However Proclus doesn’t sound very convinced by his own attribution.

If we listen to those who wish to recount ancient history, we may find some of them referring this theorem to Pythagoras and saying that he sacrificed an ox in honour of his discovery. But for my part, while I admire those who first observed the truth of this theorem, I marvel more at the writer of the Elements, not only because he made it fast by a more lucid demonstration, but because he compelled assent to the still more general theorem by the irrefragable arguments of science in the sixth Book. For in that Book he proves generally that, in right-angled triangles, the figure on the side subtending the right angle is equal to the similar and similarly situated figures described on the sides about the right angle.

Proclus would seem to want to award the credits to Euclid not Pythagoras. Those who wished to recount ancient history were Cicero writing in the first century BCE and Plutarch writing in the first century CE. One thing that makes this anecdote from antiquity somewhat dubious is the fact that the Pythagoreans rejected animal sacrifice. There is no actual contemporary evidence that associates either the Pythagoreans or Pythagoras to the theorem that we name after him. However all of this is rather academic, as the theorem existed more than a thousand years before the Pythagoreans.

There is clear evidence that the Babylonians knew of the theorem in the Old Babylonian period around 1700 BCE. However although we have several instances of them using the theorem we don’t have a Babylonia proof of the theorem Maybe they didn’t have one but there are still literally tons of Babylonian clay tablets that have never been transcribed let alone translated. It could well be that somewhere the Babylonian Pythagoras is still waiting to be discovered.

The Babylonians were not the only ones to have the theorem independently of the Greeks. A clear example of the theorem can be found in the Indian Sulba Sutras. Unfortunately the dating of early Indian texts is very problematic and the best we can do is to say the Sulba Sutras date from between 800 and 200 BCE, so if the Indian Pythagoras predated the Greek one is almost impossible to determine.

Never to be left out when it comes to ancient invention and discovery the Chinese also had their own Pythagoras. The greatest Chinese mathematical classic The Nine Chapters of the Mathematical Arts contains problems that require use of the theorem in Chapter 9. In Chinese it is known as the Gougu rule. Once again dating is a major problem, the earliest existing manuscript dates from 179 CE but the contents are probably much earlier in origin, currently thought to date to 300 to 200 BCE. A simple and elegant pictorial proof of the theorem turns up in another Chinese classic the Zhou Bi Suan

Chinese Pythagoras

Chinese Pythagoras

Jing. Also very difficult to date but probably originating around 300BCE. As can be seen this theorem doesn’t have a simple history.

Stewart now takes a massive leap into the seventeenth century CE and the invention of logarithms. Once again his simple attribution to John Napier is exactly that, simplistic and historically misleading. We can find the principle on which logarithms are based in the work of several earlier mathematicians. We can find forms of proto-logarithms in both Babylonian and Indian mathematics and also in the system that Archimedes invented to describe very large numbers. In the fifteenth century Triparty, of the French mathematician Nicolas Chuquet we find the comparison between the arithmetical and geometrical progressions that underlay the concept of logarithms but if Chuquet ever took the next step is not clear. In the sixteenth century the German mathematician Michael Stifel studied the same comparison of progressions in his Arithmetica integra and did take the next step outlining the principle of logarithms but doesn’t seem to have developed the idea further.

It was in fact John Napier who took the final step and published the first set of logarithmic tables in his book Mirifici Logarithmorum Canonis Descriptio in 1614. However the Swiss clockmaker and mathematician, Jost Bürgi developed logarithms independently of Napier during the same period although his book of tables, Arithmetische und Geometrische Progress Tabulen, was first published in 1620.

We stay in the seventeenth century for Stewart’s next equation, which is the production of a first derivative using the so-called h-method confusingly labelled calculus, confusing that is because calculus is a branch of mathematics and not an equation, and attributed to Newton 1668. To say that this line has a lot of issues would be a mild understatement. I will try to keep it relatively short. Anybody with half an idea of the history of calculus will already be asking themselves, what about Leibniz? Newton and Leibniz both developed their ideas of the calculus independently in the same period with Newton probably developing his ideas first but Leibniz being the first in print. This situation led to what is probably the most notorious priority dispute in the whole of the history of mathematics and science. What makes Stewart’s statement even more piquant is that he attributes the discovery to Newton but his equation for the first derivative is written in Leibniz’ notations. Of course there is an about two thousand year long history to the development of the calculus that I outlined in an earlier post, so I won’t repeat it now. I will however point out that the h-method to determine the first derivative is not from either Newton or Leibniz but Pierre Fermat.

Newton gets a second bite of the cherry, this time, with the equation for gravity. I’ve lost count of the number of time that I’ve pointed out that the basics of the law of gravity, the inverse square relationship, does not originate with Newton. A very quick rundown.

The first to suggest that the planets were kept in their courses by a force was Kepler who suggested a directly proportional relationship based on Gilbert’s investigations of the magnet. Borelli also speculated on forces driving the planets in his Theoricae Mediceorum Planetarum ex Causius Physicus Deductae published in 1666 and known to Newton. The first to suggest an inverse square relationship was Ismael Boulliau, a story that I’ve already told here, although I there claim erroneously that Newton admits his knowledge of Boulliau’s priority in Principia, he doesn’t, it’s in the letters he exchanged with Halley in his dispute with Hooke. In the middle of the seventeenth century Wren, Halley, Hooke and Newton all independently came to the conclusion that the force governing the planetary orbits was probably inversely proportional to the square of the distance, i.e. the law of gravity. Newton’s achievement was to show that this law was equivalent to Kepler’s third law of planetary motion and that it also allowed the deduction of Kepler’s first two laws.

Stewart’s fifth equation is his simplest i = √-1, which he attributes to Euler. Now whilst it is probably true that Euler introduced the letter “i” as the symbol for the square root of minus one, by the time he did so mathematicians had been playing with and cursing the concept for a couple of hundred years.

The first person to consciously use imaginary or complex numbers was the sixteenth century polymath Girolamo Cardano in his Ars magna, the first systematic study of the solution of polynomials published by Petreius in Nürnberg in 1545. Cardano solved cubic equation in which during the solution so-called conjugate pairs of complex numbers turned up, which when multiplied together lost their imaginary parts thus delivering real solutions. (Conjugate pairs of complex numbers are ones of the form a + b√-c and a – b√-c which when multiplied together become a2 +b2c.) Cardano thought the complex numbers were nonsensical but the solutions worked so he left them in.

Later in the century the Italian mathematician Rafael Bombelli worked quite rationally with complex numbers developing the rule for their manipulation in his Algebra published in 1572. If any one name should be attached to this equation then it’s Bombelli’s.


Of course not everybody was as happy with these very strange entities as Bombelli and it was Descartes who gave them the name imaginary in 1637. It was intended to be derogatory. Euler did much to develop the theory of complex numbers in the eighteenth century but it was first the development, independently by three mathematicians, Caspar Wessel in 1799, Jean-Robert Argand in 1806 and of course Gauss, of the geometrical interpretation of complex numbers that they became finally universally accepted.

Having ploughed your way through the historical thickets of this post some of you might be thinking that I’m just nit picking, but there is a deeper point that I’m trying to make. It is very rare in the history of mathematics or science that a theorem, theory, invention, discovery, idea, concept or hypothesis emerges in its final form, like Athena born fully armed from Zeus’ forehead. Almost always there is an, often long, period of evolution involving many thinkers and often taking long and devious routes. Very often they occur as multiple discoveries with more than one progenitor, frequently leading to priority disputes. The idea of a simple list of discoveries with one date and one name whilst superficially attractive leads inevitably to a false concept of the evolution of science and of scientific methodology. Let us get away from such lists and let students of science and mathematics really learn just how messy, complex and, I think, fascinating the histories of their disciplines really are.


Filed under History of Mathematics, Myths of Science

Looking up to Marius

One of the principle principal goals of the Simon-Marius-Anniversary-2014 has been achieved. The committee of the International Astronomical Union (IAU) responsible for the naming of minor planets, comets and natural satellites has announced that the asteroid “1980 SM” will in future be known as “(7984) Marius”. The minor planet in the so-called main belt between Mars and Jupiter was first observed at the Klet’ Observatory (Hvězdárna Kleť) on 29th September 1980.

The Minor Planet Center (MPC) announced the decision of the Committee for Small-Body Nomenclature of the International Astronomical Union (IAU) at the end of March, whereby the asteroid discovered by the Czech astronomer Zdeňka Vávrová will be named after the Ansbach Court Astronomer, Simon Marius (1573–1624). The heavenly body has an orbit of 4.27 years and is 2.63 AU distance from the sun. Its average speed is 7.57 km/s.

Marius-Solar-System Norman Schmidt

Norman Schmidt

The recognition by the International Astronomical Union is a great honour for the Franconian astronomer whose magnum opus “Mundus Jovialis” was published four hundred years ago. In this work he describes the discovery of the four largest Jupiter moons, which Galileo Galilei and Simon Marius observed for the first time in January 1610. Galileo, having published first, accused Marius of plagiarism, a charge that was only shown to be unfounded at the beginning of the twentieth-century.

Various events within the framework of the Simon-Marius-Anniversary 2014 recognise his achievements and the Nürnberger Astronomische Gesellschaft has setup the 24-Language Marius-Portal, which brings together all the electronic sources as well as the secondary literature to make them available to the international research community and all other interested parties. The naming of the asteroid is the second milestone.

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Giants’ Shoulders #70 celebrates a birthday.

Hans Sloane is one of those figures in the history of science, who deserves to be much better known than he is. Although Sloane Square in London is named after him, giving name to one of the horrors of modern English culture, the Sloane Ranger, most people would be hard put to it to say who he was.

Sir Hans Sloane Gottfried Kneller

Sir Hans Sloane
Gottfried Kneller

An Irish physician who lived through the second half of the seventeenth century and the first half of the eighteenth, he was a central figure in the English scientific community that included Hooke, Wren, Halley, Flamsteed and Newton as well as many other less well known personages. He was secretary of the Royal Society when Newton became its president in 1704 and very much shared the power with the great Sir Isaac in that august body until he resigned in 1713, after a series of power struggles with other council members over the preceding years. He got his revenge however when he was elected president following Newton’s death in 1727, a post he retained until 1741.

He served three English monarchs, Anne, George I and George II, as royal physician and was appointed baronet for his services in 1716. He was also elected president of the Royal College of Physicians in 1719 a post he would hold for sixteen years. In 1722 he also became physician-general to the army.

From the modern point of view Sloan’s most important activity was that of collector. Scientific curiosity cabinets were very much en vogue in the Early Modern Period and Sloane collected scientific curiosities on an almost unbelievable scale. When he died, in 1753, he donated his monster collection to the nation on the condition that the government build a museum to house it. The government agreed and so the venerable British Museum was born. Later Sloane’s natural history collection was given a home of its own leading to the establishment of the Natural History Museum.

Like many of his contemporaries, and in particular the collectors, Sloane was a prolific letter writer and, as is befitting in this digital age, his correspondence has its own blog. To celebrate Sir Hans’ 354th birthday, on 16 April, Giants’ Shoulders #70, the history of science, medicine and technology blog carnival  will take place at The Sloane Letters Blog hosted by our favourite blogging beagle, Lisa Smith (@historybeagle). Submission for this special birthday edition of Giants’ Shoulders should be made either direct to the host or to me here at RM or to either of us on Twitter at the latest by 15 April.


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Luca, Leonardo, Albrecht and the search for the third dimension.

Many of my more recent readers will not be aware that I lost a good Internet friend last year with the unexpected demise of the history of art blogger, Hasan Niyazi. If you want to know more about my relationship with Hasan then read the elegy I wrote for him when I first heard the news. Hasan was passionate about Renaissance art and his true love was reserved for the painter Raffaello Sanzio da Urbino, better known as Raphael. Today, 6th April is Raphael’s birthday and Hasan’s partner Shazza (Sharon) Bishop has asked Hasan’s friends in the Internet blogging community to write and post something today to celebrate his life, this is my post for Hasan.


I’m not an art historian but there were a couple of themes that Hasan and I had in common, one of these was, for example, the problem of historical dating given differing calendars. Another shared interest was the history of linear perspective, which is of course absolutely central to the history of Renaissance art but was also at the same time an important theme in Renaissance mathematics and optics. I have decided therefore to write a post for Hasan about the Renaissance mathematicus Luca Pacioli who played an important role in the history of linear perspective.


Luca Pacioli artist unknown

Luca Pacioli
artist unknown

Luca Pacioli was born in Sansepolcro in the Duchy of Urbino in 1445.

Duchy of Urbino  Henricus Hondius 1635

Duchy of Urbino
Henricus Hondius 1635

Almost nothing is known of his background or upbringing but it can be assumed that he received at least part of his education in the studio of painter and mathematician Piero della Francesca (1415 – 1492), who like Pacioli was born in Sansepolcro.

Piero della Francesca Self Portrait

Piero della Francesca
Self Portrait

Pacioli and della Francesca were members of what is now known as the Urbino school of mathematics, as was Galileo’s patron Guidobaldo del Monte (1545 – 1607). These three Urbino mathematicians together with, Renaissance polymath, Leone Battista Alberti (1404 – 1472) all played an important role in the history of linear perspective.


Leon Battista Alberti  Artist unknown

Leon Battista Alberti
Artist unknown

Whilst still young Pacioli left Sansepolcro for Venice where he work as a mathematics tutor. Here he wrote his first book, an arithmetic textbook, around 1470. Around this time he left Venice for Rome where he lived for several months in the house of Alberti, from whom he not only learnt mathematics but also gained good connections within the Catholic hierarchy. Alberti was a Papal secretary.

In Rome Pacioli studied theology and became a Franciscan friar. From 1477 Pacioli became a peripatetic mathematics teacher moving around the courts and universities of Northern Italy, writing two more arithmetic textbooks, which like his first one were never published.

Ludovico Sforza became the most powerful man in Milan in 1476, at first as regent for his nephew Gian Galeazzo, and then, after his death in 1494, Duke of Milan.

Ludovico Sforza Zanetto Bugatto

Ludovico Sforza
Zanetto Bugatto

Ludovico was a great patron of the arts and he enticed Leonardo to come and serve him in Milan in 1482. In 1496 Pacioli became Ludivico’s court mathematicus. Leonardo and Pacioli became colleges and close friends stimulating each other over a wide range of topics.


Leonardo Francesco Melzi

Francesco Melzi

Before he went to Milan Pacioli wrote his most famous and influential book his Summa de arithmetica, geometria, proportioni et proportionalità, which he published in Venice in 1494. The Summa, as it is generally known, is a six hundred-page textbook that covers the whole range of practical mathematics, as it was known in the fifteenth-century. Pacioli was not an original mathematician and the Summa is a collection of other peoples work, however it became the most influential mathematics textbook in Europe and remained so for almost the whole of the sixteenth-century. As well as the basics of arithmetic and geometry the Summa contains the first printed accounts of double entry bookkeeping and probability, although Pacioli’s account of determining odds is wrong. From our point of view the most important aspect of the Summa is that it also contains the first extensive printed account of the mathematics of linear perspective.


Pacioli Summa Title Page

Pacioli Summa
Title Page

According to legend linear perspective in painting was first demonstrated by Fillipo Brunelleschi (1377 – 1446) in Florence early in the fifteenth-century. Brunelleschi never published an account of his discovery and this task was taken up by Alberti, who first described the construction of linear perspective in his book De pictura in 1435. Piero della Francesca wrote three mathematical treatises one on arithmetic, one on linear perspective and one on the five regular Euclidian solids. However della Francesca never published his books, which seem to have been written as textbooks for the Court of Urbino where they existed in the court library only in manuscript. Della Francesca treatment of perspective was much more comprehensive than Alberti’s.

During his time in Milan, Pacioli wrote his second major work his Divina proportione, which contains an extensive study of the regular geometrical solids with the illustrations famously drawn by his friend Leonardo.


Leonardo Polyhedra


These two books earned Pacioli a certain amount of notoriety as the Summa contains della Francesca’s book on linear perspective and the Divina proportione his book on the five regular solids both without proper attribution. In his Lives of the Most Excellent Italian Painters, Sculptors, and Architects, from Cimabue to Our Timesthe Italianartist and art historian, Giorgio Vasari (1511 – 1574)


Giorgio Vasari Self Portrait

Giorgio Vasari
Self Portrait

accused Pacioli of having plagiarised della Francesca, a not entirely fair accusation, as Pacioli does acknowledge that the entire contents of his works are taken from other authors. However whether he should have given della Francesca more credit or not Pacioli’s two works laid the foundations for all future mathematical works on linear perspective, which remained an important topic in practical mathematics throughout the sixteenth and seventeenth centuries and even into the eighteenth with many of the leading European mathematicians contributing to the genre.

With the fall of Ludovico in 1499 Pacioli fled Milan together with Leonardo travelling to Florence, by way of Mantua and Venice, where they shared a house. Although both undertook journeys to work in other cities they remained together in Florence until 1506. From 1506 until his death in his hometown in 1517 Pacioli went back to his peripatetic life as a teacher of mathematics. At his death he left behind the unfinished manuscript of a book on recreational mathematics, De viribus quantitatis, which he had compiled together with Leonardo.

Before his death Pacioli possibly played a last bit part in the history of linear perspective. This mathematical technique for providing a third dimensional to two dimensional paintings was discovered and developed by the Renaissance painters of Northern Italy in the fifteenth century, one of the artists who played a very central role in bringing this revolution in fine art to Northern art was Albrecht Dürer, who coincidentally died 6 April 1528, and who undertook two journeys to Northern Italy explicitly to learn the new methods of his Italian colleagues.

Albrecht Dürer Self Portrait

Albrecht Dürer
Self Portrait

On the second of these journey’s in 1506-7, legend has it, that Dürer met a man in Bologna who taught him the secrets of linear perspective.  It has been much speculated as to who this mysterious teacher might have been and one of the favoured candidates is Luca Pacioli but this is highly unlikely. Dürer was however well acquainted with the work of his Italian colleagues including Leonardo and he became friends with and exchanged gifts with Hasan’s favourite painter Raphael.


Filed under History of Mathematics, History of Optics, Renaissance Science, Uncategorized

Did Edmond tells Robert to, “sling his hooke!”?

The circumstances surrounding the genesis and publication of Newton’s magnum opus, Philosophiæ Naturalis Principia Mathematica, and the priority dispute concerning the origins of the concept of universal gravity are amongst the best documented in the history of science. Two of the main protagonists wrote down their version of the story in a series of letters that they exchanged, as the whole nasty affair was taking place. Their explanations are of necessity biased and unfortunately we don’t have equivalent written evidence from the third protagonist Robert Hooke, although we do have the earlier exchange of letters between Hooke and Newton that led Hooke to making his claims to being the author of the idea. All of this is documented, analysed and discussed in detail by Richard S. Westfall in his authoritative biography of Newton, Never at Rest. Lisa Jardine sketches the whole sorry episode in the introduction to her Hooke biography The Curious Life of Robert Hooke: The Man Who Measured London. Beyond this there is a whole raft full of academic papers and monographs on Hooke, Newton, Halley, Principia and the Royal Society that discus the whole or various aspects of the story. Any first year history of science student should be able to write an accurate and informed essay or term paper on this important moment in the history of seventeenth-century scientific publishing. In fact it would make a very useful exercise for such students. The scriptwriters of Cosmos would however get a fat F for their efforts to present the story. Maybe they should have turned to one of those first year students for help?

Thanks to the services of a beautiful fairy princess I was finally able to watch the third episode of the much hyped American television series Cosmos and, as predicted by numerous commentators on Twitter, I was more than underwhelmed by the animation telling the story of the publication of Principia Mathematica and its significance in the history of science.

Our tale starts with an introductions to the hero of the day, Edmond Halley, an interesting choice of which I actually approve but the first error come up with the tale of the young Halley’s journey to St Helena to map the southern skies. We get told that this is the first such map. This is simply not true Dutch seamen had already started mapping the southern hemisphere at the end of the sixteenth-century. Halley’s government sponsored voyage was the English attempt to catch up. Having established Halley as a scientific hero we get presented with Robert Hooke who is to play the villain of the piece.

At the beginning we get a very positive portrait of Hooke outlining the very wide range of his scientific activities. Unfortunately this presentation is spoilt by a series of bad history of science blunders. Introducing Hooke’s microscopic investigations we get told that Hooke invented the compound microscope. Given that compound microscopes were in use twenty years before Hooke was born, I hardly think so. We then get told that Hooke improved the telescope. Whilst it is true that Hooke proposed several schemes to improve the telescope, some of them positively Heath-Robinson, none of them really proved practical and there are no real improvements to the telescope that can be laid at Hooke’s door. Next up we are informed that Hooke perfected the air pump. Hooke did indeed construct the air pump that he and Robert Boyle used for their experiments, their model was in fact ‘perfected’, although improved would be a better term as it was anything but perfect, by Denis Papin.

Moving on, we are introduced to the London coffee houses, without doubt centres of scientific communication in the late seventeenth- and early eighteenth-centuries. However Tyson claims them to be laboratories of democracy. Sorry but all I can say to this piece of hogwash is bullshit. We come to the coffee house because of a legendary conversation between Halley, Hooke and Christopher Wren that took place in one of them in January 1684, concerning the law of gravity. This conversation is indisputably a key moment in the history of science and that is the reason why it is featured in this episode of Cosmos. Given this one would expect that the scriptwriters would get the story right, however ones expectations would be dashed. According to Cosmos the three speculated as to whether there was a mathematical law governing celestial motion and then Newton, to whom I will come in a minute, produced the inverse squared law of gravity like a conjuror pulling his rabbit out of his hat. In fact all three participants were aware of speculations concerning an inverse squared law of gravity and Hooke claimed that he could deduce the motions of the heavens from it. Wren doubted this claim and offered a prize for the first to do so. Hooke persisted that he already had the solution but would first reveal it when the others had admitted defeat.

Cosmos has Halley, unable to solve the problem rushing off the Cambridge to ask Newton if he could solve it. In fact Halley being in Cambridge in August of the same year met Newton and in the course of their conversation asked Newton, “what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of their distance from it, Sr Isaac replied immediately that it would be an Ellipsis…”[1] The description of Newton given by Cosmos introducing this fateful meeting also owes more to fantasy than reality. We get told that Newton went to pieces over his dispute with Hooke concerning his theory of light, that he had become a recluse and that he was in hiding in Cambridge. Although Newton declined to have anything more to do with the Royal Society following the numerous disputes, not just with Hooke, following the publication of his theory of light in 1672 he certainly did not go to pieces, giving as good as he got and he was not hiding in Cambridge but working there as Lucasian Professor of Mathematics. Also far from being a recluse he was corresponding with a wide range of other scholars, including Hooke with whom he had sealed an uneasy truce. Blatant misrepresentations might be all right in a historical novel but not in a supposedly serious television documentary claiming to present history of science.

We now move on to the writings that Newton’s meeting with Halley provoked. First we get shown Du motu corporum in gyrum (On the Motion of Bodies in Orbit) a nine page pamphlet demonstrating the truth of Newton’s statement and quite a lot more, although Tyson doesn’t think it necessary to give us either the title or a description of the contents calling it instead, “the opening pages of modern science”, a truly crap statement. If De motu represents the opening pages of modern science what was all the stuff that Kepler, Stevin, Galileo, Pascal, Descartes, Mersenne, Huygens et al. did? Most of it before Newton was even born! There is worse to come.  In the Cosmos version of the story Halley now urges Newton to turn De motu into a book, in reality Halley wanted to enter De motu officially in the Royal Society’s register “to secure his [Newton’s] invention to himself” and it was Newton who insisted on rewriting it. It was this rewritten version that became Principia Mathematica. When almost complete the council of the Royal Society agreed that it should be published by the Society. At this point the proverbial shit hit the fan. As related in Cosmos, Hooke raised a claim to the theory of gravity and demanded that Newton give him credit for it in his book. Newton’s prickly response was to threaten to withhold volume three of the Principia, which is actually the part in which he applies his theories of motion and the law of gravity to the celestial motions i.e. the heart of the whole thing. Tyson now said, “The scientific revolution hung in the balance”! I said worse was to come.

According to convention wisdom the scientific revolution began in 1543 with the publication of Copernicus’ De revolutionibus. I’m a gradualist who doesn’t accept the term scientific revolution and for me the evolution of modern science begins around fourteen hundred although it builds on earlier medieval science. For most historians Newton’s Principia is the culmination not the beginning of the scientific revolution. It was even fashionable for a time to play down Newton’s achievement claiming that he only synthesised the result won by his predecessors. However it is now acknowledged that that synthesis was pretty awesome. However let us play a little bit of what if. If Newton had only published the first two volumes of Principia I doubt that it would have been very long before somebody applied the abstract results derived in volume one to the solar system and completed what Newton had begun. Put another way nothing hung in the balance.

In fact Halley was able to mollify Newton and the letters that the two of them exchanged at this time are the main historical source for the whole story. Cosmos paints Hooke as an unmitigated villain at this point in the story, which is again a distortion of the true facts. Hooke had indeed suggested, in print, a universal theory of gravity based on the inverse squared law and the letters he exchanged with Newton, during the uneasy truce mention above, had played a significant role in pushing Newton towards his own theories of motion and gravity. Hooke’s claim was not totally unfounded. It is true, however, that his claim was exaggerated because he did not possess the mathematical skills to turn those hypotheses into the formal mathematical structure that is the glory that is Newton’s Principia. There was blame on both sides and not just on Hooke’s. Cosmos now introduces a strange scene in which Wren and Halley meet up with Hooke and confront him on the gravity priority issues, Halley even telling Hooke to “put up or shut up”! Numerous people on Twitter commented on this sound bite, most of them betting that Halley never said it. Not only did Halley never say it, the whole scene is a product of the scriptwriter’s fantasy; in reality it never took place. Remember this is supposed to be history of science and not historical fiction.

With then get treated to the infamous History of Fish episode. In 1685 the Society had published Francis Willughby’s De historia piscium, which had been finished and edited posthumously by John Ray. The book having many lavish illustrations was costly and sold badly putting a serious strain on the Society’s, in the seventeenth-century always dodgy, finances leaving no money to fulfil the commitment to publish Newton’s Principia. This is a well-known and oft repeated story and mostly told at the cost of Willughby and his book. Cosmos did not deviate from this unfortunate pattern telling the story in a heavy handed mocking style. For the record Willughby’s book is an important publication in the history of natural history and deserves better than the treatment it got here.

Before we leave Newton and his masterwork we get presented with yet another historical clangour of mindboggling dimensions. Tyson informs us in his authoritative manner that Principia also contains Newton’s invention of the calculus. Given the amount of printer’s ink that had been used up in the academic discussion as to why Newton wrote the Principia in Euclidian geometry and not calculus this is an unforgivable gaff. I repeat for those who have not been paying attention there is no calculus in Newton’s Principia.

We now leave Newton and turn our attention to his sidekick Edmond Halley. We get a brief presentation of some of the non-astronomical aspects of the good Edmond’s life, which also contain several minor historical errors that I can’t be bothered to deal with here, before turning to the central theme of the programme, comets. There is however one major astronomical subject that I cannot ignore, the Transit of Venus. It was not, as claimed, Halley who first proposed using the Transit of Venus to determine the astronomical unit, the distance of the sun from the earth, but James Gregory in his Optica Promota published in 1663. We then get presented with the rather strange spectacle of James Cook sailing off to Tahiti in 1769 to observe the Transit. This is strange not because it’s wrong, it isn’t, Cook did indeed observe the Transit on Tahiti in 1769 but because the programme created the impression that he was the first and only person to do so. In reality Cook’s expedition was only one of many international expeditions that took place in 1769 for this purpose also there had been almost as many expeditions that had set out for the same purpose in 1761. We do not owe our knowledge of the size of the astronomical unit to some sort of solo heroic efforts of Cook in 1769 as implied by Cosmos.

The opening section of the episode was actually very well scripted with a sympathetic and understanding explanation as to how humanity came to view comets as harbingers of doom. Unfortunately this good beginning was ruined by the claim that was repeated several times throughout the script that it was Newton and Halley who were the first to view comets as astronomical objects and thus free humanity from its superstitious fear. This is just plain wrong.

In the Early Modern Period Paolo dal Pozzo Toscannelli was the first to make astronomical observations, as opposed to superstitious wonderings, of two comets in 1433 and 1456. He did not publish those observations but he did befriend Georg Peuerbach on his study journey through Renaissance Italy. Peuerbach and his pupil Regiomontanus made similar observations in Vienna in the middle of the fifteenth-century and Regiomontanus wrote an important text on the mathematical problem of measuring the parallax of a moving comet, which wasn’t published in his own lifetime.

In the 1530s several European astronomers carried out astronomical observations of a series of spectacular comets. This period led to Johannes Schöner publishing Regiomontanus’ comet text. Peter Apian published a pamphlet on his observations describing, what is incorrectly known as Apian’s Law because it was already long known to the Chinese, that the comet’s tail always points away from the sun. This series of comets and the observations of them led to an intense scientific discussion amongst European astronomers as to the physical nature of comets and their position in the heavens, above or below the moon, sub- or supra-lunar? Fracastoro, Frisius, Cardano, Jean Pena and Copernicus took part in this discussion.

In 1577 astronomers throughout Europe again observed a spectacular comet to test the theories proposed by those who had taken part in the 1530s discussions. Famously Tycho Brahe and Michael Maestlin, amongst others, determined that this comet was definitely supra-lunar. In the same period Brahe and John Dee corresponded on the subject of Regiomontanus’ comet text, the determination of cometary parallax.

Cometary observation again hit a high point in astronomical circles in 1618. The comets of this year famously led to the dispute between Galileo and the Jesuit astronomer Orazio Grassi that culminated in Galileo’s Il Saggiatore, one of the most often quoted scientific publications of all times. They also saw the publication of a much more low-key text, Kepler’s book on comets published in 1619. Kepler summarised in his work all of the astronomical knowledge on comets that had been gained in the Early Modern Period, concluding himself that comets are supralunar and travel in straight lines. Ironical someone else had suggested that comets follow Keplerian elliptical orbits eight years earlier. Thomas Harriot and his pupil William Lower had observed the comet of 1607, Halley’s comet, and were amongst the first to read Kepler’s Astronomia nova when it appeared in 1609 and to become convinced Keplerians. In a letter to Harriot, Lower suggested that comets, like the planets, have elliptical orbits. Lower’s suggestion did not become generally known until the nineteenth century but it shows that the discussion on the flight path of comets was already in full swing at the beginning of the seventeenth-century.

With the comets of the 1660’s the debate on the nature of comets and their flight paths again broke out amongst the astronomers of Europe with Kepler’s comet book at the centre of the debate, so when Newton and Halley entered the fray in the 1680s they were not initiating anything, as claimed by Cosmos, but joining a discussion that had been going on for more than two hundred years. A final omission in the Cosmos account concerns another man with whom both Halley and Newton would become embroiled in bitter disputes, the Astronomer Royal John Flamsteed. The early 1680s saw a series of spectacular comets that Flamsteed observed from Greenwich and Halley from Paris.  Flamsteed concluded that two of these were in fact one and the same comet first observed on its way to the sun and then again on its way away from the sun having passed behind it. He reported this theory to Newton who at first rejected it but then on further consideration accepted and adopted it, making comets a central theme for his research for the Principia, utilising Halley as his assistant for this work. That comets follow flight paths described by the various conic sections depending on their velocities, some of them elliptical, under the influence of the law of gravity is a central element of volume three of Principia and not something first determined by Halley in his 1705 paper as claimed by Cosmos. Halley undertook his research into the historical records of comets to see if he could find a reoccurring comet to confirm the theory already presented in Principia, as everybody knows he was spectacularly successful.

Having completely messed up the history of astronomical cometary observation Cosmos closed by returning to the Newton Hooke dogfight. We get told Hooke died in 1703 as a result of his unhealthy habits of doctoring himself with all sorts of substances. Given that Hooke lived to the age of 67, not at all bad for the seventeenth-century I found this to be an unnecessary slander on the poor man. Tyson then went on to say that Newton replaced him as President of the Royal Society. Robert Hooke was an employee of the Royal Society and never its President. Newton in fact followed Lord Somers in this august position. Although hedged with maybes, we then got the old myth of Newton burning Hooke’s portrait dished up once again. On this hoary old myth I recommend this post by good friend Felicity Henderson (@felicityhen) on her Hooke’s London Blog (always well worth reading). Given the vast amount of real history of science that they could have brought I don’t understand why Cosmos insists on repeating myths that were discredited long ago.

The history of science presented in this episode of Cosmos was shoddy, sloppy, badly researched, factually inaccurate and generally of a disgustingly low level. On Twitter the history of science hashtag is #histsci, historian of biology Adam Shapiro (@TryingBiology) suggested that the hashtag for Cosmos history of science should be #HistSigh, I concur.


[1] Richard S. Westfall, Never at Rest: A Biography of Isaac Newton, Cambridge Paperback Library, Cambridge University Press, 1983, p. 403. Quoting Abraham DeMoirve’ s account of the meeting as related to him by Newton.


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


The title is supposed to make you think of a typical article in the Daily Fail, Britain’s most obnoxious representative of the gutter press. It represents one of the dominant reactions by members of the Gnu Model ArmyTM to the Cosmos Bruno AffairTM. According to people such as Jason Rosenhouse and P Z Myer the persecution of such notable scientists as Giordano Bruno and Galileo Galilei by the Catholic Church has definitely hindered the progress of science and for good measure they or their supporters quote the words of wisdom of Über-Guru Neil deGasse Tyson that without religion science would be a thousand years more advanced. What an outrage, truly horrific the Church it seems has a lot to answer for, although I find it rather strange that they can’t dish up more examples than poor old Giordano and that universal symbol of Church oppression Galileo. I’m sure if they re-read their Draper-White they could manage to find some new names to beat the ignorant historians around the head with. I say ignorant historians because it was the historians complaining about the Bruno cartoon on the first episode of Cosmos that has brought out this charge by these stalwart defenders of scientific integrity.

Let us assume for a moment that Rosenhouse-Myer are correct and that the Catholic Church did in fact persecute Bruno and Galileo to block scientific progress does this necessarily mean that they were successful in their dastardly deeds? Did they truly manage to interrupt, slow down, or hinder the adoption, acceptance or acknowledgement of the heliocentric hypothesis or the belief in an infinite universe or the perception that the sun is a star or vice versa? No doubt about it, this is a serious charge and one that should definitely be explicated.

Now Myer and Tyson are both practicing scientists whilst Rosenhouse is a mathematician, all of them work in disciplines that require one, if one makes a substantial claim, to provide the appropriate evidence or proof to support that claim. What is with their claim that religion has blocked the advance of science in general or in the case of Bruno and Galileo the acceptance of modern astronomy and cosmology in particular? Have our scientific practitioners provided the necessary evidence to back up their claims? Do they provide a tightly argued historical thesis based on solid documentary evidence to prove their assertions? Can they demonstrate that if the Church had not intervened modern astronomy would have become accepted much earlier than it was? Given their outspoken support of the ‘scientific method’, whatever that might be, you would expect them to do so, wouldn’t you? Do they hell! They don’t waste one single word on the topic. No evidence, no proofs, no academic arguments just plain straightforward unsubstantiated claims in the style of the gutter press. A pretty poor showing for the defenders of scientific faith.

But could they still be right? Even if they don’t take the trouble to provide the historical discourse necessary to substantiate their claims, could it be true that the Church’s actions against Bruno and Galileo did in fact have a negative influence on the acceptance of heliocentricity and other aspects of modern astronomy and cosmology? Let us examine the historical facts and answer the questions that Rosenhouse-Myer and Tyson are apparently above answering, the truth being apparently so obviously clear that they don’t require answering.

To start with the poor Giordano, Bruno was one of those who advocated Copernicus’ heliocentric astronomy already in the sixteenth-century. He however went beyond Copernicus in a series of cosmological speculations and it is these that Cosmos thought to be so important that they devoted eleven minutes of a forty-five minute broadcast to them. I shall deal with the acceptance of heliocentricity separately later and only address Bruno’s cosmology now. Copernicus himself expressly left the question as to whether the cosmos is finite or infinite, as he said, to the philosophers, with good reason. This question was purely speculative and could not, with the evidence and possibilities available to the Renaissance astronomer, be addressed in anything approaching a scientific manner. To all intents and purposes the cosmos appeared finite and Renaissance scholars had no means available to prove otherwise. Bruno’s speculation was of course not new.

In his own times Nicolas Cusanus had already considered the question and earlier, in the first-century BCE, the Epicurean philosopher poet Lucretius, Bruno’s inspiration, had included it in his scientific poem De rerum natura. Lucretius of course did not invent the concept but was merely repeating the beliefs of the fifth-century BCE Greek atomists. All of this demonstrates that the idea of an infinite cosmos was fairly common at the beginning of the seventeenth century and nothing the Church said or did was likely to stop anybody speculating about it. The thing that prevented anybody from going further than speculation was the lack of the necessary scientific apparatus to investigate the question, a similar situation to that of the string-theorists and multiverse advocates of today.

This does not mean that astronomers did not address the problem of the size of the cosmos and the distance to the stars. Amongst others Galileo, Jeremiah Horrocks, Christiaan Huygens and Isaac Newton all tried to estimate/calculate the distances within the solar system and outward towards the stars. First in the middle of the eighteenth century with the transit of Venus measurements were these efforts rewarded with a minimum of success. It wasn’t until the early nineteenth century that the first stellar distance measurements, through stellar parallax, were achieved. All of these delays were not caused by anything the Church had done but by the necessity of first developing the required scientific theories and apparatus.

Bruno’s next cosmological speculation was that the sun and the stars were one and the same. Once again there was nothing new in this. Anaxagoras had already had the same idea in the fifth-century BCE and John Philoponus in the fifth-century CE. Once again the problem with this speculation was not any form of religious objection but a lack of scientific theory and expertise to test it. This first became available in the nineteenth century with development of spectroscopy. This of course first required the development of the new matter theory throughout the seventeenth and eighteenth centuries, a process that involved an awful lot of science.

Bruno’s last speculation and the one that bothered the Church was the existence of inhabited planets other than the Earth. Again this was nothing new and whatever the Church might have thought about it that speculation generated a lively debate in the seventeenth century that is still going on. We still don’t actually know whether we are alone or not.

Given my knowledge of the history of science I can’t see anywhere, where the Church hindered or even slowed down scientific progress on those things that Bruno speculated about in his cosmological fantasy. But what about heliocentricity, here surely the Church’s persecution of both Bruno and Galileo hindered science bay the hounds of anti-religious rationalism.

What follows is a brief sketch of the acceptance of the heliocentric astronomy hypothesis in the sixteenth and seventeenth centuries. This is a subject I’ve dealt with before in various posts but it doesn’t hurt to repeat the process as there are several important lessons to be learnt here. To begin with there is a common myth that acceptance of ‘correct’ new scientific theories is almost instantaneous. To exaggerate slightly, Einstein published his General Theory of Relativity in 1915 and the world changed overnight or at the latest when Eddington confirmed the bending of light rays conform with general relativity in 1919. In reality the acceptance of the general theory of relativity was still a topic of discussion when I was being educated fifty years later and that despite numerous confirmatory tests. Before it is accepted a major new scientific theory must be examined, questioned, tested, reformed, modified and shown to be superior to all serious alternatives. In the Early Modern Period with communication considerably slower this process was even slower.

Copernicus published his De revolutionibus in 1543 and there were only ten people in the entire world, including Bruno but much more importantly both Kepler and Galileo, who accepted it lock, stock and barrel by 1600. This system had only one real scientific advantage over the geocentric one; it could explain the retrograde movement of the planets. However this was not considered to be very important at the time. There were some relatively low-key religious objection but these did not play any significant role in the very slow initial acceptance of the theory. The problematic objections were observationally empirical and had already been discussed by Ptolemaeus in his Syntaxis Mathematiké in the second-century CE. Put very simple if the world is spinning very fast and hurtling through space at an alarming speed why don’t we get blown away? Copernicus had the correct answer to this problem when he suggested that the atmosphere was carried round with the earth in the form of a bubble so to speak. Unfortunately he lacked the physics to explain and justify such a claim. It would take most of the seventeenth century and the combined scientific efforts of Kepler, Galileo, Stevin, Borelli, Descartes, Pascal, Huygens, Newton and a whole boatload of lesser lights to create the necessary physics to explain how gravity holds the atmosphere in place whilst the earth is moving.  This process was not hindered by the Church in anyway whatsoever.

There was a second level of acceptance of Copernicus theory, an instrumental one, as a mathematical model to deliver astronomical data for various applications, astrology, cartography, navigations etc. Here the system based on the same inaccurate data as the Ptolemaic one did not fair particularly well. Disgusted by the inaccuracy of both systems Tycho Brahe started a new long-term observational programme to obtain new accurate data. Whilst doing so he developed a third model, the so-called geo-heliocentric model, in which the planets orbited the sun, which in turn orbited the stationary earth. This model had the advantage of explaining retrograde motion without setting the earth in motions, a win-win situation.

The first major development came with the invention of the telescope in 1608 and its application to astronomical observation from 1609 onwards. The first telescopic discoveries did not provide any proofs for either the Copernican or the Tychonic models but did refute both the Aristotelian homocentric model and the Ptolemaic model. Around the same time a new candidate, the Keplerian elliptical astronomy, entered the ring with the publications of Kepler’s Astronomia nova in 1609. For a full list of the plethora of possible astronomical models at the beginning of the seventeenth century see this earlier post.

By 1620 the leading candidate was a Tychonic model with diurnal rotation. It should be pointed out that due to the attempts of Galileo and Foscarini to reinterpret Holy Scripture in favour of heliocentricity the Catholic Church had entered the action in 1615 and forbidden the heliocentric theory but not the heliocentric hypothesis. The distinction is important. The theory says heliocentricity is a scientific fact the hypothesis says it’s a possibility. At this time heliocentricity was in fact an unproved hypothesis and not a theory. This is the point where Rosenhouse-Myers step in and claim that the Church hindered scientific progress but did they. The straightforward answer is no. The astronomers and physicist carried on looking for answers to the open questions and solutions to the existing problems. There is no evidence whatsoever of a slowing down or interruption in their research efforts.

Between 1618 and 1621 Kepler published his Epitome astronomiae Copernicanae explaining his elliptical astronomy and his three laws of planetary motion in simple terms and in 1627 the Tabulae Rudolphinae the astronomical tables based on his system and Tycho’s new accurate data. It was these two publications that would lead to the general acceptance of heliocentricity by those able to judge by around 1660. Kepler’s publications delivered the desired accurate prognoses of planetary positions, eclipses etc. required by astrologers, cartographers, navigators etc.

At no point in the 120 years between the initial publication of Copernicus’ De revolutionibus and the general acceptance of heliocentricity in the form of Kepler’s elliptical astronomy is there any evidence of the Church having slowed or hindered progress in this historical process. To close it should be pointed out that it would be another seventy years before any solid scientific evidence for the heliocentric hypothesis was found by Bradley, in the form of stellar aberration.






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