Category Archives: Renaissance Science

Comets and Heliocentricity: A Rough Guide

In the standard mythologised history of astronomy of the Early Modern Period comets are only mentioned once. We get told, in classical hagiographical manner, how Tycho Brahe observed the great comet of 1577 and thus smashed the crystalline spheres of Aristotelian cosmology freeing the way for the modern astronomy. That’s it for comets, their bit part in the drama that is the unfolding of the astronomical revolution is over and done with, don’t call us we’ll call you. The problem with this mythological account is that it vastly over emphasises the role of both Tycho and the 1577 comet in changing the view of the heavens and vastly under rates the role played by comets and their observations in the evolution of the new astronomy in the Early Modern Period. I shall deal with the crystalline spheres and their dissolution in a separate post and for now will follow the trail of the comets as they weave their way through the fifteenth, sixteenth and seventeenth centuries changing our perceptions of the heavens and driving the evolution of the new astronomy. I have dealt with various aspects of this story in earlier posts but rather than simple linking I will outline the whole story here.

In antiquity comets were a phenomenon to be marvelled at and to be feared. Strange apparitions lighting up the skies unpredictably and unexplainably, bringing with them, in the view of the astrology priests of earlier cultures, doom and disaster. As with almost all things Aristotle had categorised comets, fitting them into his grand scheme of things. Aristotle’s cosmology was a cosmology of spheres. In the centre resided the spherical earth, on the outer reaches it was enclosed in the sphere of the fixed stars. Between theses two were the spheres of the planets centred on and spreading outwards from the earth, Moon, Mercury, Venus,  Sun, Mars, Jupiter Saturn. This onion of celestial spheres was split into two parts by the sphere of the moon. Everything above this, superlunar, was perfect, unchanging and eternal, everything below, sublunar, imperfect, constantly changing and subject to decay. For Aristotle comets were a sublunar phenomenon and were not part of astronomy, being dealt with in his Meteorology, his book on atmospheric phenomena, amongst other things.

However Aristotle’s was not the only theory of comets in ancient Greek philosophy, the Stoics, whose philosophy was far more important and influential than Aristotle’s in late antiquity had a very different theory. For the Stoics the cosmos was not divided into two by the sphere of the moon but was a single unity permeated throughout by pneuma (whatever that maybe!). For them comets were not an atmospheric phenomenon, as for Aristotle, but were astronomical objects of some sort or other.

In the High Middle Ages as higher learning began to flourish one more in Europe it was Aristotle’s scientific theories, made compatible with Christian theology by Albertus Magnus and his pupil Thomas Aquinas, that was taught in the newly founded universities and so comets were again treated as atmospheric phenomena up to the beginning of the fifteenth century.

The first person to view comets differently was the Florentine physician and mathematicus Paolo dal Pozzo Toscanelli (1397–1482), best known for his letter and map supplied to the Portuguese Crown confirming the viability of Columbus’ plan to sail westwards to reach the spice islands. In the 1430s Toscanelli observed comets as if they were astronomical object tracing their paths onto star-charts thereby initiating a new approach to cometary observation. Toscanelli didn’t publish his observations but he was part of a circle humanist astronomers and mathematicians in Northern Italy who communicated with each other over their work both in personal conversation and by letter. In the early 1440s Toscanelli was visited by a young Austrian mathematician called Georg Aunpekh (1423–1461), better known today by his humanist toponym, Peuerbach. We don’t know as a fact that Toscanelli taught his approach to comet observation to the young Peuerbach but we do know that Peuerbach taught the same approach to his most famous pupil, Johannes Müller aka Regiomontanus (1436–1476), at the University of Vienna in the 1450’s. Peuerbach and Regiomontanus observed several comets together, including Halley’s Comet in 1456. Regiomontanus wrote up their work in a book, which included his thoughts on how to calculate correctly the parallax of a comparatively fast moving object, such as a comet, in order to determine its distance from earth. The books of Peuerbach and Regiomontanus, Peuerbach’s cosmology, New Theory of the Planets, published by Regiomontanus in Nürnberg in 1473, and their jointly authored epitome of Ptolemaeus’ Almagest, first published in Venice in 1496, became the standard astronomy textbooks for the next generation of astronomers, including Copernicus. Regiomontanus’ work on the comets remained unpublished at the time of his death.

Whereas in the middle of the fifteenth century, as Peuerbach and Regiomontanus were active there were very few competent astronomers in Europe the situation had improved markedly by the 1530s when comets again played a central role in the history of the slowly developing new astronomy. The 1530s saw a series of spectacular comets that were observed with great interest by astronomers throughout Europe. These observations led to a series of important developments in the history of cometary observation. Johannes Schöner (1477–1547) the Nürnberger astrologer-astronomer published Regiomontanus’ book on comets including his thoughts on the mathematics of measuring parallax, which introduced the topic into the European astronomical discourse. Later in the century Tycho Brahe and John Dee would correspond on exactly this topic. A discussion developed between various leading astronomers, including Peter Apian (1495–1552) in Ingolstadt, Nicolaus Copernicus (1473–1543) in Frauenburg, Gemma Frisius (1508–1555) in Leuven and Jean Péna (1528 or 1530–1558 or 1568) in Paris, on the nature of comets. Frisius and Pena in Northern Europe as well as Gerolamo Cardano (1501–1576) and Girolamo Fracastoro (circa 1476–1553) in Italy propagated a theory that comets were superlunar bodies focusing sunlight like a lens to produce the tail. This theory developed in a period that saw a major revival in Stoic philosophy. Apian also published his observations of the comets including what would become known, incorrectly, as Apian’s Law that the tails of comets always point away from the sun. I say incorrectly because this fact had already been known to Chinese astronomers for several centuries.

These developments in the theory of comets meant that when the Great Comet of 1577 appeared over Europe Tycho Brahe (1546–1601) was by no means the only astronomer, who followed it’s course with interest and tried to measure its parallax in order to determine whether it was sub- or superlunar. Tycho was not doing anything revolutionary, as it is normally presented in the standard story of the evolution of modern astronomy, but was just taking part in in a debate on the nature of comets that had been rumbling on throughout the sixteenth century. The results of these mass observations were very mixed. Some observers failed to make a determination, some ‘proved’ that the comet was sublunar and some, including Tycho on Hven, Michael Maestlin (1550–1631), Kepler’s teacher, in Tübingen and Thaddaeus Hagecius (1525–1600) in Prague, all determined it to be superlunar. There were many accounts published throughout Europe on the comet the majority of which still favoured a traditional Aristotelian astrological viewpoint of which my favourite was by the painter Georg Busch of Nürnberg. Busch stated that comets were fumes that rose up from the earth into the atmosphere where they collected and ignited raining back down on the earth causing all sorts of evils and disasters including Frenchmen.

On a more serious note the parallax determinations of Tycho et al led to a gradual acceptance amongst astronomers that comets are indeed astronomical and not meteorological phenomena, whereby at the time Maestlin’s opinion probably carried more weight than Tycho’s. This conclusion was given more substance when it was accepted by Christoph Clavius (1538–1612), who although a promoter of Ptolemaic astronomy, was the most influential astronomer in Europe at the end of the sixteenth century.

By the beginning of the seventeenth century comets had advanced to being an important aspect of astronomical research; one of the central questions being the shape of the comets course through the heavens. In 1607 the English astronomer, Thomas Harriot (circa 1560–1621), and his friend and pupil, the MP, Sir William Lower (1570–1615), observed Halley’s Comet and determined that its course was curved. In 1609/10 Harriot and Lower became two of the first people to read and accept Kepler’s Astronomia Nova, and Lower suggested in a letter to Harriot that comets also follow elliptical orbits making him the first to recognise this fact, although his view did not become public at the time.

The comet of 1618 was the source of one of the most famous disputes in the history of science between Galileo Galilei (1564–1642) and the Jesuit astronomer Orazio Grassi (1583–1654). Grassi had observed the comet, measured its parallax and determined that it was superlunar. Galileo had, due to an infirmity, been unable to observe the comet but when urged by his sycophantic fan club to offer an opinion on the comet couldn’t resist. Strangely he attacked Grassi adopting an Aristotelian position and claiming that comets arose from the earth and were thus not superlunar. This bizarre dispute rumbled on, with Grassi remaining reasonable and polite in his contributions and Galileo becoming increasingly abusive, climaxing in Galileo’s famous Il Saggiatore. The 1618 comet also had a positive aspect in that Kepler (1571–1630) collected and collated all of the available historical observational reports on comets and published them in a book in 1619/20 in Augsburg. Unlike Lower, who thought that comets followed Keplerian ellipses, Kepler thought that the flight paths of comets were straight lines.

The 1660s again saw a series of comets and by now the discussion amongst astronomers was focused on the superlunar flight paths of these celestial objects with Kepler’s text central to their discussions. This played a significant role in the final acceptance of Keplerian elliptical heliocentric astronomy as the correct model for the cosmos, finally eliminating its Tychonic and semi-Tychonic competitors, although some Catholic astronomers formally continued paying lip service to a Tychonic model for religious reasons, whilst devoting their attentions to discussing a heliocentric cosmos hypothetically.

The 1680s was a fateful decade for comets and heliocentricity. John Flamsteed (1646–1719), who had been appointed as the first Astronomer Royal in Greenwich in 1675, observed two comets in 1680, one in November and the second in mid December. Flamsteed became convinced that they were one and the same comet, which had orbited the sun. He communicated his thoughts by letter to Isaac Newton (1642–1727) in Cambridge, the two hadn’t fallen out with each other yet, who initially rejected Flamsteed’s findings. However on consideration Newton came to the conclusion that Flamsteed was probably right and drawing also on the observations of Edmund Halley began to calculate possible orbits for the comet. He and Halley began to pay particular attention to observing comets, in particular the comet of 1682. By the time Newton published his Principia, his study of cometary orbits took up one third of the third volume, the volume that actually deals with the cosmos and the laws of motion and the law of gravity. By showing that not only the planets and their satellite systems obeyed the law of gravity but that also comets did so, Newton was able to demonstrate that his laws were truly universal.

After the publication of the Principia, which he not only edited and published but also paid for out of his own pocket, Halley devoted himself to an intense study of the historical observations of comets. He came to the conclusion that the comet he had observed in 1682, the one observed by Peuerbach and Regiomontanus in Vienna in 1456 and the one observed by Harriot and Lower in London in 1607 were in fact one and the same comet with an orbital period of approximately 76 years. Halley published the results of his investigations both in the Philosophical Transactions of the Royal Society and as a separate pamphlet under the title Synopsis of the Astronomy of Comets in 1705. Halley determined the orbit of the comet that history would come to name after him and announced that it would return in 1758. Although long lived Halley had no hope of witness this return and would never know if his was right or not. Somewhat later the French Newtonian astronomer and mathematician Alexis Clairaut (1713–1765) recalculated the return date, introducing factors not considered by Halley, to within a one-month error of the correct date. The comet was first observed on Newton’s birthday, 25 December 1758 and reached perihelion, its nearest approach to the sun, on 13 March 1759, Clairault had predicted 13 April. This was a spectacular empirical confirmation of Newton’s theory of universal gravity and with it of heliocentric astronomy. Comets had featured in the beginnings of the development of modern astronomy in the work of Toscanelli, Peuerbach and Regiomontanus and then in the final confirmation of that astronomy with the return of Halley’s Comet having weaved their way through they whole story over the preceding 350 years.




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

Planetary Tables and Heliocentricity: A Rough Guide

Since it emerged sometime in the middle of the first millennium BCE the principal function of mathematical astronomy was to provide the most accurate possible predictions of the future positions of the main celestial bodies. This information was contained in the form of tables calculated with the help of the mathematical models, which had been derived by the astronomers from the observed behaviour of those bodies, the planets. The earliest Babylonian models were algebraic but were soon replaced by the Greeks with geometrical models based on spheres and circles. To a large extent it did not matter if those models were depictions of reality, what mattered was the accuracy of the prediction that they produced; that is the reliability of the associated tables. The models of mathematical astronomy were judge on the quality of the data they produced and not on whether they were a true reproduction of what was going on in the heavens. This data was used principally for astrology but also for cartography and navigation. Mathematical astronomy was a handmaiden to other disciplines.

Before I outline the history of such tables, a brief comment on terminology. Data on the movement of celestial bodies is published under the titles planetary tables and ephemerides (singular ephemeris). I know of no formal distinction between the two names but as far as I can determine planetary tables is generally used for tables calculated for quantitatively larger intervals, ten days for example, and these are normally calculated directly from the mathematical models for the planetary movement. Ephemeris is generally used for tables calculated for smaller interval, daily positions for example, and are often not calculated directly from the mathematical models but are interpolated from the values given in the planetary tables. Maybe one of my super intelligent and incredibly well read readers knows better and will correct me in the comments.

The Babylonians produced individual planetary tables, in particular of Venus, but we find the first extensive set in the work of Ptolemaeus. He included tables calculated from his geometrical models in his Syntaxis Mathematiké (The Almagest), published around 150 CE, and to make life easier for those who wished to use them he extracted the tables and published them separately, in extended form with directions of their use, in what is known as his Handy Tables. This publication provided both a source and an archetype for all future planetary tables.

The important role played by planetary tables in mathematical astronomy is illustrated by the fact that the first astronomical works produced by Islamic astronomers in Arabic in the eighth-century CE were planetary tables known in Arabic as zījes (singular zīj). These initial zījes were based on Indian sources and earlier Sassanid Persian models. These were quickly followed by those based on Ptolemaeus’ Handy Tables. Later sets of tables included material drawn from Islamic Arabic sources. Over 200 zījes are known from the period between the eighth and the fifteenth centuries. Because planetary tables are dependent on the observers geographical position most of these are only recalculation of existing tables for new locations. New zījes continued to be produced in India well into the eighteenth-century.

With the coming of the European translators in the twelfth and thirteenth centuries and the first mathematical Renaissance the pattern repeated itself with zījes being amongst the first astronomical documents translated from Arabic into Latin. Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī was originally better known in Europe for his zīj than for The Compendious Book on Calculation by Completion and Balancing” (al-Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabala), the book that introduced algebra into the West. The Toledan Tables were created in Toledo in the eleventh-century partially based on the work of Abū Isḥāq Ibrāhīm ibn Yaḥyā al-Naqqāsh al-Zarqālī, known in Latin as Arzachel. In the twelfth-century they were translated in Latin by Gerard of Cremona, the most prolific of the translators, and became the benchmark for European planetary tables.

In the thirteenth- century the Toledan Tables were superseded by the Alfonsine Tables, which were produced by the so-called Toledo School of Translators from Islamic sources under the sponsorship of Alfonso X of Castile. The Alfonsine Tables remained the primary source of planetary tables and ephemerides in Europe down to the Renaissance where they were used by Peuerbach, Regiomontanus and Copernicus. Having set up the world’s first scientific press Regiomontanus produced the first ever printed ephemerides, which were distinguished by the accuracies of their calculations and low level of printing errors. Regiomontanus’ ephemerides were very popular and enjoyed many editions, many of them pirated. Columbus took a pirate edition of them on his first voyage to America and used them to impress some natives by accurately predicting an eclipse of the moon.

By the fifteenth-century astronomers and other users of astronomical data were very much aware of the numerous inaccuracies in that data, many of them having crept in over the centuries through frequent translation and copying errors. Regiomontanus was aware that the problem could only be solved by collecting new basic observational data from which to calculate the tables. He started on such an observational programme in Nürnberg in 1470 but his early death in 1475 put an end to his endeavours.

When Copernicus published his De revolutionibus in 1543 many astronomers hoped that his mathematical models for the planetary orbits would lead to more accurate planetary tables and this pragmatic attitude to his work was the principle positive reception that it received. Copernicus’ fellow professor of mathematic in Wittenberg Erasmus Reinhold calculated the first set of planetary tables based on De revolutionibus. The Prutenic Tables, sponsored by Duke Albrecht of Brandenburg Prussia (Prutenic is Latin for Prussian), were printed and published in 1551. Ephemerides based on Copernicus were produced by Johannes Stadius, a student of Gemma Frisius, in 1554 and by John Feild (sic), with a forward by John Dee, in 1557. Unfortunately they didn’t live up to expectations. The problem was that Copernicus’ work and the tables were based on the same corrupted data as the Alfonsine Tables. In his unpublished manuscript on navigation Thomas Harriot complained about the inaccuracies in the Alfonsine Tables and then goes on to say that the Prutenic Tables are not any better. However he follows this complaint up with the information that Wilhelm IV of Hessen-Kassel and Tycho Brahe on Hven are gathering new observational data that should improve the situation.

As a young astronomer the Danish aristocrat, Tycho Brahe, was indignant that the times given in both the Alfonsine and the Prutenic tables for a specific astronomical event that he wished to observe were highly inaccurate. Like Regiomontanus, a hundred years earlier, he realised that the problem lay in the inaccurate and corrupted data on which both sets of tables were based. Like Regiomontanus he started an extensive programme of astronomical observations to solve the problem, initially at his purpose built observatory financed by the Danish Crown on the island of Hven and then later, through force of circumstances, under the auspices of Rudolph II, the Holy Roman German Emperor, in Prague. Tycho devoted almost thirty years to accruing a vast collection of astronomical data. Although he was using the same observational instruments available to Ptolemaeus fifteen hundred years earlier, he devoted an incredible amount of time and effort to improving those instruments and the methods of using them, meaning that his observations were more accurate by several factors than those of his predecessors. What was now needed was somebody to turn this data into planetary tables, enter Johannes Kepler. Kepler joined Tycho in Prague in 1600 and was specifically appointed to the task of producing planetary tables from Tycho’s data. Contrary to popular belief he was not employed by Tycho but directly by Rudolph.

Following Tycho’s death, a short time later, a major problem ensued. Kepler was official appointed Imperial Mathematicus, as Tycho’s successor, and still had his original commission to produce the planetary tables for the Emperor, however, legally, he no longer had the data; this was Tycho’s private property and on his death passed into the possession of his heirs. Kepler was in physical possession of the data, however, and hung on to it during the protracted, complicated and at times vitriolic negotiations with Tycho’s son in law, Frans Gansneb Genaamd Tengnagel van de Camp, over their future use. In the end the heirs granted Kepler permission to use the data with the proviso that any publications based on them must carry Tengnagel’s name as co-author. Kepler then proceeded to calculate the tables.

Put like this, it sounds like a fairly straightforward task, however it was difficult and tedious work that Kepler loathed intensely. It was not made any easier by the personal and political circumstances surrounding Kepler over the years he took to complete the task. Wars, famine, usurpation of the Emperor’s throne (don’t forget the Emperor was his employer) and family disasters all served to make his life more difficult.

Finally in 1626, twenty-six years after he started Kepler had finally reduced Tycho’s thirty years of observations into planetary tables for general use, now he only had to get them printed. Drumming up the financial resources for the task was the first hurdle that Kepler successfully cleared. He then purchased the necessary paper and settled in Linz to complete the task of turning his calculations into a book. As the printing was progressing all the Protestants in Linz were ordered to leave the city, Kepler, being Imperial Mathematicus, and his printer were granted an exemption to finish printing the tables but then Wallenstein laid siege to the city to supress a peasants uprising. In the ensuing chaos the printing shop and the partially finished tables went up in flames.

Leaving Linz Kepler now moved to Ulm where, starting from the beginning again, he was finally able to complete the printing of the Rudophine Tables, named after the Emperor who had originally commissioned them but dedicated to the current Emperor, Ferdinand II. Although technically not his property, because he had paid the costs of having them printed Kepler took the finished volumes to the book fair in Frankfurt to sell in September 1627.

Due to the accuracy of Tycho’s observational data and the diligence of Kepler’s mathematical calculations the new tables were of a level of accuracy never seen before in the history of astronomy and fairly quickly became the benchmark for all astronomical work. Perceived to have been calculated on the basis of Kepler’s own elliptical heliocentric astronomy they became the most important artefact in the general acceptance of heliocentricity in the seventeenth century. As already stated above systems of mathematical astronomy were judged on the data that they produced for use by astrologers, cartographers, navigators et al. Using the Rudolphine Tables Gassendi was able to predict and observe a transit of Mercury in 1631, as Jeremiah Horrocks succeeded in predicting and observing a transit of Venus for the first time in human history based on his own calculations of an ephemeris for Venus using Kepler’s tables, it served as a confirming instance of the superiority of both the tables and Kepler’s elliptical astronomy, which was the system that came to be accepted by most working astronomers in Europe around 1660. The principle battle in the war of the astronomical systems had been won by a rather boring set of mathematical tables, Johannes Kepler’s Tabulae Rudolphinae.

Rudolphine Tables Frontispiece

Rudolphine Tables Frontispiece




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

Galileo, the Church and Heliocentricity: A Rough Guide.

A couple of days ago on Twitter, Brian Cox asked the Twitter historians, “Did Galileo know that he would annoy the Church when he published The Starry Messenger?” The very simple answer to this question is, no but a lengthy discussion of the situation developed on Twitter. It was suggested that somebody should produce a short temperate answer to the question as a reference source and after some hesitation I have acquiesced. This will be a relative short presentation of the various stages of this historical process with a minimum of explanation and justification, as Joe Friday used to say, “the facts ma’am, just the facts!” This is of course my interpretation but it is based on a fairly good knowledge of the most recent principal secondary literature on the subject and it is one that I think would find fairly general agreement amongst those who have seriously studied the subject. Those who disagree are welcome, as always, to air their views in the comments but I expect those who choose to do so to base those views on historical facts and not on prejudice.

The first thing to make clear is the situation in terms of astronomy, cosmology and the Church in the first decade of the seventeenth-century before Galileo, Marius, Harriot, Lembo and others changed our view of the cosmos forever with the recently invented telescope. Astronomy and cosmology were not very high up on the Church’s agenda between 1600 and 1610. The vast majority of people, including the experts, still believed in a geocentric cosmos in the form developed by Ptolemaeus, the most modern version being basically that of Peuerbach and Regiomontanus. A very small handful believed in the Copernican heliocentric model, and believed is the right word because it lacked any real form of empirical proof and was burdened by all the physical problems engendered by a moving earth. A probably equally small number favoured a Tychonic geo-heliocentric model with or without a rotating earth and another small number were finding favour with Gilbert’s geocentric model with a rotating earth. All of the discussions were very academic and nothing that could or would threaten the dominance of a solid Bible conform geocentricity, so nothing for the Church to get its knickers in a twist about.

The telescopic discoveries were brand new empirical evidence and the biggest shake up in astronomy since mankind first cast its little beady eyes on the heavens. When he started to make his discoveries, late in 1609, Galileo was very much aware of the fact that he was sitting on the Renaissance equivalent of a Nobel prize, a knighthood and the keys to the treasure chest all in one and also very aware that he almost certainly wasn’t the only person making or about to make these discoveries. In the last point he was of course completely right, Harriot was ahead of him and Marius was breathing down his neck. Galileo was fully aware that if his wished to cash in then he had to get his priority claim in tout suite.

To understand this one needs to look at Galileo’s situation. In 1610 he was a forty-six year old professor of mathematics, stuck in the same rather lowly position for the last eighteen years. He was on the down hill slope to ill health, death and anonymity. He had already done his ground-breaking work on dynamics but hadn’t published it. If he were to die tomorrow nobody would remember him beyond a few close friends and his family. Now he had hit the jackpot and needed to cash in fast. He bunged his principal discoveries together in book form, in what was more a press release than a scientific report, the Sidereus Nuncius, and had it printed and published as fast as possible.

The last thing the Galileo wanted to do at this point was to annoy anybody; he wanted fame and fortune not infamy. He spent as much effort on getting permission to dedicate his small book to Cosimo Medici, the ruler of the Duchy of Florence, his home province, and his sometime private pupil, as he did on his telescopic observations. He also made very sure that the Medici would approve of the name he gave to the newly discovered moons of Jupiter; he was after preferment, which he got as a result of his clever tactical manoeuvring. He would have been mortified if his publication had caused problems with the Church in Rome because that would almost certainly have cost him any chance of an appointment to the Medici court, his main aim at the time. The Medici did in fact drop him when he finally collided with the Church in the 1620s.

The telescopic discoveries, which Galileo was the first to publish, shook up the whole of Europe and not just the Catholic Church. However the contents of Sidereus Nuncius neither disproved Ptolemaeus/Peuerbach nor did they prove Copernicus, as I’ve already explained here. Of course at first they did nothing at all because like all new scientific discoveries they needed to be confirmed by other astronomers. This proved to be somewhat difficult, as the available telescopes were very poor quality and Galileo was an exceptional telescopic observer. In the end it was the Church’s own official astronomers, the members of Clavius’ mathematical research group at the Collegio Romano, who with the active assistance of Galileo delivered the necessary confirmation of all of Galileo’s discoveries.

Hailed now as the greatest astronomer in Europe Galileo travelled in triumph to Rome where he was feted by the mathematicians of the Collegio Romano, who threw a banquet in his honour, had an audience with the Pope and was appointed a member of the Accademia dei Lincei who also threw a banquet in his honour. No signs of annoyance here. Galileo was appointed philosophicus and mathematicus to the Medici court in Florence, as well as professor for mathematics without teaching obligations at the University in Pisa. The humble insignificant mathematician had become a renowned social figure, almost overnight, feted and praised throughout Europe. High Church officials flocked to make his acquaintance and win his friendship, one of these, the Cardinal Maffeo Barberini, became a close friend and the cause of Galileo’s downfall later in his life.

Although nothing in the Sidereus Nuncius disproved the geocentric model of Ptolemaeus the discovery of the phases of Venus a short time later, by Galileo, Lembo, Harriot and Marius, did. The basic geocentric model was dead in the water and the Church had a problem because Holy Scripture clearly implied a geocentric cosmos. Riding on the wave of his fame Galileo wanted to go for the big one. He wanted to go down in history as the man who proved that the cosmos was heliocentric. Unfortunately he lacked a genuine proof. He had evidence that the cosmos was not geocentric and not homocentric but all the available empirical evidence satisfied both a heliocentric cosmos and a geo-heliocentric Tychonic one and it was the latter that most astronomers, still worried about the physical problems of a moving earth, tended to favour.

Around 1613, despite his lack of genuine proof Galileo began to canvas his newly won influential friends in Rome in an attempt to convince them to give their support to a call for the acceptance of a heliocentric cosmos, a dangerous move. The Church was a vast structure set in its ways and like a large ocean liner getting it to stop in full motion and reverse its direction was something that required a lot of time and space, Galileo eager to make his mark in history lacked the necessary patience to wait for the Church to accept the inevitable and was trying to force the pace. Several of his friends including Maffeo Barbarini advised him to calm down and not to force the Church into a corner, but Galileo, his ego inflated by his recent successes failed to heed this sound advice.

In the next couple of years both Galileo and the Carmelite father Paolo Antonio Foscarini tried to tell the Church how to reinterpret those passages of the Bible that contradict a heliocentric interpretation of the cosmos. This was a fundamental failure and guaranteed to annoy the Church extremely, which it did. One should remember that all of this was taking place in the middle of the Counter Reformation and on the eve of the Thirty Years War, which would kill off between one third and two thirds of the entire population of Middle Europe in what was basically an argument about who had the right to interpret the Bible. The Church set up a commission to investigate Foscarini’s book on the subject and the commission came down very hard on heliocentricity, calling it both philosophically (read scientifically) absurd and heretical. The accusation of heresy was not confirmed by the Pope and so was never official Church doctrine, but the damage was done. Cardinal Roberto Bellarmino was instructed to inform Galileo of the commission’s judgement. In a friendly chat Bellarmino did just this, informing Galileo that he could neither hold nor teach the theory that the cosmos was heliocentric. It is important to note that the theory was banned not the hypothesis. One could continue to discuss a hypothetical heliocentric cosmos, one could not, however, claim it to be fact. As many people have pointed out over the centuries this restriction was actually in line with the known empirical facts. The books of Kepler and other Protestants claiming that the cosmos was heliocentric were placed on the Index and Copernicus’ De revolutionibus was placed on the Index until corrected. Interestingly the Inquisition did just that. They removed the handful of passages from De revolutionibus that claimed the heliocentric cosmos to be fact and then gave the book free to be read, already in 1621. We still have Galileo’s personal censored copy of the book. This censorship was only really effective in Italy the rest of Europe not taking much notice of the Church’s efforts to suppress heliocentricity.

This setback did very little to slow down Galileo’s rise to fame and he became a very favoured celebrity throughout Northern Italy. Symptomatic for this is his notorious dispute with the Jesuit astronomer Orazio Grassi over the nature of comets that peaked in the publication of Galileo’s Il Saggiatore, in 1623. A dispute in which Grassi was scientifically right and Galileo wrong, but in which Galileo carried the laurels thanks to his superior polemic and the sycophantic cheers of his high powered fan club, which included the newly elected Pope, Urban VIII, Galileo’s old friend Maffeo Barberini.

Barberini’s elevation to the Holy Throne gave Galileo the chance he had been waiting and longing for, the chance to go down in history as the man who established the heliocentric cosmos. Using his friendship with the new Pope, Galileo convinced Barberini that the German Protestants were laughing at the Catholic Church because it had rejected heliocentricity because according to those dastardly Protestants the Catholics were too stupid to understand it. Beguiled by his silver tongued friend Barberini gave Galileo permission to write and publish a book in which he would present both the Ptolemaic and Copernican systems to demonstrate the deep astronomical knowledge of the Catholics but by no means was he to favour one of the systems. Galileo wrote the book, his Dialogo, in which he was anything but impartial and unbiased, as instructed, but instead left nobody in any doubt just how superior the Copernican system was in his opinion, however he still lacked any real empirical proof. Through a series of tricks he managed to get his book past the censors and into print. Galileo had erred very badly, you don’t play the most powerful absolutist ruler of your time for a fool, particularly not when that ruler is already displaying strong signs of the paranoia that, sooner or later, effects all absolutist rulers.

I’m not going to go into all of the contributory factors that played a part in the sorry mess that was Galileo’s trial by the Inquisitions, I’ll deal with those one day in another post, but it is safe to say that he got stamped on for his hubris. By comparison with other cases he didn’t actually get stamped on very hard and got off relatively lightly. I can already hear the screams of protest at the last sentence but within the context of the times and place where Galileo lived and moved it is an accurate description of his fate.

One thing that should be made very clear when discussing this whole sorry mess is that Galileo was never the fearless defender of scientific truth or freedom of speech that his modern fan club like to present him as. He was an extremely egotistical social climber with an eye on the main chance, his own undying fame. Through his ill-considered actions he achieved his goal but not quite in the way he had intended.

It is ironic that many people today still believe erroneously that Galileo actually proved the reality of a heliocentric cosmos in his Sidereus Nuncius.

[The original opening paragraph of this post was modified at the request of those who wish it to be used as a short simple reference source]


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

The Moons of Jupiter

As anyone interested in astronomy or its history should know Io, Europa, Ganymede and Calisto are not only the names of four of Zeus’ lovers (or rape victims!) but also the names suggested privately by Kepler and publicly by Simon Marius for the four largest of Jupiter’s moons discovered on 7th and 8th January 1610 respectively by Galileo Galilei and Simon Marius. It must have been an exhilarating experience when they were first observed by those two pioneers of Renaissance telescopic astronomy and it is still an exciting one for an amateur astronomer in the twenty-first-century as related by Clive Thompson in a blog post at The Message. Unfortunately Thompson then goes on to complete misinterpret what that original discovery, four hundred years ago, meant for the cosmology and astronomy of the times. This is a topic I’ve dealt with before but it seems to be one that needs to be addressed at regular intervals like a game of #histsci Whac-A-Mole. What exactly did Thompson say that needs to be banged on the head?

Siderius [sic] Nuncius was a powerful piece of evidence that Copernicus was right: The Earth wasn’t the center of our solar system. The sun was, and the planets revolved around it. Astronomers had been gradually warming up to the idea, and even some church authorities had accepted the Copernican system as a mathematical theory. But by showing that Jupiter had its own moonsthat a planet could be a mini-system of its ownGalileo offered something rather more: Electrifying proof [emphasis in original] of the Copernican idea. You could argue endlessly (and people did) about the geometry and math of various systems explaining how the stars moved through the sky. It was just conjecture.

But proofthat’s different. Once people put their eyes to the telescope and saw those moons circling Jupiter, they had the same whoa-dude reaction that I had on the sidewalks of Brooklyn. The solar system got real. So real, in fact, that the church began to panic; and since Galileo went on to use his telescope to amass even more evidence against geocentrism, including the phases of Venus, religious authorities eventually stepped in and demanded he recant, or else.

To explain what is wrong with the above we first need to know what the accepted view of the cosmos in the first decade of the seventeenth-century. The standard model of the age was an uneasy alliance between Aristotelian cosmology and Ptolemaic astronomy. I say uneasy because the two systems were not actually compatible, something that the scholars of the period knew but chose, mostly, to ignore. It was this geocentric mish-mash that the handful of Copernicans and Tychonians were trying to dethrone. So what exactly was the scientific significance of the Galilei-Marius discovery of the Jupiter moons?

The discovery of the four principal moons of Jupiter didn’t actually have any direct relevance, either positive or negative, for Copernican heliocentricity. What it did do was to refute a central tenet of Aristotelian cosmology that of homo-centricity. Aristotelian cosmology stated that all celestial bodies revolve around the same central point, the earth. The discovery of the moons of Jupiter of course showed this to be totally wrong. Surprisingly this did little or no damage to Ptolemaic astronomy, as this was viewed by strict Aristotelians to already contradict this fundamental principle. In Ptolemaic astronomy the seven planets revolve around the centres of their respective epicycles, which are in turn carried around the earth, actually centred on a point other than the earth, on their deferents. This in the opinion of some Aristotelians was definitely not homo-centricity. This contradiction between the two systems of thought led to various revivals of concentric or homo-centric astronomy over the centuries the most recent being in the sixteenth-century barely a decade earlier than Copernicus’ publication of De revolutionibus. In fact Christoph Clavius, the leading proponent of Ptolemaic astronomy in 1610, regarded the homocentric astronomy of Giovanni Battista Amico and Girolamo Fracastoro to be a greater threat that Copernican heliocentricity and was quite happy to have it shot down by Jupiter’s moons.

Put very bluntly the discovery of the moons of Jupiter by Galileo and Marius was in no way what so ever a proof of the Copernican idea, something of which Galileo was very much aware and he did not try to present it as being one. Marius didn’t even consider it as he was a proponent of the Tychonic system to which he remained true all of his life.

The situation is of course different with the discovery of the phases of Venus. This discovery made independently by Thomas Harriot, Simon Marius, Galileo Galilei and Giovanni Paolo Lembo, the latter a Jesuit astronomer in Rome who probably discovered the phases before Galileo, effectively killed of a pure Ptolemaic astronomy as it proved that Venus, and probably Mercury by analogy (it would be some decades before the phases of Mercury were observed), orbited the sun and not the earth. Once again this is not in anyway a proof of the Copernican system, as there were other competing systems, the Heracleidian, in which Mercury and Jupiter Venus orbit the sun, which, along with the other planets, orbits the earth and the Tychonic in which all the planets except the moon orbit the sun which then orbits the earth, that were conform with the new telescopic discovery. In fact due to the very real unsolved physical problems presented by the concept of a moving earth most astronomers now chose the Tychonic model and not the Copernican one.

Thompson’s final comment about the Church panicking and forcing Galileo to recant is just pure historical hogwash. Any new empirical evidence needs to be confirmed by independent observers. It’s all very well for Professor Galilei the little known mathematicus from Padua to come along and say that he has discovered all of these wonderful things in the heavens with this new fangled device from Holland, if nobody else can see them. What is required is that other independent observers confirm that they too can see all that Signor Galilei claims to have seen. Given the extremely poor quality of the available telescopes and the optical limits of the Dutch or Galilean telescope this was not an easy task. Popular histories criticise contemporaries who failed to see what Galileo had seen but such critics have obviously never tried to observe the moons of Jupiter with a modern Galilean telescope with state-of-the-art good quality lenses, let alone one with very shitty quality seventeenth-century lenses. It is bloody difficult to put it mildly. So who in the end did provide the scientific confirmation that Galileo so desperately needed for his telescopic claims? This confirmation was delivered by the Jesuit professors of the Collegio Romano, the Vatican’s own astronomers. Doesn’t quite fit the picture of a Church in panic, does it?

The true reasons for that oh so notorious trial are far too complex so that I’m not going to deal with them here but I will just say that they have more to do with politics and authority than science. That however is the subject for another blog post on another day.




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

Beware of hindsight!

This post is a sort of footnote to my review of Dan Falk’s The Science of Shakespeare it doesn’t really contain anything that I haven’t already said in several earlier posts but it does say something that I think bears repeating at regular intervals for those contemplating historical studies, the dangers of presentism. This time my thoughts were provoked by a comment on Twitter on my review. Jeffrey Newman (@JeffreyNewman) tweeted the following:

Is it too simplistic to suggest that Shakespeare, whose awareness of religious controversy is acute though his own views are wisely not revealed – must have been equally fascinated by contemporary scientific discoveries and controversies, news of which must have been circulating in his circles?

I had of course said something similar in the opening paragraph of my review:

Given that Shakespeare was born just twenty-one years after Copernicus’ De revolutionibus was published and lived through the period in which Kepler and Galileo, amongst others, made the heliocentric hypothesis the hottest item in the European scientific community it is not unreasonable to ask, as Falk does, in the more general sense, whether the cosmological and astronomical upheaval of the age left any traces in Will’s work.

What I wish to address here is to what extent Copernicus and heliocentricity really was actual and controversial during Shakespeare’s lifetime and how much of our perception that it must have been is actually the product of misapplied hindsight.

The common modern perception of the impact of Copernicus and his heliocentric cosmology finds its origins in the work of Immanuel Kant, one of the most influential of all European philosophers, in the late eighteenth century. Kant coined the term Die kopernikanischen Wende (The Copernican Turn) to describe what he saw as the biggest change of perception of humanities place in the cosmos that had ever taken place. In the course of the nineteenth century in English, Kant’s term mutated into the Copernican Revolution also called the Astronomical Revolution and often conflated with the Scientific Revolution, a concept also born in that century. For here on the advent of heliocentricity in the Early Modern Period was perceived as something stupendous, quite literally earth moving, a change in the intellectual climate that was almost without comparison in the history of human existence. But was it perceived as such in the second half of the sixteenth-century? The very simple answer is no, in fact rather the opposite, almost nobody took any notice of it at all.

Most astronomers and those who understood mathematical astronomy and cosmology found his book interesting but most of them remained largely unconvinced by his hypothesis and that’s all it was, an unsubstantiated hypothesis. Outside of this rather small circle of knowledgeable experts, Copernicus’ ideas received almost no attention at all. Put simply the majority of people living in Europe at that time had more important things to occupy their minds than the complex mathematical ideas of some German speaking cleric from the outskirts of civilization (Copernicus’ own estimate of his place of domicile). As I wrote in an earlier post on the same subject Copernicus’ hypothesis went off like a damp squib rather than the proverbial bombshell.

A more general discussion of the various competing systems of astronomy on offer at the beginning of the seventeenth-century first really took off in 1610 following the telescopic discoveries made by Galileo, Marius, Harriot, Lembo and others; the biggest impact being made by Galileo’s publication of his Sidereus Nuncius. I say various because there were more systems on offer than just Ptolemaic geocentricity and Copernican heliocentricity as I outlined in an earlier post. Kepler had thrown his hat into the ring one year earlier with his Astronomia nova, but his tendency to write long diatribes in convoluted Latin meant that not many people could be bothered to plough through his book. Heliocentricity, in the Keplerian version, first gained a foothold, as a viable alternative, after Kepler published his ideas in simple readable form in his Epitome Astronomiae Copernicanae, in three volumes between 1617 and 1621, and his Rudolphine Tables in 1623. Even here the acceptance, which was effectively completed by about 1660, was more gradual and low key than revolutionary.

On the negative side the common modern perception of the reception of the heliocentric hypothesis is almost totally shaped by the all too notorious dispute between Tuscany’s lamb to the slaughter, Galileo Galilei, and the big bad wolf of Early Modern history, the Catholic Church. Unfortunately here mythology rather than factual history looms large. The popular vision has the astronomers and cosmologist of Europe quaking in their shoes, only daring to discuss the new astronomy behind closed doors in fear of being used as fuel to fire the Vatican’s furnaces having first had their finger nails extracted with red hot pincers.

In reality there was almost no appreciable opposition to heliocentric astronomy before 1616. In 1616 the Catholic Church reacted to the attempts of Galileo and Foscarini to reinterpret Holy Scripture to remove the contradictions to heliocentric cosmology. This was done sotto voce and remained a purely local affair, causing hardly a ripple outside of Rome. Galileo’s trial in 1632 stirred up a lot more interest but its effect on the spread of heliocentric cosmology and astronomy in Europe was considerably less than most people imagine, in fact it was almost negligible outside of Italy, even in Catholic countries. Within Italy there was a short period of caution and then authors started producing heliocentric texts, which merely pointed out in the preface that the system whilst mathematically interesting was of course entirely hypothetical because the Holy Mother Church said so. A great battle between the Church and the astronomers never really took place and very few astronomers ever quaked in their shoes.

So what does this all mean for Dan Falk, Peter Usher and Will Shakespeare? As far as can be ascertained Shakespeare was active as a playwright from about 1590 to 1610, or possibly a couple of years longer. During this period heliocentric cosmology was not really a burning topic either scientifically or in any way socially, politically or religiously so there are no real grounds to think that Shakespeare would take up the topic in his plays, which were largely social or political commentaries. Usher argues that Shakespeare encoded the new astronomy in his plays, most notably Hamlet, rather than discussing it openly out of fear of repression. However nobody was being repressed for discussing Copernicus or Copernicanism during Shakespeare’s lifetime, he died in 1616 just as the Galileo affair was beginning, so this claim is based on a false assessment of the actual historical situation.

We now come to the crux of the matter. The arguments for a potential interest of Shakespeare in the evolving new astronomy in the closing decade of the sixteenth-century and the opening decade of the seventeenth-century and a necessity for secrecy on his part in taking an interest are based on hindsight and not on real historical research. The current view of the Copernican Revolution and its social, political and religious consequences consists largely of myths created in the late eighteenth-century and throughout the nineteenth-century. By projecting backwards from these myths, and that is committing the historical sin of presentism, rather than researching the actual historical facts Falk, Usher and Jeffrey Newman with his question on Twitter create a false scenario for Shakespeare and his potential interest in the then new but hardly present astronomy.


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

Henry and Isaac invade Oxford.

There is subject well known to all blog owners that I have never talked about, spam; I get two different varieties here at The Renaissance Mathematicus. The first is spam comments, which turn up in a never ending stream but which mostly end up in Word Press’ apparently efficient spam filter. Very occasionally one or two get through and I have to weed these out from underneath whichever post they have chosen to enrich with their presence. Otherwise the only real problem I have is remembering to regularly check the spam filter for non-spam and send the rest of its contents off to rot in cyber-hell until that day dawns when the Internet is turned off forever. Maybe I shouldn’t say this but I think that the spammers might be more successful if they didn’t have email addresses such as, just a thought.

The second type of spam I receive as a blogger is in the form of emails. These are emails from people trying to get me to either let them advertise or publish something on my blog or link something to it. Again these people might be more successful if the things that they were offering and which they are so convinced that I will find interesting were actually related in anyway to the content of my blog, they never are. As a blogger I get another type of email, ones that are invariably addressed to Professor or Doctor or even in German style to Professor Doctor. I wouldn’t mind them awarding me illusionary titles that I don’t possess, and almost certainly never will, if only they would show a little imagination in addressing me, after all professors and doctors are two a penny. Were I to get an email addressed to Our Glorious, Benevolent, Gracious, Omniscient and Wise Leader in this Age of Darkness I might just be tempted to respond, but they never do and so I don’t. The emails addressing me with imaginary academic titles usually invite me to contribute articles to their prestigious academic journal that well-known rival to Nature and Science, The East Krakatoa Journal for Island Approaches to the Philosophy of Renaissance Mathematics. Dear editors, to paraphrase Groucho Marx, “I would never submit an article to a journal that would publish anything written by me”. All of these spam emails get dispatched forthwith to cyber-hell unread, unanswered and with all links left strictly unlinked. I can spread my own viruses, thank you.

Today I received an unsolicited email asking me to advertise something, help with publicizing was the actual phrase used, and I’m actually going to do so, a first as far as I can remember here at RM. The email came from David Norbrook, Merton Professor of English Literature at the University of Oxford and he asked me very nicely to spread the word about his up coming conference Scholarship, Science, and Religion in the Age of Isaac Casaubon (1559-1614) and Henry Savile (1549-1622) at the T. S. Eliot Theatre, Merton College, Tuesday 1st – Thursday 3rd July 20124

For those not in the know Henry and Isaac are two of the Renaissance scholars who make you turn green with envy. Each of them was brainy enough to win a round of University Challenge on their own without teammates and each of them mastered enough academic disciplines to fill a small encyclopaedia on his own.

Isaac Casaubon was a French Huguenot classical scholar, philologist, historian and theologian born to refugee parents in Geneva. Home educated until he entered the University of Geneva aged seventeen were he studied Greek and was recommended for the chair in Greek only four years later. He was a consummate classical scholar and philologist whose main occupation was the translation, editing and publication of classical Greek text. He worked most of his life in Switzerland and France torn and troubled by the religious conflicts of the age. Regarded at his intellectual peak as one of the most learned men in the whole of Europe the Catholics, Lutherans, Calvinists and Anglicans all competed with offers of jobs, money and other inducements to win him as a propagandist for their cause. The situation has strong similarities to the attempts today of leading European football clubs to induce a star striker to sign for them and not one of their rivals. During the religious upheaval in Europe in the Early Modern Period a star polemicist was regarded as a good catch by the rival religious communities. In the end the political pressure in France caused him to move to England in 1610 were he died four years later. As a historian of science my main interest in Casaubon is his De rebus sacris et ecclesiasticis exercitationes XVI published in 1614 in which he proved by philological analysis that the Corpus Hermeticus, one of the most influential collection of texts in the Renaissance, was not as ancient as claimed but was in fact a product of late antiquity. This was a key moment in the evolution of the discipline of history, applying scientific, philological analysis to texts to determine their age.

I can’t leave even this brief account of Isaac Casaubon without mentioning his son Méric, who was the man responsible for ruining John Dee’s reputation. Despite all of the misfortunes that befell him in later life, in the early seventeenth-century Dee still enjoyed a good reputation in England for his work in the mathematical sciences. Around 1650 more and more people were starting to question the existence of ghosts, witches and other aspects of the occult. Deeply religious people, of whom Méric was one, were worried that this was the thin edge of the wedge that would inevitably lead to atheism. To counter this tendency Méric published John Dee’s Angel Diaries, his account of his conversations with angels, which up till then had remained largely unknown. Méric’s intention was that Dee’s accounts should act as a proof, from a reputable scholar, that the world of spirits is real and not to be questioned. Méric’s attempt backfired ruining Dee’s reputation causing people to forget the mathematicus and only remember the notorious Renaissance magus that he now became for the next four hundred years down to the present day.

Henry Savile was educated at Oxford and, self-taught, began to lecture there on astronomy at the age of 21 in 1570. He not only lectured on Ptolemaeus but also on the works of Regiomontanus and Copernicus, real cutting edge at the time. In 1578 he went on a grand tour of Europe meeting with and learning from the leading continental mathematicians; a necessary move for anyone interested in the mathematical sciences in England at that time as England was an intellectual backwater in terms of mathematics. On his return to England, in 1582, Savile was appointed Greek tutor to Queen Elizabeth. Later he became both Warden of Merton College Oxford and Provost of Eaton. Like Casaubon, with whom he was acquainted, Savile was a classical scholar and philologist but it is for his contributions to mathematics that he is best remembered. Appalled by the primitive level of mathematics teaching in England in comparison to the continent he established the first two university chairs for the mathematical sciences in England in 1619, the Savilian Chairs for Geometry and Astronomy at Oxford. In the seventeenth-century many of England’s leading mathematicians occupied one or other of these chairs including such figures as Henry Briggs, John Wallis and Edmund Halley, whose adventures sailing around the Atlantic you can follow on Twitter (@HalleysLog).

Both Casaubon and Savile are fascinating figures, who lived in and contributed to a period of great intellectual change in European history and I’m sure the Merton College conference on these two intellectual giants will be a stimulating and informative experience. If I had the time and the money, and I don’t have either, I personally would love to take part and I can only recommend that those who do have the time and the money to do so.

Unfortunately, I only got the information on the conference today and if you want to take advantage of the early booker rebate you only have until tomorrow to do so!




Filed under History of Mathematics, Renaissance Science, University History

Was Will a Copernican?

The Will of the title is England’s most notorious playwright and poet, William Shakespeare, who was supposedly born 450 years ago today. The question is the central motivation for the new book by Canadian popular science writer, Dan Falk, The Science of Shakespeare: A New Look at the Playwright’s Universe.[1] Given that Shakespeare was born just twenty-one years after Copernicus’ De revolutionibus was published and lived through the period in which Kepler and Galileo, amongst others, made the heliocentric hypothesis the hottest item in the European scientific community it is not unreasonable to ask, as Falk does, in the more general sense, whether the cosmological and astronomical upheaval of the age left any traces in Will’s work. Traditional Shakespearean scholarship says no, Falk re-examines the evidence.

The Science of Shakespeare

I must admit that when I first got offered this book to review I had a sinking feeling that somebody was going down the same garden path that Peter Usher had already trodden. For those readers who are not aware of Mr Usher’s endeavours, he is a retired astronomer who believes that he has found the secret message encoded in Shakespeare’s Hamlet and in all of the rest of his works. Usher believes that Hamlet describes the battle for supremacy between the Ptolemaic, Tychonic and Copernican system of astronomy in the Early Modern Period. What do I think of Mr Usher’s theories? Let’s put it this way, Mr Usher manages to make the Bible decoders look like rational human beings. My feelings about reading Falk’s book where not improved on discovering, upon receiving my review copy, that it was indeed an introduction to Mr Usher’s ideas that inspired Falk to research and write his book; I feared the worst. Fortunately, although I cannot totally endorse the book, Mr Falk did indeed do his research on the whole thoroughly and it turned out to be much better than I had feared. In fact on the whole I found it to be a well-written and entertaining read.

The introduction sets the scene for his book by presenting what are respectively the most expensive science and humanities rare books, Nicolas Copernicus’ De revolutionibus and The Shakespeare First Folio, given their proximity in time it is not an unreasonable question to ask if the one influenced the other and whilst acknowledging that the traditional answer is no, Falk already brings here one of the arguments used by more modern researchers, and not just Usher, to claim the opposite. I shall deal with this later along with the other supposed arguments in favour of a heliocentric Bard.

The first five chapters deal with the largely astronomical background giving a quick rundown on ancient cosmology, the emergence of Copernican theory and its reception in late sixteenth-century England. Falk has done his homework well and this part of the book is almost totally satisfying. I say almost because it does contain two serious errors.

Falk manages to walk into a trap that Copernicus laid for the unwary. Falk writes, “and it [the Copernican model] managed to bring the total number of circles down from eighty to thirty-four.” Falk is here paraphrasing a claim that Copernicus makes in the Commentariolus the pamphlet he wrote around 1514, first announcing his heliocentric system. The claim is an estimate and not a fact. Unfortunately for Falk by the time Copernicus had worked out his system in full, in De revolutionibus, he actually needed forty-eight circles, whereas Peuerbach, in his Theoricae Novae Planetarum, the most modern version of the geocentric model, which Copernicus used and consulted himself, only required forty circles. Not a victory for the new astronomy.

Whilst discussing the Copernican reception Falk quite rightly introduces William Gilbert. He goes on to explain that Gilbert, influenced by Copernicus, discusses diurnal rotation in his De magnete, explaining it as the natural motion of a spherical magnet, based on his erroneous view that a spherical magnet left to itself rotates. Unfortunately Falk then goes on to say, “He also believed that magnetic forces emanating from the sun, together with the sun’s rotation, caused the planets to move in their heliocentric orbits”. Gilbert of course believed nothing of the sort. In Book Six of De magnete, where this discussion takes place, he states quite explicitly, “ From these arguments, therefore, we infer, not with mere probability, but with certainty, the diurnal rotations of the earth; […] I pass by the earth’s other movements, for here we treat only of the diurnal rotation [my emphasis], whereby it turns to the sun and produces the natural day (of twenty-four hours) which we call nycthermeron”. Gilbert’s model is in fact not Copernican at all but a geocentric-geokinetic one. I’ve blogged about the history of such systems here. The magnetic force explanation for the movement of the planets in a heliocentric system was hypothesised by Johannes Kepler, first in his Astronomia nova and then again later in his Epitome astronomiae Copernicanae, inspired by Gilbert’s work but not taken from him. I have a sneaking suspicion that Falk got his research notes a little muddled up here.

I found it very positive that Falk does not shy away from some controversial topics concerning sixteenth century English astronomy but whilst discussing them retains a level head. For example he looks at the claims made chiefly by Colin Ronan, who strangely doesn’t get mentioned here at all, that the Digges, that’s father and son Leonard and Thomas, invented and constructed a functioning telescope forty plus years before Hans Lippershey in Holland. Whilst quoting all of the original sources that led to these speculations Falk also gives space to those experts who clearly reject Ronan’s hypothesis, as I also do.

Having presented the scientific background Falk now moves on to Shakespeare presenting the reader with an, albeit, brief but adequate biography of the Bard. A necessary section of his book for those who come to it from the history of science rather than from English philology.

We are now half way through and can at last turn our attention to the real subject of the book, Shakespeare and science and Falk dives right in with “The Science of Hamlet”, where a tortuous trail of speculation is constructed. We start with a quote from the opening scene, “When yound same star that’s westward from the pole, Had made its course to illume that part of heaven”. This is a reference to the time of night, it being common practice in the Middle Ages to measure time at night by the position of the circumpolar stars. With a lot of jiggery-pokery we are led to the conclusion that the referenced star must be the Nova from 1572. This is not completely improbable as this Nova was the most significant celestial event during Shakespeare’s lifetime. In a fantasy dialogue Falk has Shakespeare’s father taking the young Will out to view the Nova in a prologue to the book. We now get led on to the fact that this is Tycho Brahe’s Nova. This is a classic bit of presentism. Tycho did indeed observe and write about this Nova but so did every astronomer in Europe and everybody, astronomer or no, with two eyes almost certainly observed it. So why do we need to introduce Tycho?

We now come to the central argument for an astronomical Hamlet, Rosencrantz and Guildenstern. Tycho Brahe produced an engraving of himself, he did lots of that sort of thing, in 1590, which lists sixteen of his close relatives including a Rosenkrans and a Guildensteren, Q.E.D: Shakespeare took the names from Tycho. It’s obvious isn’t it? But how? Tycho sent a copy of his astronomical letters, his Epistolae, containing said engraving to Thomas Saville, which includes Tycho’s well wishes for John Dee and Thomas Digges. What if Thomas Digges also received a copy? We then get a whole heap of arguments the Shakespeare could have (must have) known the Digges family and through them seen such a Tychonic portrait. Digges, we should not forget was a Copernican. Unfortunately none of these arguments contains a single concrete fact that Shakespeare knew the Digges family. The whole chapter is an untidy heap of unsubstantiated speculations with very little real substance.

Is it possible that Shakespeare came across the names Rosencrantz and Guildenstern by other means? To be fair to Falk he answers this question in the positive. There was a Danish diplomatic mission to England in 1592 including two delegates bearing the names Rosenkrans and Guildensteren and alone on Frederick II court in Copenhagen there were nine Rs and three Gs so a connection to Tycho is not really necessary.

Because Tycho as the Danish source of Hamletian science is so important both to Falk and Usher I will now point out something that the both either ignore or possibly deliberately sweep under the carpet. In the earlier chapters on Renaissance astronomy, when discussing Tycho, Falk points out that James VI & I actually visited Tycho’s observatory on Hven during a trip to Denmark. What he neglects to mention is why James was visiting Denmark in the first place. James went to Denmark in 1589 to fetch his bride, Anne of Denmark. This means that from 1590 onwards there would have been a strong political interest in Denmark, not only in Scotland but also in England where James was already seen as the most likely heir to the childless Elizabeth. Tycho Brahe was by no means the only reason for Shakespeare and his contemporaries to be interested in all things Danish.

Let us assume that having decided to write Hamlet Shakespeare, a good author, did some research on Denmark and the Danish court. He would discover that Denmark was ruled by an oligarchy of about twenty powerful families of, which the Brahes were one. If he chose at random two names from those twenty from his play then those chosen would have been relatives of Tycho because, as is the nature of oligarchies, the families maintained their hold on power by intermarrying. The fact that two courtiers in Hamlet bear the names of two of Tycho’s relatives thus has, in my opinion, very little significance.

Enter Usher stage right: According to Peter Usher the whole of Hamlet not only contains hidden references to Copernican astronomy but is in fact a dramatic presentation of the intellectual battle between the leading astronomical systems, Ptolemaic, Copernican and Tychonic. Hamlet is the Copernican astronomer embodied by Thomas Digges, Hamlet’s murdered father is Leonard Digges, his uncle Claudius is Ptolemaeus, Rosencrantz and Guildenstern are Tycho (apparently he has a split personality!), Laertes is Thomas Harriot and so on and so on. Only the women play no role in Usher grand scheme of things, a little strange given Ophelia’s central role in the drama! Apart from the Tycho connection sketched above Usher has discovered two smoking guns in the play that he thinks justify his interpretation. The first of these is Wittenberg. This German university town gets several name checks in the play. Usher sees this as references to Copernicanism because Rheticus, who persuaded Copernicus to publish, had studied and taught at Wittenberg. There are a couple of obvious flaws in this argument. Firstly Rheticus had left Wittenberg before the publication of De revolutionibus, in which he is incidentally never mentioned, to become professor of mathematics in Leipzig. Secondly Wittenberg was by no means a centre of Copernican scholarship, Luther and Melanchthon being both on record as opposing heliocentricity.

Is there another reason for Shakespeare to feature Wittenberg in a play about the Danish court? In fact there is. The court language in Denmark was not Danish but German and although Copenhagen had its own Lutheran university it was common practice for the Danish aristocracy to send its sons abroad for their education. See a bit of the world whilst getting your degree. Because Denmark was a strongly Lutheran country Wittenberg, home of Luther and the Reformation, was the most popular destination for young Danish aristocrats to acquire their foreign university experience. There is absolutely no need to evoke a bogus Copernican connection to justify Shakespeare’s choice of Wittenberg in his play.

Usher’s second smoking gun is the famous hawk and handsaw quote, “I am but mad north-north-west. When the wind is southerly, I know a hawk from a handsaw”. (For those not in the know handsaw is thought to be a typo for hernshaw a kind of heron). For Usher this rather enigmatic passage is interpreted to mean that for someone on Hven when the wind comes from north-north-west this means Elsinore the home of Claudius and Ptolemaic astronomy, so madness, whereas a wind from the south means Wittenberg the home of Copernicanism. Having already demolished the theory that Wittenberg is the home of Copernicanism I don’t really need to say more but I do have to ask why Hamlet should be positioned on Hven, Tycho’s realm, whilst making this speech? It really doesn’t make much sense to me Mr Usher.

There are a whole series of even less convincing finds by Usher not only in Hamlet but in all of Shakespeare’s plays to justify his fantasy constructions that I’m not going to go into here, but there is one further issue that I postponed from the introduction, an argument used by those not totally convinced by Usher’s bizarre arguments but willing to accept that Shakespeare’s work possible does contain some hidden references to heliocentricity. The quote in question comes from Troilus and Cressida, “the glorious planet Sol / In noble eminence enthroned and sphered…” We get told that, “by emphasizing the role of the sun, the passage may hint at the new heliocentric astronomy.” Talk about clutching at straws. Within traditional geocentric astronomy, astrology and alchemy the sun played a special role for very obvious reasons. The sun determines day and night, it defines the year, it brings light and warmth, it is by far and away the most prominent body in the sky do I really need to go one. I will add one astronomical note for those philologists who are apparently too lazy to read up on the history of the subject. In geocentric cosmology the sun was regarded as the ruler of the planets because, in the most commonly accepted order of the orbits, it occupies the central position in the heavens with three inner plants and three outer planets below and above it.

At the end of his chapter on Usher Falk tries a bait and switch. He presents a list of off the wall papers presented at a major Shakespearean conference that he attended whilst researching his book with an argument that Usher’s thesis is no crazier than these. Just because other people spout shit doesn’t make Usher’s shit anymore palatable. I will however give Falk credit, although he does present Usher’s garbage with considerably more sympathy than he deserves he also lets Usher’s critics speak for themselves leaving it to the reader to make up her or his mind on the subject.

What now follows in a chapter on Galileo and the telescopic discoveries made around 1610; in itself not a bad retelling of well-known material. This is included because we now have Usher and others trying to convince us that Shakespeare’s late play Cymbeline contain hidden references to Galileo’s (and Marius’ but he doesn’t get a mention) discovery of the four largest moons of Jupiter. I leave it to Falk’s readers to find if the arguments are convincing.

Because the book’s title is The Science of Shakespeare and not the astronomy or cosmology of Shakespeare Falk now turns to what are now commonly known as the occult sciences. Unfortunately he doesn’t seem to have done his homework here anywhere near as well as he did for the astronomy and cosmology in the main part of the book. We start with astrology and here he fall on his nose at the first hurdle. Falk tells us:

In England, astrology came to have two more or less distinct branches, known as “natural astrology” and “judicial astrology”. Natural astrology was, in fact, something like straight-ahead astronomy; it focused on tracking and predicting the motions of the sun, moon, and planets. Judicial astrology was closer to what we think of today as just plain “astrology – the attempt to link celestial happenings to earthly affairs, and to use astronomical knowledge to predict terrestrial happenings.

Wrong! Astronomy focused on tracking and predicting the motions of the sun, moon, and planets. That’s the difference between astronomy and astrology, although in Shakespeare’s time the two words were still used interchangeably. In fact astrology has four major divisions that go back to antiquity and were not first developed in Renaissance England. These are judicial astrology, electional astrology, horary astrology and natural astrology. Judicial or natal astrology is more or less as Falk describes it. Electional astrology is the casting of horoscopes to determine the correct or propitious time or date to start an undertaking. When should one marry, when lay the foundation stone of a building or new town, when to undertake a journey or even when to start a military campaign. Horary astrology is the attempt to answer questions by astrologers casting horoscopes upon receipt of the question. This is the classic detective story astrology used to detect thieves or to discover the hiding place of stolen goods. Natural astrology is the branch of astrology that deals with the things of the natural world i.e. astro-medicine and astro-meteorology. Theses division are important in the history of astrology, as there were extensive debates and disputes as to the validity of each of them, each of the four having its own champions and opponents. Interestingly even the strongest opponents of astrology in general in the High Middle Ages and the Renaissance tended to accept the validity of natural astrology whilst simultaneously launching vitriolic invective against the widespread judicial astrology.

Although having got off to a bad start Falk’s discussion of judicial astrology in Shakespeare is reasonably good. He acknowledges that Shakespeare’s work is permeated by astrological references, whilst being a good mirror of his own society he also lets the opponents of astrology speak their piece. Unfortunately I got the feeling that Falk was trying to persuade the reader that Shakespeare was an opponent of astrology and that despite the fact that in his biographical chapter on the Bard he warns the reader against trying to determine Shakespeare’s character or personality from his works. I was particularly irritated by statements that Carl Sagen or Richard Dawkins would find favour with a particular anti-astrology speech or Neil deGrasse Tyson and Laurence Krauss would applaud a piece of scepticism. I found these comments out of place and quite frankly somewhat bizarre.

After astrology we turn to magic. This chapter slightly disturbs me, as it is largely about demonic magic, Macbeth’s witches and all that, which unlike natural magic was never considered scientia and thus not science. Towards the end of the chapter Falk does briefly discuss the difference between demonic and natural magic but his definition of natural magic is even more wrong than his definition of natural astrology. I’m not even going to go there, as an attempt to explain natural magic would probably end up as long as this already over long review. Even worse Falk talks about astrology as being magic. This is within the context of a book on Renaissance history a serious category mistake. Astrology is not a form of magic. Falk makes the same category mistake as he discusses alchemy in this chapter. Alchemy gets dismissed in a couple of short paragraphs somewhat of a disappointment as alchemy played a very central role in Elizabethan learned society, with even Elizabeth herself a practicing alchemist. Falk closes out the chapter by stating that “Astrology, witchcraft, alchemy, magic … and science. It was all part of a package; all were thoroughly intertwined in the sixteenth century, and even into the early years of the seventeenth.” This was indeed true although it went much further into the seventeenth century than the early years. However I find it slightly sad that Falk choses to illustrate this with a quick sketch of the live and work of Johannes Kepler. This sketch whilst basically correct doesn’t do Kepler’s scientific achievements justice. We also get the following old myth dished up, “We might note that Kepler was a practicing astrologer, and that he cast horoscopes for the German nobility. It’s not clear, however, how much faith he put in the power of the starts to influence our lives” [my emphasis]. Just for the record Kepler was a 100% convinced astrologer and any claims to the contrary are wishful thinking from those who would prefer their scientific heroes free of the taint of the occult.

Next up is Renaissance medicine a recurring theme in Shakespeare’s plays. An adequate treatment of the subject as far as it goes but neither here nor in his discussion of astrology does Falk even mention let alone discuss astro-medicine. This is a strange omission as astrological medicine was one of the dominant directions in medical practice in Shakespearean times. This chapter contains the strangest claim in the whole book. In his discussion of the differences between physicians, surgeons, apothecaries, and midwifes Falk produces the following gem, “Since the Middle Ages, the practice of medicine had been associated with the Catholic Church and so physicians were forbidden to shed blood”. Now I’m not a historian of medicine but I’ve read a lot of literature on the history of medicine and I’ve never come across anything of the sort in fact I will go as far as to say that this statement is a total myth of the same sort as the claim that the Church had banned dissection. I’m quite prepared to admit that I’m wrong should any of my highly educated readers show Falk to be in the right but somehow I don’t think I’m going to have to.

In the penultimate chapter Falk takes a sharp left turn. The chapter opens with a brief discussion of Lucretius’ De rerum natura and a free advert for Stephen Greenblatt’s The Swerve. As Falk correctly says De rerum natura was a highly popular and influential book in Shakespeare’s time so one might well expect to find this popularity reflected in Shakespeare’s writings. All that Falk can deliver is one instance of the word atomi in Romeo and Juliet. This doesn’t stop him discussing Lucretius and recommending Greenblatt’s book. Greenblatt is one of the experts on Shakespeare that Falk consulted for his book, as he tells us on numerous occasions in the text and he gives an enthusiastic endorsement to Greenblatt’s work on the rediscovery of Lucretius’ poem in the Middle Ages. Unfortunately, this high opinion of The Swerve is not shared by many historians of medieval philosophy including one guest author here at The Renaissance Mathematicus.

Falk now introduces us to the sixteenth-century French essayist Montaigne trying to conceive him as a modern scientific skeptic, again gratuitously name dropping some actual ones, this time Laurence Krauss and Stephen Hawking. He does however admit that the attempt is at best dubious. He lets us know that Montaigne briefly refers to Copernicus, noting that there are now two possible cosmologies however reflecting that maybe in a thousand years a third model will come along and overthrow both of them. For this insight Falk credits Montaigne with being a sixteenth-century Karl Popper. There is however method in all this. We now get shown that Shakespeare was a diligent reader of the English translation of Montaigne’s essays traces of them turning up all over his own writings. This leads Falk to the categorical claim that at least here Shakespeare must have [my emphasis] come across Copernicus and Copernicanism. I always react allergically when somebody writing a historical text having failed to produce a direct link between two things sets up a plausible but speculative link and then says, “must”. There is no must about it. We simply do not know if Shakespeare read all of Montaigne’s voluminous output or only selected essays or if reading the essay in question skipped over the brief lines referring to Copernicus or even reading them gave them no significance and promptly forgot them again. What makes Falk’s last ditch attempt to link Shakespeare and Copernicus all the more questionable, having failed earlier in his book to produce a genuine smoking gun, is that he has spent a lot of words trying to convince the reader that Hamlet is the Bard’s Copernican work, whereas the English translation of the Montaigne essay first appeared in 1603 after Hamlet was written.

The final chapter of the book goes off on another tangent, this time in the direction of atheism. We get a potted history of atheism in the Early Modern Period and parallel to it a synopsis of how lacking in hope King Lear is. Combining this with the fact the Will’s friend Kit Marlowe was accused of atheism Falk ventures the hypothesis that Shakespeare had abandoned a belief in god. At the latest here, it becomes clear that Falk wishes to recreate Shakespeare as a sort of sixteenth-century Richard Dawkins. Enthusiastically embracing, albeit secretly, the new mode of scientific thinking and rejecting humanities dependency on god. However having come this far Falk baulks at the final hurdle hurriedly qualifying his own hypothesis, “We can’t definitely label Shakespeare an atheist, just as we can’t call him a scientist – even if we suspect we are seeing hints of such a world view.” In my opinion Falk has made a valiant effort to find facts to support his thesis but for me his argument is far too full of gaping holes to be really convincing.

Although this is not a an academic book its subject matter is of an academic nature so I think it is fair to ask about the academic apparatus, foot- or endnotes, bibliography and index. The book is equipped with, what I’m told, are hanging endnotes. That is endnotes giving sources for direct quotes in the text but without indications (quote numbers) in the text that they exist. This is possibly the worst solution to the notes problem that exists and I abhor it. I also found several direct quotes in the text for which no endnote exists. What makes this choice even stranger is that the text also has spasmodic footnotes referring to quotes in the text. Why some quotes earn footnotes and others hanging endnotes is not at all clear to me. The bibliography is quite extensive and gives ample evidence of the work that Falk has obviously invested in his book. There is no index! I find the omission of an index in this age of advance word processors, which make the compilation of an index child’s play, unforgivable.

I realise that if anybody has stayed with me up to here that they might think that having made so many negative comments I would not recommend Falk’s book, they would be wrong. On the whole I found the book well written, entertaining and informative. It is not free of errors but very few popular books on the history of science ever are. One of the very positive aspects of the book is that when even Falk presents a speculative theory concerning some aspect of science and a Shakespearean play he makes very clear that it is speculative and also presents alternative explanations for the text in question leaving it up to the readers to decide for themselves whether to accept the proffered hypothesis or not. On the whole I enjoyed reading this book and would recommend it as a stimulating read for anybody interested in the subject matter, although they should be on their toes whilst reading.



[1] Dan Falk, The Science of Shakespeare: A New Look at the Playwright’s Universe, Thomas Dunne Press, St. Martin’s Press, New York, 2014.


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

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

Cartoons and Fables – How Cosmos Got the Story of Bruno Wrong

One of the joys of writing this blog is that I have a number of readers/commentators who are more intelligent, more knowledgeable, more erudite and above all more sensible than I. Every now and then I succeed in trapping, blackmailing, bullying or conning one of them into writing a guest post in order to give you the readers an alternative perspective on the world of the history of science and the chance to read something of quality. This time I have succeeded in acquiring the literary services of Tim O’Neill, historian and inexhaustible warrior against the misuse and abuse of the history of science. In his post Tim adds his tuppence worth to the debate raging far and wide about the Bruno cartoon in the first edition of the Cosmos reboot. Enjoy! 

A few months ago while visiting Rome I did something a tourist should not do in a strange city – I took a short cut.  Walking back from the Forum to my apartment over the Tiber, I should have taken the obvious route down the Corso Vittorio Emanuele II toward the Castel  Saint ‘Angelo, but I decided I knew where I was going, so I took a more direct path through some back streets and soon became completely lost.  After winding my way through a maze of smaller laneways trying to find a major road I saw a piazza up ahead and so decided to use that to get my bearings.  I stopped under a statue in the middle of the square to get out a map, looked up at the statue and immediately knew where I was.  I realised I was in the Campo de’Fiori, because the statue was the famous monument to Giordano Bruno, raised on the spot where he was burned at the stake in February 1600.

Bruno 2013 Photo: Tim O'Neill

Bruno 2013
Photo: Tim O’Neill

Bruno is the poster boy of the Draper-White Thesis – the idea that science and religion have always been at war and an idea beloved by the New Atheist movement despite the fact it was rejected by actual historians of science about a century ago.  Try to engage in an attempt at intelligent discussion of the real and much more complex and nuanced interrelations between religion and what was to emerge as modern science in the medieval and early modern periods and Bruno is usually brandished as “proof” that the Church was the implacable and ignorant foe of early science.  After all, why else did they burn him for daring to say the earth wasn’t the centre of the universe and that the stars were other suns with planets?  For those who prefer simple slogans and caricatures to the hard work of actually analysing and understanding history, Bruno is a simple answer to a intricate question.  Nuance and complexity are the first casualties in a culture war.

So when I saw the first preview clips of the revamped version of Carl Sagan’s Cosmos, this time presented by Sagan’s genial protégé Neil deGrasse Tyson, and noticed an animated sequence of someone being menaced by Inquisitors and burned at the stake, I knew that the revived Cosmos was going to be presenting some bungled history.  This was also following in Sagan’s footsteps, I suppose, since in the original series he veered off into a mangled version of the story of Hypatia of Alexandria that fixed the false idea of her as a martyr for science in the minds of a generation, as I’ve discussed elsewhere.

So when the first instalment of the new series – Cosmos: A Spacetime Odyssey -  went to air last week, at its heart was an eleven minute version of the Bruno myth.  I often refer to the simplistic moral fable that people mistake for the history of the relationship between the Church and early science as “the cartoon version”, because it’s oversimplified, two-dimensional and reduced to a black and while caricature.  But in this case it really is a cartoon version – the sequence was animated, with the voice of Bruno provided by the series’ Executive Producer, Seth MacFarlane, of Family Guy fame, which seems to be why Bruno has an Italian accent of a kind usually heard in ads for pizza or pasta sauce.

The clichés didn’t end with the silly accents.  In the weirdly distorted version of the story the program tells, Bruno is depicted as an earnest young friar in Naples who was a true seeker after truth.  But DeGrasse Tyson assures us that he “dared to read the books banned by the Church and that was his undoing.”   We then get a sequence of Bruno reading  a copy of Lucretius’ On the Nature of Things which he has hidden under the floorboards of his cell.  The first problem here is that Lucretius’ work was not “banned by the Church” at all and no-one needed to hide it under their floor.  Poggio Bracciolini had published a printed edition of the book a century before Bruno was born and it had never been banned when the medieval manuscripts Bracciolini worked from had been copied nor was it banned once his edition made it widely available.  The idea that the Church banned and/or tried to destroy Lucretius’ work is a myth that Christopher Hitchens liked to repeat and which has been given a lease of popular life via Stephen Greenblatt’s appalling pseudo historical work The Swerve, which somehow won a Pulitzer Prize despite being a pastiche of howlers.

The DeGrasse Tyson cartoon goes on to depict Bruno having his mind opened to the idea of an infinite universe by Lucretius’ book but then being kicked out of his friary by a mob of Disney villain-style Church types who turn up unexpectedly like Monty Python’s Spanish Inquisition.  This, of course, makes for a much better parable than the truth – Lucretius’ work wasn’t “banned by the Church” and Bruno actually ran away from his religious house and wasn’t thrown out for reading naughty books.

It would also have complicated this simplistic cartoon fable to note where Bruno got his ideas about a vast cosmos where the earth was not the centre, where the stars were other suns, where there was a multiplicity of worlds and where some of these other worlds could even have been inhabited just like ours.  Because this was not something Bruno got from Lucretius nor was it something he dreamed up himself in a vision, as the Cosmos cartoon alleges.  It’s something he drew directly from the man he called “the divine Cusanus” – the fifteenth century natural philosopher and theologian Nicholas of Cusa.

If the writers of the series were actually interested in the real history of the origins of scientific thought, there are many people whose stories would have been far more worthy of telling than Bruno – people who actually were proto-scientists.  The writers of the show, Stephen Soter and Sagan’s widow Ann Druyan, seem to have known enough about Bruno to know they could not present him as a scientist and DeGrasse Tyson’s narration does mention that he was “no scientist” at one point.  But they delicately skim over the fact that the guy was, to our way of thinking, a complete mystical loon.  In his defence of the criticism the Bruno sequence has since attracted Soter notes that several  other early science figures also pursued studies that we find abjectly unscientific, such as Newton’s obsessions with alchemy and apocalyptic calculation.  But the difference is that Newton and Kepler pursued those ideas as well as studies that were based on real empirical science, whereas Bruno’s hermetical mysticism, sacred geometry and garbled and largely invented ancient Egyptian religion were all of his studies – he did no actual science at all.

But if they wanted to be truly accurate they should have detailed or even merely acknowledged Bruno’s debt to Nicholas of Cusa, who expounded on a non-finite cosmos without a centre 109 years before Bruno was even born.  Here is Cusanus on the subject in his book De docta ignorantia :

” The universe has no circumference, for if it had a centre and a circumference there would be some and some thing beyond the world, suppositions which are wholly lacking in truth. Since, therefore, it is impossible that the universe should be enclosed within a corporeal centre and corporeal boundary, it is not within our power to understand the universe, whose centre and circumference are God. And though the universe cannot be infinite, nevertheless it cannot be conceived as finite since there are no limits within which it could be confined.”

That’s the insight that the Bruno cartoon attributes solely to Bruno.  So why not attribute it to “the divine Cusanus”?  Well, that would ruin the whole parable.  Because far from being kicked around by grim-looking Disney villains imprisoned and burned at the stake, Cusanus was revered and actually made a cardinal.  So that doesn’t lend itself very well to a moral fable about free-thinking geniuses being oppressed by dogmatic theocrats.

The cartoon then goes on to depict brave Bruno lecturing at Oxford, with grumpy and aristocratic-sounding scholars there objecting to his espousal of Copernicanism and eventually throwing fruit at him and driving him away.  Again, the reality wasn’t quite as worthy.  There is zero record of any objection to heliocentrism and the problem the Oxford scholars had with Bruno was actually his plagiarism of another scholar’s work.  But, again, that doesn’t lend itself to a fable about a pure and persecuted freethinker.

Throughout the cartoon the idea is that he is afflicted because he supports heliocentrism and the idea of an unbounded cosmos  where the earth is not the centre.  As we’ve seen, the latter idea was not new and not controversial.  By the 1580s Copernicus’ heliocentric hypothesis wasn’t particularly new either, though it was more controversial – virtually no astronomers accepted it because it was recognised as having severe scientific flaws.  The important point to remember here is that at  that stage it was not considered heretical by religious authorities, even though some thought it had some potentially bothersome implications.

Copernicus had not even been the first proto-scientist to explore the idea of a moving  earth.  The medieval scholar Nicholas Oresme had analysed the evidence that supported the idea the earth rotated way back in 1377 and regarded it as at least plausible.  The Church didn’t bat an eyelid.  Copernicus’ calculations and his theory had been in circulation long before his opus was published posthumously and and it had interested several prominent churchmen, including Pope Clement VII, who got Johan Widmanstadt to deliver a public lecture on the theory in the Vatican gardens, which the Pope found fascinating.  Nicholas Cardinal Schoenburg then urged Copernicus to publish his full work, though Copernicus delayed not because of any fear of religious persecution but because of the potential reaction of other mathematicians and astronomers.  Heliocentrism didn’t become a religious hot topic until the beginning of the Galileo affair in 1616, a decade and half after Bruno’s death.

Again, the Cosmos writers seem to be at least vaguely aware of all this and so do some fancy footwork to keep their parable on track.  In the cartoon’s depiction of Bruno’s trial we get the first hint that the Church’s beef with Bruno might actually have been to do with ideas that had zero to do with an infinite cosmos, multiple worlds or any cosmological speculations at all.  So the Disney villain Inquisitor reads out a list of accusations such as “questioning the Holy Trinity and the divinity of Jesus Christ” and a few other purely religious charges.  The depiction gives the impression that these are somehow less important or even trumped up accusations, when in fact these are the actual reasons Bruno was burned at the stake, along with others beside.  As horrific as it is to us, denying the virginity of Mary, saying Jesus was merely a magician and denying Transubstantiation did get you burned in 1600 AD, though only if you refused repeated opportunities to recant.

But the cartoon wants to stick to its parable, so they tack on the final and, we are led to believe, most serious charge – “asserting the existence of other worlds”.  As we’ve already seen, however, this was not actually a problem at all.  Here’s NIcholas of Cusa on these other worlds in the book that inspired many of Bruno’s beliefs:

“Life, as it exists on Earth in the form of men, animals and plants, is to be found, let us suppose in a high form in the solar and stellar regions. Rather than think that so many stars and parts of the heavens are uninhabited and that this earth of ours alone is peopled – and that with beings perhaps of an inferior type – we will suppose that in every region there are inhabitants, differing in nature by rank and all owing their origin to God, who is the center and circumference of all stellar regions …. Of the inhabitants then of worlds other than our own we can know still less having no standards by which to appraise them.”

Again, remember that Cusanus was not burned at the stake, he was revered, praised and made a cardinal.

The only mention of other worlds in the accusations against Bruno specifies that he believed in “a plurality of worlds and their eternity“.  It was that last part that was the problem, not subscribing to an idea that a prince of the Church had espoused a century earlier.

The cartoon concludes with DeGrasse Tyson’s caveats about Bruno being “no scientist” and his ideas being no more than a “lucky guess”.  Some commenters seem to think that this somehow absolves the whole sequence of its distortions and that it means the show depicts Bruno only as a martyr to free thought and a lesson on the dangers of dogmatism.  But the problem with the cartoon is that it makes up a silly pastiche of real history, fantasy and oversimplified nonsense to achieve this aim.  The real story of Cusanus would actually have been a much more interesting one to tell and wouldn’t have had the Draper-White inspired baggage of the Bruno myths.  But the whole sequence seems to have had an agenda and a burned heretic story served that agenda’s purpose in a way that a revered and untrammelled medieval cardinal’s story would not have.

The objective here was to make a point about free thought and dogmatism in the context of the culture wars in the US about Creationism.  That Bruno was a believer in God was an idea that was repeated several times in the cartoon, even though he was actually more of a pantheist than anything.  But he is depicted as an open-minded and unconstrained believer who is oppressed and finally killed by the forces of dogmatic literalism.  The cartoon Bruno’s cry to the fruit-throwing Oxford scholars  – “Your God is too small!” – is actually the point of the whole parable.  This entire sequence was aimed at the dogmatic literalists in the American culture war while still trying to appeal to believers, given the majority of the show’s American audience would have been theists.  That’s the framework of this fable and the writers chopped up bits of the actual historical Bruno story and then clumsily forced them into this modern message.

This sequence wasn’t history or anything remotely like it – it was politics, pure and simple.

Which brings me back to my encounter with the statue in the Campo de’Fiori.  The statue was created by Ettore Ferrari and erected in 1889 in the wake of the unification of Italy in the face of Church opposition.  The monument, raised by members of the Grande Orient d’Italia Masonic order, was a deliberate political symbol of anti-clericalism.  Atheists and free thinkers revere it to this day and commemorate Bruno’s execution on Febrary 17 each year.

Of course, anyone who points out that Bruno is a rather ridiculous icon for atheists, given his kooky mystical views and magical practices is usually ignored.  And anyone who has the temerity to point out that he was executed for purely religious ideas and not any speculation about multiple worlds or a non-finite cosmos is usually (bizarrely) told they are somehow justifying his horrific execution.  As I’ve often noted, for people who call themselves rationalists, many of my fellow atheists can be less than rational.  Unfortunately, Neil deGrasse Tyson, Ann Druyan, Steven Soter and Seth MacFarlane’s silly Bruno cartoon will definitely not help in that regard.


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