Category Archives: Renaissance Science

“…realigning the heavens with a single stroke of the brush.“ – Really?

Recently on twitter I stumbled across a problematic discussion, as to which single image had most changed the course of science. Although the various participants made stimulating and interesting suggestions, Darwin’s tree diagram, Franklin’s photo of DNA etc. I found this discussion problematic because it suffers from the same difficulties as discussion in the history of science as “the first”, “the greatest”, “the father of” and all similar hyperbolic claims, just how do you measure and compare the numerous candidates that spring to mind?

This discussion didn’t just appear out of cyberspace on somebody’s whim but was provoked by Joe Hanson at It’s OK to be Smart and his post Message from the Moon, which in turn was provoked by the set of washes of the moon by Galileo that had been circulating on Twitter a couple of days before.

Galileo's washes of the moon.

The watercolour sketches that Galileo made of his initial telescopic observations of the moon in 1609/10 are iconic images in the history of science that did have a major impact on the way humanity viewed the cosmos but there are an awful lot of inaccuracies in Hanson’s description of that impact that I am going to analyse here.

Hanson’s first minor error is to claim that the images he has posted on his blog are included in the Sidereus Nuncius. Galileo’s legendary publication does indeed included woodcuts of five of his lunar watercolours but the sheet displayed by Hanson, and here above, was not included, a trivial but important point.

Hanson informs us:

But hiding in their shadows lies a greater significance. The squiggled edges of that bleeding ink bear an observation that altered the heavens themselves. Or at the very least, our view of them.

And then goes on to explain why:

In 1610, cosmology, not that it had much to show for itself as a science, was still based on the ideas of Aristotle, who by this time had been dead for 18 centuries. So current! Copernicus’ observation that the Earth orbited the sun, first published in 1543, had begun to challenge Aristotelian supremacy, it wasn’t exactly a popular idea. 

Aristotle’s cosmological beliefs were based on the idea that the heavens were made of a perfect substance called “aether”, and therefore the circular motions and spherical shapes of heavenly bodies were also perfect. Earth, he claimed, was inherently imperfect, as were all the things that existed upon it. Everything in the heavens was awesome, and Earthly matter was inherently “just okay”, even if its name was Aristotle. This was one of the reasons people found Copernicus’ claims so hard to swallow. The imperfect Earth among the perfect heavens? Heresy! [emphasis in original]

Somewhat sloppily expressed but so far so good, although placing the earth in the heavens didn’t really play that much of a role in the initial rejection of Copernican cosmology being insignificant in comparison to the physical problems engendered by a moving earth. Hanson’s argument is that because Galileo’s interpretations of what he saw through his telescope, and don’t forget that they are interpretations, clearly suggested that the moon was not smooth and perfect but had a landscape like the earth he had realigned “the heavens with a single stroke of the brush”; a nice literary figure of speech but unfortunately one that doesn’t fit the historical facts.

Already in antiquity people, had speculated that the differing shades of the moons surface were the result of a mountainous landscape. This viewpoint was expressed most notably by Plutarch in his On The Face Which Appears in the Orb of the Moon, one of his collection of essays, the Moralia. This was well known and widely read in the sixteenth-century and was even used by Kepler as a springboard for his own “lunar geography”, the Somnium, written but not published before Galileo made his telescopic discoveries. This widespread alternative concept of the lunar surface made it much easier to accept Galileo’s discovery and considerably weakened any impact that it might have had on Aristotelian cosmology. However this was not the only factor that gives the lie to Hanson’s “single stroke of the brush” postulate. Aristotle’s division of the cosmos into two spheres one superlunar, which was perfect, unchanging and eternal, everything below, and the other sublunar, which was imperfect, constantly changing and subject to decay had been under attack for most of the century preceding Galileo’s discoveries, as I have already outlined in my post on Comets and Heliocentricity.

In the 1530s observations of several comets had led many leading European astronomers to the conclusion that comets were superlunar phenomena and not sublunar ones as Aristotle’s cosmology required. Comets are of course anything but perfect, unchanging and eternal. In the 1570s another generation of European astronomers, Tycho Brahe and Michael Maestlin to the fore, confirmed this conclusion making life more than somewhat difficult for any cosmologist who wished to maintain a strict Aristotelian party line. To make matters worse the stellar novae of 1572 and 1604 observed once again by Europe’s finest watchers of the heavens and determined by them to be unquestionably superlunar really put the kibosh on Aristotle’s wonderful division of the cosmos. All in all by 1610 Aristotle’s cosmology was already looking distinctly unhealthy and Galileo’s discovery of the lunar landscape far from being an unexpected deadly bolt out of the blue was just another blow helping it on its way to its grave.

Hanson might be forgiven for his over emphasis of the impact of Galileo’s lunar watercolours based obviously on his ignorance of Renaissance astronomical and cosmological history but the content of his closing paragraph displays an ignorance that I, for one, find hard to forgive. Our intrepid non-historian writes:

Galileo’s Sidereus Nuncius [emphasis in original] also included newly detailed maps of the constellations and the mention of four moons of Jupiter (although detailed observations of those were still centuries away), [my emphasis] but it was his drawings of our moon that bore the most impact on future astronomical science, realigning the heavens with a single stroke of the brush.

Having over emphasised the significance of the impact of Galileo’s lunar watercolours Hanson dismisses his discovery of the moons of Jupiter in a throwaway comment. He couldn’t demonstrate his ignorance of the material more spectacularly.

It was of course Galileo’s discovery of the four largest moons of Jupiter that caused the sensation and also did the most damage to Aristotelian cosmology, when he published the Sidereus Nuncius in 1610. Central to Aristotelian cosmology was the principle of homo-centricity, i.e. the concept that all celestial bodies, the sphere of the fixed stars and the seven planets, revolve around a common centre, the earth. The discovery of the Galilean moons, as they came to be known, was a direct empirical proof that the principle of homo-centricity was wrong. It lent indirect support to heliocentricity, which required two centres of revolution the sun for the fixed stars and the six planets and the earth for the moon. It was Galileo’s discovery of the Medician Stars, as he called them, which led to his much desired appointment as court philosophicus and mathematicus in Florence and professor of mathematics at the University of Pisa without teaching duties. Catapulting him almost overnight from being an obscure, ageing professor of mathematics to being Europe’s most notorious astronomer. The four moons of Jupiter are not “mentioned” in Sidereus Nuncius they are the reason for its hurried and secretive, to prevent anybody else beating him to the punch, composition and publication.

The illustrations of the moon in the Sidereus Nuncius are the eye candy, which the reader can admire but the far less visually spectacular diagrams of the positions of the four moons relative to Jupiter are the explosive content that make this slim pamphlet one of the most important scientific publications of all time and elevated Galileo into the pantheon of scientific heroes.

Page from Galileo's observation log displaying position of the moons relative to Jupiter

Page from Galileo’s observation log displaying position of the moons relative to Jupiter

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

How much can you get wrong in an eight hundred word biographical sketch of a very famous sixteenth and seventeenth-century mathematicus and philosophicus? – One helluva lot it seems?

If someone is doing the Internet equivalent of being a big-mouthed braggart and posting an article with the screaming title, “10 Absurdly Famous People You Probably Don’t Know Enough About” you would expect them to at least get their historical facts right, wouldn’t you? Well you would be wrong at least as far as “absurdly famous” person number seven is concerned, Galileo Galilei. Tim Urban the author of this provocative article on the ‘Wait But Why’ blog appears to think that history of science is something that you make up as you go along based on personal prejudice mixed up with some myths you picked up some night whilst drunk in a bar. Having not had a real go at somebody else’s terrible history of science for sometime now and not having deflated my favourite punching bag, Galileo or rather the hagiographic imbeciles who write about him, for even longer I thought I would kill two birds with one stone and correct Mr Urban’s little piece as it were a high school term paper. The blue text is original Urban the black comments are mine.

Galileo-300x263

Lived: 1564 – 1642

He makes a promising start in that he at least got the years of birth and death right, although with the same amount of effort he could have given us the exact dates – 15 February 1564 – 8 January 1642

In 11 words: Rare giant of scientific advancement fighting against hopelessly-backward Catholic Church

After that reasonably good beginning we go rapidly down hill. As I have commented on a number of occasions Galileo was by no means as rare or as gigantic as he is usually painted. He also spent most of his life getting along very happily with the Catholic Church with whom he was on good terms and which was in a lot of things, including scientific one, anything but hopelessly-backward. Just to quote one example about which I’ve blogged in the past, it was the Jesuit astronomers at the Collegio Romano who delivered the very necessary scientific confirmations of Galileo’s telescopic astronomical discoveries and then invited Galileo to Rome to celebrate them.

His main thing: Einstein called Galileo “the father of modern science,” which sums things up pretty nicely.

Einstein, as a leading historian of Renaissance science is of course highly qualified to make such a judgement. Regular readers of this blog should by now know my opinion of such expressions as “the father of” and in particular their use to describe Galileo. For those that don’t I recommend my post, “Extracting the stopper”, as a good starting-point.

Galileo made major discoveries about the motion of planets and stars, the motion of uniformly accelerated objects (i.e. that two objects would fall at the same rate regardless of their masses), sound frequency, and the basic principle of relativity, among other things

I must admit to being somewhat perplexed by the claim that Galileo made “major discoveries about the motion of planets and stars”; I’m not aware of any achievements by the good man in this direction, perhaps somebody could enlighten me?

—and major advancements in technology, including inventing or improving upon the telescope, microscope, thermometer, pendulum, and the compass.

Galileo made an improved telescope and might have been one inventor of the microscope, although this is clouded in uncertainty. He experimented with a thermoscope, not a thermometer, but probably did not invent it. He neither invented nor improved the pendulum and I don’t think he or anybody else ever claimed that he did so. He did however investigate the properties of the pendulum, although the law he set out for the pendulum is actually wrong.

The last claim is quite funny and turns up time and time again quoted by people who literally don’t know what they are talking about. Galileo had nothing to do with the (magnetic) compass but manufactured and marketed an improved version of the sector, or proportional or military compass. This is a hinged ruler with numerous scales used for making mathematical calculations particularly by artillery officers. This instrument has several independent inventors; the one improved by Galileo was invented by his mentor, Guidobaldo del Monte.

Galileo's military compass

Galileo’s military compass

His work was central to most future developments in science, including those of Newton and Einstein, and most of what he discovered was in contradiction with conventional wisdom—his work was as shocking and revolutionary in the 1600s as Einstein proclaiming that “time is relative” was in the 1900s.

This is typical of the hagiographical hogwash dished up by people writing about Galileo. The only part of Galileo’s work ‘central’ to Newton was the parabolic flight path of projectiles, which was discovered independently by other including Thomas Harriot. His only connection to Einstein is the rejection of Galilean relativity in the theory of the latter. Very little of Galileo’s own work was shocking and the only parts that were in anyway revolutionary were the laws of fall, discovered independently and earlier by Benedetti, and heliocentricity, a field in which Galileo was not the discoverer or inventor but merely the polemicist, who probably did more damage than good through his advocacy.

But the most impressive part about Galileo, other than his ability to make such a cranky facial expression in the above painting, is that he did everything he did in the face of threats and repression by the Catholic Church and their inane loathing of ground breaking scientific advancements.

I begin to get the impression that our author has a personal problem with the Catholic Church, which did not have an “inane loathing of ground breaking scientific advancements”, and except in the one case Galileo did nothing in “the face of threats and repression by the Catholic Church” but actually received much support and encouragement from many leading figure in the Church hierarchy for the vast majority of his life and work.

The main thing the Church kept yelling at Galileo for was his backing and advancement of Copernicus’s heliocentric model of the universe, which puts the sun, instead of the Earth, in the center of the solar system and suggests that the Earth’s spinning is why the sun appears to revolve around the Earth. The Church declared heliocentrism to be “foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture”—in particular, the parts of scripture that said things like, “the world is firmly established, it cannot be moved” and “the Lord set the earth on its foundations; it can never be moved”—and ordered Galileo “to abstain completely from teaching or defending this doctrine and opinion or from discussing it… to abandon completely… the opinion that the sun stands still at the center of the world and the earth moves, and henceforth not to hold, teach, or defend it in any way whatever, either orally or in writing. “That would be like modern-day governments imprisoning geologists who studied ancient rocks because their findings conflicted with the Bible’s accounts of the Great Flood. Or like preventing gay people from getting married because of passages in the Bible about sexual orientation. Thankfully, those times are over.

The above paragraph contains the real reason that Mr Urban is frothing at the mouth about the Catholic Church, Galileo’s clash with the Church on heliocentricity. Once again I’m not going to go into great detail about the whole sad sorry affair but will for the umpteenth time repeat that the central problem had very little to do with science, astronomy, cosmology or whatever but with the fact that in 1615 Galileo tried to tell the Church how to interpret the Bible. If he had not done this and instead bided his time patiently, as suggested by his friends, including Cardinal Maffeo Barberini the later Pope Urban VIII, the Church would in its own time almost certainly have adopted heliocentricity. Instead of which through Galileo’s pig-headedness the acceptance of heliocentricity by the Catholic Church was delayed by about one hundred and fifty years.

So the Church repressed the greatest genius of the century,

There’s no such thing as the greatest!

… finding him “vehemently suspect of heresy,” and placed him under house arrest for the rest of his life. Luckily, Galileo just hung out on his couch and kept doing his thing, publishing some of his most important works while under house arrest.

I know Galileo fans and militant atheists don’t like to hear this but, for the ‘crime’ of which he was found guilty, Galileo was treated very, very gently and his sentence was very mild.

Other things:

  • Galileo never married, having all three of his children out of wedlock with the same woman.
  • We got something right!
  • One of the reasons Galileo started inventing things (like the telescope) in the first place was that he badly needed money to deal with all the money his starving artist little brother kept “borrowing” from him.
  • Like many Renaissance mathematicians Galileo supplemented his income by designing, manufacturing and selling scientific instruments. He didn’t invent the telescope! Galileo was notoriously always short of money not because he supported his little brother financially, which he did, but because he enjoyed the good life and tended to live beyond his means.
  • He was briefly a professor at the University of Pisa, but he was inappropriate with his students and the university didn’t renew his contract.
  • The second part of the above sentence is a pure fabrication. Galileo was professor of mathematics in Pisa from 1589 till 1592 when he applied for and received the more prestigious and better-paid professorship for mathematics in Padua where he remained until 1610.
  • Despite his conflicts with the Church, Galileo was a devout Catholic. He briefly became a priest before his father convinced him to go into medicine, and his two daughters were nuns. But he was critical of the Church’s repression of science, stating, “Holy Writ was intended to teach men how to go to Heaven, not how the heavens go.”
  • That Galileo was a devout Catholic is a standard claim in the history of science repeated, I think, to make the Church look worse for their persecution of the man. This claim has been strongly challenged by Renaissance historian; David Wootton in his biography “Galileo: Watcher of the Skies” (Yale University Press, 2010), which paints Galileo convincingly as a very lax Catholic and possibly an unbeliever. Galileo was never a priest but did spend a few months in a monastery as a teenage novice, although he never took holy orders. Galileo’s two daughters were placed in a monastery because, being illegitimate, he considered them unmarriageable and also to spare him the cost of their dowries, a standard procedure in that period.
  • One of Galileo’s worst offenses against the Church was creating a character called Simplico in his famous book Dialogue Concerning the Two Chief World Systems, who always presented the old, incorrect, geocentric view. Simplico suggests “simpleton” in Italian just like it does in English, and in the book, Simplico does not come off very well. The issue is that a lot of what Simplico says in the book were well known to be the direct views of the Pope (Urban VIII), indirectly insulting the Pope and hastening Galileo’s path toward house arrest.
  • The character in the Dialogo who presents the case for geocentricity is called Simplicio not Simplico. The insult of the Pope was much more direct than suggested here. When Urban VIII granted Galileo permission to write a book explaining both geocentricity and heliocentricity, in order to prove that Catholics were not ignorant of the latter theory, he specifically instructed Galileo to include his own theological argument against deciding for one system over the other because this would “limit and restrict the Devine power and wisdom to some particular fancy of my own”. A not unreasonable viewpoint given that there were no proofs for the heliocentric system at that time. Galileo did as instructed including exactly those words in the final speech of Simplicio, the simpleton, on the last page of the book, who had had seven kinds of intellectual shit kicked out of him in the preceding four hundred pages (in the edition I own) by the other two characters. This really reduced Urban’s argument to a joke! Not a smart move, Signore Galilei.
  • It wasn’t until 200 years later in 1835 that the Church finally stopped its prohibition of books advocating heliocentrism and not until 1992 that the Vatican officially cleared Galileo’s name of any wrongdoing.
  • The church allowed the publication of an edition of Galileo’s works, excluding the Dialogo, in 1718 just 76 years after his death. In 1741 a complete edition of his works was authorised by Pope Benedict XIV. The general ban on works advocating heliocentricity was lifted in 1758.
  • It should be noted that Galileo’s church difficulties occurred in the heart of the Renaissance. You can only imagine what it was like to be a scientist in the far more repressive Middle Ages (and how much potential scientific advancement was stifled).
  • We’re back in anti-Church bullshit city! Within the history of science Galileo’s difficulties with the Church, which he largely brought down on his own head, remain a largely isolated incident. The Middle Ages were by no means more repressive than the Renaissance and in fact much scientific progress was made during the Middle Ages, following the re-establishment of an urban culture around 1000 CE. Also it should be noted that the majority of that progress was made by members of the Catholic Church. Galileo was very much aware of the work of his medieval predecessors and built his own work on the foundations that they had constructed.
  • Some weirdo cut the middle finger off of Galileo’s corpse a century after his death, and it is currently on display at the Museo Galileo in Florence.
  • He got something right again!
  • Galileo’s dad begrudgingly allowed him to leave medicine in favor of mathematics and died a few years later when Galileo was an amateur math professor—he had no idea his son was anything special, let alone “the Father of Modern Science.”
  • It is true that Vincenzo Galilei was not particularly enthusiastic when his son abandoned his medical studies, however Galileo was never an “amateur math professor” but a fully paid professional. On the “Father of Modern Science”, see above.

2014 equivalent: Elon Musk

I find the concept of Elon Musk being the 2014 equivalent of Galileo Galilei quite simply mindboggling!

Mr Urban your term paper does not meet the required standards. Your research is to put it mildly very sloppy and personal prejudice is not a substitute for scholarly endeavour, therefore I cannot award you anything but an F!

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

 

 

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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

 

 

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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]

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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.

 

 

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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.

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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 purchase@cheapviagra.com, 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!

 

 

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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.

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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.

RaphaelHasanBadge

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

Leonardo
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

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.

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