Category Archives: Renaissance Science

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

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

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

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

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

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

Bruno 2013 Photo: Tim O'Neill

Bruno 2013
Photo: Tim O’Neill

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

A strange defence

This week saw the broadcast of the first episode of the remake of the legendary television series COSMOS, originally hosted by Carl Sagan and now being presented by Neil deGasse Tyson. Although I have now had the chance to view it thanks to the good offices of the man for all things Darwinian, Michael Barton (@darwinsbulldog), I’m not going to blog about it as Tim O’Neill, Renaissance Mathematicus reader and commentator, and fellow invincible warrior in the struggle against bad history of science,  is writing a guest post on the subject, which if all goes well will appear here on next Monday. However this post is directly concerned with one part of the show.

The centrepiece of the episode was an anime style carton on the life and thoughts of infamous Renaissance heretic Giordano Bruno. This immediately led to a raising chorus of voices on Twitter wondering what my views on this would be. Having in the mean time seen it I labelled it on Twitter an “Anime Draper-White for the Twenty-First Century”. For anybody who doesn’t know John William Draper (1811 – 1882) and Andrew Dickson White (1832 – 1918) are the two nineteenth century American academics who created the myth of a war (their term) between science and religion. A myth still unfortunately believed in by many a gnu atheist.  I’m not going to say anything more about this unfortunate piece of animated bollocks, as I’m sure that Tim will comment extensively in his guest post.

However the rest of the Intertubes has not remained silent on the issue and I can recommend the eminently sensible post on the subject by Meg Rosenburg (@trueanomalies) and the wonderfully provocative post by Becky Ferreira (@beckyferreira) “What ‘cosmos’ got wrong about Giordano Bruno, the heretic scientist, which contains the absolutely brilliant description of Bruno: “Bruno was a walking, talking shit storm, with a black belt in burning bridges”.  How I wish that I had coined that sentence!

The debate continued at Discovery Magazine with a blog post by Cory S. Powell, “Did “Cosmos” pick the wrong hero?”, in which Powell suggests that Thomas Digges would have made a better subject for the cartoon than Bruno. Personally I side with Meg Rosenburg who asks whether we need any heroes at all when discussing the history of science; a rhetorical question to which the answer is no.

Powell’s post finally provoked a response from the makers of “Cosmos” in the form of a post by Steven Soter, astrophysicist and co-writer of “Cosmos”, titled The Cosmos of Giordano Bruno (now with added response from Powell) and it is to this post that I now wish to reply, as it contains a number of very questionable statements.

In his second paragraph Soter writes the following:

Powell’s critique dwells on the well-known facts that Bruno was a mystic and an extremely difficult person. Well, so was Isaac Newton, who devoted as much time to alchemy and biblical numerology as to physics. But that has no bearing whatever on his good ideas.

I could write a whole post just about this one paragraph. First off Soter is putting Bruno a man who had one half correct cosmological idea during an intoxicating religious fantasy, that makes you wonder if he’d been hitting the magic mushrooms, with Isaac Newton who produced some of the most important new mathematics, astronomy, and mathematical physics in the history of mankind. That’s one hell of a lopsided analogy Mr Soter! Secondly as anybody knows, who is up to date on his Newton research, or who has simply read some of my blog posts on the man, Newton’s theology and his alchemy did have a massive bearing on his ‘good ideas’.

Soter then corrects Powell as to who first claimed that the universe was infinite, which to be fair Powell got wrong, although neither of them remarks that Lucretius, Bruno’s source, didn’t think of this himself but actually got the idea from the Greek atomists.

We now come to the core of the matter and the reason why Soter et al claim to have included the Bruno cartoon in their show:

Bruno’s originality lies elsewhere. He was indisputably the first person to grasp that the Sun is a star and the stars are other suns with their own planets. That is arguably the greatest idea in the history of astronomy. Before Bruno, none of the other Copernicans ever imagined it.

Leaving aside the hyperbole about ‘the greatest idea in the history of astronomy’, as he says the question is highly debateable, this paragraph still has several issues. Firstly the Greek philosopher Anaxagoras had already suggested that the sun and the stars were one and the same in the fifth century BCE, although he didn’t hypothesise the presence of other planets. Secondly if this was the real reason for including the Bruno cartoon in this episode, why was the main emphasis of the cartoon placed on the Church’s treatment of Bruno as a heretic even to the extent of presenting the Church officials as demons with red glowing eyes, I smell a rat.

If you think I’m misinterpreting the message of the cartoon I offer this comment from Meg Roserburg’s post, Albeit says:

No offense, but I think you’re missing the point here. The moral of the story, as stated in Cosmos, is: don’t let your beliefs stand in the path of reality. Bruno’s necessarily oversimplified story is just a warning about anti-science and dogmatic thinking.

Throughout the Internet you can find similar interpretations, so either the message of the cartoon was other than claimed by Soter or they really made a balls up of scripting it.

Soter than attacks Powell’s suggestion that Thomas Digges should have been featured rather than Bruno, after all he did suggest that the universe is infinite before Bruno. Soter’s argument is a little strange he writes:

But Digges regarded the stars as “the court of the celestial angels” not as the suns of other material earths. And that was a big step backwards. In contrast, Bruno wrote, “the composition of our own stars and world is the same as that as many other stars and worlds as we can see.” His profound intuition had to wait three centuries to be verified by the spectroscope.

First off Digges’ claim that the stars were the court of the celestial angels is just bog standard medieval cosmology, so in that sense is not a step backwards. Secondly Digges wrote and published earlier than Bruno, so in that sense it is also not a step backwards.

That the composition of everything in the cosmos was the same is neither new nor original to Bruno. The Stoics had believed this in antiquity and there had been a major revival in Stoic scientific philosophy in the sixteenth century making Bruno considerably less original on this count than Soter would like to see him.

Soter is also guilty here of quote mining, selecting those parts of Bruno’s fantasy that fit with our modern concepts and quietly ignoring those that don’t. This is a form of presentism known as searching for predecessors. One takes an accepted scientific idea and filters through history to see if somebody had the same idea earlier, then crying eureka and declaring the discovered thinker to be a genius ahead of his or her times. This activity can best be observed in popular histories of atomism where everybody who ever believed that matter consists of some sort of particles are all swept up into one glorious heap and declared to be predecessors of John Dalton. In Bruno’s case one has to ignore the rather inconvenient fact that he thought that the whole of space was filled with identical solar systems placed throughout space at equal intervals, a conception that doesn’t quite fit with our actually understanding of the universe.

Soter now attacks Powell for saying that neither Kepler nor Galileo thought much of Bruno. Soter mocks and ridicules Kepler for believing in a finite universe.  This is ironic given that Soter thinks it is irrelevant that Bruno produced fifty tons of shit including rejecting the use of mathematics in science because he produced one tiny little diamond of thought.

Soter then quote mines again making Kepler to a supporter of Bruno. He correctly quotes a passage from Kepler’s Dissertatio cum Nuncio Sidereo (1610) his response to Galileo’s telescopic discoveries.

What other conclusion shall we draw from this difference, Galileo, than that the fixed stars generate their lights from within, whereas the planets, being opaque, are illuminated from without; that is, to use Bruno’s terms, the former are suns, the latter, moons or planets?

Here Kepler is referring to the difference in the images of planets and stars when viewed through the new invention the telescope. Kepler would here be appearing to support Bruno’s theory and that is the impression that Soter wisher the reader to have but this is actually an illusion. Kepler says let us use Bruno’s term, he doesn’t say let us adopt Bruno’s theory. You might think I’m splitting hairs and that by adopting Bruno’s term Kepler is of course adopting Bruno’s theory but this is very definitely not the case. How can I be so sure? Because Kepler himself tells us so, he does so by evoking what is now known as Olbers’ paradox.  Kepler argues, as did Heinrich Olbers, a German astronomer, in the nineteenth century, that if the heavens were filled with an infinity of suns equally distributed in all direction, as Bruno claimed, then there would never be a night, these suns lighting up the skies twenty-four hours a day. His, incorrect but rational solution, to the paradox was that the Sun and the stars are fundamentally different and thus Bruno was wrong. Far from being a tacit supporter of Bruno’s hypothesis, as Soter would have us believe, Kepler actually refuted it with a good solid, if incorrect, scientific argument. A further irony in this situation is that Kepler was not the first to realise that an infinity of suns would lead to Olbers’ paradox, thus seeming to invalidate Bruno’s hypothesis, Thomas Digges, who hypothesised an infinity of stars before Bruno, also explicitly recognised the problem.

Having abused Kepler Soter now moves on to Galileo accusing him of plagiarism and cowardice, in the process again making a false claim:

Galileo never once mentioned Bruno’s name. Of course in the land of the Inquisition he had good reasons. But in his “Dialogue on the Two Chief World Systems” (the book that got him into deep trouble), he discretely accepted Bruno’s greatest idea, writing that the fixed stars are other suns.

Don’t let anybody tell you that being a pedantic history of science blogger is an easy life. Although I possess two different translations of Galileo’s magnum opus I don’t know it off by heart and was not aware of Galileo “discretely accepting Bruno’s greatest idea”, so I spent about four hours yesterday evening going through every single reference to star, stars or sun listed in the index to the Drake translation comparing with the Finocchiaro translation and searching for further information in five volumes of secondary literature. The only consolation for all of this effort was that I found the passage to which Soter is probably referring. On The Second Day in a discussion on the movement of the heavenly bodies Salviati makes the following observation:

Now behold how nature, favoring our needs and wishes, presents us with two striking conditions no less different than motion and rest; they are lightness and darkness – that is, being brilliant by nature or being obscure and totally lacking in light. Therefore bodies shining with internal and external splendour are very different in nature from bodies deprived of all light. Now the earth is deprived of light; more splendid in itself is the sun, and the fixed stars are no less so. The six moving planets entirely lack light, like the earth; therefore their essence resembles the earth and differs from the sun and the fixed stars: Hence the earth moves and the sun and the stellar sphere are motionless.

This passage is, like the Kepler quote above, very clearly based on Galileo’s telescopic observations of the stars and planet and their respective telescopic images and is not borrowed from Bruno. It is also clear that here Galileo is only referring to the stars and the sun both being self-illuminating, his discussion only treats of one attribute, lightness or darkness, but he doesn’t take the next step of saying that therefore they are the same. He might possibly have thought so but then again he might not. It is also clear here that with his reference to the stellar sphere Galileo s still accepting a traditional bounded finite cosmos.

I now turn to the implicit argument that Galileo didn’t reference Bruno because of the Inquisition, either through caution or, as I provocatively said above, through cowardice. This argument is not unique to Soter but has been used by numerous commentators in the Internet in the last few days. In the Roman Inquisition had, like the FBI, had a Most Wanted list, then during the first part of Galileo’s life Numero Uno on that list would have, without any doubt, been the Servite monk Paolo Sarpi (1552 – 1623).  To quote John Heilbron’s Galileo biography, “…the Servite Sarpi, would present the Vatican with a graver threat than Bruno”. During his years in the Republic of Venice, as professor of mathematics at the University of Padua, Galileo’s best mate and intellectual sparing partner was Sarpi, a fact that was publically well known. Unlike Bruno, who they regarded as a nuisance, the Venetian authorities, who were very proud of their intellectual rebel, Sarpi, who was Venetian born and bred, refused to deliver him to the Roman Inquisitions. Making him even more of a thorn in the side of the Church. Galileo’s close friendship to Sarpi was far more dangerous to his relations with the Church than any casual scientific reference to Bruno would have been. Galileo did not quote Bruno because he didn’t want to, not because he was scared of the Inquisition.

It is worth noting in this context that when Galileo applied for and was granted the position of court philosophicus and mathematicus to the Medici in Florence his Sarpian friends in Venice warned him against leaving the comparatively safe haven of thr Republic, where he was free to think and say almost anything he liked, for the shark infested waters of court intrigue and religious orthodoxy of Florence and Rome. However fame, fortune and social status were more important to Galileo than freedom of thought and speech so he ignored his friends’ warnings with the well known historical consequences.

To close this already over long post I would like to address a historiographical point related to Soter’s deification of Bruno in the history of science. Wirkungsgeschichte is a German term that refers to the historical impact of a scientific theory, invention, or discovery. Some ideas make little or no impact and disappear from the historical stage requiring them to be rediscovered at a later date. A classic example of this is the correct explanation of the cause of the rainbow. Theodoric of Freiberg discovered the correct explanation through empirical experiments in the thirteenth century. However his discovery had almost no impact and got lost, meaning that it wasn’t until the seventeenth century, when Descartes rediscovered it, that the correct explanation of the rainbow became generally known. Bruno’s lucky guess that the stars are suns or that the sun is a star had almost no impact and was largely ignored and forgotten. This makes him in a historical sense a dubious figure to elevate to the status of a scientific hero, as Soter apparently wished to do with his very strange animation in the COSMOS broadcast.

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Where does the AD/BC dating convention come from?

I was already on record as expressing scepticism about Neil deGrasse Tyson’s forthcoming Cosmos television series, as I view his knowledge of the history of science as at least as bad if not worse than Carl Sagan’s was and that was pretty terrible. Yesterday evening my Twitter stream was full of people wondering what I would have thought of N dG T’s elevation of Giordano Bruno to the status of a great scientific thinker. Fortunately I can’t view Cosmos here in Germany and so I was spared this particular piece of history of science inanity. However I came across another wonderful example of N dG T’s fantasy version of the history of science today.

Massimo Pigliucci’s Rationally Speaking has a new podcast interview, Neil deGrasse Tyson on Why He Doesn’t Call Himself an Atheist. Tyson rejects the label atheist because of the expectations that radical atheists place on him, an attitude that I can more than sympathise with. The particular trigger for this discussion was Tyson being volubly criticised for using the expression god speed in a video, which he quite rightly regards as being an imposition. In the course of the discussion Tyson then goes on to list other Christian things that he likes, uses, accepts despite not believing in the Christian God. Again I have no argument with him in this. However he then let off a minor tirade about the calendar and those who reject the use of AD/BC.

Tyson’s argument was roughly as follows, The Gregorian Calendar is a great invention and should be respected. It was a Christian invention, created by Jesuit scientist. Accept it! (A paraphrase not a direct quote) This brief outburst contains a whole series of historical errors that are unfortunately typical for Tyson.

First off his main bone of contention the origins of the AD/BC dating system has nothing to do with Gregorian Calendar. The use of Anno Domini goes back to Dionysius Exiguus  (Dennis the Short) in the sixth century CE in his attempt to produce an accurate system to determine the date of Easter. He introduced it to replace the use of the era of Diocletian used in the Alexandrian method of calculating Easter, because Diocletian was notorious for having persecuted the Christians. Dionysius’ system found very little resonance until the Venerable Bede used it in the eight century CE in his Ecclesiastical History of the English People. Bede’s popularity as a historian and teacher led to the gradual acceptance of the AD convention. BC created in analogy to the AD convention didn’t come into common usage until the late seventeenth century CE. There is a certain irony in the fact that Dionysius miscalculated the birth of Christ who was most probably born sometime between six and four BCE. Whatever, the AD/BC dating convention has nothing to do with the Gregorian Calendar, although this did take it over.

Tyson’s little outburst however contains more historical errors. The Gregorian Calendar is indeed a Christian invention but it was not created by Jesuit scientists. First off to refer to anybody who existed before 1834 as a scientist is a historical anachronism to be avoided if at all possible. Personally I’m coming to the conclusion that the word scientist should be generally avoided, as it’s a highly ambiguous word, but that is the subject for another post. The people who created the Gregorian Calendar should be referred to as astronomers. Calendar creation and calculation has been the task of astronomers since the early years of antiquity.

Unfortunately for our intrepid science communicator the Gregorian Calendar was not created by the Jesuits. The original scheme for the calendar was worked out by Aloysius Lilius (vernacular either Luigi Lilio, or Luigi Giglio) who was a physician and astronomer from Calabria in Italy. Lillius was not a cleric of any sort let alone a Jesuit. His scheme was examined, contemplated and finally recommended by a committee that met irregularly over a period of more than ten years. The exact composition of this committee is not known, as it varied over the years, but nine members signed the final recommendation to the Pope of whom only one, the least significant member Christoph Clavius, was a Jesuit. Following the introduction of the calendar by the Catholic Church Clavius, at the request of the Pope, took over the defence of the new system of time measurement against its many critics, writing six books on the subject over the next thirty odd years, thus becoming closely associated with the calendar although he did not create it.

These are all facts that are easily accessible to anybody with use of a good library or who knows their way around the Internet (hint, hint Wikipedia!) and there is absolutely no excuse for Tyson to spout his fully incorrect version of history, which will unfortunately be accepted as gospel by his army of worshipers.

Addendum: Both the Jewish and the Islamic calendars are older than the Gregorian calendar so why should these two non Christian peoples accept the AD/BC dating convention? There are other older calendars in use in India, China, Persia, same argument. Also the Gregorian calendar is only a slightly modified version of the Julian calendar, which was distinctly non Christian and it was nothing more or less than the Egyptian solar calendar in use since about four thousand BCE, again anything but Christian.

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Sliding to mathematical fame.

William Oughtred born on the 5th March 1575, who Newton regarded along with Christopher Wren and John Wallis as one of the three best seventeenth-century English mathematicians, was the epitome of the so-called English School of Mathematics. The English School of Mathematics is a loose historical grouping of English mathematicians stretching over several generations in the sixteenth and seventeenth centuries who propagated and supported the spread of mathematics, mostly in the vernacular, through teaching and writing at a time when the established educational institutions, schools and universities, offered little in the way of mathematical tuition. These men taught each other, learnt from each other, corresponded with each other, advertised each other in their works, borrowed from each other and occasionally stole from each other building an English language mathematical community that stretched from Robert Recorde (c. 1512 – 1558) who is regarded as its founder to Isaac Newton at the close of the seventeenth century who can be regarded as a quasi member.  Oughtred who died in 1660 spanned the middle of this period and can be considered to be one of its most influential members.

Oughtred was born at Eton College where his father Benjamin was a writing master and registrar and baptised there on 5th March 1575, which is reputedly also his birthdate. He was educated at Eton College and at King’s College Cambridge where he graduated BA in 1596 and MA in 1600. It was at Cambridge that he says he first developed his interest for mathematics having been taught arithmetic by his father.  Whilst still at Cambridge he also started what was to become his vocation, teaching others mathematics.  He was ordained priest in 1603 and appointed vicar of Shalford in Surry. In 1610 he was appointed rector of nearby Albury where he remained for the rest of his life. He married Christgift Caryll in 1606, who bore him twelve or possibly thirteen children, accounts differ. All in all Oughtred lived the life of a simple country parson and would have remained unknown to history if it had not been for his love of mathematics.

William Oughtred by Wenceslas Hollar 1646

William Oughtred
by Wenceslas Hollar 1646

Oughtred’s first claim to fame as a mathematician was as a pedagogue. He worked as a private tutor and also wrote and published one of the most influential algebra textbooks of the century his Clavis Mathematicae first published in Latin in 1631. This was a very compact introduction to symbolic algebra and was one of the first such books to be written almost exclusively in symbols, several of which Oughtred was the first to use and which are still in use today. Further Latin edition appeared in 1648, 1652, 1667 and 1698 with an English translation appearing in 1647 under the title The Key to Mathematics.

The later editions were produced by a group of Oxford mathematicians that included Christopher Wren, Seth Ward and John Wallis. Seth Ward lived and studied with Oughtred for six months and Wallis, Wren and Jonas Moore all regarded themselves as disciples, although whether they studied directly with Oughtred is not known. Wallis probably didn’t but claimed to have taught himself maths using the Clavis.

Title page Clavis Mathematicae 5th ed 1698  Ed John Wallis

Title page Clavis Mathematicae 5th ed 1698
Ed John Wallis

The Latin editions of the Clavis were read throughout Europe and Oughtred enjoyed a very widespread and very high reputation as a mathematician.

Although he always preached the importance of theory before application Oughtred also enjoyed a very high reputation as the inventor of mathematical instruments and it is for his invention of the slide rule that he is best remembered today. The international society for slide rule collectors is known as the Oughtred Society. I realise that in this age of the computer, the tablet, the smart phone and the pocket calculator there is a strong chance that somebody reading this won’t have the faintest idea what a slide rule is. I’m not going to explain although I will outline the historical route to the invention of the slide rule but will refer those interested to this website.

The Scottish mathematician John Napier and the Swiss clock and instrument maker Jobst Bürgi both invented logarithms independently of each other at the beginning of the seventeenth century although Napier published first in 1614. The basic idea had been floating around for sometime and could be found in the work of the Frenchman Nicolas Chuquet in the fifteenth century and the German Michael Stifel in the sixteenth. In other words it was an invention waiting to happen. Napier’s logarithms were base ‘e’ now called natural logarithms (that’s the ln key on your pocket calculator) and the English mathematician Henry Briggs (1561 – 1630), Gresham Professor of Geometry, thought it would be cool to have logarithms base 10 (that’s the log key on your pocket calculator), which he published in 1620. Edmund Gunter (1581 – 1626), Gresham Professor of Astronomy, who was very interested in cartography and navigation, produced a logarithmic scale on a ruler, known, not surprisingly, as the Gunter Scale or Rule, which could be read off using a pair of dividers to enable navigators to make rapid calculations on sea charts.

Briggs introduced his good friend Oughtred to Gunter, remember that bit above about teaching, learning etc. from each other, and it was Oughtred who came up with the idea of placing two Gunter Scales next to each other to facilitate calculation by sliding the one scale up and down against the other and thus the slide rule was born. Oughtred first published his invention in a pamphlet entitled The Circles of Proportion and the Horizontal Instrument in 1631, which actually describes an improved circular slide rule with the scales now on circular discs rotating about a central pin. This publication led to a very nasty dispute with Richard Delamain, a former pupil of Oughtred’s who claimed that he had invented the slide rule and not his former teacher. This led to one of those splendid pamphlet priority wars with both antagonists pouring invective over each other by the bucket load. Oughtred won the day both in his own time and in the opinion of the historians and is universally acknowledged as the inventor of the slide rule, which became the trusty companion of all applied mathematicians, engineers and physicist down the centuries. Even when I was at secondary school in the 1960s you would never see a physicist without his trusty slide rule.

It still seems strange to me that more than a whole generation has grown up with no idea what a slide rule is or what it could be used for and that Oughtred’s main claim to fame is slowly but surely sliding into the abyss of forgetfulness.

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Rehabilitating Simon Marius

Simon_Marius 

The Ansbach court mathematicus, Simon Marius (1573-1624) acquired a telescope in 1609 and began to make astronomical observations. These proved to be very fruitful and he discovered the four largest moons of Jupiter just one day later than Galileo Galilei. Unlike his Tuscan rival, Marius did not rush into print, the world first becoming aware of his discoveries when he published his magnum opus, Mundus Iovialis, in 1614*. This of course led to Galileo accusing Marius of plagiarism vitriolically in his Il Saggiatore in 1623. Being by now the most famous astronomer in Europe, Galileo’s charge stuck ruining Marius’ reputation down to the present day, although he was shown to be innocent at the beginning of the twentieth century.

2014 brings the four hundredth anniversary of the publication of Mundus Iovialis. To celebrate this anniversary the Nürnberger Astronomische Gesellschaft e.V. (NAG) with the active support of the municipal authorities of Gunzenhausen (his place of birth), Ansbach and Nürnberg as well as the Friedrich-Alexander-University of Erlangen-Nürnberg, the Julius-Maximilians-University of Würzburg, the University of Hamburg, the Hochschule Ansbach, the Technische Hochschule Nürnberg Georg Simon Ohm and the Max-Planck-Institute for the History of Science Berlin together with a whole raft full of sponsors and active and passive partners is presenting a wide range of activities throughout the whole year.

Today, 18th February, is the four hundredth anniversary of the signing of the dedication in the Mundus Iovialis to celebrate which the Simon Marius Internet Portal is being officially launched.

This internet presence is intended to be a guide through the anniversary year of 2014 and will bring together electronically retrievable sources, secondary literature, lectures and news on Simon Marius and – whenever possible – provide convenient links. We the initiators invite you the public to make use of this multilingual portal and also to make your own contributions.

The high point of the year will be a one day conference on the life and work of Simon Marius, Simon Marius und seine Zeit, which will be held in the Nicolaus-Copernicus-Planetarium in Nürnberg on Saturday, 20th September 2014. The proceedings of this conference will be published in book form, hopefully in 2015.

* He had already published his discovery of the moons of Jupiter in his Prognosticon Astrologicum auf das Jahr 1612however this was almost certainly only distributed locally in  Southern Germany and Galileo and the rest of the astronomical community of the period were not aware of its existence.

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Dying to make life easier for historians.

There is a clichéd view of history encouraged by bad teaching that presents the subject as the memorising of long lists of dates that somebody has designated as being significant, 55 BC, 1066, 1492, 1687, 1859, 1914 etc., etc. Now whilst in reality history is much more concerned with what happened and why it happened than with when it happened dates are the scaffolding on which historians hang up their historical facts for inspection.

When presenting biographies of scientists two key dates that the historical biographer has to remember are those of the birth and the death of her or his subject. One of my favourite Renaissance mathematici mathematics teacher, astronomer, astrologer, cartographer and globe maker, Johannes Schöner, about whom I have already blogged in the past, made life easier for historians by dying on his seventieth birthday. He was born on 16th January 1477 in Karlstadt am Main and died on 16th January 1547 in Nürnberg.  This means one only has to remember his birthdate and them simply add seventy to get his date of death.

 

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Christmas Trilogy 2013 Part III: A New Year’s Offering.

Johannes Kepler wrote more than eighty books and pamphlets covering a wide range of mathematical and scientific topics. One of the most fascinating is the pamphlet he wrote as a New Year’s offering at the beginning of 1611. We’ll let Kepler introduce it for us:

The highly regarded Court Councillor of His Imperial Majesty, Herr Johannes Matthäus Wacker von Wackenfels, Golden Knight …, Supporter of the Sciences and Philosophy, my Gracious Benefactor.

Yes, I know that especial you love nothingness; however certainly not because of its slight value but rather much more because of the joyful and charming games, which one can, with lively jest, play with this word. It is easy for me to fancy that a present for you is all the more desirable and welcome the closer it approaches nothingness.

Wacker von Wackenfels Aegidius Sadeler

Wacker von Wackenfels
Aegidius Sadeler

Johannes Matthäus Wacker von Wackenfels (1550 – 1619) was lawyer, diplomat, humanist scholar and courtier, who having worked his way up the greasy pole of Renaissance absolutist court politics had, since 1597, been a member of one of the highest legal councils at the imperial court of Rudolph II, the Holy Roman German Emperor and Kepler’s employer. Wacker was an intelligent and well educated and widely read humanist scholar and Kepler’s closest friend at Rudolph’s court and the two Johanneses very much enjoyed chewing the intellectual cud with each other. It was Johannes Wacker, for example, who first brought Kepler the news of Galileo’s telescopic discoveries. It was good manners in those time for friends to give presents to each other at New Year and the pamphlet of which I have quoted the very flowery opening paragraphs was Kepler’s New Year’s offering to his friend Wacker in 1611.

This opening is followed by two pages of the various forms of nothingness that Kepler knows his friend to already possess. We then arrive at the core of Kepler’s offering to his friend:

As I went over the bridge deep in thought and full of worry and annoyed about my poverty, that is to come to you without a New Year’s offering, always following the same thoughts, to present this nothingness, or to find something that come closest to it, and exercised the astuteness of my thoughts on it, by chance the water vapour thickened through the cold to snow, and single small snowflakes fell on my coat, all were six-cornered with feathered spokes. Yes, by Heracles, that’s it, yes a phenomenon, smaller than a drop, and thereto of regular form. Yes, that is the wished for New Year’s offering for a friend of nothingness! Just as snow falls from the heavens and looks like the stars, so it is also suitable as the present of a mathematician who has nothing and receives nothing. Now quickly bring the present to my benefactor, as long as it exists and hasn’t through body warmth disappeared into nothingness.

Snowflake photo Alexey Kljatov  The Atlantic Dec 4 2013

Snowflake photo
Alexey Kljatov
The Atlantic Dec 4 2013

Here we have the subject of the pamphlet already expressed in its title, Strena seu de Nive sexangula, in English, New Year’s Offering or The Six-Cornered Snowflake. From here Kepler sets out to investigate the question, why are snowflakes six-cornered?

What follows is a rambling, at time fascinating, at others delightful discourse not just on six-cornered snowflakes but also the hexagonal cells of a honeycomb, the shape of pomegranate seeds, the arrangement of peas in a pod, the regular Platonic solids, the semi-regular Archimedean solids, three and six petaled flowers and various other things. Kepler discusses the tiling of planes and the filling of spaces. As one aspect of the latter he considers the best way to stack canon balls to occupy the least space. He had discussed this subject in his correspondence with Thomas Harriot who had been presented with this highly practical problem by his patron and employer, Sir Walter Raleigh. Kepler’s suggested solution, for which he could offer no proof, entered the history of mathematics as Kepler’s conjecture. Hilbert included it as problem eighteen in his famous list of twenty-three unsolved mathematical problems in 1900. The American mathematician Thomas Hales finally produced a generally accepted proof of Kepler’s conjecture that relies on a computer in 1998. Hales started on a more formal version of his proof, which he estimates will take twenty years, in 2003. Great oaks do truly from little acorns grow!

The Kepler conjecture makes The Six-Cornered Snowflake an important document in the history of mathematics. This is however not its only claim to scientific fame. Although comparatively primitive it is considered the first published scientific work in the discipline of crystallography.

But what of Kepler’s question, why is the snowflake six-cornered? In the end after all his considerations and diversions he is forced to admit defeat and acknowledge that he is unable to produce a satisfactory answer to his own question.

In the seventeenth century Kepler was not the only natural philosopher to consider the snowflake. René Descartes turned his attention to them in his Discourse on the Method

Sketch of snow crystal  René Descartes

Sketch of snow crystal
René Descartes

As did Robert Hooke in his microscopical investigations, which you can read about here.

Hooke's snowflakes

Hooke’s snowflakes

The first person to successfully photograph snowflakes was Wilson Alwyn “Snowflake” Bentley (February 9, 1865 – December 23, 1931).

Snowflakes Wilson Bentley

Snowflakes
Wilson Bentley

 

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