Category Archives: Book Reviews

A little learning is a dangerous thing

“A little learning is a dangerous thing

Drink deep, or taste not the Pierian spring: 

There shallow draughts intoxicate the brain,

And drinking largely sobers us again. 

Fired at first sight with what the muse imparts,

In fearless youth we tempt the heights of arts 

While from the bounded level of our mind 

Short views we take nor see the lengths behind 

But more advanced behold with strange surprise,

New distant scenes of endless science rise!”

In a recent New Yorker essay Adam Gopnik delivered up his view of Galileo Galilei. The essay is long and meandering and I don’t intend to do a complete analysis but there is one central point of Gopnik’s that I do wish to discuss. He gets off to a lousy start by calling Galileo “The founder of modern science”. I’ve already dealt with this elsewhere and don’t intend to repeat myself here. However Gopnik returns to the theme towards the end of his essay with proof! He begins with the following:

Contemporary historians of science have a tendency to deprecate the originality of the so-called scientific revolution, and to stress, instead, its continuities with medieval astrology and alchemy. And they have a point. It wasn’t that one day people were doing astrology in Europe and then there was this revolution and everyone started doing astronomy. Newton practiced alchemy; Galileo drew up all those horoscopes. But if you can’t tell the difference in tone and temperament between Galileo’s sound and that of what went before, then you can’t tell the difference between chalk and cheese.

Those historians of science can make their claims but Gopnik, a literary critic/humourist/art critic [please choose the appellation for Gopnik that best fits your prejudices or lack of them: see comments] knows better! He has read a book!

The difference is apparent if you compare what astrologers actually did and what the new astronomers were doing. “The Arch-Conjuror of England” (Yale), Glyn Parry’s entertaining new biography of Galileo’s contemporary the English magician and astrologer John Dee, shows that Dee was, in his own odd way, an honest man and a true intellectual. He races from Prague to Paris, holding conferences with other astrologers and publishing papers, consulting with allies and insulting rivals. He wasn’t a fraud. His life has all the look and sound of a fully respectable intellectual activity, rather like, one feels uneasily, the life of a string theorist today.

Now I have read the same book and although that book is excellent it, in my opinion, suffers from a major deficiency that I actually discussed on twitter a while back with Ted Hand (@t3dy) a historian of alchemy. However before we turn to Parry’s book and its deficiency let us see how Gopnik uses it to justify his belief in Galileo’s modernity.

The look and the sound of science . . . but it does have a funny smell. Dee doesn’t once ask himself, “Is any of this real or is it all just bullshit?” If it works, sort of, and you draw up a chart that looks cool, it counts. Galileo never stopped asking himself that question, even when it wasn’t bullshit but sounded as though it might well be. That’s why he went wrong on the tides; the-moon-does-it-at-a-distance explanation sounds too much like the assertion of magic. The temperament is not all-seeing and curious; it is, instead, irritable and impatient with the usual stories.

So there we have it. Galileo may have been a practicing astrologer but he was also a questioning scientist whereas his near contemporary John Dee was just a gullible pseudo-scientist. Case closed. Galileo is different. He is the founder of modern science as claimed. Gopnik 1 historians of science 0.

Unfortunately for Gopnik reading one book on Dee, no matter how good, isn’t enough. He has fallen head first into the error illustrated by the famous quote from Alexander Pope with which this post is headed, “a little learning is a dangerous thing”. If instead he had drunk deep of the springs of Dee scholarship he would not have so confidently labelled Dee chalk to Galileo’s cheese.

What is Parry’s deficiency and why is Gopnik wrong?

To understand the problem we have to look at how John Dee’s image has changed over the centuries. In the 16th century Dee was a highly respected member of the European scientific community highly involved in mathematics, astronomy, astrology, alchemy, cartography, navigation and history. By the middle of the 17th century his star was fading fast and he was largely forgotten then Meric Casaubon published the so-called Angel Diaries, Dee’s supposed conversations with angels through the medium Edward Kelly. Through this publication of previously unknown material Dee became the archetypal Renaissance magus in the popular imagination, a dabbler in magic probably in league with the devil.

This remained the public persona of Dee right up to the beginning of the twentieth century and he became a notorious trans-continental figure turning up as the essence of sorcery in several works of fiction. In the twentieth century, however, historians began to investigate and re-assess the real historical John Dee and the role that he played in European Renaissance culture. What emerged was a very different figure from the archetypal Renaissance magus. The last forty or fifty years has seen the publication of many academic papers and a series of monographs containing biographical studies of Dee, illustrating various aspects of his highly complex character. Glyn Parry’s The Arch Conjuror of England: John Dee is the latest such biography to be published.

Parry’s book, which is excellent and highly recommended for those interested in the subject, is a well researched and minutely documented study of the role played by alchemy and magic in the European royal courts of the sixteenth century, in particular the court of Elizabeth I of England, structured around the life story of John Dee. This is not the first such study but follows in the tradition of R. J. W. Evan’s excellent Rudolph II and his World: A study in intellectual history, 1576–1612 and Bruce T. Moran’s equally excellent The Alchemical World of the German Court: Occult Philosophy and Chemical Medicine in the Circle of Moritz of Hessen (1572–1632) both of which also feature John Dee, albeit in a less central role, who was active on both courts. Both books are regarded as classics and standard works on the role of the occult in Renaissance culture and Parry’s book is a more than worthy companion but there is a minor and important difference. Both Evan’s and Moran’s books were marketed as academic books written for specialists and although Parry’s volume is equally academic his publishers have seized upon Dee’s public popularity and marketed it as a popular book. They have also, and this is the crucial point, marketed it as a biography. This marketing strategy has led Gopnik to the belief that having read Parry’s book he now knows all about John Dee but unfortunately he is highly mistaken.

Parry actually only deals with one aspect of Dee’s multi-faceted nature, his activities as a magus almost completely ignoring Dee the mathematicus and it is here that Gopnik walks straight into a trap of his own making. If instead of just reading Parry’s book he had done some basic research on Dee he would have discovered that Dee and Galileo are by no means so far apart as he would like to think.

Several times in his book Parry alludes to the fact that mathematics plays a very central role in Dee’s whole philosophy but never bothers to elucidate what or why, concentrating instead on Dee’s occult activities leading Gopnik to a totally false picture of Dee the mathematical scientist. Early in his book Parry explains that after graduating from Cambridge Dee paid two visits to the University of Leuven, in the Spanish Netherlands, one short and one substantially longer to study under Gemma Frisius and Gerard Mercator. Parry discusses the astrology that Dee studied under the two Netherlanders but makes no mention of the mathematics. In fact Frisius was one of the leading teachers of the cutting edge mathematical sciences of the age and Dee came back to Britain with the best mathematical education available anywhere in the world at the time. He introduced into Britain, which lagged far behind the rest of Europe in the development of the mathematical sciences, the newest procedures in mathematics, astronomy, cartography and navigation as well as bringing with him the newest terrestrial and celestial globes and astronomical instruments from the workshops of Frisius and Mercator. On his early journeys through Europe Dee also got to know and to learn from other leading European mathematical practitioners such as Pedro Nunes in Portugal and Federico Commandino in Italy.

In his house in Mortlake Dee set up a research centre for the mathematical sciences, which contained the largest private scientific library in Europe, including at least two copies of Copernicus’ De revolutionibus, where other interested scholars could and did come to learn and discuss the latest in mathematical knowledge. Dee’s foster son Thomas Digges wrote and published one of the first works on Copernican astronomy in English, which contained the first published partial translation of De revolutionibus into the vernacular. Another acolyte of Dee’s John Feild (sic) published, at Dee’s urging, the first ephemeris based on Copernicus’ work. Dee himself wrote the extensive preface to Henry Billingsley’s English translation of The Elements of Euclid. This preface is an important early work on the philosophy of mathematics. Dee corresponded on mathematical topics with many of the leading mathematicians and astronomers in Europe including a correspondence with Tycho Brahe on the problems of determining the parallax of moving celestial bodies, i.e. comets, a topic at the cutting edge of contemporary astronomical research. Dee was also a close friend and colleague of Thomas Harriot the greatest of English Renaissance mathematicians whose scientific discoveries easily rivalled those of Galileo but because he never published anything remained unknown and unacknowledged.

His English language preface to Billingley’s Euclid was not a one off but is symbolic for one of Dee’s most important contribution that of co-founder of the so-called English school of mathematics. As already mention in the second half of the sixteenth century England lagged behind the rest of Europe in the mathematical sciences. The first person to undertake series efforts to correct this deficit was Robert Recorde who wrote and published a series of textbooks in English covering the mathematical sciences including Copernican astronomy. After Recorde’s death Dee brought out several revised and expanded editions of those textbooks. The two of them started a tradition of English mathematics that stretched through the second half of the sixteenth century all the way through the seventeenth century up to Newton, which encompasses such important figures as William Oughtred, Seth Ward, John Wallis, Christopher Wren and even Newton himself.

Far from being the naïve magician that Gopnik imagines him to have been John Dee was acknowledged and recognised as one of the leading European mathematical practitioners in the third quarter of the sixteenth century. Whose mathematical heritage echoed all the way through the seventeenth century and the creation of modern science.

Contrary to the commonly held myth Galileo did not invent modern mathematical science but built his research on a solid foundation a Renaissance mathematical advances that goes back all the way to Georg Peuerbach and Regiomontanus in the middle of the fifteenth century. One of the Renaissance mini-giants on whose shoulders Galileo and his contemporaries constructed their contributions to the evolution of modern science was John Dee. Far from being the contrast obsolescent model to Galileo’s shiny new show room model as Gopnik would have us believe John Dee, in his own way, contributed as much to the creation of modern science as Galileo himself.


Filed under Book Reviews, History of Astrology, History of Astronomy, History of Cartography, History of science, Myths of Science, Renaissance Science

Science in Antiquity: A book review

In the last few weeks everybody else has been nominating books of the year or recommending books for Christmas so I thought I would follow the trend and at the same time try to improve my somewhat negative image by actually writing a positive book review. In fact this is not a review of one book but of a whole series of seven books, The Routledge Sciences of Antiquity series. These books are not new but have been available for some years now although one of them saw the release of its second expanded edition on the 1st of November this year. The books are, in no particular order, Ancient Natural History by Roger French (who was before his death also the original general editor of the series), Time in Antiquity by Roland Hannah, Ancient Astrology by Tamsyn Barton, Cosmology in Antiquity by M. R. Wright, Ancient Mathematics by S. Cuomo, Ancient Meteorology by Liba Taub (who is the current general editor) and finally Ancient Medicine by Vivian Nutton. I now own five of the series only missing the volumes by Taub and Hannah, which are high up on my book purchase list, so if anybody wishes to buy The Renaissance Mathematicus a Christmas present…

I’m not going to do a blow-by-blow account of all the five volumes that I do own but I’ll start with some general comments about Nutton’s Ancient Medicine, which was the one whose second edition appeared this year. Nutton is one of the leading English historians of medicine and a great expert on medicine in antiquity and especially Galen. This book, which became a standard work on the subject when it first appeared and an instant classic, is now even better in its improved second edition. If you are a student of the history of medicine and this book is not on your bookshelf then something is seriously wrong with your book buying policy.

This brings us to the intended or potential readership for this series. In his general introduction to the series Roger French writes the following:

The purpose of this series of volumes is to provide the reader who is not necessarily a classical scholar with a broad view of some areas of ancient interest to which the term ‘science’ has customarily been attached.

I personally would see the potential readership in undergraduate and postgraduate students of general history, philosophy and both the history and philosophy of science. Of course any reasonably well read scholar with a general interest in antiquity could and would benefit from reading one or more of the volumes in this series. I personally find them very useful as a slightly more advanced historian of science whose area of expertise lies somewhere else (the Early Modern Period) but who vainly attempts to maintain a broad and general picture of the whole of the history of science. A hopeless endeavour but one that I think all historians of science should follow to some extent.

All of the books that I possess in this series are excellently written by top experts in their field (an appellation that also applies to both Hannah and Taub whose volumes I don’t possess) in a style that makes them accessible to the reasonably educated general reader. All of them also posses a full academic apparatus of endnotes (I still prefer footnotes), extensive bibliography and index making it possible for the reader to deepen their knowledge of any points that catch their interest.

One particular aspect of the series that for me increases their value is that they are not standard re-iterations of the supposed facts and myths of the subjects with which they deal but are up to date reassessments of what is known presented in context. French writes:

The ancient material used by philosophers and other in later periods is here described in its ancient context. But the needs of the modern reader, who may want information on one particular area of the sciences, has been kept in mind.

These two purposes, to give ancient ‘science’ in its context and to direct the reader’s attention to fields of study that he recognises, coincides with a fresh look at ancient ‘science’.

This fresh look is wonderfully illustrated for me by Cuomo’s volume, Ancient Mathematics a subject in which I had read extensively before I came to her book. Books on mathematics tend to be strongly internalist dealing with which theorems were first discovered by whom and also often dangerously speculative stretching the often very small set of real facts available, mostly without informing the reader that this is the case. Cuomo’s book is wonderfully contextual giving all of the sources where mathematical knowledge was not only produced but also used and discussed in antiquity whilst continuously reminding the reader just how thin the blanket of available facts really is. A wonderful corrective to all those books that go on for pages about the achievements of one or other of the Greek mathematicians from whom we have absolutely no extant works and whose appearance in the oft many centuries later works of others are at best scant. I heartily recommend this book to anybody who thinks they already ‘know’ about mathematics in antiquity. It’s is startling to discover how much of our standard ‘knowledge’ repeated in numerous reference works is at the best dubious and often plain myths.

If you are looking for a last minute gift for the historian or philosopher of science in your life then one or other of the volumes in this series would I’m sure be gratefully received. One small word of warning whilst the paperbacks are, whilst not cheap, reasonably priced for academic books of this quality the hardbacks are exorbitantly expensive.



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Filed under Book Reviews, History of science

Phrases in the history of science that should be abolished, banned, forbidden, eradicated, annihilated, obliterated, eliminated, jettisoned, extirpated…

Patricia Fara has written a new biography of Erasmus Darwin, Charles’ paternal grandfather and a significant eighteenth century intellectual figure in his own right. Ms Fara is an excellent historian of science and a skilful and entertaining writer whose books are usually to be recommended. Rebekah “Becky” Higgitt also tells me that she is an excellent teacher but I digress. I for one welcome this publication and look forward, in the fullness of time, to acquiring a copy and reading it. So I was pleased when I stumbled across the article on the Oxford University Press’ blog advertising it. Pleased that is until I read the phrase out of the text used as a header for the article:

Erasmus Darwin’s views on evolution, politics and religion were so controversial that he was written out of history [My emphasis] for nearly two centuries.

I don’t know about you but the phrase “written out of history” evokes in me images of George Orwell’s 1984 and the re-writing of the history books, newspapers etc. every time the countries involved in the global war switched alliances. Or maybe those Stalinist era Politburo Mayday Parade photographs in which prominent politicians have been airbrushed out because they have, in the meantime, been shipped off to the Gulag for some real or imagined offense against the ruling party.

Whatever else might have happened to him in the last two hundred plus years, dear OUP, Erasmus Darwin has at no time been “written out of history”. If you mean that, in your opinion, he has not received the attention that he deserves from historians then say so, but don’t try to express your opinion in some sort of meaningless and completely false hyperbolic bovine excreta.


Filed under Book Reviews

Dava Sobel tries her hand at historical fantasy.

Dava Sobel’s Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time is almost certainly the most successful popular history of science book published in the last fifty years. This is to some extent understandable as it is a well written enthralling tale of one mans battle against the establishment to solve a great scientific challenge, the determination of longitude at sea. It suffers however from a major flaw, it is a distortion of the real history it is claiming to relate. Sobel makes this tale of a complex episode in the history of science into a struggle between good, represented by John Harrison, and evil represented by Nevil Maskelyne, a severe distortion of the historical facts. To discover more about what really took place I recommend reading the posts at The Board of Longitude Project Blog, my concern here is Sobel’s latest history of science outing A More Perfect Heaven: How Copernicus Revolutionized the Cosmos.

When I first read her Longitude I was very impressed by the story that she told about a period and a development in the history of science about which I then knew very little. Unfortunately for Ms Sobel I was so impressed that I decided to investigate further and started to acquire and read the academic literature on the subject and fairly quickly learnt that Sobel’s version of the story was anything but accurate. Having made this experience I was more than sceptical when I first discovered that Sobel had chosen the life and work of Copernicus as the subject for her latest book. I feared that she would make a mess of it and unfortunately my fears have been confirmed. One can get a first impression of how Sobel deals with the subject from an interview she gave about the book earlier this year in Cosmos.

Cosmos: What is A More Perfect Heaven about

Sobel: It’s about Copernicus and how he was talked into publishing his crazy idea, heliocentrism. It was an idea he developed in his youth and told only a few people about and promised he would write a book on the subject. He eventually did, but he worked on the book for decades and became increasingly fearful he would be laughed at and that people would use the Bible to claim his idea was irreligious.

Here we have Sobel repeating the old myth that Copernicus didn’t want to publish because he feared the religious reaction; this has been dismissed by historians of science for decades. Copernicus didn’t publish because he couldn’t deliver. In his Commentariolus he had claimed he would provide proof that the world (read universe or solar system) was heliocentric. He was nowhere near being able to deliver that proof and that is why he hesitated to publish his book.

Sobel: He seems to have decided not to publish it, but then he was surprised to get a visit from a young German mathematician, a brilliant man called Rheticus, who was a colleague of Martin Luther. Rheticus was on a self-improvement journey and he learned about Copernicus’s work while in Nuremberg, so he went off to see him – a journey of 500km. Copernicus’s region of Poland was Catholic, and the bishop had banished all Lutherans, so when this fellow showed up it was a conflict on several levels.

Except in the formal sense that they were both professors at the same university Rheticus was not a colleague of Luther’s and the suggestion that he was is part of Sobel’s disinformation tactic.

Sobel: I remember learning that story in 1973 – the 500th anniversary of Copernicus’s birth. There was an article by science historian Edward Rosen in a magazine called Sky and Telescope, and I remember thinking what a great play it would make. The characters are different in every way, but they came together on this one idea and somehow Copernicus managed to keep them there for two years, and Rheticus helped him complete the book.

Here we have the core of Sobel’s distortion of history, which I will deal with later but I find it significant that Sobel bases her work on a source that is anything but up to date or accurate for that matter.

After a lot of hesitation as to whether I really wanted to waste my money on a book that I was fairly certain was not very good I finally succumbed and bought the Kindle edition. Sadly, to have my worst suspicions confirmed.

The book is in three sections. The first is a conventional biography of Copernicus, which however doesn’t really deal with his astronomy. The second, and major, part of the book is written in the form of a play and is a fictional reconstruction of what occurred between Copernicus and Rheticus when the latter visited Frauenburg and persuaded the reluctant author to part with his manuscript and allow it to be published. The final part deals with the reception and further developments of the heliocentric hypothesis, Kepler, Galileo etc.

The biography at the beginning of the book is actually quite good although given the nature of the material it is anything but scintillating. Sobel deals with the material well and presents a rounded picture of Copernicus the political administrator and physician, which is what he was. There is nothing new here but as there isn’t a good modern English language biography of the man it might have made for a good book if not for the following section. My only quibble with the first section is that Sobel keeps emphasising Copernicus’ astronomical observations as if they were highly significant. This was not the case. In fact Copernicus made comparatively few observations in his forty odd years as an active astronomer and most of those that he did make were of a comparatively trivial nature. He was not an observational astronomer he was a theoretician.

It is with the second, central, part that the book unravels very spectacularly. Sobel claims to be writing historical fiction in this section, creating a plausible reconstruction of what took place between the two mathematicians during their time together, a period that we know very little about. However what she has produced could at best be called historical fantasy, although the use of the word historical here is very much stretching the point. What we have is a collection of ahistorical cardboard cut out figures spouting soap opera dialogue that is at time so bad it’s embarrassing.

The problems start with the opening scene where Copernicus comes home to find the newly arrived Rheticus sleeping on his doorstep. Rheticus is presented as a sort of naïve, simpleton, teenage astronomical groupie who has just hitch-hiked in from Wittenberg in the clothes he is standing up in and with a bag slung over his shoulder to pay his respects to his hero Copernicus. Historically plausible? Like hell it is. Although relatively young, 25, and given to hero worship Rheticus was the independently wealthy son of a minor Italian aristocrat who was professor of mathematics at a leading European university that was a major centre of humanistic learning. He was travelling with a servant and alone the folio editions of the books that he had brought with him, as a gift for Copernicus would have required the services of a pack mule if not a horse. He in fact checked into a hostelry like any other wealthy and educated visitor and sent a message to Copernicus requesting an audience. Sobel now proceeds to play the religious card for all that it’s worth repeating a standard myth that because we are in the middle of the Reformation and Rheticus is a Lutheran Protestant from Wittenberg visiting a Catholic Prince Bishopric that some how his life must be in danger. What we have here in reality is actually an interesting historical phenomenon because throughout the Reformation and Counter Reformation scholars, who weren’t fire breathing preachers, were treated with consideration and respect on both sides of the divide. As long as they kept their noses out of religious affairs they were free to come and go and to correspond as they pleased. All of the time that Rheticus spent in Ermland he was treated, as what he was, an honoured scholarly guest. Before moving on there is one minor point that relates back to those observations. The naïve groupie on being allowed to view Copernicus’ manuscript asks, so many observations did you make them all yourself? Well no, the vast majority of the observations used in De revolutionibus are taken from other sources. As I said Copernicus was a theoretician not an observer.

The situation in Sobel’s mini-drama gets even worse when we come to Copernicus and the Bishop of Frauenburg. Here we get a repeat of the Longitude scenario with Copernicus presented as a wise and caring saint, a sort of Prussian Albert Schweitzer, who hides the Protestant groupie in his attic like a sixteenth century Anne Frank. As I’ve already pointed out there was no need what so ever for Rheticus to hide anywhere. Even worse is Sobel’s vision of the Bishop of Frauenburg, he, who is never given a name, is presented as a snivelling, paranoid, anti-science cretin, who is determined to bring about the downfall of both Copernicus and his book. A fair representation? Like hell it is.

The real life Bishop of Frauenburg at the time of Rheticus’ visit was Johannes Dantiscus an acknowledge humanist scholar and a crowned poet laureate. He had served for many years as a diplomat for various kings, emperors and princes throughout Europe before entering the church and maintained an extensive correspondence with many leading European scholars. He had personally met Phillip Melanchthon, Rheticus’ superior and mentor, respected him as one of the most learned men of the age but regretted that he was a Protestant. One of his correspondents had been Johann Reuchlin Melanchthon’s uncle and the leading humanist Hebrew scholar in Europe. Dantiscus was a cultivated, highly educated and very knowledgeable man. Far from being anti-science and trying to block Copernicus’ work he sent a copy of Rheticus’ Narratio Prima, the first published account of Copernicus’ heliocentric hypothesis, to Gemma Frisius in Leuven and tried to persuade him to come to Frauenburg to work together with Copernicus. The real Bishop of Frauenburg didn’t fit Sobel’s simplistic fairy tale of saints and demons and religious and scientific persecution so she invented a completely fictional character who bears no resemblance to Johannes Dantiscus.

All of this would be all well and good if Sobel wasn’t claiming to be producing a plausible reconstruction of what took place in Frauenburg between 1539 and 1541.  However what she presents has absolutely nothing to do with the known facts and whatever did take place was certainly nothing like Sobel’s warped distortion of history.

Reading the third section of the book I got the impression that this was filler material added to bulk out a rather thin volume. It is a very uninspired retelling of standard myths and falsehoods about the history of heliocentrism between 1543 and 1630, which contributes absolutely nothing towards redeeming a truly bad book. If you were thinking of reading or even buying this book save your time and money it’s not worth either the cost or the effort.



Filed under Book Reviews, History of Astronomy, Renaissance Science

When you’re in a hole, stop digging!

Somebody made a comment at Scientific American on Ken Shulman’s article pointing to my criticism and providing a link. Not unexpectedly, Mr Shulman has reacted and posted a sort of defence of his excruciating piece on the history of astronomy. He did not join the comments column here to post his retort but did so under his article at Scientific American. As I have no desire to register at Scientific American in order to be allowed to respond I have transferred the whole of Mr Shulman’s latest screed here where I shall subject it to the same careful analysis with which I rewarded his original effort.

Thony Christie’s writes that words fail him, but in truth they merely betray his as rash and mostly wrong.

Yes! Slapdash, ill considered, rash and without a doubt wrong! Guilty as charged your honour. Somebody spends a long-time and expends a lot of effort carefully analysing why your text is factually wrong and the best you can do Mr Shulman is to dismiss it as rash! A rather weak level of criticism for a professional journalist. However you do go on to make some specific comments; let’s see what you think I got wrong. Before doing so I would point out that you have only answered some and by no means all of my criticisms. Does that mean all the others are right?

For starters: 

Cambridge University records show Jeremiah Horrocks entering Emmanuel College on May 18, 1632 as a sizar–a student who supplemented his tuition by performing menial tasks. Why would a wealthy father subject a gifted son to this indignity? And as far as the nature and location of Horrocks’ observatory, we can only speculate, although they were clearly not as elaborate as Tycho’s.

The Horrocks-Aspinwall clan, his mother was an Aspinwall, were strict and active puritans, which also explains why he studied at Emmanuel College Cambridge, as this was the leading Puritan educational establishment of the age. Given their beliefs and their moral attitudes it would in fact be more than probable that they would expect their son to work his way through college. There is another very good example of another leading seventeenth century British astronomer with a Puritan background entering Cambridge as a sizar, although his family were wealthy, Isaac Newton. Before anybody says that he was only the son of a farmer I will point out that when Newton inherited the family estate after the death of his mother it generated an income of £600 p.a. This at a time when the annual income of John Flamsteed, the Astronomer Royal, was only £100. Newton’s family could more than afford to pay for his studies.

You were the one claiming to know that Horrocks observed from a cottage. I pointed out that his place of observation is not known. It is however known that Horrocks did not possess or use an observatory, again as I have already pointed out, just like nearly all of his fellow contemporary astronomers.

The device Gassendi used during the 1631 transit of Mercury is properly defined as a camera obscura.

I would direct your attention to the exchange between Rebekah “Becky” Higgitt and myself at the start of the comments to my post criticising you article. It is a debatable point of terminology, as to whether the sun focussed through a telescope should be referred to as a camera obscura or not. Kepler who coined the term camera obscura would almost certainly have said no, as he discriminates in his writings between camera obscuras and telescopes. This, as I have already pointed out in my remarks in the comments, is not the central point of my criticism. Due to your form of expression you definitely imply, intentionally or unintentionally (and I’m not sure, which is worse) that Gassendi’s mode of transit observation was different and inferior to Horrocks’. As I pointed out it wasn’t they both utilised the same method of observation.

Keeping track of dates can be difficult for one who straddles centuries. Every author deserves at least one mulligan. I offer one here for Mr. Christie. Copernicus published De Revolutionibus in 1543 (although he had circulated draft versions of his heliocentric theory to friends and colleagues on or before 1514.) Both dates fall well within the 16th century. Again, the 16th century. Kepler worked with Tycho Brahe in 1600, published Astronomia Nova in 1609,and his third law in 1619. His major contributions all occur in the 17th century, the one in which Kepler lived from age 28 until his death in 1630. 

Keeping track of dates is the bread and butter of historical research. I’m quite happy to admit that my original comment on the short centuries in the Early Modern Period was a cheap shot that I would not normally have taken if the rest of your article were not so atrocious. However I find it somewhat strange that you now admit that I’m right whilst at the same time trying rather lamely to justify yourself. You claimed incorrectly in your article that Tycho and Kepler worked together in the 1590s, which I corrected and despite the fact that I supplied you with the right information you still get it wrong. They only worked together in 1601. If we are going to be picky Kepler published his Mysterium Cosmographicum, which he considered, right up to his death, to be his most important work in 1596 so not all of his major contributions occur in the seventeenth century.

Sure, Copernicus explained retrograde motion. So did Ptolemy, and Aristotle. They just didn’t explain it right. Of course the heliocentric model is light years better than those with jury-rigged epicycles or nesting spheres to illustrate why planets seem to move backwards in their orbits. But the phenomenon of retrograde motion wasn’t fully understood until Kepler.

We now come to the reason for the title of this post. You, Mr Shulman are deep down in a hole and don’t realise it and so go on digging like the Duracell Bunny*. It was this, quite frankly, bizarre claim that led me to criticise your article in the first place and you go on insisting that it’s correct. Just for your benefit a short discourse on the cause of retrograde motion and its explanation.

Retrograde motion is an illusion observed in heliocentric planetary systems. All planets travel in the same directions on their orbits but inner planets travel faster than outer planets. When an inner planet overtakes an outer planet the outer planet first appears to halt then to reverse its direction of travel, to stop again and then continue in the original direction. These apparent loops are retrograde motion and are as I say an illusion. The Eudoxian homocentric system, which was the one propagated by Aristotle and the Ptolemaic deferent epicycle system, both of them geocentric, produced geometrical models that were capable of reproducing the retrograde motion but not of explaining it. All heliocentric systems automatically explain retrograde motion irrelevant of the shape of the orbits. Copernicus’ system completely explains retrograde motion and none of the changes that Kepler introduced in his heliocentric system added anything to that explanation. If you can’t or wont accept that then you definitely should not be writing about the history of astronomy.

As far as Galileo goes, my bad. Mr. Galilei worked with the 10x scopes in 1608. By 1610, during his observation of the phases of Venus, he did have a 30x. And it is true that in 17th century astronomy the known bodies were referred to as stars. But these bodies were divided into two categories: Galileo himself refers to fixed stars (still known as stars,) and wandering stars (known today as planets) in Sidereus Nuncius. In a 1610 letter to Cosimo II, Grand Duke of Tuscany, he refers to the moons of Jupiter as planets, and later as Medician stars. I’m happy to parse the language further, but the matter here is that Galileo’s observations of the phases of Venus confirmed that Venus orbited the sun and was, just like the earth, a planet. 

The Duracell Bunny* is still shovelling away with no regard for the depth of the hole. The status of Venus as a wandering star, i.e. planet (Greek for wanderer), had never been in doubt since sometime deep in antiquity and your claims that Galileo proved it was a planet and not a star are just ridiculous. Your last half sentence also displays a lack of historical sensitivity as when Galileo, Harriot, Lembo and Marius observed the phases of Venus the Earth was not regarded by the majority of astronomers as a planet; it didn’t wander but sat at the middle of the universe. Turning the Earth into a planet is the essence of the so-called Copernican Revolution, which didn’t become the accepted majority view amongst astronomers until after 1660.

I don’t think I’m telling Mr. Christie anything he doesn’t already know. But I will tell him if he cares as much about the stars and the truth as he professes to, he certainly should know better.

Unlike yourself Mr Shulman I do know better and as a historian of astronomy I actually know what I’m talking about something that could not be said about yourself on the evidence available.

* My readers, who are much better informed than I am, have told me that the “Duracell Bunny” is known as the “Energizer Bunny” in the US of A.


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

Scientific American craps out.

Just in case you haven’t noticed yet next Wednesday an astronomical “once in a lifetime” “event of the century”, a transit of Venus, will take place. This has naturally provoked a flood of media interest resulting in lots and lots of reports running the gamut from good to totally miserable with the average, from the history of science standpoint, tending to ropey at best. Under normal circumstances I might have taken one or the other of these articles to task here but as I was busy writing my own Transit of Venus article, for a local astronomy society journal, and public lecture, held last Wednesday in Nürnberg, I didn’t really feel like blogging about it as well. However the appallingly bad book extract on the subject posted yesterday on the Scientific American website made me change my mind. Just how bad is it? This post is a very serious candidate for the worst piece of history of science writing of the year. In fact any competitor is going to have to try very, very hard to beat it for this title.

The piece in question is titled The Man Who Knew Venus Would Transit the Sun and is an excerpt from a book entitled Venus in Sole Visa by Ken Shulman. Some simple advice for my readers, “Do not read this article! Do not buy this book!” It is a total waste of both your time and your money and an insult to your intelligence. As is my wont on such occasions I will reproduce passages from the offending article and then point out the errors contained there in.

The article deals with the prediction and observation by the young English astronomer Jeremiah Horrocks of the Transit of Venus in 1639, a worthy and important subject for a history of astronomy article. The author starts with a bit of biographical background:

Son of craftspeople and perhaps farmers—there were also a few watchmakers among his forbears—Horrocks had been a local wunderkind who entered Emmanuel College in Cambridge at age 14 as a sizar—a poor student whose duties, along with studies, included the preparation of meals, waiting on tables, and custodial work. In 1635, three years after his arrival, Horrocks left the university—in all probability due to lack of funds–and returned to Lancashire, where he continued to observe the heavens with a small telescope he either purchased or received as a gift from one of the landed families whose children he tutored.

There were not just watchmakers amongst his forebears; Horrocks’ own father was a watchmaker. Although his future development definitely shows that Horrocks was an extremely intelligent young man there is no historical evidence what so ever to support the claim that he was recognised as a “wunderkind” or child prodigy. If as I suspect, due to the juxtapositioning, the author is inferring this from the fact that Horrocks entered Emanuel College at the age of 14 then he is mistaken; throughout the Early Modern Period 14 was the normal age for university matriculation. Horrocks did indeed leave the university in 1635 without graduating but we don’t know why. The claim that it was probably due to poverty is a myth created in the nineteenth century. This claim is highly unlikely as Horrocks’ family were known to have been wealthy, his entering university as a sizar was probably due to puritan ethics rather than financial necessity, and such a radical change in their circumstances would probably have been documented. We know that he purchased his first telescope, for 2s. 6d., himself because he says so in his correspondence. By the time he observed the transit he had acquired his third telescope, an above average model according to his own account. All of this is, of course, just nit picking but we have only just started; it gets worse, much worse.

Having dealt with the biographical we now move on to the astronomy of the period, to Kepler, Brahe and Copernicus:

The revolutionary discovery was Kepler’s, and would be his most memorable contribution to science. One century before Kepler, Nicolas Copernicus stated that the sun—not the Earth—was the center of our planetary system. Heliocentrism helped astronomers reconcile cosmic theory with the real-life cosmos they saw before them. Yet there were still many phenomena that Copernicus’ bold shift did not explain: retrograde motion—the apparent backtracking of planets—was one; others included eclipses and planetary conjunctions that should not have occurred if the Copernican model of the solar system was accurate.

Copernicus’ De revolutionibus was published in Nürnberg in 1543. Johannes Kepler was born in 1571. I didn’t realise that centuries were so short in the Early Modern Period.

Yet there were still many phenomena that Copernicus’ bold shift did not explain: retrograde motion—the apparent backtracking of planets—was one…

History of Astronomy 101:

Question: What is the principle feature of Copernicus’ heliocentricity that increases its explanatory power as a theory of planetary motion in comparison to the geocentric theory of Ptolemaeus?

Answer: It provides a natural explanation for retrograde motion.

In case any of my readers don’t recognise the enormity of the authors mistake here and why it completely disqualifies him to write about the history of astronomy it’s as if a football writer would say that Germany won the World Cup Final against England in 1966 or a historian would write that Charles I won the English Civil War against Cromwell.

…others included eclipses and planetary conjunctions that should not have occurred if the Copernican model of the solar system was accurate.

The sentence quoted above is just mind bogglingly stupid. I’m not even sure what it’s supposed to mean. Whatever it is it is just plain and simple rubbish.

Kepler intuited that these discrepancies were due to the true shape of planetary orbits.

No he didn’t! First of all, the “discrepancies”, as quoted above, are a figment of our author’s imagination. Secondly, Kepler was initially only concerned with the accurate size and duration of the planetary orbits; he only stumbled across his shape changing innovations during his analysis of the orbit of Mars.

After a prolonged and trying period analyzing Brahe’s data (Kepler gained access to Brahe’s figures while working as Tycho’s assistant in Prague in the 1590′s,) Kepler concluded that Mars traveled around the sun in an ellipse and not in a circle.

Tycho and Kepler first met in 1600. They didn’t start working together until 1601; a partnership that was very short, as Tycho died in the same year.

Horrocks cottage observatory in Much Hoole was a far cry from Tycho Brahe’s palatial skylabs in Denmark and Bohemia

It is not actually known from where in Much Hoole Horrocks observed the 1639 Transit. However the house that is traditionally assumed to have been his “observatory” is a three-story country mansion and not a cottage.

But Horrocks was not delusional. In 1610, Galileo had used a telescope of just 10x magnifying power to confirm that Venus was a planet and not a star; the finding cast the nature of the entire universe into doubt. In 1631 Pierrre (sic) Gassendi had successfully observed a transit of Mercury with a makeshift camera obscura he’d mounted in a spartan (sic) Paris garret.

Galileo was using 20x and 30x telescopes in 1610 to observe the heavens and we can assume, given his comments about the superiority of his instrument, that Horrocks was probably using a 30x telescope for his transit observations. Gassendi used a telescope to project the image of the sun onto a scaled sheet of paper to observe the 1632 Transit of Mercury and not a camera obscura; the same technique employed by Horrocks for his transit observations.

…to confirm that Venus was a planet and not a star; the finding cast the nature of the entire universe into doubt.

Words fail me! In seventeenth century astronomical terminology all heavenly bodies are stars but the seven planets, Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn, were planets and had been since the Greeks coined the word. What Galileo, as well as Marius, Harriot and Lembo all independently, discovered telescopically was that Venus has phases like the Moon; phases of a type that proved that Venus orbits the Sun and not the Earth. Again this is an error is on a level that completely disqualifies the author from writing on the subject.

It wasn’t that the German’s math was flawed, Horrocks saw. It was that Kepler had misunderstood the nature of the force that causes the planets to travel around the sun in ellipses. Kepler believed the sun first pulled the planets toward it, and then, when they were close, repelled them. This alternating push and pull, according to Kepler, was the force that generated the elliptical orbits. Horrocks believed this was wrong, and that the error had skewed Kepler’s calculations. 

The Englishman was a very unlikely challenger for such a heavyweight. Kepler had studied with the finest professionals of his day, had enjoyed royal patronage, and had access not only to Tycho’s magnificent data set but to his equally magnificent facilities. In contrast, Horrocks was a poor university dropout working in a remote provincial town that most likely did not even have a library, let alone an observatory. His mind, of course, was keen. But it was also a mind that worked in almost total isolation, and in a country that had never attributed great importance to the study of the stars.

Kepler, in fact, only had one teacher, Michael Maestlin, who was however one of the leading European astronomers of the age. He did have Tycho’s data but so did Horrocks in the form of the Rudolphine Tables. Kepler didn’t have access to Tycho’s facilities as these belonged to Tycho’s heirs who sold them off after his death. He didn’t however need them, as he was a theoretical astronomer and not an observational one. Kepler’s royal patronage was a curse rather than a blessing as his employers seldom paid him his retainer and he spent almost all of his life fighting debt and poverty. We don’t know which books Horrocks actually owned but it is very clear from his papers that he knew and had studied all of the leading astronomical literature of the period. Very few working astronomers in the first half of the seventeenth century had or used observatories. Their few instruments were all highly portable and they just carried them to wherever they wished to observe, set them up and observed. Horrocks’ observation conditions were no different to those of Galileo, Thomas Harriot, Simon Marius or many others who wrote astronomical history in this period and to claim otherwise is misleading pathos. Far from being isolated Horrocks was a close friend of John Wallis one of the leading mathematical scholars of the age. He also corresponded extensively with the Gresham Professor of Astronomy Henry Gellibrand and his successor Samuel Foster both of whom were integral members of the English mathematical community of the time.

Still, Horrocks continued to trust his own eyes and his intuition. He constructed a pendulum and studied its Earthward and upward swings; from this simple experiment he concluded that a planet, left to its own devices, would always travel in a straight line. And that the sun, conversely, would attempt to cause the planet to revolve around it in a circle. (Horrocks’ description of the dynamic between sun and planet is very close to the force that his compatriot Isaac Newton would identify as gravity some four decades later.) It was the ongoing dialogue between these two forces, Horrocks concluded, that dictated the elliptical orbits, not the push me–pull you sun of Kepler’s cosmos. More importantly, it was this difference in dynamic that accounted for the inaccuracies he’d found in the Rudolphine Tables.

The distinction between the theories—and the distortions that distinction might produce—was minor, Horrocks knew. But scaled against the solar system, at distances that could be cadenced in thousands of Earth radii, it was just large enough to turn a non-event into a full-blown transit of Venus. Kepler’s Rudolphine Tables had Venus passing just above the sun on November 24, 1639. Horrocks predicted that Venus would pass in front of the sun, just as it had eight years earlier.

Horrocks did indeed develop an alternative theoretical model to Kepler’s to explain the planetary orbits but he did not use a pendulum to do so. (His theory is however much, much further removed from Newton’s theory of gravitation than the author suggests)  In order to explain his model he made a verbal analogy to the movement of a pendulum. These differing models have absolutely nothing to do with the numerical errors in the Rudolphine Tables or Horrocks’ corrections of them. Horrocks discovered the errors through empirical observations, he was using a telescope Tycho’s observations the basis for the tables were naked eye observations, and he made the necessary corrections based on those observations.

This book extract presented by a university student as an essay in a history of astronomy 101 course would earn a big fat F and the suggestion that the student should perhaps choose another minor. If the course were his major then he would have really big problems. Published on the website of one of the worlds leading popular science journals it is nothing short of a scandal and an insult to every serious historian of science working in the world today.







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

Mapping the history of triangulation

One of my interests as a historian of practical mathematics is the history of the invention of triangulation and its applications in both cartography and geodesy, a subject on which I have, in the meantime, read a small library of academic books and papers. Now, at first glance, it would seem that the measuring of large triangles across the landscape is not the sort of exciting scientific endeavour that would inspire an author to put pen to paper or fingers to keyboard to produce a work of popular science history, however appearances can be deceptive. I possess five popular historical volumes on the application of triangulation to the solution of geodetic and cartographic problems, of which I have read the first three They are John Keay, The Great Arc: The Dramatic Tale of How India was Mapped and Everest was Named, HarperCollins, 2000, Ken Alder, The Measure of All Things: The Seven Year Odyssey and Hidden Error That Transformed the World, Free Press, 2002, Rachel Hewitt, Map of a Nation: A Biography of the Ordnance Survey, Granta Books, 2010, Larrie D. Ferreiro, Measure of the Earth: The Enlightenment Expedition that Reshaped the World, Basic Books, 2011 and Paul Murdin, Full Meridian of Glory: Perilous Adventures in the Competition to Measure the Earth, Copernicus Books, 2009. The first, as the title says, deals with the measurement of the meridian arc in India in the 19th century and the resulting mapping of this sub-continent. The second deals with the re-measurement of the meridian arc in France to determine the basic unit of the metre for the metric system in the late 18th century. The third is self-explanatory but also includes the measurement of a meridian arc in Britain. The last two deal with the history of the measurement, mostly by the French, of meridian arcs in France, Peru and Lapland to determine whether the earth is a prolate or an oblate spheroid, a story that I have already blogged about.

Given the fact that triangulation is a very major, or even the major, player in all of these books one could as reader expect the authors to have researched and in their respective books to explain the historical origins of this technique or methodology. This expectation is not really fulfilled. Let us examine what each of them has to say on the subject.

Paul Murdin writes the following:

[Willebrod] Snell (sic)[1] had proposed the technique of triangulation as a way to measure the relative locations of points on the surface of the Earth (Smith 1986). The method, which is still the standard one, starts by the surveyors measuring a reference line between two stakes on a flat plain using standard sized sticks or chains (Fig. 7). A third stake is placed somewhere else on the plain at a significant location. From each end of the line, a surveyor sights the stake at the other end as well as the third stake, measuring the angle between with a theodolite. [emphasis in original] The third stake is located relative to the other two by trigonometry of the triangle. From the reference points the surveyor can also sight natural vertical features in the landscape.  […]  All these features can be located relative to the others building a chain of triangles across the country – hence the term triangulation (Murdin, p. 15)

Snell’s techniques were demonstrated by relatively small-scale projects by him and other Dutch cartographers. The first survey by triangulation is regarded to be Snell’s survey prior to 1615 of the Netherlands from Alkmaar via Amsterdam, Leiden, Utrecht, Dordrecht and Breda to Bergen-op-Zoom, accumulating an overall distance of 120 km. (Murdin p. 17)

Although he doesn’t actually directly say so Murdin implies that the technique of triangulation was invented by Snel; it wasn’t. Although Snel was almost certainly the first to measure a meridian arc using triangulation he certainly wasn’t the first to carry out a triangulation survey. I have included so much of the first quote because it saves me the bother of explaining the basic principles of triangulation. Let see whether Ferreiro does any better.

Writing about The Academy of Science’s proposal to extend Picard’s first triangulation survey in the late 17th century he writes:

The method for carrying out long-distance surveys had been around for several centuries and used a basic Euclidean premise: Given two angles of a triangle and the length of one side, the remaining sides and angles can be computed. This principle can be employed to measure over long distances by establishing a geodesic chain of triangles between two fixed points.

 Here nobody in credited with the invention and the couple of lines quoted contain a number of serious errors. The method had not been around for several centuries but was, as we will see, invented in the first half of the 16th century. It does not use a basic Euclidean premise. Given two angles and one side of a triangle one can construct the triangle using Euclidean geometry but if you wish to compute the rest of the triangle, and the subsequent chain of triangles, which is indeed what is done in triangulation, you need trigonometry, which you will search for in vain in the Elements of Euclid. The oldest surviving source for trigonometry is Ptolemaeus’ Syntaxis Mathematiké from the middle of the 2nd century CE more than 400 years later than Euclid. The trigonometry used in the Early Modern Period for triangulation came into Europe from India via the Islamic Empire during the High Middle Ages.

How do our other authors fair fare? Alder like Murdin plumps incorrectly for Snel, also misspelling his name:

The modern technique for using triangles to measure earthly distances, however, was introduced in 1617 by Willebrod Snell, “The Dutch Eratosthenes,” on the frozen fields outside Leyden, and his [my emphasis] method persisted for the next 360 years.

To be fair to both Murdin and Alder many academic sources, that should know better, attribute the invention of triangulation to Snel.

Keay ignores the subject completely giving a brief description of the principles of the technique but wasting no thoughts on its origins. Of our five authors only Hewitt gets the attribution right, she writes:

Triangulation had first emerged as a map-making method in the mid sixteenth century when the Flemish mathematician Gemma Frisius set out the idea in his Libellus de locorum describendum ratione (Booklet concerning a way of describing places),…

So who was Gemma Frisius?

Gemma Frisius 17th C woodcut

E. de Boulonois

He was born Jemma Reinierzoon or Jemma son of Reinier to poor parents in Dokkum in Friesland on 9th Dec 1508. His nom de plume Gemma Frisius is a Latinised onomatopoeic version of his birth name plus the toponym Frisius for Friesland. His parents died whilst he was still very young and he moved to relatives in Groningen, where he was educated in a cloister school. On 26th February 1926 1526 he matriculated as a poor scholar at the University of Louvain where he graduated Master of Arts in 1528. In 1529 there followed one of the strange unexplained episodes in the history of science. In 1924 1524 the then young German graduate of the University of Vienna Peter Apian published his Cosmographia, a textbook on astronomy, astrology, surveying, cartography and other aspects of applied astronomy. Apian not only wrote this book but printed and published himself, as part of his efforts to establish himself as a scientific publisher. In 1529 a second improved edition of Apian’s Cosmographia was published but not by Apian, the second and all the subsequent highly successful extended and improved thirty-two editions of this book, in many different languages, were edited by Gemma Frisius. This was one of the most successful mathematical textbooks published in the sixteenth century and it is not known why Gemma and not Apian edited and published all but the original edition.

Following up on his edition of Apian’s Cosmographia Gemma Frisius began to make printed terrestrial and celestial globes moving the tradition of their manufacture from Nürnberg to the northern Germanic area and through his pupil Gerard Mercator into Holland, where the Dutch would dominate the European globe making industry for most of the seventeenth century. He also set up as an instrument maker and through his own efforts and those of his nephews, the Arsenius brothers, Louvain became a major centre for high quality mathematical instruments.

In 1934 1534 he married and started to study medicine, graduating MA in 1536, which allowed him to practice medicine, going on to obtain his MD in 1541. At some point he became Professor of Medicine at the University of Louvain. During his medical studies he famously helped his fellow medical student Andreas Vesalius to steal a corpse from the gallows to conduct a bit of illicit dissection. Vesalius would of course go on to publish the most famous anatomy book of all times, his De fabrica, in 1543, in which he praises Gemma as a doctor and a mathematician.

Teaching medicine at the university, Gemma only taught mathematics privately producing in his time several famous pupils. I have already mentioned Gerard Mercator possibly the most well know of Gemma’s students but amongst other names known only to historians of mathematics and astronomy can be found the name of John Dee who came to Louvain after graduating at Cambridge to study at the feet of the master.

Gemma published nothing on medicine but lots of works on mathematics including, alongside the Cosmographia, the most successful arithmetic textbook of the sixteenth century. His Radio astronomico, a handbook on a new form of cross-staff of his own invention, published in 1545, contains the earliest printed, largely positive, discussion of Copernicus’ De revolutionibus.

Gemma was very successful and highly respected in his own lifetime and was one of the leading mathematical practitioners of Europe when he died of kidney stones on 25th May 1555 not yet 47 years old.

Many of his innovations in the mathematical sciences were published as appendices to his various editions of the Cosmographia and it is here attached to the 1533 third edition (Gemma’s second) that we find the Libellus de locorum describendum ratione, his pamphlet outlining completely and in detail the technique of triangulation.

Gemma himself did not enjoy good health and was a thinker and not a doer so he almost certainly didn’t carry out any surveying work himself. We do know that Mercator used Gemma’s method when he surveyed the Duchy of Lorraine later in the century. Tycho Brahe who knew Gemma’s work well being a customer of his instrument workshop also conducted a survey of his island of Hven using Gemma’s triangulation, which was never actually finished. Willebrod Snel would also have been well acquainted with Gemma’s work and it is almost certainly the Libellus that was the source of his knowledge of triangulation.

Some sources claim rather vaguely that triangulation was acquired by the Europeans from the Arab mathematicians during the Renaissance but fail to give any source for these claims or to reference any Arabic works on the subject. More directly some sources claim that the great Islamic scholar al-Biruni, who wrote extensively on geography and geodesy, used triangulation. This claim is simply false. He used geometrical methods to determine the longitude and latitude of various cities but his calculations did not just use triangles and he had no measured base line and made no sightings. He merely constructed geometrical models of the positions of the towns respective to each other based on travellers’ tales of the scale of their separations.

Historically there is very little doubt that the technique of triangulation emerged once and once only in a pamphlet written and published by Gemma Frisius in 1533. It is a strange fact that relatively insignificant scientific discoveries and inventions proudly carry the names of their discoverers and inventors but most people, including the people who write books about it, never stop to consider who invented triangulation, which until the invention of GPS, was the only tool, and a very powerful one, capable of producing accurate maps with their incredible economic, political, military and scientific significance. Gemma Frisius belongs in the pantheon of great modern scholars for his invention and not forgotten and ignored even by those who earn money writing about the incredible applications that this invention made possible.


[1] Snel is written with only one ‘l’, a common mistake in English texts. In his Latin publications Snel Latinised his name, as had his father also an academic mathematician, as Snellius. English authors translating back into the vernacular made the mistake of retaining the second ‘l’.


Filed under Book Reviews, History of Astronomy, History of Mathematics, History of science, Renaissance Science

How not to write about Renaissance mathematics

This is a book review. It is a review of Mark A. Peterson’s Galileo’s Muse: Renaissance Mathematics and the Arts (Harvard University Press, 2011) that I have to admit I’m writing with some reluctance. Why? I’m writing this review with some reluctance because it is going to be an extremely negative review. Now regular readers of this blog are probably asking themselves, “is he ill?” “There’s nothing the Renaissance Mathematicus likes more than putting the boot in, so why not now?” These would of course be justified questions so before I review Mr Peterson’s book I want to take some time to explain why I am in this case reluctant to put the boot in.

Some time back my Internet histsci soul buddy, Darin Hayton of the PACHS Network wrote a really good piece on book reviewing. He compared different reviews of Robert Westman’s new Copernicus book and explained why, in his opinion, the review written by Renaissance historian David Wootten Wootton is relatively worthless. Darin then goes on to give a set of guidelines for what he considers to be the right way to review (history of science) books. The whole article is well worth a read and I think his guidelines are absolutely spot on. One of his recommendations reads as follows:

Do not accept for review a book you are predisposed to dislike, or committed by friendship to like. Do not imagine yourself a caretaker of any tradition, an enforcer of any party standards, a warrior in any ideological battle, a corrections officer of any kind. (The bold emphasis is Darin’s).

Now the publisher’s blurb for Peterson’s book had instantly predisposed me to dislike it, which I’ll explain later. This being the case I felt a certain reluctance to even read it let alone review it. However not every book is as bad as the publisher’s blurb makes it out to be and the author often has very little control in how the publisher markets his efforts. This being the case I ignored my feelings of doubt and read the book. It turned out to be worse than I had feared. Worried that given my reaction to the publisher’s blurb I had read the book with prejudicial eyes I put it aside for several weeks and then re-read it trying very had to view it objectively and not to let my, possibly, prejudices get in the way. This didn’t improve my opinion of Peterson’s tome, what to do?

I have had several exchanges with various history of science colleagues in particular with Becky Higgitt, who as well as being a very good historian of science is also the book review editor of an important history of science journal, on the subject of bad popular history of science books and their reviews. On the whole real working historians of science refuse to review popular books on their subject written by non-historians. The reviews get written instead by fiction authors, journalists, professors of Italian[1] and other non-experts who often praise the reviewed volumes for their literary and entertainment qualities completely ignoring the fact that they are historical rubbish. Said volumes go on to become best sellers and the professional historians of science moan about the fact that they are factually incorrect, misleading and so on and so forth. Weighing up both points I have in the end decided to write my highly negative review of Peterson’s Galileo’s Muse, because although I had a negative view of this book before I even read it, it is a book that in my opinion should not be offered to the general public without saying that it is very, very far from being good history of science.

Prejudice! Why was I put off this book by the publishers blurb? On the flyleaf one can read the following statement:

Mark Peterson makes an extraordinary claim in this fascinating book focused around the life and thought of Galileo: it was the mathematics of Renaissance arts, not Renaissance sciences that became modern science. Galileo’s Muse argues that painters, poets, musicians, and architects brought about a scientific revolution that eluded the philosopher-scientists of the day, steeped as they were in a medieval cosmos and its underlying philosophy.

 This is an example of what I call the “my God Newton was an alchemist” syndrome. Every few years a new book or newspaper or magazine article trumpets out “Shock, Horror, Outrage Isaac Newton the father of modern science was a secret alchemist!” That Newton was a practicing alchemist has been known since at least the middle of the 19th century and that his alchemy even influenced his scientific work is also no longer new. It’s actually a rather sad comment on peoples’ knowledge of the history of science that such stories can be recycled about every five years.

That there was a vital and extensive interchange of knowledge between the artisan and scientific communities in the Renaissance has been the subject of extensive research for several decades and has produced a significant amount of literature. Peterson claim is not extraordinary or in anyway new but is the daily bread of a fairly large number of Renaissance historians of art, science, culture, literature and mathematics. Just to name a couple of the better-known products of these efforts we have Pamela H. Smith’s very impressive The Body of the Artisan: Art and Experience in the Scientific Revolution, Chicago University Press, 2004. The complete life’s work of art historian Samuel Edgerton who has written numerous books and articles on the discovery of linear perspective in the Renaissance and his, highly disputed, theory that this triggered the scientific revolution. We have Martin Kemp’s masterpiece The Science of Art: Optical Themes in Western Art from Brunelleschi to Seurat, Yale University Press, 1990. Horst Bredekamp’s Galilei der Kunstler, Berlin 2007 and a whole lot more. Peterson is not doing anything new he is following an already well-worn path and doing it badly.

This article is already quite long and I haven’t even started on the review proper. If I were to go into detail on everything in Peterson’s book that annoys, worries or angers me then my review would be substantially longer than the book itself. Instead I shall make some remarks about various aspect of the book that are in my opinion are wrong but with the caveat that there is more of the same that I haven’t commented on.

The book opens with a biographical sketch of Galileo’s youth and his decision to become a mathematician. Strangely Peterson does not reference modern scholarly biographies of Galileo but uses as his sources the two contemporaneous partial accounts of Galileo’s life. What’s wrong with that you might ask? Very simply both accounts are known to be at best dubious and at worse false. So why does Peterson use them? He uses them to sustain the myth that Galileo came to mathematics by accident as an adult and against opposition to his choosing this career. Why will Peterson sustain this myth? Because he is in reality writing a hagiographical account of how Galileo the autodidact singlehandedly re-introduced ‘real’ mathematics into science. The first and only person to do so since the classical age of Greek mathematics! This is the real message of Peterson’s book and it is historical rubbish. To achieve this aim Peterson proceeds to twist, misrepresent and falsify the history of science and mathematics. He starts by explaining that Galileo’s apparent ignorance of mathematics until he was an adult and university drop out although implausible can be verified by the similar experience of Thomas Hobbes. Peterson relates Hobbes’ exhilaration on first viewing an open page of Euclid’s Elements, as an adult. Peterson argues so Hobbes, so Galileo. Unfortunately the comparison doesn’t work, which Peterson would know if he had really studied the history of Renaissance mathematics. Galileo grew up and went to university in Northern Italy where the universities had had specialist chairs for the mathematical sciences since the last quarter of the 15th century and a well developed network of private schools for commercial mathematics since the 14th century, that is a well established and well developed mathematical culture. As a student of medicine at Pisa Galileo would have taken the same courses in mathematics, astronomy and astrology as every other medical undergraduate, course that he himself would then teach as professor of mathematics both at Pisa and Padua starting only a few years later. Hobbes grew up in England and graduated from Oxford University in 1609. The first university chairs for the mathematical sciences in England were established in Oxford in 1620! Something akin to the Italian abbacus schools for commercial mathematics only began to emerge in England during Hobbes’ youth thanks to the efforts of Robert Record and John Dee. In Hobbes’ youth England had no mathematical culture!

Peterson continues his campaign of misinformation with his account of the various forms of Renaissance mathematics. I can’t even begin to explain in the space of this review everything that’s wrong with this account other than to repeat that its aim is to justify his claims for Galileo’s mathematical uniqueness.

There then follows a section on science and mathematics in classical antiquity that I can only sum up with the phrase “half read, half understood, half forgotten!” It’s as if an undergraduate had half read the assigned literature for a course in classical studies, only really understood half of what he had read and the forgotten half of it anyway. The result is horrendous! I think the worst aspect is a sort of Animal Farm belief mantra that Peterson insinuates in his account of antiquity  “mathematics good, philosophy bad”. Aristotle hasn’t got a leg to stand on because he wasn’t a fan of mathematics and poor Ptolemaeus gets taken to task for daring to start a book on mathematical astronomy with a philosophical discussion. I would draw a veil over the whole sorry mess but there is one point that I have to illuminate.

In his writings Galileo praises the Pythagorean philosophy. Now Peterson is aware that modern scholars tend to write off the Pythagoreans as a rather weird religious sect who practiced a strange form of number veneration. His Galileo couldn’t possibly be a fan of something like that! So Peterson proposes that the ‘real’ Pythagoreans were the mathematical giants of antiquity, Euclid, Appolonius, Archimedes etc. and that they kept their identity as Pythagoreans secret. We have left the realm of popular history of science and entered the world of Dan Brown. Mr Peterson the explanation is much simpler and much more rational. Galileo’s Pythagoreans were not the historical sect in Southern Italy but an idealised Renaissance view of a mathematized world, very simple.

The next two chapters of the book also owe more to a Dan Brown view of the world than to a historical one. We get treated to Dante the geometer. This is actually stuff that Peterson has published before and is being recycled here. Peterson has decoded Dante’s Paradiso and discovered that it’s really a text about advanced geometry. Dante’s description of heaven is really a description of the 3-sphere! For the non-mathematicians amongst my readers, if you’re still awake at the back there, a 3-sphere in the geometrical equivalent to the sphere in four dimensions, as the sphere is the geometrical equivalent to the circle in three dimensions. What in fact happens is that Dante arriving at the boundary to heaven describes what he sees in a way than can be interpreted, and is so by Peterson, as a non-mathematical description of a 3-sphere. Thus so Peterson Dante is the discoverer of the 3-sphere! There is again a much simpler and much more rational explanation for Dante’s description. For a mediaeval Christian heaven is literally indescribable, it is beyond human comprehension so when Dante arrives at the boundary of heaven he does just that. He describes something impossible, something beyond comprehension, little imagining that a few hundred years in the future that, which he has described will become for all intents and purposes the mathematicians 3-sphere. Dante is not its discoverer. Peterson argues that Dante was a knowledgeable geometer because he quotes two Euclidean theorems in his Paradiso. Unfortunately for Peterson both the theorems quoted by Dante are from the very beginning of the Elements and are such that any undergraduate at a mediaeval university would have studied/learnt in his liberal studies course and do not demonstrate that “Dante knew his Euclidean geometry very well”.

Peterson goes even further with his Paradiso Code fantasies claiming that the closing stanzas of the Paradiso are actually an encoded version of Archimedes’ proof of the incommensurability of the circle! I wont do a blow-by-blow account of this bizarre claim but I will make one trenchant comment. Peterson writes:

In all Dante’s writings he never mentions the name Archimedes, but there is a surviving treatise of Archimedes called On the Measure of the Circle. It is only a few pages long, and thus easily copied. It was widely circulated in Dante’s day, and even well before. [An exaggeration on Peterson’s part] We have seen how intensely Dante was interested in the measure of the circle [One brief reference in an unfinished work] – it is inconceivable that he would not have known the Archimedes treatise.

It is perfectly conceivable and highly probable.

Having supposedly dealt with geometry in poetry Peterson now moves on to painting and to what I consider to be the only halfway good section of his book. Here he deals with the Renaissance discovery of linear perspective, which is indeed an important episode in the development of Renaissance mathematics. However here he can’t refrain from falsifying history to suit his prejudices. Alberti who actually wrote the first treatise on linear perspective is dismissed as not really understanding what he’s writing about and Luca Pacioli is dismissed as a showy braggart who’s not really a mathematician. This being the author of the Summa de arithmetica, geometria, proportioni et proportionalità one of the most important mathematics books published in the period as well as being Leonardo’s mathematics teacher. The purpose of these degradations is to raise the profile of Piero della Francesca who is the main subject of the section. Once again Peterson is recycling work that he has already published elsewhere but it is nice to see somebody giving both della Francesca’s work in linear perspective and in mathematics the attention it richly deserves. However it should be noted that Peterson contributes nothing original here he is merely recycling the researches of others, most notably Martin Kemp and Judith Field. This section closes with a real clanger, having explained how Pacioli plagiarised della Francesca’s work on the Platonic solids Peterson opinions the following about Leonardo who provided the wonderful geometrical illustrations for Pacioli’s work. He writes:

It is painful to think how vulnerable Leonardo might have been to the seductions of Pacioli’s geometry. In the end, Leonardo produced sixty careful drawings of the Platonic solids and other polyhedra, representing physical models of these figures fashioned as hollow frameworks, so you could see through them to the back. Leonardo was at the height of his powers – the Mona Lisa was still to come – but here he is doing something utterly mechanical, and almost embarrassing.

 Here Peterson displays an ignorance of Renaissance art at the beginning of the 16th century that is almost embarrassing. After the discovery of linear perspective, starting with della Francesca, the correct perspective presentation of three-dimensional geometrical figures became almost a fetish amongst artists who were proud to demonstrate their mastery of perspective with such studies. Far from being embarrassing Leonardo would have revelled in the chance to demonstrate he very obvious superior skills as a draughtsman and if Peterson thinks that such drawing exercises are mechanical I would suggest that he tries to draw a copy of one of Leonardo’s figures.

Following painting we are presented with music another area where mathematics was applied in the Renaissance and for the first time in many pages we encounter Galileo again. This time we are more concerned with his father Vincenzo who was one of the leading music theorists of the period and involved in an infamous dispute over the divisions of the scale and the size of musical intervals. Again Peterson adds nothing new to a story that has been told many times although for the first time in the book we have Galileo the experimental physicist working together with his father on the laws governing the pitches of stretched strings, experiments that found their way into his Two New Sciences.

Music is used to introduce us to Johannes Kepler whose magnum opus was famously entitled The Harmony of the World and actually contains an extensive discussion of the dispute involving Vincenzo Galilei. We get a fairly standard account of the handful of letters the two men exchanged laced with Peterson’s attempt to denigrate Kepler’s mathematical achievements whilst praising Galileo’s:

Although higher mathematics in 1610 was still entirely identified with astronomy, [it wasn’t of which more later] Galileo meant to extend mathematics to earthly things, a philosophical revolution for which he needed the title Court Philosopher as much as Court Mathematician. For Kepler earthly mathematical problems simply could not compete with astronomical ones for beauty and importance.

 Peterson completely ignores the brilliant general mathematical advances in Kepler’s astronomical works, his presentation and analysis of the 13 semi-regular Archimedean solids, he demonstration that the conic sections are actually all the same general function, his extraordinary use of proto-integration in his ‘proof’ of his second planetary law. Instead we are treated with a bizarre presentation of his Dioptrice, his Six-Cornered Snowflake and his pamphlet on measuring wine barrels. Of the Dioptrice Peterson writes:

Kepler returns in Dioptrice to a problem he had omitted from his 1604 Optics, the use of lenses in astronomy, and especially the theory of the telescope, since the telescope had turned out to be useful in astronomy after all. His treatment of the subject is a practical, semi-quantitative account of what you see when you look through two lenses, undeniably the result of systematic experimental work, not something one usually thinks of in connection with Kepler.

 There is so much wrong with this passage it is hard to know where to begin. The Optics from 1604 does include the first account of the geometrical optics of lenses, the first such account ever to be published and it was this that enabled Kepler to publish his Dioptrice, a definitive account of the optics of telescopes so soon after Galileo had published his Sidereus Nuncius. His Optics had not included an account of the telescope because it didn’t exist in 1604 being first invented in 1608!  In the Dioptrice his treatment is totally theoretical displaying Kepler’s total mastery of the theory of geometrical optics, not a single hint of an experiment anywhere. The Dioptrice also includes accounts of optical systems with more than two lenses most notably the so-called terrestrial telescope with its third inverter lens one of Kepler’s three significant inventions in the book; the other two are the astronomical telescope and the telephoto lens.

Peterson will have us believe that Kepler was unaware of the mathematical and scientific significance of his snowflake pamphlet because he writes it in a deprecating humorous style. I beg to differ. Peterson also wilfully ignores or is ignorant of the fact that Kepler’s pamphlet on measuring wine barrels in an important early example of the use of integration to determine volumes.

Kepler was a vastly superior mathematician in comparison to Galileo and his contributions to the evolution of modern mathematics are manifold but Peterson tries desperately to play this fact down because it totally contradicts his central theme than Galileo was unique in the period in his use of mathematics to solve problems in physics.

Next up in Peterson’s survey of Renaissance arts and crafts is architecture and the Renaissance artist engineers adherence to the Pythagorean theories of harmonic proportions in design. His presentation is very superficial and not very illuminative but he still manages to make a serious failure. At the end of the section he discusses Copernicus’ claim as to why his heliocentric system was superior to the Ptolemaic geocentric one, which Copernicus frames in terms of the natural harmony of his system. Peterson writes:

There is nothing in the Ptolemaic description to determine the third dimension, however – the distance from us to the various planets.

 Although the relative size of the planetary orbits is automatically dictated by the heliocentric system it is true that this is not the case with the geocentric system. However the geocentric astronomy did have a convention for determining those distances so to say, as Peterson does, “there is nothing” is historically false. Copernicus argument is that in his system the determination follows from the system whereas in the Ptolemaic one it is only decided by convention.

This introduction to Renaissance architectural theory is only a lead in to what Peterson obviously regards as one of the high points of his book, his discussion of Galileo’s public lecture on the dimensions of hell in Dante’s Inferno. Here Peterson thinks that he has made an important discovery that Galileo uses physical scaling arguments in his description of the structure of hell. This, according to Peterson, is an important major new scientific method that Galileo is introducing here. I think he is over egging the cake. Apart from anything else as he himself admits Galileo got the argument wrong.

We are now approaching the conclusions of the book and they are prefaced with a survey of “mathematics old and new”. This survey as with all the accounts of Renaissance mathematics in the book is to put it mildly highly inaccurate and inadequate. First we get a rather tired retelling of the Tartaglia – Cardano episode and the solution of the cubic equation at the end of which we are told that Galileo had no interest in the new algebra. Other workers in the field such as Bombelli or Stiffel don’t even get a mention. The section on geometry starts rather bizarrely with the Gregorian calendar reform and we are informed that Peuerbach and Regiomontanus did their work in trigonometry as a contribution to this reform, which is complete historical rubbish. Having described their contributions to the development of trigonometry, Peterson then dismisses them as irrelevant and insignificant. Again we have no mention of the others who made contributions to the evolution of trigonometry in the 16th century; contributions that led Ivor Gratten-Guiness, one of the leading historians of mathematics, to label the period “the age of trigonometry”.  This chapter on mathematics closes with a section on translations, highly appropriate as the Renaissance is all about the recovery of original Greek and Latin texts and here Peterson drops one of the biggest clangours in the entire book whilst discussing the first printed edition of Archimedes. This is important to him as he presents Galileo, quite correctly, as taking Archimedes as his mathematical role model. Peterson writes:

Tartaglia produced the first printed Archimedes in 1543, the one that Galileo studied so intensively on the advice of Ostilio Ricci, but it was just the thirteenth-century translation of Wilhelm Moerbeke. (The comment about the old translation is that it is therefore a highly defective translation.)

 In 1543 Tartaglia published the first Italian translation of Euclid’s Elements, from the Latin and not the Greek original, but he never published an edition of Archimedes in any form what so ever. The first printed edition of the works of Archimedes was published by Johann Herwagen in Basil in 1544. It is a bilingual edition Greek with the Latin translation of Gerard of Cremona edited and corrected from the Greek by Regiomontanus and then edited for publication by Thomas Geschauff known as Venatorius, a cleric and scholar from Nürnberg. I really don’t understand how Peterson could have got it so completely wrong.

The penultimate chapter now promises to reveal Peterson’s main claim the uniqueness of Galileo’s contribution to mathematics. I have reread the chapter several times and I can’t find anything what so ever to justify this claim. He also here wants to demonstrate how Galileo’s training as an artist influenced his scientific discoveries. On this the only real evidence he produces is Galileo’s telescopic illustration of the moon a subject that has been dealt with exhaustively by Albert van Helden in numerous papers and Horst Bredekamp in the very thick book mention very early on in this review. The New Scientist reviewer of Peterson’s book even wrote the following:

All this is true, but Peterson does not show in any detail how this cultural background led Galileo to make the two great discoveries for which he is famous in physics: the law of freely falling bodies, and the fact that the trajectory of a projectile is a parabola.

 Peterson even manages to confuse these “two great discoveries”. He writes that Pierre Duhem says that the parabola law had already been discovered in the fourteenth century. What in fact Duhem and others say, perfectly correctly, is that the mean speed theorem, the core element of the laws of fall, was discovered by the Oxford mathematician William Heytesbury in the fourteenth century and that this was demonstrated by the Paris physicist Nicolas Oresme, in the same century, with a graph identical to the one used by Galileo to demonstrate the same law. Peterson doesn’t even mention the fact that almost the complete laws of fall were published by the Italian mathematician Benedetti in the 1550s. Peterson also completely ignores the fact that the Dutch mathematician Simon Stevin was doing very similar work contemporaneously to Galileo in mathematical physics; facts that rather spoils his uniqueness claims for Galileo. This section also contains what I regard as the most revealing mistake in the book. In his attempt to negate the achievements of Galileo’s mediaeval predecessors Peterson writes:

The medieval theory was not so much a theory of motion as it was a theory of any quality that varied with position or time, the quality of color for example.

 Remember that earlier quip about “half read, half understood, half forgotten!” Here we have a perfect example. In his philosophy Aristotle did in fact regarded terrestrial motion, celestial motion is completely different, as one example of change. The earthly or sub-lunar sphere being characterised by impermanence, decay and change as opposed to the supra-lunar sphere which was permanent, eternal, unchanging. All forms of change were therefore properties of the sub-lunar sphere. However when discussing change he did not put up a general theory but dealt with the different forms of change separately. His theory of motion dealt with motion and only with motion. This theory was highly unsatisfactory and was already challenged in the Early Middle Ages by John Philliponus and in the High Middle Ages by both Islamic and European scholars who developed the so-called impetus theory of motion; a theory that even Galileo used in his early investigations of motion. The mathematical treatment of motion carried out by the Oxford Calculatores and the Paris Physicists in the 14th century was just that, a mathematical theory of motion and not as Peterson claims a general Aristotelian theory of change.

Following, what is, a rather disappointing conclusion to his stated claims for his book Peterson closes with a rather strange chapter in which he thinks he can prove that an oration on the virtues of mathematics held by a student of a student of Galileo’s was actually written by Galileo. Here his arguments are somewhat less than convincing and even if he is right the oration is nothing more than a puff piece of no real significance so one is left asking, “so what?”

The book closes with an epilogue, which contains probably the best conclusion by Peterson concerning Galileo in the whole book. He writes:

It is not easy to write about Galileo and yet ignore the Copernican controversy, as I have done until now. In the end I feel a responsibility to record my view, namely that the importance of the Copernican controversy in Galileo’s biography is overstated. [my emphasis]

I couldn’t agree more.

It is actually a very important historical fact to realise that Galileo was actually a typical Renaissance artist-engineer in the very strong tradition of such people as Brunelleschi, Alberti, Leonardo, Michelangelo, to a lesser extent Dürer and many lesser known figures such as Ignazio Danti or even, later than Galileo, Nicholas Mercator rather than the “modern scientist” as he is most often presented. It is also very important if we are ever going to really understand the emergence of modern science in the Early Modern Period to study the working practices of these artisans and to see where their methodologies led to those that we now recognise as scientific. Galileo, given his contributions to the evolution of science, would seem to be a perfect object for such a study and that is what Peterson’s book seemed to be promising. Maybe I’m being to hard in my judgement but I think he has failed totally to do so. Even more worrying in his attempt to achieve his second stated aim, that is to show that Galileo’s use of mathematics was ground breaking and in some way unique, he has presented a warped, distorted and I’m afraid to say deliberately false picture of mathematics and its use in the Early Modern Period before Galileo. I cannot honestly recommend this book to anyone.

I said that a study of Galileo as a Renaissance artist-engineer and how this affected his scientific work would be very interesting and although Peterson has in my opinion failed to deliver somebody else has. Appearing to late for Peterson to have read it whilst writing his own book is Matteo Valleriani, Galileo Engineer, Springer, 2010. Unlike Peterson’s book this is not aimed at the popular reader but is in fact the author’s doctoral thesis. It is also not made more readable by the fact that the author, an Italian, wrote it in English and did not allow anybody to, shall we say, smooth out his language. However the book is actually fairly readable and for anybody who is really interested in how the training of a Renaissance artist-engineer translated into scientific methodology I heartily recommend Valleriani’s book.





[1] One of the reviews on the cover of Peterson’s book is by a professor of Italian.


Filed under Book Reviews

The Swerve is really a full-frontal crash.

Today  we have a new guest post from regular commentator and Renaissance Mathematicus fan Baerista. Whereas I am an Englishman living in Germany who blogs in English Baerista is a German living in London who normally blogs in German. Today he has delivered up a post in English explaining why he thinks the highly praised The Swerve by Stephen Greenblatt ought to be viewed somewhat more critically

Marvelous Distortions: Greenblatt and the Transmission of Lucretius

For all the obsessive preoccupation with classical antiquity that has characterized our modern culture, it is at times disconcerting to see how little the average aficionado of Greece and Rome knows about the way his beloved classics have reached his modern bookshelf. This general ignorance is well exemplified by the frequently heard statements to the effect that “we owe Islamic civilization the preservation of Greek literature, which would have otherwise been lost during the Dark Ages.” The problem with this claim is not that we owe nothing to Islamic civilization (we certainly do), but much rather that the people who make these pronouncements are usually fully cognizant that textual editions from the whole gamut of Greek literature in their original language are easily available at the local library (in the case of the Loeb series, they are recognizable from afar by their green covers). Do they really think that these are all re-translations from Arabic?

I suspect that one factor that makes it hard for the average observer to get a clear grasp of the transmission of classical texts, be they Greek or Latin, is the ubiquitous use of the term “Renaissance,” which essentially transports a skewed view of cultural history. The implication is that, when antiquity ended, classical culture went to sleep and lay dormant in a cigar box for a good thousand years, until it was re-discovered by a bunch of Italian bonvivants, who thought it would be a neat idea if everyone spoke like Cicero again. Historians who are wont to counter this view are often eager to point out that there has been not one, but many “re-births” of classical literature, one of which took place in the late eighth and early ninth century and is known as the “Carolingian Renaissance.” In a nutshell, the “Carolingian Renaissance” denotes a general revival of intellectual culture in the Frankish empire that had its epicenter in Charlemagne”s court in Aachen. Besides giving rise to the direct forerunner to most Western styles of handwriting, in form of the Carolingian minuscule, this early medieval “rebirth” of European learning also led to a greatly increased rate of manuscript production and dissemination, which included many important works from classical antiquity.

Among the ancient Latin jewels that were thus saved from oblivion is the poem De rerum natura by the Roman poet Lucretius-a comprehensive description of the “facts of life” as seen from an Epicurean point of view, which spans some 7,400 hexameters. As is well known, this philosophy was strikingly at odds with the Christian worldview that dominated the Middle Ages, in that it emphasized the pursuit of earthly pleasures, denied the immortality of the soul and reduced the universe to an infinite number of atoms that randomly moved through empty space. According to Epicurus and Lucretius, the way these atoms collide and hook together accounts for the creation, growth and decay of all material things, including human beings. On the surface, DNR thus comes across as a remarkably “modern” piece, which helps to explain its ongoing popularity in the twenty-first century. One of the many modern fans of DNR is Stephen Greenblatt, a literary critic and professor at Harvard, who makes Lucretius”s masterpiece the protagonist of his latest book The Swerve: How the World Became Modern (2011), which has already earned its author both the 2011-National Book Award for Nonfiction and, more impressively still, this year”s Pulitzer Prize in the same category.

What is this “swerve” all about and how did it make the world modern? As it turns out, one of the big problems with this book is that the second part of this question is never sufficiently addressed. At its core, The Swerve tells the story of the Renaissance humanist Poggio Bracciolini (1380-1459), who, in 1417 visited the libraries of several Southern German monasteries on a hunt for “lost” texts from classical antiquity. One of the manuscripts he happened upon during this book-hunt contained Lucretius”s DNR, which was soon re-copied multiple times and caused a sensation among the reading public of the Italian Renaissance. Greenblatt makes no bones about the fact that he himself regards the Epicurean philosophy of radical materialism combined with unapologetic hedonism that is encoded in DNR as the best thing since sliced bread and one of the defining sources of our modern way of thinking.

His idea that Epicureanism was present at the birthpangs of modernity is far from original and has only recently found a vocal defender in Catherine Wilson”s confidently titled 2010-book Epicureanism at the Origins of Modernity. As with most attempts to reduce complex historical phenomena to monocausal explanations, Wilson”s book has not been everywhere well received, as can be seen from this scathing review by Margaret J. Osler (1942-2010), a widely respected expert on early modern science. Given these very recent discussions among historians, it is very disappointing to discover that Greenblatt”s own “defence” of the mentioned proposition consists of little more than a series of brief excursuses on figures such as Thomas More, Michel de Montaigne and Giordano Bruno, who all read DNR and therefore…what? However the world may have become modern, The Swerve definitely is not the book to turn to if you are interested in an answer.

Realizing that the original subtitle was a misnomer, the book”s publisher in the United Kingdom (a Random House imprint named “The Bodley Head”) went for a little more understatement and retitled it as The Swerve: How the Renaissance Began, not realizing that this technically makes things even worse. While the assertion that the re-discovery of Epicureanism is at the sole root of modern science and philosophy is certainly dubious, it at least makes some chronological sense. By contrast, to declare DNR the source of Renaissance humanism puts the cart entirely before the horse. The very fact that Poggio Bracciolini discovered DNR on a book tour through Germany, undertaken to satisfy the ever-growing desire of Italian courts and scholars for ancient texts, should alert us to the fact that Poggio and his discovery were products of the Renaissance and not its cause. While Greenblatt rightly focuses on Petrarca as Poggio”s most important fourteenth century predecessor, some modern historians would be inclined to trace the beginnings of the Renaissance “movement” even further back-to a growing interest in the classics that already started in the second half of the thirteenth century and that had some of its early proponents by English friars such as Nicholas Trevet (c. 1257-c. 1334), who had ties to Italy and produced commentaries on the whole corpus of tragedies by Seneca the Younger at the instigation of his patron, Nicholas of Prato, cardinal bishop of Ostia (1303-21).

I have deliberately mentioned Trevet, a theologian and member of the Dominican order, because he is a good example for the kind of scholar that, according to the picture of history presented in The Swerve, should not have existed. In Greenblatt”s worldview, which is a disconcerting throwback to the heyday of John William Draper and Andrew Dickson White, the protagonists of Western intellectual history always appear on stage clad in white or black robes, depending on which team they support. Needless to say, Epicurus and Lucretius, as the fragile heroes of “team reason,” are constantly at the brink of destruction thanks to the malicious interference of “team Church,” whose intrinsic evilness is evident from the fact that Jan Hus and Giordano Bruno were burnt at the stake-episodes on which Greenblatt dwells for several pages (pp. 166-72, 233-41), despite their being only tenuously related to the subject of his book.

Neither does he forget to slip in an account of the library of Alexandria, the destruction of the Serapeion and the murder of Hypatia of Alexandria, which is essentially a rehash of old Gibbonian (and Saganian) tropes that have been debunked so well by Tim O”Neill over at Armarium Magnum. True, Greenblatt”s account of these events does contain some hints that he did enough research to realize that Hypatia”s death was probably just the result of partisan politics and that no ancient account mentions the destruction of books when the Serapeion was sacked. But, as if to honour the principle of “never change a winning story,” he goes on to blabber: “The murder of Hypatia signified more than the end of one remarkable person; it effectively marked the downfall of Alexandrian intellectual life and was the death knell for the whole intellectual tradition that underlay [De rerum natura]” (p. 93). I am not sure whether Greenblatt simply never heard of people like Hierocles, Asclepius of Tralles, Olympiodorus the Younger, Ammonius Hermiae, Hermias, or the woman philosopher Aedesia (who managed to pursue her philosophy without being physically harmed) or whether they were not intellectual enough for his taste, but if I was a representant of fifth and sixth century Alexandria, I would doubtlessly be pissed at his lack of consideration.

Another group that would not have been pleased by the way they are depicted in The Swerve are the men and women of the medieval monasteries, whose manifold cultural achievements are largely ignored in favour of the practices of self-torment and asceticism, which Greenblatt imagines in irritatingly lurid detail. The resulting caricature of medieval monastic life was rightly criticized by Anthony Grafton in an article for the New York Review of Books, who very appositely calls it a “a curious blend of Gibbonian irony and Sadean relish,” only to later remark with a brief, but audible, sigh: “The Swerve is not always as accurate as one would wish.” From a world-class scholar like Grafton, who is widely known as an extremely generous man, always careful to wrap even the faintest criticism in a wadding of praise, such clear-cut words can be taken as the verbal equivalent to a bitchslap.

Without wanting to get into a prolongued critique of Greenblatt”s many distortions of medieval and Renaissance history, I shall presently focus on what is arguably one of the most annoying of all the misrepresentations in his book annoying, because it is ostensibly there for no other reason than to furnish his narrative with additional momentum: as it turns out, the book”s title The Swerve alludes to the English equivalent to the Latin word clinamen, which Lucretius used to describe the erratic and unpredictable movement of atoms in the void. According to Greenblatt, the textual history of DNR was itself marked by a remarkable number of unexpected “swerves” that, taken together, supposedly account for its “miraculous” survival:

“It was by chance that a copy of On the Nature of Things made it into the library of a handful of monasteries, places that had buried, seemingly forever, the Epicurean pursuit of pleasure. It was by chance that a monk laboring in a scriptorium somewhere or other in the ninth century copied the poem before it moldered away forever. And it was by chance that this copy escaped fire and flood and the teeth of time for some five hundred years until, one day in 1417, it came into the hands of [Poggio].” (p. 109)

As becomes clear from this and other pages of his book, Greenblatt wants his readers to believe that the manuscript discovered by Poggio in 1417 contained the only surviving copy of DRN and that the text would have doubtlessly been lost forever, had it not been for this one serendipitous discovery. Furthermore, he heavily implies that the text”s survival was constantly endangered, not just by “fire and flood and the teenth of time,” but also by malignant monks and churchmen, who despised pagan learning and all too often destroyed ancient texts by turning their manuscripts into palimpsests (e.g. pp. 42-44). How realistic is this account?

The situation concerning the manuscript transmission of DNR can be roughly summarized like this: the text today found in critical editions rests chiefly upon two ninth-century manuscripts at Leiden”s Universiteitsbibliotheek, which are both products of the aforementioned “Carolingian Renaissance”: Voss. Lat. F. 30, known as the Oblongus (O) due to its format, which was copied shortly after 800 at the Palace School of Charlemagne in Aachen and is the ancestor (direct or at one remove) to the manuscript later discovered by Poggio; and Voss. Lat. Q. 94, the so-called Quadratus (Q), which derives from north-east France. A further ninth-century copy from south-west Germany is attested by two fragments of only a few leaves each, now housed at libraries in Copenhagen and Vienna (a second Viennese fragment may have sprung from the same book or from yet another ninth-century copy). The fact that only three or four manuscripts from this period are still attested in the flesh need not and does not mean that they were the only ones copied. Our preserved number of early medieval manuscript is generally only the tip of a lost iceberg. Indeed, stemmatic analysis (the construction of a family tree for manuscript copies on the basis of discrepancies and scribal errors in the preserved copies) postulates not only a late antique (fourth or fifth century) archetype in rustic capitals, but no less than three further medieval copies that came before O, Q and the fragments.

Moreover, it is simply not true that this text had lain “dormant and forgotten for more than a thousand years” (p. 13) and was never read or used during the Middle Ages until Poggio happened upon it: from excerpts in a variety of medieval manuscripts, especially from the ninth and tenth century, we can tell that Lucretius was no stranger to scholars in the Low Countries, northern France and the Rhineland area. In about 825, Mico of Saint-Riquier, a scholar at Reichenau, an island monastery in Lake Constance, put together a metrical florilegium contaning lines from DNR. Lucretius is also present at the monastery of St. Gall, where he is quoted around 850 in a letter written by Ermenrich of Ellwangen and also appears in another florilegium produced there in c. 900. Another famous scholar from this period whose works contain citations from DNR is Rabanus Maurus (d. 856), who, aside from being a prolific writer, also served as the archbishop of Mainz. For the rest of the history of the Middle Ages up until Poggio”s time, the textual history of Lucretius admittedly becomes more sketchy. From medieval library catalogues we know that copies were held in the north Italian monastery of Bobbio in the ninth and at the abbeys of Lobbes (Belgium) and Corbie (Northern France) in the twelfth century, while a gloss that references Lucretius appears in a work of Sigebert of Gembloux (c. 1030-1112).

Unsurprisingly, Greenblatt suppresses almost all of this fascinating information, despite the fact that it is very readily available in the standard hand books such as L. D. Reynold”s and N. G. Wilson”s Scribes and Scholars (1968/1974/1991) and L. D. Reynold”s Texts and Transmission (1983) as well as Michael Reeve”s article in the relatively recent Cambridge Companion to Lucretius (2007). The latter rightly points out that the fate of DNR (being copied several times during the “Carolingian Renaissance,” followed by a largely dormant tradition between the ninth and fifteenth century) is shared by so many other classical texts that there is no reason to suppose this had anything to do with deliberate censorship, motivated by”Christian scruples” about Lucretius”s a-religiosity.

The fact that an essential research aid like the Cambridge Companion appears nowhere in Greenblatt”s bibliography may be telling, but not quite as telling as the fact that the former two books are in fact listed. With other words: there is every reason to assume that Greenblatt knew fully well that he was distorting the facts when he decided to contruct a whole sweeping narrative on the motif of DNR”s “miraculous” survival. He therefore ended up telling the story the way he did not (simply) because he is a poor scholar, but because of the nature and purpose of his book, which is not an offering on the altar of truth, but a carefully calculated “bestseller,” whose author had some very precise ideas of what his readers would expect-and reward.

It is indeed worth observing that Greenblatt”s book comes to us at the height of a “renaissance” of general interest in Lucretius”s work, not just on the part of scholars, but also and especially among lay readers, many of them members of a large social movement that is very active on the internets and that can be roughly categorized as “secularist” or “new atheist.” This movement attracts a great deal of young people, who use the world wide web as their main resource to increase their intellectual standing in what they perceive as a daily struggle against the dark forces of religious obscurantism. Unfortunately, the sources they avail themselves to are such that many of them end up with an extremely impoverished picture of the human past that often relies on fringe theories such as “Jesus mytherism” and a comic-book idea of the history of science that is well-exemplified by this monstrosity.

The reasons why this demographic might be interested in DNR are not difficult to see: it is certainly reassuring to know that about seven centuries before the Quran and still a century before the New Testament there used to be a Roman guy who (seemingly) saw the world very much like oneself. For a modern-day admirer of Lucretius, who perceives history as an eternal struggle of reason against religion, the idea that this crucial text was rescued almost miraculously from oblivion in the hands of self-castigating monks, who were burning pagan books when they were not burning heretics, is clearly an eminently sexy one. It is precisely this intellectual climate that Greenblatt decided to take advantage of when he wrote The Swerve. Being faced with the choice between intellectual honesty (which, being a literary critic and therefore steeped in pomo-philosophy, he probably regards as an outmoded concept anyway) and the prospect of laughing all the way from the bank, he chose the latter. If there is something we should be worried about, it is not the fact that people make such choices, but that garbage of this kind is awared with a Pulitzer Prize.


Filed under Book Reviews, Myths of Science, Renaissance Science

Pictures of Isaac.

I have recently finished reading the book Recreating Newton1 by my Whewell’s Ghost co-blogger Rebekah ‘Becky’ Higgitt and I have decided to write a brief review of her efforts2. The book based on Ms Higgitt’s doctoral thesis deals with the changing perceptions of Isaac Newton in the historical literature in the first half of the 19th century. What at first look sounds like a subject of fairly limited interest turns out to be a fascinating journey from the largely mythical hagiographical image of England greatest science icon created in the 18th century towards a deeply researched, fact based picture of the real Isaac Newton, warts and all by the middle of the 19th.

First of all I will simply say that this is a truly excellent book with which I can find no fault, at least none that is attributable to its author. I do however have two points of disagreement with the publishers both of them probably moot points but I shall state them anyway. The first, as unfortunately all too often with academic books, is the price, weighing in at £60 (Amazon, UK), €84,99 (Amazon, Germany) and $99 (Amazon America) for an octavo volume of not quite 200 pages plus notes, bibliography and index it is just too expensive. This is a highly readable and interesting book and it should in this age of computerised publishing be possible to make it available at a price that a normal reader would consider paying. By setting the price so high the publishers claim that academic books don’t sell will become a self-fulfilling prophecy. At this price even my university library, which has a remarkable collection of literature on Newton including first editions of the works discussed by Ms Higgitt, probably wont buy a copy in this age of budget cuts and expenditure restraints. At the time of writing there are only five copies available in the German inter-library loan system three years after publication.

My second point concerns those notes, bibliography and index or what is known as the academic apparatus. On page 118 the author writes, “De Morgan’s ‘References for the History of Mathematical Sciences’ gives further insights into what he considered good history. He admired books that referred to primary materials, had clear accurate references and that provided a good index.” De Morgan would have loved this book. All quote and paraphrases are scrupulously sourced and the sources are given in accurate detail in the endnotes, all sources used also being listed in the extensive bibliography. I would add the index is also extensive and as far as I can tell accurate. I could do a whole post on books that have caused me extreme anguish because the page number given in the index for a particular theme was wrong! However I do have a quibble and that is endnotes. I’m one of those readers who reads the notes whilst I am reading the text often also referring to the bibliography at the same time to check the full details of a source given in the notes with just author and year; this means that I’m permanently flipping back and fourth within the book whilst I read. Footnotes3 instead of endnotes make life much more comfortable for me and in this age of text formatting computers are no more difficult to produce than endnotes so why the hell have the majority of academic publishers abandoned the footnote for the endnote?

Back to the book, Ms Higgitt reviews the, mostly English, biographies of Newton that appeared between 1820 and 1870 and shows how new methods of research and the use of new sources led to an almost complete revision of the historical image of Isaac Newton, very much laying the foundation stones for the currently accepted perception of the man. This analysis is not just conducted on the texts themselves but shows very clearly how these researches were motivated and directed by the external concerns of the authors. The disputes over the nature of light, wave or particular, the then actual discussion on the decline of science, in particular in Britain, the associated discussion on the scientific institutions in Britain, Royal Society, Royal Astronomical Society etc., theological concerns this being the age of religious emancipation in Britain, the very lively debate of the age on the nature of genius and half a dozen other contemporary topics. The author also uses the development of the Newton biographies to demonstrate how the biographers in their attempts to prove that their Newton was the one and only true Newton developed and utilised the modern methods of historiographical research. Interestingly at the same time showing that British historians of science were already utilising the methodologies supposedly invented by the so-called father of historiography Ranke before his work had become known in Britain.

This is a deeply researched and complex book that juggles half a dozen themes, skilfully weaving them together into a fascinating and stimulating narrative. Although always correctly academic and never superficial the author manages to present her arguments in a style that is very readable and highly enjoyable, for those unlike myself who are not too concerned with the endnotes, this book, although serious history, can be read as popular history of science and many authors of such books could do worse than to take Ms Higgitt as a role model.

In her conclusion the author writes, “This book was not conceived as a contribution to the modern field of Newton studies. While it does unpick the original appearance of various stories and sources that have become standard in any consideration of his life, it is not concerned with understanding Newton or his thoughts. The primary concern was to use the writings of Newton as a means of revealing nineteenth-century attitudes regarding the role of science and its practitioners within contemporary society. Developing from this research, however, was an appreciation of the innovations within both scientific biography and historical practice that these writings represent.” She has perfectly captured the essence of her book in these few lines and her book more than adequately fulfils her ‘primary concern’. I would unreservedly recommend this book to anybody with a serious interest in the biography of Isaac Newton, the development of (British) science in the nineteenth century or the historiography of science all of them can only profit from reading this excellent tome.

1)    Recreating Newton: Newtonian Biography and the Making of Nineteenth-Century History of Science, Rebekah Higgitt, Pickering & Chatto, London, 2007.

2)    I am strangely qualified to review this book, as two of my serious excursions into the history of science are/were extensive researches into the life and work of Isaac Newton and research into the history of British algebra of logic in the nineteenth- century. I have actually read and studied a large number of Newton biographies including several of those dealt with by Rebekah. At first glance it may seem the nineteenth-century Newton studies and the algebra of logic have little in common but appearance deceive. Like Rebekah I am more of an external than internal historian of science that is I research the social, cultural, economic etc environments in which science is created rather than the content that the scientists generate. In fact the research project in which I worked for several years was titled ‘social history of formal logic’. The time and milieu in which the algebra of logic was created is exactly the same as that researched by Rebekah in fact reading her book awoke a lot of half forgotten memories. There are even closer connections in the person of De Morgan who is one of the principle agents in Rebekah’s book and who was one of my main research objects. I too researched the Society for the Diffusion of Useful Knowledge, of which De Morgan was a prominent member, and whose English translation of Biot’s Newton biography starts Rebekah’s journey. I even researched in my study of De Morgan his dispute with Sir David Brewster on details of the Newton biography that forms the central part of Recreating Newton. There are other parallels as well but I will stop here before this footnote becomes longer than the main text.

3)    An interesting discussion of the footnote can be found in The Footnote a Curious History, Anthony Grafton, Faber & Faber, London, 1997. A book that I would heartily recommend to all lovers of intellectual trivia.


Filed under Book Reviews, History of science, Newton