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A Different Royal Society

What do the Penny Post, the Great Exhibition of 1851, the Albert & Victoria Museum, GCSEs, the iMac and the art works on the fourth plinth in Trafalgar Square all have in common? Their origins are all in someway connected to the Royal Society for the Encouragement of Arts, Manufactures and Commerce. The Royal Society for what, I hear you ask, or at least that was my reaction when I first read the name.

Few people have heard of the Royal Society for the Encouragement of Arts, Manufactures and Commerce. Even fewer know what it does. Many assume, as its name is usually abbreviated to the Royal Society of Arts, that it is all about art. It has certainly done a lot to promote art, but it has also done much more than that. In fact, the Society is by its very nature difficult to define. There is no other organisation quite like it, and nor has there ever been. It is in a category of its own.

The quoted paragraph is the opening paragraph to the introduction to Anton Howes’ Arts and MindsHow the Royal Society of Arts Changed a Nation[1], which is the fourth official history of the Society and the first written by an independent, professional historian. The first three were written by society secretaries. Howes’ book will answer any and all question that you might have about the Royal Society of Arts. In little more than three hundred pages he takes his readers on a whirl wind tour of three centuries of British political, social, cultural and economic history and the at times complex and influential role that the Society played in it. To describe Howes’ work as a tour de force barely does this superb piece of interdisciplinary history justice. 

One would be forgiven for assuming that the Royal Society of Arts (RSA) had nothing to do with the Royal Society that more usually features on this blog, but you would be mistaken. The RSA owes its existence very directly to its Royal cousin and not just in the sense of a society for the arts modelled on the one for science. The Royal Society of London was modelled on the natural philosophical concepts of Francis Bacon. A very central element of Bacon’s utopian vision of natural philosophy was that advances in the discipline would and should serve the improvement of human society, i.e. science in the service of humanity. This ideal got lost, pushed aside, forgotten fairly rapidly as the Royal Society evolved and in the eighteenth century various people discussed revitalising this Baconian utopian aim and after much discussion the result was the founding of the RSA, whose aims were to support efforts to improve human society. As a side note the Royal Society became royal on the day it was founded, whereas the RSA only acquired its royalty in the nineteenth century and didn’t actually call itself Royal until the early twentieth century.

The Society was founded as a subscription and premium society. Membership was open to all and members paid a yearly subscription. This money and other donations were then used to pay premiums to help people to develop ideas that were seen as improvements. From the beginning the whole concept of improvement and what could or should be improved was left very vague, so over the three centuries of its existence the Society has launched a bewildering assortment of projects over a very wide range of disciplines. A standard procedure was to select an area where improvement was thought necessary and then to write out a call for suggestions. The suggestions were then examined and those thought to be the best were awarded a premium. The areas chosen for improvement varied wildly and were mostly determined by powerful individuals or pressure groups, who managed to persuade the membership to follow their suggestions. Often those pressure groups, brought together by common aims within the RSA, moved on to found their own separate societies; one of the earliest was the Royal Society of Chemistry. Over the three centuries many other societies were born within the RSA.

Howes guides he readers skilfully through the meandering course that the Society took over the decades and centuries. Presenting the dominant figures, who succeeded in controlling the course of the Society for a period of time and the various schemes both successful and unsuccessful that they launched. One area that played a central role throughout the history of the RSA was art, but predominantly in the form of art applied to industrial design. However, the Society also encouraged the development of art as art putting on popular exhibitions of the art submitted for premiums. 

We follow the society through its highs and lows, through its periods of stagnation and its periods of rejuvenation. As the well-known cliché goes, times change and the society had to change with them. Howes in an excellent guide to those changes taking his readers into the depth of the societies’ problems and their solutions. Here one of his strengths is his analysis of the various attempts by the society to define a new role for itself since World War II and up to the present.

Having grown up in the second half of the twentieth century, I was pleasantly surprised to be reminded of two important socio-cultural developments from my youth, where I was not aware of the strong involvement of the RSA. The first was the beginning of the movement to conserve and preserve historical building and protect them from the rapacious post-war property developers. The Society was active in arranging the purchase of such buildings to place them out of harm’s way, even at one point buying an entire village. The second was the birth and establishment of environmentalism and the environmental protection movement in the UK, which was led by Peter Scott, of the Wildfowl Trust, and Prince Philip, who was President of the Society. It was for me a timely reminder that Phil the Greek, who these days has a well-earned bad reputation amongst left wing social warriors, actually spent many decades fighting for the preservation of wildlife and the environment. I was aware of this activity at the time but had largely forgotten it. I was, however, not aware that he had used his position as President of the RSA, and the Society itself, to launch his environmental campaigns. 

To go into great detail in this review would produce something longer than the book itself, so I’ll just add some notes to the list in my opening question. The Penny Post was a scheme launched by the society to make affordable and reliable written communication available to the general public. The Great Exhibition of 1851, the first ever world fair, was set in motion by the Society in imitation of and to overtrump the industrial fairs already fairly common in various cities on the continent. Howes takes us through the genesis of the original idea, the initial failure to make this idea a reality and then the creation of the Great Exhibition itself. This probably counts as the Societies greatest success. Two things I didn’t know is one that the Societies’ committee played a significant role in setting up and promoting later world fairs other countries in the nineteenth century and was responsible for the British contributions to those fairs. Secondly the desire to preserve much of the content of the Great Exhibition led to the setting up of the museums in South Kensington, including the V&A. 

To help working people acquire qualifications in a wide range of subjects and disciplines that they could then use to improve their positions, the Society set up public examinations, in the nineteenth century. As they became popular and widespread Oxford and Cambridge universities took over responsibility for those in academic disciplines and these are the distant ancestors of todays GCSEs. Jonathan Ive was Apple’s chief designer and the man behind the iMac, as a polytechnic student he won the RSA Student Design Award, which afforded him a small stipend and a travel expense account to use on a trip to the United States, which took him to Palo Alto and his first contact with the people, who would design for Apple. I was surprised to discover that the, at time controversial, scheme to present art works on the empty fourth plinth in Trafalgar Square also originated at the RSA.

This is just a small selection of the projects and schemes launched by the RSA and I found it fascinating whilst reading to discover more and more things that are attributable to the RSA’s efforts. Howes’ book is a historical and intellectual adventure story with many surprising discoveries waiting to be made by the reader. Despite being densely packed with details the book is highly readable and I found it a pleasure to read. It has extensive endnotes, which are both references to the very extensive bibliography, as well containing extra details to passages in the text. The whole is rounded out by a good index. As one would expect of a book about the greatest active supporter of design in UK history the book is stylishly presented. A pleasant and easy to read type face, a good selection of grey in grey illustrations and a good collection of colour plates. 

If you like good, stimulating and highly informative history books or just good books in general, then do yourself a favour and acquire Aton Howes’ excellent tome. No matter how much you think you might know about the last three centuries of British political, social, cultural and economic history, I guarantee that you will discover lots that you didn’t know. 


[1] Anton Howes, Arts and MindsHow the Royal Society of Arts Changed a Nation, Princeton University Press, Princeton & Oxford, 2020.

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Galileo was insufficiently woke?

We haven’t had a good Galileo rant here at the Renaissance Mathematicus for some time, but when you just begin to think that maybe people have stopped misusing the Tuscan natural philosopher for their own ends, up pops a new example and we’re off again.

My attention was drawn to today wonderful example by the following exchange on Twitter:

Seb Falk (@Seb_Falk): I’ve heard a lot of nonsense about Galileo, but persecuted by the Church for being insufficiently woke? That’s a new one on me.

Is there a Galileo-related law equivalent to Godwin’s Law? If not, Falk’s Law states that as a culture war continues, the probability that someone will invoke a mythologised account of the trial of Galileo in a specious defence of academic freedom approaches 1.

Dave Hitchcock (@Hitchcokian): Amazing. it shall definitely be known henceforth as Falk’s Law.

Seb Falk: I’m honoured – though I was just thinking that @rmathematicus has been calling this stuff out for so long we should call it Christie’s Law. Bloody history of science, always naming things after the wrong person

James Sumner (@JamesBSumner): Well, now, that’s perfectly consonant with Stigler’s law of eponymy

For those not aware of Stigler’s Law, it states that no scientific discovery is named after its original discoverer. Stigler’s law itself was in fact discovered by Robert K Merton and not Stephen Stigler.

So what was the piece about Galileo that provoked the creation of Falk’s Law?

Trevor Phillips (@MTREVORP) opens an article in the Times newspaper titled University bigots want to control minorities with the following:

Every scientist knows the Galileo story. When one of the greatest minds of the 17th (or any other) century concluded that, contrary to the Catholic Church’s teaching, the Earth was not the still centre of the universe but just one satellite of the sun he was for the high jump.

Subjected to six years at the hands of the Inquisition, character assassination and house arrest, he finally gave in and admitted his “wrongthink” but is reputed to have muttered under his breath “E pur si muove” – “Still, it moves”. The man whom Einstein called the father of modern science was said to be hurt most by the way his fellow philosophers abandoned him for fear of suffering the same fate.

I find it fascinating just how much a supposedly intelligent, educated, well informed writer can get wrong in just two very short paragraphs. We start with the opening sentence; experience has clearly shown that very few scientists know the actual Galileo story; most of them know one or other very mangled version of what might be termed the Galileo myth, which all have something in common, a factual, historical truth content on a par with an episode of Game of Thrones.

We then get the statutory hyperbollocks as soon as Galileo becomes the subject of discourse, “one of the greatest minds of the 17th (or any other) century.” This leads me to the thought, what if Galileo had not been hyped up to this larger than life, once in a century genius, would people be just as outraged if he had been mistreated by the Inquisition. Is it a worse crime if those in power mistreat a brilliant scientist, than if they mistreat Giuseppe, the guy who empties the trash cans? Not just here but in lots of things that I have read, I get the impression that is exactly what a very large number of people think. Are some lives really worth more than others? Their argument seems to be something along the lines of but Galileo changed the world, Giuseppe the trash can guy didn’t. What if the fact that Giuseppe was rotting in an Inquisition dungeon, instead of cleaning the streets led to an outbreak of cholera that wiped out half the population of the city? But I digress.

What follows is a significant misrepresentation of the facts that is dished every time somebody present their mythical version of the Galileo story and one that I have dealt with many times. It wasn’t just the Catholic Church’s teaching that we live in a geocentric cosmos but was the considered, majority opinion of informed astronomers based on the then available empirical evidence. Galileo was involved in a complex scientific debate on the astronomical and cosmological status of the solar system and was not this brilliant scientist taking on the ignorant, non-scientific, religious prejudices of the Catholic Church.  There are a couple of grammatical and lexigraphical anomalies in Phillips’ sentence that should have been picked up by a good sub-editor. If he is going to write Earth with a capital ‘E’ then he should also write sun with a capital ‘S’ and the earth is not a satellite of the sun it is a planet. Satellites orbit planets, planets orbit suns.

Subjected to six years at the hands of the Inquisition? Really? Galileo’s interrogation, trial and the passing of judgement by the Roman Inquisition lasted not quite four months, so I have literally no idea what Phillips is talking about here. I also have absolutely no idea what he means when he writes, “character assassination”, through out the whole affair he was treated with care and consideration and the respect due to him both because of his age and his reputation. Does one really need to repeat that Galileo was not tried for supporting the heliocentric hypothesis but for breaking an injunction from 1616 not to hold or teach the heliocentric theory as fact rather than, as a hypothesis? There was literally no question of “wrongthink”, Galileo was fully entitled to think what he liked about heliocentricity and even to express those thoughts verbally but he was not permitted to claim that heliocentricity was a proven fact. Just for the record, for the umpteenth time, it wasn’t. I find it almost funny that Phillips includes house arrest amongst the mistreatments before Galileo adjured. Having adjured he was, in fact, sentenced to imprisonment, which was immediately commuted to house arrest by the Pope, so after the fact not before.

Of course, having dished up a totally fictional account of Galileo’s dispute with the Church, Phillips doesn’t not spare us the “E pur si muove” – “Still, it moves” myth, in for a penny in for a pound. If we going to present fairy tales in place of historical accuracy then why not go the whole hog? We, natural, get that leading expert on the history of science, Albert Einstein, quoted on Galileo’s status in that history. Why ask a historian when you can ask Uncle Albert, the font of all wisdom? Another reminder, the expression ‘father of’ is a meaningless piece of crap.

Phillips’ last claim leaves me, once more, totally bewildered. “[Galileo] was said to be hurt most by the way his fellow philosophers abandoned him for fear of suffering the same fate.” There are two aspects to this claim. Firstly, the man, who is a serious candidate for the most egotistical and arrogant arsehole in the entire history of science and who spent a large part of his life actively insulting, denigrating and alienating ‘his fellow philosophers’ was hurt because they didn’t support him, really? Secondly, I have spent a life time reading about and studying Galileo and the historical context in which he lived and worked and I have never ever come across anybody claiming anything remotely like this claim made by Phillips. Put differently, Phillips is just making shit up to bolster the argument that he is going to present in his article. This is not history or journalism this is quite simply lying!

People used to refer to the Galileo Gambit, when somebody, almost always a crank, compared having his ‘fantastic ideas’ rejected to the Catholic Church’s persecution of Galileo. To this Bob Dylan delivered up the perfect retort:

He said, “They persecuted Jesus too.”

I said, “You’re not him.”

“I said you know, they refused Jesus, too. He said you’re not him.”

[Correct version of Dylan quote curtesy of Todd Timberlake]

Trevor Phillips delivers up a slightly different variation on the theme. He is using a totally mythical version of the Galileo story to beat people, who he disapproves of or disagrees with around the head. If he can’t make the points that he wishes to make without resorting to lies and deception in that he misuses an episode in the history of science then he should give up pretending to be a journalist.

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The emergence of modern astronomy – a complex mosaic: Part XXXVIII

At the end of the last section Isaac Newton was still a student, who had embarked on a six-year period of intensive study teaching himself the modern analytical mathematics, the basics of mechanics and optics.In 1666 during the phase when he was learning mechanics, principally from the works of Descartes and where like Huygens he corrected Descartes theories of elastic collision and Galileo’s false value for g, the acceleration due to gravity, he had his legendary flash on inspiration, possibly inspired by the equally legendary falling apple, in which he asked himself if the force that causes an object to fall to the ground is the same as the force that prevents the Moon from flying off at a tangent, as the law of inertia, acquired from Descartes, said it should. Newton made a back of an envelope calculation, which gave an interesting correlation but was somewhat inaccurate due to inaccurate input data. Newton dropped the line of enquiry and didn’t take it up again for almost twenty years. However, one aspect of his calculation was very important for the future. In order to calculate the force holding the Moon he plugged Kepler’s third law into Huygens’ formula for centripetal force, which led to the inverse square law of gravity.

In 1669, on the recommendation of Isaac Barrow the retiring incumbent, Newton was appointed Lucasian Professor of Mathematics at Cambridge University.The appointment was not as impressive as it appears today and Newton remained still largely under the radar, although the mathematics fan John Collins (1625–1683) had circulated some of his mathematical manuscripts awaking the world to his immense mathematical talent. This changed in the early 1670s when he presented the world with his reflecting telescope, the first functioning one, and published his first paper on the nature of white light. A new leading natural philosopher had arrived on the European stage.

In 1680 and 1681 two new great comets lit up the skies and once again the astronomers all turned their attentions into trying to determine their flight paths. The 1680 comet was discovered by the German astronomer Gottfried Kirch (1639–1710) from Coburg, who lived from writing and publishing almanacs, on 4 November.

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The Comet C/1680 V1 as seen over Nürnberg just south of Coburg with Georg Christoph Eimart’s observatory in the foreground Source

It was the first ever comet to be discovered by telescope, that is before it became visible to the naked eye. It remained visible until 7 December when it disappeared. The comet of 1681 first appeared on 20 December. One astronomer, John Flamsteed (1646–1719), who had been appointed Astronomer Royal for the new Royal Observatory at Greenwich in 1675, had the bright idea that these were not two separate comets but one single comet on its way to and from the sun (modern designation C/1680 V1). Unsure of his assumption Flamsteed turned to Isaac Newton to ask his opinion. Flamsteed did not know Newton personally so the contact, by letter, was initially through a mutual acquaintance at Cambridge.

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Historical picture of the first comet ever discovered using telescope,  the Great Comet of 1680 (C/1680 V1), as painted by Lieve Verschuier: Source

Flamsteed’s hypothesis was that the comet turned in front of the Sun upon reaching it; he, echoing Johannes Kepler, suggested that the comet was attracted to the Sun magnetically and then through a change in polarity as it neared the Sun repulsed. In two letters in February 1881 Newton dismantled Flamsteed’s hypothesis, concentrating on his magnetic argument but also not accepting that the two comets were actually just one. Newton had applied the inverse square law of gravity to a theoretical system consisting of a single planet and the Sun, a year earlier, but did not apparently consider applying it to the comet at this point in time. However, in a draft of his second letter to Flamsteed, which he never sent, he did sketch a dynamic system of the comet circling behind the Sun but in terms of magnetic attraction.

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John Flamsteed by Godfrey Kneller, 1702 Source. Wikimedia Commons

Later in the year Newton received new observational data on the comet from an old school acquaintance, Arthur Storer (c. 1648–1686) an amateur astronomer, who had emigrated to Maryland in 1679. He also later sent Newton data on the 1682 comet (Comet Halley), which he was amongst the first to observe in North America and which was named after him there for some time. Edmond Halley (1656–1741), an excellent astronomer and mathematician, who observed the comet of 1680/81, whilst travelling in France, also believed, like Flamsteed, that the two comets were one. In 1682 he came to Cambridge to visit Newton and the two of them discussed the comets.

Edmund_Halley

Source: Wikimedia Commons

Newton observed the comet of 1682 and at some point after 1680 he systematically collected together data on all recorded comets and decided that comets did indeed obey the inverse square law of gravity just like planets, their paths being oval if they returned and hyperbola if not. This was possibly the point where Newton’s thoughts on gravity became a universal theory of gravity. Comets and their flight paths would go on to play a significant role in the Principia. Newton apparently didn’t think to inform Flamsteed of his change of mind and acknowledge that Flamsteed had been right, at least in principle, until 1685.

Newton_Comet1680

The orbit of the comet of 1680, fit to a parabola, as shown in Isaac Newton’s Principia Source: Wikimedia Commons

Newton and Flamsteed were not the only people to reconsider the flight paths of comets in the early 1680s and Newton was not the only person to think that the inverse square law of gravity applied to them, Newton’s rival Robert Hooke also did so. Robert Hooke had been investigating the effects of gravity for many years and had discovered the inverse square law for himself and became convinced of a universal gravity. He thought that the flight paths of comets, like planets, were determined by gravity and that the inverse square law also applied to them. However, unlike Newton he didn’t do the mathematics. This mutual independent discovery of universal gravity would lead to renewed conflict between the two natural philosophers, who had already crossed swords over the nature of light.

 

 

 

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Eleven

Eleven is a number word in English that derives from the Old English ęndleofon, which is first attested in Bede’s Ecclesiastical History of the English People. There are cognates in all the Germanic languages, all of which have the same meaning of ‘one is left’. Left that is having counted up to ten. This is of course, a clear linguistic indication that we use, and have long used, a ten based, or decimal, number system contingent on the fact that through evolutionary chance we possess ten fingers or digits. Just to round up the picture twelve and its equivalents in other Germanic languages originally meant ‘two are left’ before we move onto thirteen, fourteen etc., which are simply three plus ten, four plus ten and so on and so fourth.

number-11-clipart

Coming back to eleven, on this day one year ago we celebrated, in our own inimitable way, the glorious tenth anniversary of the Renaissance Mathematicus that we are still here 366 days later, don’t forget that 2020 is a leap year, means that your favourite malcontent, #histSTM blogger has managed to fill yet another year with his incoherent scribblings. Counting up to ten we have one left. Ignoring such trivial matters, as the current world pandemic not much has changed in the world of the Renaissance Mathematicus. I have somehow managed, against my usually tendency to wander off and start something else, to complete another twenty-five slices of my, in the meantime, monumental series on the emergence of modern astronomy, bringing the word count up to a guesstimated fifty to sixty thousand. An end is actually in sight even if we haven’t quite reached it yet. This will be when the real work starts if I really want to turn it into a book. I need to go back to the beginning and basically rewrite the entire thing!

Turning to other matters, today is purely by chance the religious festival Corpus Christi or to give it it’s official title Dies Sanctissimi Corporis et Sanguinis Domini Iesu Christi (Day of the Most Holy Body and Blood of Jesus Christ the Lord), a Christian liturgical solemnity celebrating the Real Presence of the Body and Blood, Soul and Divinity of Jesus Christ in the elements of the Eucharist, to quote Wikipedia.

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Corpus Christi procession. Oil on canvas by Carl Emil Doepler Source: Wikimedia Commons

Now you might think that this particular piece of Catholic mumbo-jumbo (you might remember that one of the things that divided Catholics and Protestants during the Reformation, is that Protestants stopped believing that the bread and wine actually changed into the body and blood of Christ) has little or nothing to do with the history of science, you would be wrong.

To start with we need to address the chance bit. Corpus Christi, which is anchored to Easter, is one of those movable feasts in the Church calendar the irregular occurrences of which are determined by the Gregorian calendar, the introduction of which involved some very intricate astronomy and mathematics, which have the been the subject of a couple of blog posts here.

The actually Church feast was suggested by and campaigned for, thirty years long by Juliana of Liège (c. 1192–1258) prioress of the double canonry of Liège and her wish was granted by Pope Urban IV, who commissioned his chief theologian Thomas Aquinas (1225–1274) to compose an office for the Feast of Corpus Christi to be celebrated on the Thursday after Pentecost, which is itself celebrated fifty days after Easter Sunday. Thomas Aquinas plays a very central role in the history of European science, as it was he together with his teacher Albertus Magnus (before 1200–1280), who made Aristotelian natural philosophy acceptable for the Catholic Church, thus establishing it as the predominant scientific corpus in the European High Middle Ages.

The next #histSTM connection with the feast of Corpus Christi actually occurred in the life of Galileo. In his Il Saggiatore Galileo speculated a little bit with the ancient Greek theory of atomism. Because of this he was denounced anonymously to the Inquisition. The denunciation claimed that atomism contradicted the Church’s teaching on transubstantiation, which was based on the medieval Aristotelian theory of matter.  This distinguished between substantial and accidental properties of matter. In this theory the appearance of a piece of matter is accidental but its true nature is substantial. According to the transubstantiation theory the bread and the wine change in their substance into the body and blood of Christ whilst retaining the accidental appearance of bread and wine. If, however, the Aristotelian theory of matter were to be replaced with atomism this theory would no longer function. The Inquisition never proceeded against Galileo in this matter but it is of note that in England Thomas Harriot and Sir Walter Raleigh were held and questioned on a similar charge somewhat earlier.

Returning to personal matters, as is usually my wont in my birthday posts, I recently had an acrimonious exchange with one of my readers, whose comments were from the beginning aggressive, insulting and historically false. I tried to reason with him and he just got more abusive in his tone. In the end I blocked him and erased his comments but I found his parting shot insult, and it was clearly meant as an insult, fascinating; he stated that I was not a historian but a storyteller.

This is interesting because, as is very clear to see history and story share the same etymological root, the Latin historia, “narrative of past events, account, tale, story,” from Greek historia “a learning or knowing by inquiry; an account of one’s inquiries; knowledge, account, historical account, record, narrative.” It is not until the late 15thcentury that the two differentiated meanings for history and story began to slowly appear. In German the same word, Die Geschichte means both story and history, the different meanings depending on context.

Book of ideas

If I get asked in a formal or semi-formal context how I describe what I do, my answer is that I’m a narrative historian of the contextual history of science. That quite a mouthful and might sound, to some, rather pretentious. If I get asked what that means, my answer is I’m a storyteller. I don’t regard being called a storyteller as an insult; I regard it as a compliment.

 

 

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Another Negative Review

For those, who don’t always read the comments, Renaissance Mathematicus friend and sometime guest blogger, Chris Graney, who is also a leading expert on the arguments pro and contra heliocentricity in the early 17th century, has written another negative review of Galileo and the Science Deniers. More moderate in tone, than your favourite HIST_SCI HULK, but not in content, he also takes Mario Livio to the cleaners.

We will combat science denial by showing how vigorous scientific debate over a universally accepted set of facts was present at the very birth of modern science, as it often is in science today. Galileo and the Science Deniers does not do this, despite its author being a scientist. It retells a tale that is central to the genre of conspiracy and science denial, and so it will in all likelihood contribute to the very science denial problem it purports to help solve.

It is well worth a read, so pop on over and boost Professor Graney’s reader figures.

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My name is Bond, Jamie Bond.

Today we have a first at the Renaissance Mathematicus, a book review of two interrelated books that have nothing, or at least very little, to do with the histories of science and mathematics. They, however, both deal with England during the Revolution (Civil War) and Interregnum in the middle of the seventeenth century, so very much home territory for this blog.

The word spy is one that for most people instantly evokes a male figure, for someone of my generation, a man in a dinner jacket with a martini glass in one hand and a Beretta pistol in the other. Very few people would immediately associate the word spy with a woman, although there have been some notable female spies throughout history. Dutch historian of early modern English literature Nadine Akkerman, Reader at Leiden University, stumbled across a female spy during her research into the correspondence of Elizabeth Stuart, Queen of Bohemia (1596–1662), who lived out the last forty years of her life in The Hague. Inspired by this discovery Akkerman, who believed that female spies were perhaps not so rare as one might suspect, began to systematically search archives for traces of other women involved in espionage in the seventeenth century. The result of her researches appeared in a book two years ago, Invisible Agents: Women and Espionage in Seventeenth-Century Britain. [1] The paperback, that I’ve been reading, was published just this month.

Invisible Agents001

Akkerman’s book is a truly excellent piece of historical scholarship. Her, apparently tireless, excavations of the archives have turned up a large amount of evidence for the existence and activities of female spies, or as she prefers to call them she-intelligencers, as they were then commonly known, in the three decades of the seventeenth century, 1640s to1660s, in Britain. She has sorted, analysed and interpreted this flood of data to produce a coherent narrative about her she-intelligencers. From the start she explains that there is both too much data and too much of it fragmentary to produce a complete picture of the women involved in espionage in this period so instead she presents the reader with a series of case studies.

The first chapter deals with the mostly aristocratic women who worked as she-intelligencers for Charles I during his imprisonment by the parliamentary forces acting as couriers in the various plots to free the king. These women, on the whole, engaged in these activities out of loyalty to king and country. This is contrasted in the second chapter with accounts of the largely working class women, who sold information to Thurloe the parliamentary spymaster. Here we should note in particular, for later, her account of Diana Stewart, who appears to have supplied information to both sides, a double agent perhaps, or was she simply some sort of early modern con artist?

The third chapter is dedicated to the story of Susan Hyde, the sister of Sir Edward Hyde, a prominent royalist politician, who became 1st Earl of Clarendon and Lord Chancellor under Charles II. Susan Hyde was an active royalist she-intelligencer but has till now remained under the radar and Akkerman is the first to entangle and tell her story, giving it the attention it deserves. The next two chapters deal with Elizabeth Murray, who unlike Susan Hyde is a well-documented historical figure. Here Akkerman displays her analytical talents to the full. In the first chapter she deconstructs the accepted historical narrative about Murray and shows why it is at best dubious and at worst false. In the second chapter she reconstructs Murray’s story using the sources that she has excavated in her research.

Following Murray we have another Elizabeth, Elizabeth Carey, Lady Mordaunt. A she-intelligencer, who together with her husband was involved in espionage during the late phases of the Interregnum. Of particular interest here is Akkerman’s analysis of Carey through her correspondence with the gardener and diarist John Evelyn. Next up, is Anne, Lady Halkett and another deconstruction by Akkerman. This time she deconstructs the interpretations by other literary historians of Halkett’s own extensive written account of her espionage activities. The final figure in the book is probably the most well known female English author of the seventeenth century Aphra Behn, who was also a she-spy, or was she? Another deconstruction job by Akkerman.

Each subject in the book is presented in the full political and social context of her times. Her activities are described in as much detail as the sources allow and we, the readers, are introduced to the full array of early modern espionage activities. The post offices and the post routes the coded letters, the cyphers used, the secret societies, the counter espionage activities of the other side and the fate of those, who were trapped by those counter espionage activities. After having read Akkerman’s book one comes away with a rich knowledge of the activities of the seventeenth century English she-intelligencers.

Akkerman’s book is a masterpiece in the assimilation, ordering and interpretation of archival sources within a given historical area and can be held up as an example of how to do and present historical research. The book bristles with extensive footnotes, no endnotes, and has an equally extensive bibliography of both primary and secondary sources. The index is first class and is followed by an Index Occultus, a key to all the code names used in the original source documents for the historical characters in the book.

At the beginning I said this was a review of two interrelated book, the second is the novel Killing Beauties by Pete Langman[2].

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As far as I know this is Langman’s first novel but it is not, by a long chalk, his first artistic endeavour. A one time rock guitarist and then music teacher, he has worked as a music journalist, is a cricketer and along the way acquired a doctorate in early modern literature with a thesis about Francis Bacon. On a side note he gently and politely corrects me when I say something stupid about the Viscount St. Alban. Pete Langman also suffers from early-onset Parkinson’s disease and is the author of the highly acclaimed Slender Threads: A young person’s guide to Parkinson’s Disease.[3]

Pete Langman is also Nadine Akkerman’s partner and has borrowed two of the central figures from Invisible Agents, Diana Stewart and Susan Hyde, to weave a semi-fictional tale of espionage in the Interregnum, imaginatively filling out the gaps in Akkerman’s research.

Langman takes his readers on a fascinating journey through the streets, alleyways, drinking holes, apothecaries and seats of espionage of Interregnum London, evoking an authentic picture of life in the capital city in Cromwell’s time. A wide cast of fascinating and captivating characters lead the readers through the twists and turns of a risky espionage coup and the counter espionage moves to prevent that coup from being put into effect. None of the characters is entirely good or entirely bad but each of them is a real human being with all the normal faults and virtues, meaning that one doesn’t end up rooting for one side or the other, or at least I didn’t. There are enough twists and turns in the narrative to delight Agatha Christie fans and things don’t necessarily turn out, as you might have expected during the earlier chapters.

Langman’s voice is the authoritative voice of the seventeenth century historian but is is the voice of the story teller and not the lecturer, the artist and not the teacher. He recreates a visceral and authentic picture of a period of English history when the populous was torn between two philosophies of life and politics and some paid for their beliefs in one or other of those systems with their honour and even their lives.

His book is both an excellent historical novel and an excellent espionage novel that should delight fans of both genres and is also a wonderful companion to Akkerman’s historical presentation of the material. I would recommend both books to anybody interested in seventeenth century Britain, the history of espionage or simply just good writing. According to taste a potential reader can choose one or the other, but if you should choose to read both then I would recommend first reading Langman’s novel and then Akkerman’s historical presentation as the back story.

Disclosure: As should be obvious from various comments in this review, Pete Langman is an Internet friend, known as @elegantfowl on Twitter, with whom I share a mutual interest in the guitar playing of Gary Lucas and the history of seventeenth century science, amongst other things. Unbound is a crowd funding book publisher and when Pete announced on Twitter that he was trying to publish a novel on Unbound I became a subscriber, which is why I came to read Killing Beauties. Having read it, I was intrigued enough to acquire Invisible Agents when it appeared in paperback. Some might therefore not regard me as a neutral reviewer but as I have said in the past in similar circumstances if I didn’t like the book then I wouldn’t have reviewed it.

[1] Nadine Akkerman, Invisible Agents: Women and Espionage in Seventeenth-Century Britain, OUP, Oxford, 2018, ppb. 2020

[2] Pete Langman, Killing Beauties, Unbound, London, 2020.

[3] Pete Langman, Slender Threads: A young person’s guide to Parkinson’s Disease, Self Published, 2013. On a personal note, Pete said some very sensible and comforting things when I discussed my own problems with coming to terms with my brother’s Parkinson’s with him.

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Christmas Trilogy 2019 Part I: Would the real Mr Newton please stand up?

Probably the more wide spread and popular image of Isaac Newton is of him discovering the law of gravity after being hit on the head by a falling apple.

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For many generations of school kids throughout the world the name Newton is associated with his laws of motion and that law of gravity, often with unpleasant thoughts of having to solve physics home work problem involving them. For many Newton is the ‘father of modern science’ or the ‘father of physics’ or in some way synonymous with the scientific revolution. Also for those worldwide, generations of school kids he was the inventor/discoverer of the bane of mathematics the calculus. In reality, as well as his most well known achievements in mathematics, astronomy and physics, Newton took a lively interest in a surprising range of topics and, never a dabbler, he invested the full power of his vast intellect in whatever he undertook to investigate.

GodfreyKneller-IsaacNewton-1689

Portrait of Newton by Godfrey Kneller, 1689 Source: Wikimedia Commons

Born in Woolsthorpe Manor on 25 December 1642, the son of a yeoman farmer, who died before he was born, Newton grew up in a strongly puritan environment and remained deeply religious throughout his entire, very long life. He devoted an immense amount of time and energy to studying the Bible that tradition claims he could recite off by heart. He would learn both Greek and Hebrew in order to further his theological studies. His religious views were anything but orthodox and he was in fact probably an Arian i.e. he denied the concept of the Trinity believing in a Unitarian concept of God instead. He would have normally been required to take holy orders in order to become a professor at Cambridge and even considered leaving the university because he was not prepared to do so. Through the assistance of Isaac Barrow he was granted a special dispensation and was thus able to accept the Lucasian Chair without having to take holy orders. Although he wrote many papers on his religious beliefs, including his belief that the Catholic Church had corrupted the text of the Bible in order to justify their belief in the Holy Trinity, he largely kept his heterodox religious views to himself, sharing them only with selected sympathetic correspondents.

His religious views played a central role in his scientific endeavours as he believed that he was uncovering God’s plan of the universe. He went further than this in that he believed that he, and he alone, had been chosen by God to reveal that plan. He was also a prisca theologian, who believed that Adam and the early generations of humanity had had perfect knowledge of God’s creation and that this knowledge had been lost down through the succeeding generations. He was not discovering the plans of God’s creation but rediscovering them.

Newton was also, like many others in the High Middle Ages and the Early Modern Period, a millennialist that is he believed in a second coming and the end of the world. This led to the second of his great intellectual passions, history. Newton was a Bible chronologist, who thought that if he could accurately determine the date of creation and thus the current age of the Earth then he could also determine the time of the second coming. In order to do this he devoted a lot to the study of history in order to establish the time and durations of the great civilisations based, of course, around an analysis of the Old Testament as a historical source. He also tried, as an astronomer, to tie historical descriptions of astronomical phenomena, eclipses etc., to mathematically determined dates of those phenomena. This led other chronologists to eagerly await access to Newton’s chronological writings after his death hoping that the great astronomer mathematician would provide solid scientific evidence for his historical dating scheme. On the whole those hopes were disappointed when Newton’s chronological manuscripts did finally see the light of day.

Newton’s prisca theological beliefs also led to another of his better-known intellectual activities his alchemical investigations. He believed that alchemy was the oldest of all the sciences and that if he could unravel the secrets of this arcane discipline then it would bring him closer to knowledge of God’s creation plan. You will often see the highly incorrect assertion that the scientist Newton only turned to the occult alchemy in his dotage, after his scientific creativity had been drained; this is far from the truth. Newton began his alchemical studies in about 1666 at the height of his intellectual powers. He built a hut in the gardens of Trinity College, which served as his laboratory and devoted the winter months of the next thirty years to the serious study of alchemy. He read and annotated hundreds of alchemical manuscripts, carried out numerous experiments and wrote his own thoughts on the subject none of which he ever published. On interesting side note to this intensive engagement is that he used the knowledge of chemical processes that he had won to develop new and better methods of assaying when he was running the Royal Mint later in life.

The years that Newton devoted to the study of alchemy were also the years that he devoted to the study of mathematics, physics and astronomy. Those people who reached a high enough level in mathematics in their own education usually know than Newton is credited with being the co-creator, together with Leibniz, of the calculus. What most people don’t realise is just how vast Newton’s output of creative mathematics was. The edited edition of his collected mathematical papers runs to eight very thick, large format volumes covering a very wide range of mathematical topics. His scientific crowning glory is, of course, his Principia Mathematica (1687) combining, as it does a definitive, uniform presentation of the physical mechanics that had been developed piecemeal over the preceding two centuries adding much that was new in the process, as well as a complete consistent heliocentric model of the solar system. With this one book he established himself as Europe’s number one physicist and number one astronomer. He second masterpiece was his Opticks, created and written largely before the mathematics, mechanics and astronomy but first published, due to negative reactions to his first papers on the subject, in 1704. It was of course in this period that Newton was also Lucasian Professor of mathematics at Cambridge University. This however was not that much of a burden, as Newton famously had virtually no students attending his lectures. Mathematics was not particularly popular at English universities during the seventeenth century.

In 1696 Newton left the world of academia, and to some extent his scientific investigations, to start a completely new career as a government servant, first as warden then later as comptroller of the Royal Mint in London. He obtained this appointment through the services of one of his former students, Charles Montagu, later 1st Earl of Halifax, one of the most powerful Whig politicians and for a time Chancellor of the Exchequer. Newton’s association with Montagu illustrates another aspect of his life that of politician. Newton was a member of the Whig Party, who sat as an MP for Cambridge University, the universities were their own parliamentary constituencies, at the convention to settle the revolution of 1689. This was however one activity where Newton remained very passive and did nothing to distinguish himself. In 1705 Montagu persuaded him to stand again and even arranged for him to be knightedto increase his chances of election but he lost the election and thus ended his active political career.

The job at the Royal Mint, which Newton desired because he thought being a mere university professor did not fit his status as a leading European intellectual, was actually normally considered a political sinecure, i.e. the office holder was not actually expected to do anything, just hold the title and collect the pay. Others would actually do the work. Newton was not a man for sinecures. He plunged right in taking over the day-to-day running of the mint. He personally supervised the recoining of the nation, a monstrous task, which Montague had introduced as a measure to combat the debasement of the English currency. Newton applied his scientific mind to modernising the Mint, introducing as indicated above, new methods of chemically assaying metals. One of the responsibilities of the Warden of the Mint was to track down and bring to trial coiners, i.e. those who forged coin of the realm, and clippers, i.e. those who clipped are shaved metal of the edges of coins. The milling of the edges of coins was introduced in Newton’s times to make life more difficult for clippers. Normally a Warden would employ others to track down these criminals, Newton took on the job himself working as a sort of seventeenth century gumshoe[1]. He was very much a hands on boss and remained so until late in his life, when he began to hand over the reigns to John Conduit, the husband of his niece and housekeeper, Catherine Barton.

From 1704 onwards until his death, he was also President of the Royal Society, which he ruled in a very autocratic manner. Once again he was not prepared to be merely some sort of figurehead but was deeply engaged in shaping the society’s profile and business. In this role he also became a tourist attraction, foreign visitors to London attending meetings of the Royal Society in order to witness Sir Isaac Newton Europe’s greatest, living natural philosopher.

Although the term natural philosopher signifies what we would now call a scientist, Newton was also a philosopher in the true sense. Although, unlike Leibniz, he didn’t publish separate philosophical texts, his major works, the Principia Mathematica and the Opticks, both contain a lot of serious thoughts on the philosophy and methodology of science. He was also very much pulling the strings, as the puppet master, in the philosophical debate about Newton’s natural philosophy between Leibniz and Samuel Clarke, who acted as Newton’s mouth piece. Newton’s philosophical approach to science influenced, not necessarily positively, John Locke, David Hume and Immanuel Kant amongst others.

Last but perhaps by no means least there is an aspect to Newton that often gets overlooked, Newton the family man. This might seem like a contradiction in terms given that Newton lost his father before he was born and was abandoned as a small child by his mother, to be looked after by relatives, when she remarried. Newton, also, never married and had no children. However, he inherited the family’s not insubstantial holdings in Lincolnshire, they generated a yearly income of six hundred pounds at a time when the annual salary of the Astronomer Royal was one hundred pounds per annum. Newton brought his niece Catherine Barton to London to be his housekeeper and by no means treated her as a servant but as the lady of the house, who enjoyed the status of a lady in London’s high society. Newton also managed the family holdings personally and took good care of those members of his extended family living in Lincolnshire. Newton has acquired a historical reputation for being cantankerous and unfriendly but towards his extended family but also towards his scientific acolytes, the first so-called Newtonians, he could be and often was warm and generous.

Although the above is at best an inadequate sketch I hope I have made it clear that the real Isaac Newton was much more than a caricature of a scientist with an apple falling on his head. He was a theologian, historian, Bible chronologist, alchemist, mathematician, physicist, astronomer, public servant, detective, politician, society president, philosopher, farm manager and family man quite a lot for any individual.

[1] For an excellent account of this activity read Thomas Levenson’s Newton and the Counterfeiter, Houghton Mifflin Harcourt, 2009

 

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The Renaissance Mathematicus Christmas Trilogies explained for newcomers

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Being new to the Renaissance Mathematicus one might be excused if one assumed that the blogging activities were wound down over the Christmas period. However, exactly the opposite is true with the Renaissance Mathematicus going into hyper-drive posting its annual Christmas Trilogy, three blog posts in three days. Three of my favourite scientific figures have their birthday over Christmas–Isaac Newton 25thDecember, Charles Babbage 26thDecember and Johannes Kepler 27thDecember–and I write a blog post for each of them on their respective birthdays. Before somebody quibbles I am aware that the birthdays of Newton and Kepler are both old style, i.e. on the Julian Calendar, and Babbage new style, i.e. on the Gregorian Calendar but to be honest, in this case I don’t give a shit. So if you are looking for some #histSTM entertainment or possibly enlightenment over the holiday period the Renaissance Mathematicus is your number one address. In case the new trilogy is not enough for you:

The Trilogies of Christmas Past

Christmas Trilogy 2009 Post 1

Christmas Trilogy 2009 Post 2

Christmas Trilogy 2009 Post 3

Christmas Trilogy 2010 Post 1

Christmas Trilogy 2010 Post 2

Christmas Trilogy 2010 Post 3

Christmas Trilogy 2011 Post 1

Christmas Trilogy 2011 Post 2

Christmas Trilogy 2011 Post 3

Christmas Trilogy 2012 Post 1

Christmas Trilogy 2012 Post 2

Christmas Trilogy 2012 Post 3

Christmas Trilogy 2013 Post 1

Christmas Trilogy 2013 Post 2

Christmas Trilogy 2013 Post 3

Christmas Trilogy 2014 Post 1

Christmas Trilogy 2014 Post 2

Christmas Trilogy 2014 Post 3

Christmas Trilogy 2015 Post 1

Christmas Trilogy 2015 Post 2

Christmas Trilogy 2015 Post 3

Christmas Trilogy 2016 Post 1

Christmas Trilogy 2016 Post 2

Christmas Trilogy 2016 Post 3

Christmas Trilogy 2017 Post 1

Christmas Trilogy 2017 Post 2

Christmas Trilogy 2017 Post 3

Christmas Trilogy 2018 Post 1

Christmas Trilogy 2018 Post 2

Christmas Trilogy 2018 Post 3

 

 

 

 

 

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On Becoming German

Ten days ago I got my Personalausweis (identity card), which kind of make me feel like a real German citizen for the first time, although my certificate of naturalisation was issued on the 15 October and I officially became a German citizen when it was handed to me 21 October. It’s a rather strange feeling to become a citizen of another country, although as a EU citizen I retain my British citizenship and am thus a dual national.

It is a move I have been considering making for several years now, but as a ADDer with dysgraphia I hate, fear and loathe all bureaucracy, so my innerer Schweinehund (translates roughly as internal lazy hound) kept me from making it. The result of the Brexit referendum finally pushed me to get off my fat arse and do something but even then my inertia held me back. Last autumn I paid two hundred plus euro and took my German language and German citizenship exams. The first shouldn’t have been necessary, as I took and passed the much harder university German Language exam three decades ago but couldn’t prove it, the records have got lost, so I spent a whole day proving that I could master the German language. The citizenship exam was a joke. You have to answer 33 multiple-choice questions, 28 of which are taken from a catalogue of 3000 questions that you can read and learn on the Internet (I didn’t bother) and 5 specific to the German State in which you live, in my case Bavaria. To pass you have to get at least 17 right. You have 60 minutes for the exam; I took 4 minutes and I wasn’t the fastest. I got 31 right and am annoyed because I know one that I got wrong but have no idea what the other one was!

Having taken this step I still kept putting off having to actually deal with the bureaucracy. Eventually on 27 March just four days before the final Brexit deadline (remember that?!) I finally pulled myself together and submitted my application for German citizenship; with all the forms, documents and whatever that I had to submit, the pile was literally three centimetres thick; the Germans are very thorough. And then you sit and wait! I was actually fairly convinced that my application would be rejected because of lack of financial support. Having led a rather fucked up life, I live on a basic state pension, which is a pittance and have no financial resources whatsoever. I got more and more nervous as the next Brexit deadline approached fearing, I would become an undesirable alien in my country of residence. I breathed a deep sigh of relief when I received the letter telling me to come and collect my certificate of naturalisation.

Having changed my nationality or rather acquired a second one as I am now a dual national, as I said above, I suppose I should feel something but I don’t and don’t really know what I’m supposed to feel.

I’m a white, middle class male born of British parents in Clacton-on-Sea of all places, so I suppose I couldn’t really be more British. However, as I pointed out in an earlier post my mother, although British, was born in Burma and grew up in British India first coming to Europe at the age of thirty-one. I’ve never really identified as British. It’s a word I fill in, in the appropriate section on official forms that ask for my nationality and it’s what is on the front of my passport. I enjoy watching sport but have never been particularly or even mildly fanatical about any team. Except for in rugby, which I played and enjoyed at school, and the Olympics there are no British sports teams but separate ones for England, Scotland, Wales and Northern Ireland. I take an Englishman’s perverse pleasure, I think the term is schadenfreude, in watching the inevitable English bating collapse in test matches or another golden generation of English soccer players crashing out of yet another European/World Cup. But that’s about it. I’ve never understood sentiments like “my country right or wrong” or dying for “king and country.” I’m a lifelong pacifist, who would adopt Bertrand Russell’s policy if those that I love and care for were threatened by fascism or anything similar and do what ever was necessary to oppose.

I vaguely identify as a West European; I have lived in England, Wales, Belgium, Sweden and the largest part of my life in Germany, Middle Franconia to be precise. Beyond that, I have travelled and holidayed in Denmark, Holland, France, Spain, Italy, Luxembourg, Andorra and Lichtenstein. However, my family background and my upbringing have led me to regard all culture and peoples to be fundamentally the same and to abhor discrimination of any sort.

I identify Middle Franconia in general and the area in and around Erlangen in particular, as being my Wahlheimat, Heimat is the German for home, home town, home country but has connotations of belonging that can’t really be translated into English and Wahlheimat is Heimat of choice. It’s where I feel at home, comfortable and everything else considered where I would like to live out the rest of my life. All of this was true before I applied for German citizenship and being granted it hasn’t really changed anything.

Going through the process of acquiring a new nationality has shown me that the word nationality really doesn’t have any deep meaning for me at all. I probably shouldn’t but I worry slightly about this realisation.

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Finding your way on the Seven Seas in the Early Modern Period

I spend a lot of my time trying to unravel and understand the complex bundle that is Renaissance or Early Modern mathematics and the people who practiced it. Regular readers of this blog should by now be well aware that the Renaissance mathematici, or mathematical practitioners as they are generally known in English, did not work on mathematics as we would understand it today but on practical mathematics that we might be inclined, somewhat mistakenly, to label applied mathematics. One group of disciplines that we often find treated together by one and the same practitioner consists of astronomy, cartography, navigation and the design and construction of tables and instruments to aid the study of these. This being the case I was delighted to receive a review copy of Margaret E. Schotte’s Sailing School: Navigating Science and Skill, 1550–1800[1], which deals with exactly this group of practical mathematical skills as applied to the real world of deep-sea sailing.

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Schotte’s book takes the reader on a journey both through time and around the major sea going nations of Europe, explaining, as she goes, how each of these nations dealt with the problem of educating, or maybe that should rather be training, seamen to become navigators for their navel and merchant fleets, as the Europeans began to span the world in their sailing ships both for exploration and trade.

Having set the course for the reader in a detailed introduction, Schotte sets sail from the Iberian peninsular in the sixteenth century. It was from there that the first Europeans set out on deep-sea voyages and it was here that it was first realised that navigators for such voyages could and probably should be trained. Next we travel up the coast of the Atlantic to Holland in the seventeenth century, where the Dutch set out to conquer the oceans and establish themselves as the world’s leading maritime nation with a wide range of training possibilities for deep-sea navigators, extending the foundations laid by the Spanish and Portuguese. Towards the end of the century we seek harbour in France to see how the French are training their navigators. Next port of call is England, a land that would famously go on, in their own estimation, to rule the seven seas. In the eighteenth century we cross the Channel back to Holland and the advances made over the last hundred years. The final chapter takes us to the end of the eighteenth century and the extraordinary story of the English seaman Lieutenant Riou, whose ship the HMS Guardian hit an iceberg in the Southern Atlantic. Lacking enough boats to evacuate all of his crew and passengers, Riou made temporary repairs to his vessel and motivating his men to continuously pump out the waters leaking into the rump of his ship, he then by a process of masterful navigation, on a level with his contemporaries Cook and Bligh, brought the badly damaged frigate to safety in South Africa.

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In each of our ports of call Schotte outlines and explains the training conceived by the authorities for training navigators and examines how it was or was not put into practice. Methods of determining latitude and longitude, sailing speeds and distances covered are described and explained. The differences in approach to this training developed in each of the sea going European nations are carefully presented and contrasted. Of special interest is the breach in understanding of what is necessary for a trainee navigator between the mathematical practitioners, who were appointed to teach those trainees, and the seamen, who were being trained, a large yawning gap between theory and practice. When discussing the Dutch approach to training Schotte clearly describes why experienced coastal navigators do not, without retraining, make good deep-sea navigators. The methodologies of these two areas of the art of navigation are substantially different.

The reader gets introduced to the methodologies used by deep-sea navigators, the mathematics developed, the tables considered necessary and the instruments and charts that were put to use. Of particular interest are the rules of thumb utilised to make course corrections before accurate methods of determining longitude were developed. There are also detailed discussions about how one or other aspect of the art of navigation was emphasised in the training in one country but considered less important in another. One conclusion the Schotte draws is that there is not really a discernable gradient of progress in the methods taught and the methods of teaching them over the two hundred and fifty years covered by the book.

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As well as everything you wanted to know about navigating sailing ships but were too afraid to ask, Schotte also delivers interesting knowledge of other areas. Theories of education come to the fore but an aspect that I found particularly fascinating were her comments on the book trade. Throughout the period covered, the teachers of navigation wrote and marketed books on the art of navigation. These books were fairly diverse and written for differing readers. Some were conceived as textbooks for the apprentice navigators whilst others were obviously written for interested, educated laymen, who would never navigate a ship. Later, as written exams began to play a greater role in the education of the aspirant navigators, authors and publishers began to market books of specimen exam questions as preparation for the exams. These books also went through an interesting evolution. Schotte deals with this topic in quite a lot of detail discussing the authors, publishers and booksellers, who were engaged in this market of navigational literature. This is detailed enough to be of interest to book historians, who might not really be interested in the history of navigation per se.

Schotte is excellent writer and the book is truly a pleasure to read. On a physical level the book is beautifully presented with lots of fascinating and highly informative illustrations. The apparatus starts with a very useful glossary of technical terms. There is a very extensive bibliography and an equally extensive and useful index. My only complaint concerns the notes, which are endnotes and not footnotes. These are in fact very extensive and highly informative containing lots of additional information not contained in the main text. I found myself continually leafing back and forth between main text and endnotes, making continuous reading almost impossible. In the end I developed a method of reading so many pages of main text followed by reading the endnotes for that section of the main text, mentally noting the number of particular endnotes that I wished to especially consult. Not ideal by any means.

This book is an essential read for anybody directly or indirectly interested in the history of navigation and also the history of practical mathematics. If however you are generally interested in good, well researched, well written history then you will almost certainly get a great deal of pleasure from reading this book.

[1] Margaret E. Schotte, Sailing School: Navigating Science and Skill, 1550–1800, Johns Hopkins University Press, Baltimore, 2019.

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