Category Archives: Book Reviews

Reading Euclid

This is an addendum to yesterday review of Reading Mathematics in Early Modern Europe. As I noted there the book was an outcome of two workshops held, as part of the research project Reading Euclid that ran from 2016 to 2018. The project, which was based at Oxford University was led by Benjamin Wardhaugh, Yelda Nasifoglu (@YeldaNasif) and Philip Beeley.

The research project has its own website and Twitter account @ReadingEuclid. As well as Benjamin Wardhaugh’s The Book of Wonders: The Many Lives of Euclid’s Elements, which I reviewed here:


And Reading Mathematics in Early Modern EuropeStudies in the Production, Collection, and Use of Mathematical Books, which I reviewed yesterday.

Reading Maths01

There is also a third online publication Euclid in print, 1482–1703: A catalogue of the editions of the Elements and other Euclidian Works, which is open access and can be downloaded as a pdf for free.

All of this is essential reading for anybody interested in the history of the most often published mathematics textbook of all times.

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There’s more to reading than just looking at the words

When I first became interested in the history of mathematics, now literally a lifetime ago, it was dominated by a big events, big names approach to the discipline. It was also largely presentist, only interested in those aspects of the history that are still relevant in the present. As well as this, it was internalist history only interested in results and not really interested in any aspects of the context in which those results were created. This began to change as some historians began to research the external circumstances in which the mathematics itself was created and also the context, which was often different to the context in which the mathematics is used today. This led to the internalist-externalist debate in which the generation of strictly internalist historians questioned the sense of doing external history with many of them rejecting the approach completely.

As I have said on several occasions, in the 1980s, I served my own apprenticeship, as a mature student, as a historian of science in a major research project into the external history of formal or mathematical logic. As far as I know it was the first such research project in this area. In the intervening years things have evolved substantially and every aspect of the history of mathematics is open to the historian. During my lifetime the history of the book has undergone a similar trajectory, moving from the big names, big events modus to a much more open and diverse approach.

The two streams converged some time back and there are now interesting approaches to examining in depth mathematical publications in the contexts of their genesis, their continuing history and their use over the years. I recently reviewed a fascinating volume in this genre, Benjamin Wardhaugh’s The Book of Wonder: The Many Lives of Euclid’s Elements. Wardhaugh was a central figure in the Oxford-based Reading Euclid research project (2016–2018) and I now have a second volume that has grown out of two workshops, which took place within that project, Reading Mathematics in Early Modern Europe: Studies in the Production, Collection, and Use of Mathematical Books[1]. As the subtitle implies this is a wide-ranging and stimulating collection of papers covering many different aspects of how writers, researchers, and readers dealt with the mathematical written word in the Early Modern Period.

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In general, the academic standard of all the papers presented here is at the highest level.  The authors of the individual papers are all very obviously experts on the themes that they write about and display a high-level of knowledge on them. However, all of the papers are well written, easily accessible and easy to understand for the non-expert. The book opens with a ten-page introduction that explains what is being presented here is clear, simple terms for those new to the field of study, which, I suspect, will probably the majority of the readers.

The first paper deals with Euclid, which is not surprising given the origin of the volume. Vincenzo De Risi takes use through the discussion in the 16th and 17th centuries by mathematical readers of the Elements of Book 1, Proposition 1 and whether Euclid makes a hidden assumption in his construction. Risi points out that this discussion is normally attributed to Pasch and Hilbert in the 19th century but that the Early Modern mathematicians were very much on the ball three hundred years earlier.

We stay with Euclid and his Elements in the second paper by Robert Goulding, who takes us through Henry Savile’s attempts to understand and maybe improve on the Euclidean theory of proportions. Savile, best known for giving his name and his money to establish the first chairs for mathematics and astronomy at the University of Oxford, is an important figure in Early Modern mathematics, who largely gets ignored in the big names, big events history of the subject, but quite rightly turns up a couple of times here. Goulding guides the reader skilfully through Savile’s struggles with the Euclidean theory, an interesting insight into the thought processes of an undeniably, brilliant polymath.

In the third paper, Yelda Nasifoglu stays with Euclid and geometry but takes the reader into a completely different aspect of reading, namely how did Early Modern mathematicians read, that is interpret and present geometrical drawings? Thereby, she demonstrates very clearly how this process changed over time, with the readings of the diagrams evolving and changing with successive generations.

We stick with the reading of a diagram, but leave Euclid, with the fourth paper from Renée Raphael, who goes through the various reactions of readers to a problematic diagram that Tycho Brahe used to argue that the comet of 1577 was supralunar. It is interesting and very informative, how Tycho’s opponents and supporters used different reading strategies to justify their standpoints on the question. It illuminates very clearly that one brings a preformed opinion to a given text when reading, there is no tabula rasa.

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We change direction completely with Mordechai Feingold, who takes us through the reading of mathematics in the English collegiate-humanist universities. This is a far from trivial topic, as the Early Modern humanist scholars were, at least superficially, not really interested in the mathematical sciences. Feingold elucidates the ambivalent attitude of the humanists to mathematical topics in detail. This paper was of particular interest to me, as I am currently trying to deepen and expand my knowledge of Renaissance science.

Richard Oosterhoff, in his paper, takes us into the mathematical world of the relatively obscure Oxford fellow and tutor Brian Twyne (1581–1644). Twyne’s manuscript mathematical notes, complied from various sources open a window on the actual level and style of mathematics’ teaching at the university in the Early Modern Period, which is somewhat removed from what one might have expected.

Librarian William Poole takes us back to Henry Savile. As well as giving his name and his money to the Savilian mathematical chairs, Savile also donated his library of books and manuscripts to be used by the Savilian professors in their work. Poole takes us on a highly informative tour of that library from its foundations by Savile and on through the usage, additions and occasional subtractions made by the Savilian professors down to the end of the 17th century.

Philip Beeley reintroduced me to a recently acquired 17th century mathematical friend, Edward Bernard and his doomed attempt to produce and publish an annotated, Greek/Latin, definitive editions of the Elements. I first became aware of Bernard in Wardhaugh’s The Book of Wonder. Whereas Wardhaugh, in his account, concentrated on the extraordinary one off, trilingual, annotated, Euclid (Greek, Latin, Arabic) that Bernard put together to aid his research and which is currently housed in the Bodleian, Beeley examines Bernard’s increasing desperate attempts to find sponsors to promote the subscription scheme that is intended to finance his planned volume. This is discussed within the context of the problems involved in the late 17th and early 18th century in getting publishers to finance serious academic publications at all. The paper closes with an account of the history behind the editing and publishing of David Gregory’s Euclid, which also failed to find financial backers and was in the end paid for by the university.

Following highbrow publications, Wardhaugh’s own contribution to this volume goes down market to the world of Georgian mathematical textbooks and their readers annotations. Wardhaugh devotes a large part of his paper to the methodology he uses to sort and categorise the annotations in the 366 copies of the books that he examined. He acknowledges that any conclusions that he draws from his investigations are tentative, but his paper definitely indicates a direction for more research of this type.

Boris Jardine takes us back to the 16th century and the Pantometria co-authored by father and son Leonard and Thomas Digges. This was a popular book of practical mathematics in its time and well into the 17th century. Jardine examines how such a practical mathematics text was read and then utilised by its readers.

Kevin Tracey closes out the volume with a final contribution on lowbrow mathematical literature and its readers with an examination of John Seller’s A Pocket Book, a compendium of a wide range of elementary mathematical topics written for the layman. Following a brief description of Seller’s career as an instrument maker, cartographer and mathematical book author, Tracey examines marginalia in copies of the book and shows that it was also actually used by university undergraduates.

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The book is nicely presented and in the relevant papers illustrated with the now ubiquitous grey in grey prints. Each paper has its own collection of detailed, informative, largely bibliographical endnotes. The books referenced in those endnotes are collected in an extensive bibliography at the end of the book and there is also a comprehensive index.

As a whole, this volume meets the highest standards for an academic publication, whilst remaining very accessible for the general reader. This book should definitely be read by all those interested in the history of mathematics in the Early Modern Period and in fact by anybody interested in the history of mathematics. It is also a book for those interested in the history of the book and in the comparatively new discipline, the history of reading. I would go further and recommend it for general historians of the Early Modern Period, as well as interested non experts.

[1] Reading Mathematics in Early Modern Europe: Studies in the Production, Collection, and Use of Mathematical Books, eds. Philip Beeley, Yelda Nasifoglu and Benjamin Wardhaugh, Material Readings in Early Modern Culture, Routledge, New York and London, 2021

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A book is a book is a book is a book


I assume that most of the people reading this would agree that a book is for reading. The writer of the book puts their words down on the page and the reader reads them; it is a form of interpersonal communication. However, if one stops to think about it books also fulfil many other functions and book historian Tom Mole has not only thought long and deeply about it but has put those thoughts down, as a series of essays, in the pages of a book to read, his delightful The Secret Life of Books: why they mean more than words[1], which has recently appeared in paperback.


I will say a bit more about Mole’s book about books not just being books to read in a bit, but first I want to sketch what books have meant in my life, thoughts provoked by his opening essay. Mole describes a university professor, he had as a student, whose office slowly disappeared under steadily increasing number of books. Ever more books meant ever more bookcases until the weight threatened the structural integrity of the building. This is a scenario that speaks volumes to me, and I suspect to many other lifelong book consumers.

I grew up in a house full of books. My father was a university teacher, and my mother was a voracious book reader. Reading books was an integral part of our family life, as long as I can remember. We, the four kids in the family, had a playroom, when we were small. In this playroom there was a book cupboard containing a collection of several hundred children’s books, a collection that grew steadily every year. I had taught myself to read by the time I was about three years old and at around the same age I acquired my first library card. Once a week the family would walk the short stretch to the village library, housed in the primary school, and each one of us would choose new reading matter for the following seven days. My mother always returned from these trips with four new novels, which would be consumed before the next outing. That library was a treasure trove; I can still remember the joy I experienced the first time I discovered Crockett Johnson’s Harold and the Purple Crayon. Later I was always excited to take home a new volume of Mary Norton’s The Borrowers or Richmal Crompton’s William Brown series.

Moving forward in time, when my mother died I, as the only child still living at home, was pushed off to boarding school, there was an excellent school library, and my father and I left our Essex village and moved to London, where my father worked. At the beginning we didn’t have a house, so we lived in the Royal Anthropological Institute on Bedford Square, which my father ran in those days. He had a small bedsitting room with an attached kitchen, that was his office and during the school holidays or weekends home I slept, on an inflatable mattress, on the floor of the Sir Richard Burton Library, that’s the nineteenth century explorer infamous for his translation of The Perfumed Garden. I can assure you that the bookshelves only contained boring tomes on geography, anthropology etc., and no porn, I checked.

When we did finally acquire a house in Colville Place, one of the most beautiful streets in London. My father and I spent several weeks lining the walls of the house with self-constructed bookshelves to house not only his books from our family home but from his office at the RAI and his office at SOAS, where he taught. That house didn’t need any wall paper. During the time that I lived there, now a maturing teenager, I perused many of the fascinating volumes on those shelves covering a bewildering range of topics.

Over the years, books continued to play a very central role in my life and I still own quite a few of the volumes that I acquired over the next decade that very much shaped the historian I am today. For example, Hofstader’s Gödel, Escher, Bach: an Eternal Golden Braid, Bronowski’s The Ascent of Man, Lakatos’ Proofs and Refutations, Criticism and the Growthof Knowledge edited by Lakatos & Musgrave, Polya’s How to Solve It, and Boyer’s A History of Mathematics. They are old friends and have shared my living spaces for more than forty years.

As regular readers of this blog will know, I moved to Germany forty years ago and one year later I started to study at the University of Erlangen. The professor, who most influenced and shaped me, Christian Thiel, is also a serious book consumer. The walls of his university office were completely covered with books and over the years his desk, the windowsills and the floor all acquired steadily growing piles of books. Thiel is the owner of a fairly large house and he is also a serious collector of logic books, he is said to own the second largest such private collection in the world. The walls of most of the rooms in his house are lined with this collection. It reached a point where his wife dictated that he could only acquire new volumes if he sold the same width in centimetres of the old ones.

The walls of my small appartement, where I am sitting typing this, are also lined with bookshelves, except for the 2,60 metres covered by my CD shelves. Those bookshelves are filled, to overflowing and the piles of not shelved books continue to grow. I keep telling myself that I must stop acquiring books or at least dispose of some of them but the thought of parting with one of them is on a par with the thought of having teeth extracted without anaesthetic and as I write, four new books are winging there way to my humble abode from various corners of the world.

My name is Thony and I am a bookaholic.

Returning to the volume that inspired this autobiographical outburst, as already mentioned above, Tom Mole’s book is really a collection of eight essays each of which deals with a different aspect of the book as not reading matter. There are also three interludes that take a look at books depicted in paintings, surely a topic for a whole book. I’m not going to go into detail because that would spoil the pleasure that the reader will get out of these carefully crafted gems, but I will list the topics as given in the essay titles: 1) Book/Book, 2) Book/Thing, 3) Book/Bookshelf[2] 4) Book/Relationship 5) Book/Life 6) Book/World 7) Book/Technology 8) Book/Future

 The book is completed with a relatively small number of endnotes for each chapter, which include bibliographical references for deeper reading on the given theme and an adequate index.

If you are a book lover then this is definitively a book you will want to own and read. Both the original hardback and the paperback are at almost throwaway prices and this small volume would make a perfect stocking filler for the bookaholic in your life. However, be warned if you do give them this book for Christmas, they probably won’t speak anymore after unpacking it, as their nose will be buried in The Secret Life of Books.


[1] Tom Mole, The Secret Life of Books: why they mean more than words, ppb., Elliot & Thompson, London 2020

[2] Mole is going to push me to buy Henry Petroski’s classic study (Mole’s term) The Book on the Bookshelf, London: Vintage, 2000. I already own Petroski’s The Pencil, Alfred A. Knopf, New York, 2004 and it’s brilliant.


Filed under Autobiographical, Book Reviews

You can con all of the people some of the time, and some of the people all of the time, but you can’t con all of the people all of the time. However, you can con enough people long enough to cause a financial crisis.


The name Isaac Newton evokes for most people the discovery of the law of gravity[1] and if they remember enough of their school physics his three laws of motion. For those with some knowledge of the history of mathematics his name is also connected with the creation of calculus.[2] However, Newton lived eighty-four years and his life was very full and very complex, but most people know very little about that life. One intriguing fact is that in 1720/21 Newton lost £25,000 in the collapse of the so-called South Sea Bubble. A modern reader might think that £25,000 is a tidy sum but not the world. However, in 1720 £25,000 was the equivalent of several million ponds today. Beyond this, when he died about eight years later his estate was still worth about the same sum. Taken together this means that Isaac Newton was in his later life a vey wealthy man.

These details out of Newton’s later life raise a whole lot of questions. Amongst other, how did he become so wealthy? What was the South Sea Bubble and how did Newton come to lose so much money when it collapsed? Science writer and Renaissance Mathematicus friend,[3] Tom Levenson newest book, Money for Nothing [4], offers detailed answers to the last two questions but not the first[5].


Both Newton and the South Sea Bubble play central roles in Levenson’s book but they are actually only bit players in his story. The real theme of the book is the birth of the modern world of political and capitalist finance in which both the creation of the South Sea Company and its eventual collapse played a dominant role. You can find explanations and the origins of all the gobbledegook that gets spouted in tv, radio and print-media finance reports, derivatives, call and put options, etc. It is also here that the significance Newton as a central figure becomes clear. There were other notable figures in the early eighteenth century, who made or lost greater fortunes than the substantial loses that Newton suffered, but he is really here for different and important reasons.

One reason for Newton’s presence is, of course, his role as boss of the Royal Mint during this period and his secondary role as financial consultant and advisor. Another reason is that central feature of this new emerging world of finance was the application of mathematical modelling, parallel to the mathematical modelling in physics and astronomy, in which Newton is very much the dominant figure, not just in the very recently created United Kingdom.  

We get introduced the work of William Petty and Edmond Halley, who applied the recently created branches of mathematics, statistics and probability, to social and political problems.


I found particular interesting the work of Archibald Hutchinson, who I’d never come across before, who carried out a deep and extensive mathematical analysis of the South Sea Company scheme, basically to turn the national debt into shares of a joint stock company, which promised a dividend, could not work as it existed because the South Sea Company would never generate enough profit to fulfil its commitments to its shareholders. Whilst the South Sea Company was booming and everybody was scrabbling to obtain shares at vastly inflated prices, Hutchinson’s cool analytical warnings of doom were ignored, he was truly a prophet crying in the wilderness. After the event when he had been proved right nobody was interested in hearing, I told you so.


Another fascinating figure, who was new to me, is John Law, a brilliant mathematician and felon[6], who landed up in France and through his mathematical analysis became the most powerful figure in French financial politics. Law created the comparatively new concept of paper money (new that is in Europe, the Chinese had had printed paper money for centuries by this time) and the Mississippi Company, which served a similar function to the South Sea Company, to deal with the French national debt. The Mississippi Company collapsed just as spectacularly as the South Sea Company and Law was forced to flee France.


Levenson goes on to show how the French and UK governments each dealt with the financial disasters that their experiments in modern finance had delivered up. The French government basically returned to the old methods, whereas the UK government now moved towards the future world of capitalist finance, which gave them a financial advantage over their much greater and richer rival in the constant wars that the two colonial powers waged against each other throughout the eighteenth century.

The book features a cast that is a veritable who’s who of the great and the infamous in England in the early eighteen century. As well as Isaac Newton and Edmund Halley we have, amongst many others, Johnathan Swift, Daniel Defoe, Alexander Pope, John Gay, Georg Handel, William Hogarth, Sarah Churchill, Duchess of Marlborough (who played the market and made a fortune), Charles Montagu, 1st Earl of Halifax (Newton’s political patron), Christopher Wren and Uncle Bob Walpole and all.


The book closes with an epilogue, which draws the very obvious parallels between the financial crisis caused by the South Sea Bubble and the worldwide one caused in in 2008 but the collapse of the very rotten American derivative market based on mortgages. Echoing the adage that those who don’t know history are doomed to repeat it. History really does have its uses.

The hard back is nicely presented, with an attractive type face and the apparently, in the meantime, obligatory grey in grey prints. There are not-numbered footnotes scattered throughout the text, which explain various terms or expand on points in the narrative but otherwise the book has, what I regard as the worst option, hanging endnotes giving the sources for the direct quotes in the text. There is an extensive bibliography, which our author has very obviously read and mined and an excellent index.

Levenson has written a big in scope and complex book with multiple interwoven layers of mathematical, financial, political and social history that taken together, illuminate an interesting corner of early eighteenth-century life and outline the beginnings of our modern capitalist world. The result is a dense story that could be a challenge to read but, as one would expect of the professor for science writing at MIT, Levenson is a first class storyteller with a light touch and an excellent feel for language, who guides his readers through the tangled maze of the material with a gentle hand. There is much to ponder and digest in this fascinating and rich slice of truly interdisciplinary history, which will leave the reader, who braves its complexities, enriched and possibly wiser than they were before they entered the world of the notorious South Sea Bubble.

[1] As I have pointed out in the past, he didn’t discover the law of gravity he proved it, which is something different.

[2] As I pointed out long ago in a blog post that is no longer available, neither Newton nor Leibniz invented/discovered (choose your term according to your philosophy of mathematics) calculus, even created is as step too far.

[3] Disclosure: Several years ago, I read through Tom’s original book proposal and more recently one chapter of the book, to see if the facts about Newton were correct, but otherwise had nothing to do with this book apart from the pleasure of reading it.  

[4] Money for Nothing: The South Sea Bubble and the Invention of Modern Capitalism, Head of Zeus ltd., London, 2020.

[5] For this you will have to read other books including, perhaps, Tom’s earlier excellent Newton book, Newton and the Counterfeiters: The Unknown Detective Career of the World’s Greatest Scientist, Houghton Mifflin Harcourt, Boston & New York, 2009.

[6] Why I refer to John Law as a felon is a much too intriguing story that I’m going to spoil in in this review; for that you are going to have to read Professor Levenson’s book


Filed under Book Reviews, History of Mathematics

A book or many books?

If you count mathematics as one of the sciences, and I do, then without any doubt the most often reissued science textbook of all time has to be The Elements of Euclid. As B L van der Waerden wrote in his Encyclopaedia Britannica article on Euclid:

Almost from the time of its writing and lasting almost to the present, the Elements has exerted a continuous and major influence on human affairs. It was the primary source of geometric reasoning, theorems, and methods at least until the advent of non-Euclidean geometry in the 19th century. It is sometimes said that, next to the Bible, the “Elements” may be the most translated, published, and studied of all the books produced in the Western world.

The Elements have appeared in numerous editions from their inceptions, supposedly in the fourth century BCE down to the present day. In recent years, Kronecker-Wallis issued a new luxury edition of Oliver Byrne’s wonderful nineteenth century, colour coded version of the first six books of The Elements, extending it to all thirteen books.


There are far too many different editions of this fundamental geometry textbook to be able to name them all, but this automatically raises the question, are they all the same book? If we take a random example of a book with the title The Elements of Euclid, will we always find the same content between the covers? The simple answer to this question is no. The name of the author, Euclid, and the title of the book, The Elements, are much more a mantle into which, over a period of more than two thousand years, related but varying geometrical content has been poured to fit a particular time or function, never quite the same. Sometimes with minor variations sometimes major ones. The ever-changing nature of this model of mathematical literature is the subject of Benjamin Wardhaugh’s fascination volume, The Book of WonderThe Many Lives of Euclid’s Elements.[1]


To write a detailed, complete, chronological history of The Elements, would probably produce something with the dimensions of James Frazer’s twelve volume The Golden Bough and Wardhaugh doesn’t attempt the task here. What he does do is to deliver a selective series of episodes out of the long and complex life of the book. These episodes rather than book chapters might best be described, as essays or even short stories. In total they sum up to a comprehensive, but by no means complete, overview of this fascinating mathematical tome. Wardhaugh’s essay collection is split up into four section, each of which takes a different approach to examining and presenting the history of Euclid’s opus magnum. 

The first section opens with Euclid’s Alexandria, the geometry of the period and the man himself. It clearly shows how little we actually know about the origins of this extraordinary book and its purported author. The following essays deliver a sketch of the history of the book itself. We move from the earliest surviving fragments over the first known complete manuscript from Theon in the fourth century CE. We meet The Elements in Byzantium, in Arabic, in Latin and for the first time in print. 


In the latter case I tripped over the only seriously questionable historical claim that I was aware of in the book. Wardhaugh repeats the nineteenth century claim that Erhard Ratdolt, the printer/publisher of that first printed edition, had been apprenticed to Regiomontanus. This claim is based on the fact that Ratdolt printed and published various manuscripts that had previously belonged to Regiomontanus, including the Euclid. However, there is absolutely no other evidence to support this claim. Regiomontanus was famous throughout Europe both as a mathematicus and as a printer/publisher, people were publishing books, which weren’t from him, more than one hundred years after his death, under his name. If Ratdolt had indeed learnt the printing trade from Regiomontanus he would, with certainty, have advertised the fact, he didn’t.

The first section closes with the flood of new editions that Ratdolt’s first printed edition unleashed in the Early Modern Period. 

The second section deals with the various philosophical interpretations to which The Elements were subjected over the centuries. We start with Plato, who supposedly posted the phrase, “Let no man ignorant of geometry enter” over the entrance to his school. Up next is Proclus, whose fifth century CE commentary on The Elements was the first source that names Euclid as the author. We then have one of Wardhaugh’s strengths as a Euclid chronicler, in his book he digs out a series of women, who over the centuries have in some way engaged with The Elements; here we get the nun Hroswitha (d. c. 1000CE), whose play Sapientia included sections of Euclidian number theory. Following Levi ben Gershon and his Hebrew Euclid, we get a section that particularly appealed to me. First off Christoph Clavius’ Elements, possibly the most extensively rewritten version of the book and one of the most important seventeenth century maths textbooks. This is followed by the Chinese translation of the first six books of Clavius’ Elements by Matteo Ricci and Xu Guangqi.


The second continues with an English stage play on geometry written for the carnival in Rome in 1635. Wardhaugh’s Euclidean research has dug very deep. Baruch Spinoza famously wrote a book on ethics in the style of Euclid’s Elements and of course it’s included here. The section closes with another woman, this time the nineteenth century landowner, Anne Lister.

The third section of the book deals with applied geometry. We start with ancient Egyptian surveyors, move onto music theory and the monochord, Roman field surveyors and the Arabic mathematician Muhammad abu al-Wafa al-Buzjani, who work on the theory of dividing up surfaces for the artisans to create those wonderful geometrical patterns so typical of Islamic ornamentation. Up next are medieval representations of the muse Geometria, which is followed by Piero della Francesca and the geometry of linear perspective. There is a brief interlude with the splendidly named seventeenth century maths teacher, Euclid Speidel before the section closes with Isaac Newton. 

The fourth section of the book traces the decline of The Elements as a textbook in the nineteenth century. We start with another woman, Mary Fairfax, later Mary Sommerville, and her battles with her parents to be allowed to read Euclid. We travel to France and François Peyrard’s attempts to create, as far as possible, a new definitive text for the Elements. Of course, Nicolai Ivanovich Lobachevsky and the beginnings of non-Euclidian geometry have to put in an appearance. Up next George Eliot’s The Mill on the Floss is brought in to illustrate the stupefying nature of Euclidian geometry teaching in English schools in the nineteenth century. We move on to teaching Euclid in Urdu in Uttar Pradesh. A survey of the decline of Euclid in the nineteenth century would no be complete without Lewis Carroll’s wonderful drama Euclid and his Modern Rivals. Carroll is followed by, in his time, one of the greatest historians of Greek mathematics, Thomas Little Heath, whose superb three volume English edition of The Elements has graced my bookshelf for several decades.


The book closes with an excursion into the arts. Max Ernst’s Euclid’s Mask morphs into a chapter on Euclidean design, including Oliver Byrne’s colour coded Elements, mentioned earlier. The final chapter is some musing on the iconic status of Euclid and his book.

There are no foot or endnotes and the book contains something that I regard as rather inadequate. Notes on Sources, which for every chapter gives a short partially annotated reading list. Not, in my opinion the most helpful of tools. There is an extensive bibliography and a good index. The book is illustrated with the now standard grey in grey prints.

Benjamin Wardhaugh is an excellent storyteller and his collected short story approach to the history of The Elements works splendidly. He traces a series of paths through the highways and byways of the history of this extraordinary mathematics book that is simultaneously educational, entertaining and illuminating. In my opinion a highly desirable read for all those, both professional and amateur, who interest themselves for the histories of mathematics, science and knowledge or the course of mostly European intellectual history over almost two and a half millennia.  

[1] Benjamin Wardhaugh, The Book of WonderThe Many Lives of Euclid’s Elements, William Collins, London, 2020


Filed under Book Reviews, History of Mathematics

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.


Filed under Book Reviews, Uncategorized

A scientific Dutchman

For many decades the popular narrative version of the scientific revolution started in Poland/Germany with Copernicus moving on through Tycho in Denmark, Kepler in Germany/Austria, Galileo et al in Northern Italy, Descartes, Pascal, Mersenne etc., in France and then Newton and his supporters and opponents in London. The Netherlands simply didn’t get a look in except for Christiaan Huygens, who was treated as a sort of honorary Frenchman. As I’ve tried to show over the years the Netherlands and its scholars–Gemma Frisius, Simon Stephen, Isaac Beeckman, the Snels, and the cartographers–actually played a central role in the evolution of the sciences during the Early Modern Period. In more recent years efforts have been made to increase the historical coverage of the contributions made in the Netherlands, a prominent example being Harold J Cook’s Matters of Exchange: Commerce, Medicine and Science in the Dutch Golden Age.[1]

A very strange anomaly in the #histSTM coverage concerns Christiaan Huygens, who without doubt belongs to the seventeenth century scientific elite. Whereas my bookcase has an entire row of Newton biographies, and another row of Galileo biographies and in both cases there are others that I’ve read but don’t own. The Kepler collection is somewhat smaller but it is still a collection. I have no idea how many Descartes biographies exist but it is quite a large number. But for Christiaan Huygens there is almost nothing available in English. The only biography I’m aware of is the English translation of Cornelis Dirk Andriesse’s scientific biography of Christiaan Huygens, The Man Behind the Principle.[2] I read this several years ago and must admit I found it somewhat lacking. This being the case, great expectation have been raised by the announcement of a new Huygens biography by Hugh Aldersey-Williams, Dutch Light: Christiaan Huygens and the Making of Science in Europe.[3]


So does Aldersey-Williams fulfil those expectations? Does he deliver the goods? Yes and no, on the whole he has researched and written what is mostly an excellent biography of the Netherland’s greatest scientist[4] of the Early Modern Period but it is in my opinion marred by sloppy history of science fact checking that probably won’t be noticed by the average reader but being the notorious #histSTM pedant that I am I simply can’t and won’t ignore.[5]

My regular readers will known that I describe myself as a narrative contextual historian of science and I personally believe that if we are to understand how science has evolved historical then we have to tell that story with its complete context. This being the case I’m very happy to report that Aldersey-Williams is very much a narrative contextual historian, who tells the complete story of Christiaan Huygens life within its wider context and not just offering up a list of his scientific achievements. In fact what the reader gets for his money is not just a biography of Christiaan but also a biography of his entire family with some members being given more space than other. In particular it is a full biography of Christiaan and his father Constantijn, who played a significant and central role in shaping Christiaan’s life.

The book opens by setting the scientific scene in the early seventeenth-century Netherlands. We get introduced to those scientists, who laid the scientific foundations on which Christiaan would later build. In particular we get introduced to Simon Steven, who shaped the very practice orientated science and technology of the Early Modern Netherlands. We also meet other important and influential figures such as Hans Lipperhey, Isaac Beeckman, Willebrord Snel, Cornelius Drebbel and others.

There now follows what might be termed a book within a book as Aldersey-Williams delivers up a very comprehensive biography of Constantijn Huygens diplomat, poet, composer, art lover and patron and all round lover of knowledge. Constantijn was interested in and fascinated by almost everything both scientific and technological. His interest was never superficial but was both theoretical and practical. For example he was not only interested in the newly invented instruments, the telescope and the microscope, but he also took instruction in how to grind lenses and that from the best in the business. Likewise his love for art extended beyond buying paintings and patronising artists, such as Rembrandt, but to developing his own skills in drawing and painting. Here Aldersey-Williams introduces us to the Dutch term ‘kenner’ (which is the same in German), which refers to someone such Constantijn Huygens, whose knowledge of a subject is both theoretical and practical. Constantijn Huygens married Suzanna von Baerle for love and they had five children over ten years, four sons and a daughter, Christiaan was the second oldest, and Suzanna died giving birth to their daughter, also named Suzanna.

Constantijn Huygens brought up his children himself educating them in his own polymathic diversity with the help of tutors. When older the boys spent brief periods at various universities but were largely home educated. We now follow the young Christiaan and his older brother, also Constantijn, through their formative young years. The two oldest boys remained close and much of Christiaan’s astronomical work was carried out in tandem with his older brother. We follow Christiaan’s early mathematical work and his introduction into the intellectual circles of Europe, especially France and England, through his father’s widespread network of acquaintances. From the beginning Christiaan was set up to become either a diplomat, like his father, grandfather and brothers, or a scientist and it is the latter course that he followed.

Aldersey-Williams devotes an entire chapter to Christiaan’s telescopic observations of Saturn, with a telescope that he and Constantijn the younger constructed and his reputation making discovery of Titan the largest of Saturn’s moons, and the first discovered, and his determination that the strange shapes first observed by Galileo around Saturn were in fact rings. These astronomical discoveries established him as one of Europe’s leading astronomers. The following chapter deals with Huygens’ invention of the pendulum clock and his excursions into the then comparatively new probability theory.

Saturn and the pendulum clock established the still comparatively young Huygens as a leading light in European science in the second half of the seventeenth century and Aldersey-Williams now takes us through ups and downs of the rest of Christiaan’s life. His contact with and election to the Royal Society in London, as its first foreign member. His appointment by Jean-Baptist Colbert, the French First Minister of State, as a founding member of the Académie des sciences with a fairy generous royal pension from Louis XIV. His sixteen years in Paris, until the death of Colbert, during which he was generally acknowledged as Europe’s leading natural philosopher. His initial dispute over light with the young and comparatively unknown Newton and his tutorship of the equally young and unknown Leibniz. His fall from grace following Colbert’s death and his reluctant return to the Netherlands. The last lonely decade of his life in the Netherlands and his desire for a return to the scientific bustle of London or Paris. His partial rapprochement with Newton following the publication of the Principia. Closing with the posthumous publication of his works on gravity and optics. This narrative is interwoven with episodes from the lives of Constantijn the father and Constantijn his elder brother, in particular the convoluted politics of the Netherlands and England created by William of Orange, whose secretary was Constantijn, the younger, taking the English throne together with his wife Mary Stewart. Christiaan’s other siblings also make occasional appearances in letters and in person.

Aldersey-Williams has written a monumental biography of two generations of the Huygens family, who played major roles in the culture, politics and science of seventeenth century Europe. With a light, excellent narrative style the book is a pleasure to read. It is illustrated with 37 small grey in grey prints and 35 colour plates, which I can’t comment on, as my review proof copy doesn’t contain them. There are informative footnotes scattered through out the text and the, by me hated, hanging endnotes referring to the sources of direct quotes in the text. Here I had the experience more than once of looking up what I took to be a direct quote only to discover that it was not listed. There is an extensive bibliography of both primary and secondary sources and I assume an extensive index given the number of blank pages in my proof copy. There were several times when I was reading when I had wished that the index were actually there.

On the whole I would be tempted to give this book a glowing recommendation were it not for a series of specific history of science errors that simple shouldn’t be there and some general tendencies that I will now detail.

Near the beginning Aldersey-Williams tells us that ‘Stevin’s recommendation to use decimals in arithmetical calculations in place of vulgar fractions which could have any denominator [was] surely the sand-yacht of accountancy … Thirty years later, the Scottish mathematician John Napier streamlined Stevin’s notation by introducing the familiar comma or point to separate off the fractional part…” As is all too often the case no mention is made of the fact that Chinese and Arabic mathematicians had been using decimal fractions literally centuries before Stevin came up with the concept. In my opinion we must get away from this Eurocentric presentation of the history of science. Also the Jesuit mathematician Christoph Clavius introduced the decimal point less than ten years after Stevin’s introduction of decimal fractions, well ahead of Napier, as was its use by Pitiscus in 1608, the probable source of Napier’s use.

We also get told when discussing the Dutch vocabulary that Stevin created for science that, “Chemistry becomes scheikunde, the art of separation, an acknowledgement of the beginnings of a shift towards an analytical science, and a useful alternative to chemie that severs the etymological connections with disreputable alchemy.” This displays a complete lack of knowledge of alchemy in which virtually all the analytical methods used in chemistry were developed. The art of separation is a perfectly good term from the alchemy that existed when Stevin was creating his Dutch scientific vocabulary. Throughout his book Aldersey-Williams makes disparaging remarks about both alchemy and astrology, neither of which was practiced by any of the Huygens family, which make very clear that he doesn’t actually know very much about either discipline or the role that they played in the evolution of western science, astrology right down to the time of Huygens and Newton and alchemy well into the eighteenth century. For example, the phlogiston theory one of the most productive chemical theories in the eighteenth century had deep roots in alchemy.

Aldersey-Williams account of the origins of the telescope is a bit mangled but acceptable except for the following: “By the following spring, spyglasses were on sale in Paris, from where one was taken to Galileo in Padua. He tweaked the design, claimed the invention as his own, and made dozens of prototypes, passing on his rejects so that very soon even more people were made aware of this instrument capable of bringing the distant close.”

Firstly Galileo claimed that he devised the principle of the telescope and constructed his own purely on verbal descriptions without having actually seen one but purely on his knowledge of optics. He never claimed the invention as his own and the following sentence is pure rubbish. Galileo and his instrument maker produced rather limited numbers of comparatively high quality telescopes that he then presented as gifts to prominent political and Church figures.

Next up we have Willebrord Snel’s use of triangulation. Aldersey-Williams tells us, “ This was the first practical survey of a significant area of land, and it soon inspired similar exercises in England, Italy and France.” It wasn’t. Mercator had previously surveyed the Duchy of Lorraine and Tycho Brahe his island of Hven before Snel began his surveying in the Netherlands. This is however not the worst, Aldersey-Williams tells us correctly that Snel’s survey stretched from Alkmaar to Bergen-op-Zoom “nearly 150 kilometres to the south along approximately the same meridian.” Then comes some incredible rubbish, “By comparing the apparent height of his survey poles observed at distance with their known height, he was able to estimate the size of the Earth!”

What Snel actually did, was having first accurately determined the length of a stretch of his meridian using triangulation, the purpose of his survey and not cartography, he determined astronomically the latitude of the end points. Having calculated the difference in latitudes it is then a fairly simple exercise to determine the length of one degree of latitude, although for a truly accurate determination one has to adjust for the curvature of the Earth.

Next up with have the obligatory Leonard reference. Why do pop history of science books always have a, usually erroneous, Leonardo reference? Here we are concerned with the camera obscura, Aldersey-Williams writes: “…Leonardo da Vinci gave one of the first accurate descriptions of such a design.” Ibn al-Haytham gave accurate descriptions of the camera obscura and its use as a scientific instrument about four hundred and fifty years before Leonardo was born in a book that was translated into Latin two hundred and fifty years before Leonardo’s birth. Add to this the fact that Leonardo’s description of the camera obscura was first published late in the eighteenth century and mentioning Leonardo in this context becomes a historical irrelevance. The first published European illustration of a camera obscura was Gemma Frisius in 1545.

When discussing Descartes, a friend of Constantijn senior and that principle natural philosophical influence on Christiaan we get a classic history of mathematics failure. Aldersey-Williams tells us, “His best known innovation, of what are now called Cartesian coordinates…” Whilst Descartes did indeed cofound, with Pierre Fermat, modern algebraic analytical geometry, Cartesian coordinates were first introduced by Frans van Schooten junior, who of course features strongly in the book as Christiaan’s mathematics teacher.

Along the same lines as the inaccurate camera obscura information we have the following gem, “When applied to a bisected circle (a special case of the ellipse), this yielded a new value, accurate to nine decimal places, of the mathematical constant π, which had not been improved since Archimedes” [my emphasis] There is a whole history of the improvements in the calculation of π between Archimedes and Huygens but there is one specific example that is, within the context of this book, extremely embarrassing.

Early on when dealing with Simon Stevin, Aldersey-Williams mentions that Stevin set up a school for engineering, at the request of Maurits of Nassau, at the University of Leiden in 1600. The first professor of mathematics at this institution was Ludolph van Ceulen (1540–1610), who also taught fencing, a fact that I find fascinating. Ludolph van Ceulen is famous in the history of mathematics for the fact that his greatest mathematical achievement, the Ludophine number, is inscribed on his tombstone, the accurate calculation of π to thirty-five decimal places, 3.14159265358979323846264338327950288…

Next up we have Christiaan’s correction of Descartes laws of collision. Here Aldersey-Williams writes something that is totally baffling, “The work [his new theory of collision] only appeared in a paper in the French Journal des Sçavans in 1669, a few years after Newton’s laws of motion [my emphasis]…” Newton’s laws of motion were first published in his Principia in 1687!

Having had the obligatory Leonardo reference we now have the obligatory erroneous Galileo mathematics and the laws of nature reference, “Galileo was the first to fully understand that mathematics could be used to describe certain laws of nature…” I’ve written so much on this that I’ll just say here, no he wasn’t! You can read about Robert Grosseteste’s statement of the role of mathematics in laws of nature already in the thirteenth century, here.

Writing about Christiaan’s solution of the puzzle of Saturn’s rings, Aldersey-Williams say, “Many theories had been advanced in the few years since telescopes had revealed the planet’s strange truth.” The almost five decades between Galileo’s first observation of the rings and Christiaan’s solution of the riddle is I think more than a few years.

Moving on Aldersey-Williams tells us that, “For many however, there remained powerful reasons to reject Huygens’ discovery. First of all, it challenged the accepted idea inherited from Greek philosophers that the solar system consisted exclusively of perfect spherical bodies occupying ideal circular orbits to one another.” You would have been hard put to it to find a serious astronomer ín 1660, who still ascribed to this Aristotelian cosmology.

The next historical glitch concerns, once again, Galileo. We read, “He dedicated the work [Systema Saturnium] to Prince Leopoldo de’ Medici, who was patron of the Accademia del Cimento in Florence, who had supported the work of Huygens’ most illustrious forebear, Galileo.” Ignoring the sycophantic description of Galileo, one should perhaps point out that the Accademia del Cimento was founded in 1657 that is fifteen years after Galileo’s death and so did not support his work. It was in fact founded by a group of Galileo’s disciples and was dedicated to continuing to work in his style, not quite the same thing.

Galileo crops up again, “the real power of Huygens’ interpretation was its ability to explain those times when Saturn’s ‘handles’ simply disappeared from view, as they had done in 1642, finally defeating the aged Galileo’s attempts to understand the planet…” In 1642, the year of his death, Galileo had been completely blind for four years and had actually given up his interest in astronomy several years earlier.

Moving on to Christiaan’s invention of the pendulum clock and the problem of determining longitude Aldersey-Williams tells us, “The Alkmaar surveyor Adriaan Metius, brother of the telescope pioneer Jacob, had proposed as long ago as 1614 that some sort of seagoing clock might provide the solution to this perennial problem of navigators…” I feel honour bound to point out that Adriaan Metius was slightly more than simply a surveyor, he was professor for mathematics at the University of Franeker. However the real problem here is that the clock solution to the problem of longitude was first proposed by Gemma Frisius in an appendix added in 1530, to his highly popular and widely read editions of Peter Apian’s Cosmographia. The book was the biggest selling and most widely read textbook on practical mathematics throughout the sixteenth and well into the seventeenth century so Huygens would probably have known of Frisius’ priority.

Having dealt with the factual #histSTM errors I will now turn to more general criticisms. On several occasions Aldersey-Williams, whilst acknowledging problems with using the concept in the seventeenth century, tries to present Huygens as the first ‘professional scientist’. Unfortunately, I personally can’t see that Huygens was in anyway more or less of a professional scientist than Tycho, Kepler or Galileo, for example, or quite a long list of others I could name. He also wants to sell him as the ‘first ever’ state’s scientist following his appointment to the Académie des sciences and the accompanying state pension from the king. Once again the term is equally applicable to Tycho first in Denmark and then, if you consider the Holy Roman Empire a state, again in Prague as Imperial Mathematicus, a post that Kepler inherited. Galileo was state ‘scientist’ under the de’ Medici in the Republic of Florence. One could even argue that Nicolas Kratzer was a state scientist when he was appointed to the English court under Henry VIII. There are other examples.

Aldersey-Williams’ next attempt to define Huygens’ status as a scientist left me somewhat speechless, “Yet it is surely enough that Huygens be remembered for what he was, a mere problem solver indeed: pragmatic, eclectic and synthetic and ready to settle for the most probable rather than hold out for the absolutely certain – in other words. What we expect a scientist to be today.” My ten years as a history and philosophy of science student want to scream, “Is that what we really expect?” I’m not even going to go there, as I would need a new blog post even longer than this one.

Aldersey-Williams also tries to present Huygens as some sort of new trans European savant of a type that had not previously existed. Signifying cooperation across borders, beliefs and politics. This is of course rubbish. The sort of trans European cooperation that Huygens was involved in was just as prevalent at the beginning of the seventeenth century in the era of Tycho, Kepler, Galileo, et al. Even then it was not new it was also very strong during the Renaissance with natural philosophers and mathematici corresponding, cooperating, visiting each other, and teaching at universities through out the whole of Europe. Even in the Renaissance, science in Europe knew no borders. It’s the origin of the concept, The Republic of Letters. I suspect my history of medieval science friend would say the same about their period.

In the partial rapprochement between Huygens and Newton following the Publication of the latter’s Principia leads Aldersey-Williams to claim that a new general level of reasonable discussion had entered scientific debate towards the end of the seventeenth century. Scientists, above all Newton, were still going at each other hammer and tongs in the eighteenth century, so it was all just a pipe dream.

Aldersey-Williams sees Huygens lack of public profile, as a result of being in Newton’s shadow like Hooke and others. He suggests that popular perception only allows for one scientific genius in a generation citing Galileo’s ascendance over Kepler, who he correctly sees as the more important, as another example. In this, I agree with him, however he tries too hard to put Huygens on the same level as Newton as a scientist, as if scientific achievement were a pissing contest. I think we should consider a much wider range of scientists when viewing the history of science but I also seriously think that no matter how great his contributions Huygens can’t really match up with Newton. Although his Horologium oscillatorium sive de motu pendularium was a very important contribution to the debate on force and motion, it can’t be compared to Newton’s Principia. Even if Huygens did propagate a wave theory of light his Traité de la lumière is not on a level with Newton’s Opticks. He does have his Systema saturniumbut as far as telescopes are concerned Newton’s reflector was a more important contribution than any of Huygens refractor telescopes. Most significant, Newton made massive contributions to the development of mathematics, Huygens almost nothing.

Talking of Newton, in his discussion of Huygens rather heterodox religious views Aldersey-Williams discussing unorthodox religious views of other leading scientists makes the following comment, “Newton was an antitrinitarian, for which he was considered a heretic in his lifetime, as well as being interested in occultism and alchemy.” Newton was not considered a heretic in his lifetime because he kept his antitrinitarian views to himself. Alchemy yes, but occultism, Newton?

I do have one final general criticism of Aldersey-Williams’ book. My impression was that the passages on fine art, poetry and music, all very important aspects of the life of the Huygens family, are dealt with in much greater depth and detail than the science, which I found more than somewhat peculiar in a book with the subtitle, The Making of Science in Europe. I’m not suggesting that the fine art, poetry and music coverage should be less but that the science content should have been brought up to the same level.

Despite the long list of negative comments in my review I think this is basically a very good book that could in fact have been an excellent book with some changes. Summa summarum it is a flawed masterpiece. It is an absolute must read for anybody interested in the life of Christiaan Huygens or his father Constantijn or the whole Huygens clan. It is also an important read for those interested in Dutch culture and politics in the seventeenth century and for all those interested in the history of European science in the same period. It would be desirable if more works with the wide-ranging scope and vision of Aldersey-Williams volume were written but please without the #histSTM errors.

[1] Harold J Cook, Matters of Exchange: Commerce, Medicine and Science in the Dutch Golden Age, Yale University Press, New Haven & London, 2007

[2] Cornelis Dirk Andriesse, The Man Behind the Principle, scientific biography of Christiaan Huygens, translated from Dutch by Sally Miedem, CUP, Cambridge, 2005

[3] Hugh Aldersey-Williams, Dutch Light: Christiaan Huygens and the Making of Science in Europe, Picador, London, 2020.

[4] Aldersey-Williams admits that the use of the term scientist is anachronistic but uses it for simplicity’s sake and I shall do likewise here.

[5] I have after all a reputation to uphold


Filed under Book Reviews, History of Astronomy, History of Mathematics, History of Navigation, History of Optics, History of Physics, History of science, Newton

Our medieval technological inheritance.

“Positively medieval” has become a universal put down for everything considered backward, ignorant, dirty, primitive, bigoted, intolerant or just simply stupid in our times. This is based on a false historical perspective that paints the Middle Ages as all of these things and worse. This image of the Middle Ages has its roots in the Renaissance, when Renaissance scholars saw themselves as the heirs of all that was good, noble and splendid in antiquity and the period between the fall of the Roman Empire and their own times as a sort of unspeakable black pit of ignorance and iniquity. Unfortunately, this completely false picture of the Middle Ages has been extensively propagated in popular literature, film and television.

Particularly in the film and television branch, a film or series set in the Middle Ages immediately calls for unwashed peasants herding their even filthier swine through the mire in a village consisting of thatch roofed wooden hovels, in order to create the ‘correct medieval atmosphere’. Add a couple of overweight, ignorant, debauching clerics and a pox marked whore and you have your genuine medieval ambient. You can’t expect to see anything vaguely related to science or technology in such presentations.

Academic medieval historians and historians of science and technology have been fighting an uphill battle against these popular images for many decades now but their efforts rarely reach the general lay public against the flow of the latest bestselling medieval bodice rippers or TV medieval murder mystery. What is needed, is as many semi-popular books on the various aspects of medieval history as possible. Whereby with semi-popular I mean, written for the general lay reader but with its historical facts correct. One such new volume is John Farrell’s The Clock and the Camshaft: And Other Medieval Inventions We Still Can’t Live Without.[1]


Farrell’s book is a stimulating excursion through the history of technological developments and innovation in the High Middle Ages that played a significant role in shaping the modern world.  Some of those technologies are genuine medieval discoveries and developments, whilst others are ones that either survived or where reintroduced from antiquity. Some even coming from outside of Europe. In each case Farrell describes in careful detail the origins of the technology in question and if known the process of transition into European medieval culture.

The book opens with agricultural innovations, the deep plough, the horse collar and horse shoes, which made it possible to use horses as draught animals instead of or along side oxen, and new crop rotation systems. Farrell explains why they became necessary and how they increased food production leading indirectly to population growth.

Next up we have that most important of commodities power and the transition from the hand milling of grain to the introduction of first watermills and then windmills into medieval culture. Here Farrell points out that our current knowledge would suggest that the more complex vertical water mill preceded the simpler horizontal water mill putting a lie to the common precept that simple technology always precedes more complex technology. At various points Farrell also addresses the question as to whether technological change drives social and culture change or the latter the former.


Having introduced the power generators, we now have the technological innovations necessary to adapt the raw power to various industrial tasks, the crank and the camshaft. This is fascinating history and the range of uses to which mills were then adapted using these two ingenious but comparatively simple power take offs was very extensive and enriching for medieval society. One of those, in this case an innovation from outside of Europe, was the paper mill for the production of that no longer to imagine our society without, paper. This would of course in turn lead to that truly society-changing technology, the printed book at the end of the Middle Ages.


Along side paper perhaps the greatest medieval innovation was the mechanical clock. At first just a thing of wonder in the towers of some of Europe’s most striking clerical buildings the mechanical clock with its ability to regulate the hours of the day in a way that no other time keeper had up till then gradually came to change the basic rhythms of human society.

Talking of spectacular clerical buildings the Middle Ages are of course the age of the great European cathedrals. Roman architecture was block buildings with thick, massive stonewalls, very few windows and domed roofs. The art of building in stone was one of the things that virtually disappeared in the Early Middle Ages in Europe. It came back initially in an extended phase of castle building. Inspired by the return of the stonemason, medieval, European, Christian society began the era of building their massive monuments to their God, the medieval cathedrals. Introducing architectural innovation like the pointed arch, the flying buttress and the rib vaulted roof they build large, open buildings flooded with light that soared up to the heavens in honour of their God. Buildings that are still a source of wonder today.


In this context it is important to note that Farrell clearly explicates the role played by the Catholic Church in the medieval technological innovations, both the good and the bad. Viewed with hindsight the cathedrals can be definitely booked for the good but the bad? During the period when the watermills were introduced into Europe and they replaced the small hand mills that the people had previously used to produce their flour, local Church authorities gained control of the mills, a community could only afford one mill, and forced the people to bring their grain to the Church’s mill at a price of course. Then even went to the extent of banning the use of hand mills.

People often talk of the Renaissance and mean a period of time from the middle of the fifteenth century to about the beginning of the seventeenth century. However, for historians of science there was a much earlier Renaissance when scholars travelled to the boundaries between Christian Europe and the Islamic Empire in the twelfth and thirteenth centuries in order to reclaim the knowledge that the Muslims had translated, embellished and extended in the eight and ninth centuries from Greek sources. This knowledge enriched medieval science and technology in many areas, a fact that justifies its acquisition here in a book on technology.

Another great medieval invention that still plays a major role in our society, alongside the introduction of paper and the mechanical clock are spectacles and any account of medieval technological invention must include their emergence in the late thirteenth century. Spectacles are something that initially emerged from Christian culture, from the scriptoria of the monasteries but spread fairly rapidly throughout medieval society. The invention of eyeglasses would eventually lead to the invention of the telescope and microscope in the early seventeenth century.

Another abstract change, like the translation movement during that first scientific Renaissance, was the creation of the legal concept of the corporation. This innovation led to the emergence of the medieval universities, corporations of students and/or their teachers. There is a direct line connecting the universities that the Church set up in some of the European town in the High Middle Ages to the modern universities throughout the world. This was a medieval innovation that truly helped to shape our modern world.

Farrell’s final chapter in titled The Inventions of Discovery and deals both with the medieval innovations in shipbuilding and the technology of the scientific instruments, such as astrolabe and magnetic compass that made it possible for Europeans to venture out onto the world’s oceans as the Middle Ages came to a close. For many people Columbus’ voyage to the Americas in 1492 represents the beginning of the modern era but as Farrell reminds us all of the technology that made his voyage possible was medieval.

All of the above is a mere sketch of the topics covered by Farrell in his excellent book, which manages to pack an incredible amount of fascinating information into what is a fairly slim volume. Farrell has a light touch and leads his reader on a voyage of discovery through the captivating world of medieval technology. The book is beautifully illustrated by especially commissioned black and white line drawing by Ryan Birmingham. There are endnotes simply listing the sources of the material in main text and an extensive bibliography of those sources. The book also has, what I hope, is a comprehensive index.[2]

Farrell’s book is a good, readable guide to the world of medieval technology aimed at the lay reader but could also be read with profit by scholars of the histories of science and technology and as an ebook or a paperback is easily affordable for those with a small book buying budget.

So remember, next time you settle down with the latest medieval pot boiler with its cast of filthy peasants, debauched clerics and pox marked whores that the paper that it’s printed on and the reading glasses you are wearing both emerged in Europe in the Middle Ages.

[1] John W. Farrell, The Clock and the Camshaft: And Other Medieval Inventions We Still Can’t Live Without, Prometheus Books, 2020.

[2] Disclosure: I was heavily involved in the production of this book, as a research assistant, although I had nothing to do with either the conception or the actual writing of the book that is all entirely John Farrell’s own work. However, I did compile the index and I truly hope it will prove useful to the readers.


Filed under Book Reviews, History of science, History of Technology, Mediaeval Science

We just don’t know!

Matthew Cobb is one of those people that you can’t help but admire but also secretly hate just a little bit for being so awesome. He is professor for zoology at the University of Manchester with a sizable teaching load that he apparently masters with consummate skill. He’s a scientific researcher, who researches the sense of smell of fruit fly maggots; I kid you not!  He’s also an attentive and loving family father but he still finds time and energy to write brilliant history of science books, three to date. His first, The Egg and Sperm Race, describes the search for the secret of human reproduction in the seventeenth and eighteenth centuries and is one of my favourite history of science books, on the period. His second, Life’s Greatest Secret is a monster, both in scope and detail, description of the hunt to decipher the structure and function of DNA that along the way demolishes a whole boatload of modern #histSTM myths. The most recent, and the subject of this review, is The Idea of the Brain: A History. Actually I don’t really need to review it, on the cover there is a quote from Adam Rutherford, who is also a brilliant science communicator, This is a masterpiece. Agreed, end of review!


You want a bit more detail before you commit your shekels and purchase a copy? OK! What Cobb presents us with is a history of the various attempts by researchers to understand the brain and its functions, which of course also includes such concrete things as the nervous system and abstract ones as thought, memory, consciousness, all of those things that we think make us human. The book is divided into three sections past, present and future. The first deals with those attempts to explain the brain offered up roughly from the seventeenth century up to about 1950. The second deals with approximately the last 70 years, which saw a major change in the tools available to the researchers and in the final section Cobb offers us his opinions on where the research might go from here; a brief survey that he admits is highly speculative.

Astute readers of this review might wonder why Cobb’s book only gets going in the seventeenth century, when humans of some sort or another have been around for a couple of million years, their brains also. This gets explained in the first chapter, which at first glance is confusingly entitled Heart and not Brain! Whilst reading this introductory chapter I found myself humming old pop songs by Cilla Black and Bonnie Tyler, the lyrics of which contain the answer to my question. Anyone Who had a Heart, and Total Eclipse of the Heart reflect a belief that existed for most of humanity’s existence. It was believed that the heart was the seat of emotions, thoughts, consciousness etc. and not the brain. As those pop songs nicely illustrate, much of our everyday speech still reflects that belief. ‘He thought with his heart and not his head’ ‘If you weren’t so hard hearted’ and many, many more. It was first in the seventeenth century that the attention of the natural philosophers turned from the heart to the brain to try and solve the conundrums thrown up by thoughts about thinking. Here the developing empirical approach to science in general kicked in as nicely illustrated by the book’s motto supplied by Nicolaus Steno (1638–1686) in his On the Brain (1669), which also supplies the leitmotif for the whole book:

The brain being indeed a machine, we must not hope to find its artifice through other ways than those which are used to find artifice in other machines. It thus remains to do what we would do for any other machine; I mean to dismantle it piece by piece and to consider what these can do separately and together.

I did briefly muse on the fact that Steno, a truly fascinating figure, also played a leading role in Cobb’s first book, The Egg and Sperm Race, but I digress.

It is well known that the brain is a glibbery, grey mass that you can’t really take apart, let alone put back together again. The best you can do is cut it up into slices, which I’m sure some early investigators did, but without high power microscopes that is not going to tell you an awful lot. All you can really do is fry the slices in breadcrumbs and eat them with a good sauce. What the early brain researchers did do was to set up analogies to other scientific systems and technologies and hypothesize that the brain functions in the same or a similar way. Then try to find some way to test your hypothesis. Cobb takes us through a whole series of these analogy models of the brain and shows clearly how they all failed. What is interesting is that the models were almost always based on the newest scientific theories or technological development within each generation. Hey we’ve got this wonderful new whatsit, I bet the brain functions like that too. This first section of the book is a fascinating journey through a couple of centuries of science and technology and failed and abandoned models of the brain. However not all was lost or totally wrong. This process produced, for example, the valid information that the nervous system and with it the brain are somehow powered by electricity.

Following WWII Cobb takes us into what he terms the present of brain research. Here a whole lot of new investigatory possibilities begin to be developed, computer tomography scans for examples. But of course the analogy game doesn’t stop and we what is probably the most widespread and well-known analogy of all, the brain is a computer, which harks back to earlier technological analogies, the telegraph network and the telephone exchange.


Cobb devotes quite a lot of space to showing the efforts invested in the computer analogy and why in the end those efforts also all failed. Within the present section of his book Cobb lays out the whole battery of modern neurological research and the immense effort that has been invested in the last circa seventy years to try and understand the brain, the nervous system and related questions about the nature of memory, consciousness etc.

The strongest impression that I took away from this section was the complexity of the task. Before I read this book my thoughts about the brain were related to the saying, if the brain was simple enough that we could understand it, we wouldn’t be intelligent enough to do so. I sort of knew that the brain was mind bogglingly complex, but having read Cobb’s book I now know that mind bogglingly complex doesn’t come anywhere near describing just how complex it is. One aspect that was new to me is that some researchers, who have accepted the complexity problem (paradox?), have stopped trying to understand the human brain and are trying their luck with smaller less complex brains, in fact the smallest and simplest that they can find. Remember Cobb’s research on the sense of smell of fruit fly maggots? What is the summa summarum of all these efforts? How does the brain really function? The answer that emerges at the end of Cobb’s book is, we just don’t know!

Having stunned us with the science and its inability to answer fundamental questions about the brain the book now takes us into the future, where do we go from here? There are probably as many answers to this question as there are people currently researching the brain or hoping to do so in the future. Cobb takes us through some of the, perhaps, more hopeful approaches but admits that there in no real clean line for the researchers of the future to follow.

The book is beautifully presented the English edition has a wonderful cover and stunning end papers, black and white line illustrations throughout the text and a section of photos in the middle. There is an extensive bibliography and endnotes that are mainly simple bibliographical references. It is rounded off with a good index.

The astute reader, and this blog only has astute readers, will have noticed that this review is strong on general waffle but low on detail; this is intentional. Matthew Cobb is an excellent writer and a highly skilled storyteller. Each chapter of the book is presented as a scientific adventure story with much humour and enough bad jokes and snide comments to keep any reader happy. I found that the individual chapters made for good bedtime stories. To have gone into more detail would have been the equivalent of revealing the murderer in an Agatha Christie novel and I really don’t want to spoil the fun you the readers are going to have following Professor Cobb down the winding and contorted paths of the historical attempts to understand what is perhaps the most complex object on the planet, the human brain. The final page is I think the best final page that I have ever read in a history of science book.

I can only repeat what I said at the beginning, quoting Adam Rutherford, This is a masterpiece, so get hold of a copy and read it, you won’t regret it.





Filed under Book Reviews

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.


Filed under Book Reviews, Uncategorized