Category Archives: Book Reviews

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.

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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]

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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. 

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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.

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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.

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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

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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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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]

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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

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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]

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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.

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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.

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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.

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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.

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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!

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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.

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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.

 

 

 

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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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Galileo sources: a starter kit

Following my last post, numerous people have asked me for book recommendations on Galileo and his opponents. What follows is a list of books that I have and have consulted to create my Galileo. I should add that over the years I have also read a cartload of academic papers on Galileo and related topics. What I list here is only a small fraction of the available literature on the topic. My friend Pierre, the editor of the Simon Marius book, who is a real Galileo expert, I’m not, has currently 1514 items listed in his Galileo bibliography and even that is only a small fraction.

L. Heilbron, Galileo, OUP, 2010

David Wootton, Galileo: Watcher of the Skies, Yale University Press, 2010

Mario Biagioli, Galileo Courtier: The Practice of Science in The Culture of Absolutism, University of Chicago Press, 1993

Mario Biagioli, Galileo’s Instruments of Credit: Telescopes, Images, Secrecy, University of Chicago Press, 2006

William R. Shea & Mariano Artigas, Galileo in Rome: The Rise and Fall of a Troublesome Genius, OUP, 2003

Maurice A. Finocchiaro, On Trial for Reason: Science, Religion, and Culture in the Galileo Affair, OUP, 2019

 

Galileo Galilei, trans. Albert van Helden, Sidereus Nuncius or The Sidereal Messenger, University of Chicago Press, 1989

Galileo Galilei, trans. Stillman Drake, Dialogue Concerning the Two Chief World Systems, University of California Press, 1967

Galileo Galilei, trans. Henry Crew & Alfonso de Salvio, Dialogues Concerning Two New Science, Dover, 1954

Discoveries and Opinions of Galileo, translated with an Introduction and Notes by Stillman Drake, Anchor Books, 1957. (Starry Messenger, Letter to the Grand Duchess Christina, plus excerpts from Letters on Sunspots & The Assayer)

The Essential Galileo, Edited and Translated by Maurice A. Finocchiaro, Hackett Publishing Company, 2008

Galileo on the World Systems: A New Abridged Translation and Guide, Maurice A. Finocchiaro, University of California Press, 1997

Galileo Galilei & Christoph Scheiner, On Sunspots, Translated and Introduced by Eileen Reeves & Albert van Helden, University of Chicago Press, 2010

Eileen Reeves, Galileo’s Glassworks: The Telescope and the Mirror, Harvard University Press, 2008

Massimo Bucciantini, Michele Canmerota, Franco Giudice, Galileo’s Telescope’s: A European Story, Harvard University Press, 2015

James M Lattis, Between Copernicus and Galileo: Christoph Clavius and the Collapse of Ptolemaic Cosmology, University of Chicago Press, 1994

Franz Daxecker, Der Physiker und Astronom Christoph Scheiner, Universitätsverlag Wagner, 2006 (I don’t know of anything good on Scheiner in English)

Christopher M Graney, Setting Aside All Authority: Giovanni Battista Riccioli and the Science against Copernicanism in the Age of Galileo, University of Notre Dame Press, 2015

Mordechai Feingold, Jesuit Science and the Republic of Letters, MIT Press, 2002

Hans Gaab & Pierre Leich eds., Simon Marius and His Research, Springer, 2018

 

 

 

 

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How to create your own Galileo

Writing this book review caused me a great deal of of stress, even leading to sleepless night when I made the mistake of reading the offending piece of literature as bedtime reading. The review itself has become horrendously long and I must at times fight my instinct to add even more explanations, as to why this or that was wrong. It is in the words of that excellent history of science author, Matthew Cobb, ‘baggy and rambling’ and should actually be radically edited but I just can’t be arsed to do it, so I’m simply posting the whole monstrosity. For those, who don’t want to read the whole thing, and I wouldn’t blame you, the first three and the last five paragraphs offer a sort of synopsis of the whole thing.

Since I began writing book reviews on a more regular basis I have tried only to review books that I personally find good and which I think might be of interest to those who come here to read my weekly scribblings. I decided that on the whole it isn’t worth wasting time and energy writing about uninteresting, mediocre or simply bad books. However, occasionally a book come along that I feel duty bound, given my reputation as a #histSTM grouch, to debunk as a favour to my readers so that they don’t waste their time and energy reading it; today’s review is one such.

Some time back I wrote a post about the Alexandrian mathematician and philosopher Hypatia, which started with the fact that she has been used as a sort of blank slate onto which numerous people down the centuries have projected their images of what they would have wanted her to be. In the case of Hypatia this is fairly easy, as the rest of my post pointed out we know next to nothing about the lady. Another figure, who has been used extensively over the years as a silhouette, which people fill out according to their own wishes is Galileo Galilei; in his case this is more difficult as we actually know an awful lot about the Tuscan mathematician’s life and work. However, this has not prevented numerous authors from creating their own Galileos.

The latest author, who has decided to present the world with his Galileo, is the astrophysicist and very successful author of popular books on mathematics and science, Mario Livio with his Galileo and the Science Deniers.[1] I might not have bothered with this book but Livio is a very successful pop science book author, as is made very clear by the fact that the hardback and paperback were both issued simultaneously and at very low prices; the publishers expect it to sell well, so it will unfortunately have a big impact on uninformed peoples perceptions of Galileo. I say unfortunately, which, of course, gives readers of this review a very strong clue as to what I think of this book. Quite simply don’t bother, it brings nothing new to our knowledge of Galileo and in fact is full of, at times, quite serious historical errors, serious that is if you’re a historian, who takes getting the facts right seriously.

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The opening sentences starts with a couple of wonderful errors and also lays out Livio’s version of Galileo:

Being an astrophysicist myself, I have always been fascinated by Galileo. He was, after all, not only the founder of modern astronomy and astrophysics–the person who turned an ancient profession into the universe’s deepest secrets and awe-inspiring wonders–but also a symbol of the fight for intellectual freedom.

I think Copernicus, Tycho Brahe and Johannes Kepler might want a word with Livio about, who exactly is the founder of modern astronomy. Also, excuse the language, but what the fuck did Galileo ever do for astrophysics? The final half sentence tells us into which silhouette Livio has decided to pour his Galileo; Livio’s Galileo is the white knight of freedom of speech and freedom of thought, who has mounted his charger and taking up his lance sets off to kill the anti-science dragon of the Holy Roman Catholic Church. This is, of course not a new Galileo but a well-known old model, which historians of science have spent a lot of time and effort dismantling over the last fifty plus years.

Central to the problems with Livio’s book is that he completely ignores the historical context in which the Galileo story took place. His is totally a presentist view in which he applies the social rules and moral judgements of the twentieth-first century to the various occurrences he sketches in the early seventeenth century. This is quite simply very bad historiography. He compounds this error by trying to draw parallels between Galileo’s conflict with the Catholic Church and the current problems with science denialists in our times, hence the title of his book. To do this he simply denies Galileo’s critics any scientific basis for their criticism whatsoever, Galileo is science, his critics are anti-science. A rather simplistic and historically highly inaccurate presentation of the known facts.

Just to make clear what exactly the historical context was, there existed no freedom of speech or freedom of thought under any civil or religious authority anywhere in Europe at the beginning of the seventeenth century; such social concepts still lay in the future. There is a slight irony in the fact that the current wave of science denialists, against whom Livio’s book is directed, are in fact exercising their, protected by law, rights of freedom of thought and speech. More importantly the Holy Roman Catholic Church was not just a religion and a church but also a powerful political and judicial body with judicial rights over all within its dominion and this in an age of absolutism with the Pope as the most absolute of all absolute rulers. All authorities both civil and religious reserved for itself the right to determine what its subject were permitted to express in public, the Catholic Church was in no way unique in claiming and exercising this right.

Still in the preface to Livio’s book we find his first distortion of the historical scientific facts, he writes that Galileo’s telescopic discoveries, “All but destroyed the stability of the Earth-centered Ptolemaic universe.” Here Livio, and not only here, fails to differentiate between Aristotelian cosmology and Ptolemaic astronomy. All of the telescopic discoveries, with the exception of the phases of Venus, demolished aspects of Aristotelian cosmology but had no significance for Ptolemaic geocentric astronomy. The discovery of the phases of Venus, of course, refuted a pure geocentric system but was perfectly compatible with a Tychonic geo-heliocentric system, which then became the default alternative to a heliocentric system. With two notable exceptions that I will deal with later Livio makes no clear mention of the fact that the telescopic discoveries were made within the same approximately three year period not only by Galileo but simultaneous by others, so if Galileo had never used a telescope it would have made very little difference to the subsequent history of astronomy. This makes rather a mockery of Livio’s next dubious claim, “his [Galileo’s] ideas became the basis on which modern science has been erected.” This is much less true than Livio and other Galileo groupies would have us believe. Galileo made a contribution but others in the seventeenth century actually contributed significantly more.

One last comment from the preface, Livio writes:

He insisted on publishing many of his scientific findings in Italian [actually Tuscan not Italian] (rather than Latin), for the benefit of every educated rather than for a limited elite.

In the early seventeenth century almost every educated person would per definition have been able to read and write Latin; Latin was the default language of education.

Reading the opening chapter of Livio’s book, Rebel with a Cause, I constantly had the feeling that I had been transported back to the 1960s and 70s, when I first began to read books about the history of science in general and Galileo in particular. It as if the last fifty plus years of history of science research had never taken place, he even relies on Einstein and Bertrand Russell as his historical authorities, at times I shuddered. He goes so far as to tell us that the Renaissance happened because people discovered that they were individuals! I can’t remember when I last read this particular piece of inanity and I would be curious who actually put it into the world. The final page of this chapter contains all of the classic Galileo clichés.

Perhaps most important, Galileo was the pioneer and star of advancing the new art of experimental science. He realised that he could test or suggest theories by artificially manipulating various terrestrial phenomena. He as also the first scientist whose vision and scientific outlook incorporated methods and results that were applicable to all branches of science.

There is a long historical list of people who would disagree–Archimedes, Ptolemaeus, al-Haytham, Grosseteste, Roger Bacon, William Gilbert and a whole host of alchemists starting with Abū Mūsā Jābir ibn Hayyān (for Livio opinion on alchemy see below)–just to name the most prominent. Modern research has also conclusively shown that artisanal practice in the fifteenth and sixteenth centuries played a significant role in the development of empirical, experimental science. Livio’s last sentence here is also rather dubious, apart from some rather trivial aspects, there are no methods and results that are applicable to all branches of science.

…in four areas he revolutionised the field: astronomy and astrophysics; the laws of motion and mechanics; the astonishing relationship between mathematics and physical reality […]; and experimental science.

Despite everything, Galileo’s contributions to astronomy were rather minimal and he certainly didn’t revolutionise the field, others such as Kepler, whom he ignored, did. I am still trying to work out what his contributions to astrophysics could possibly be? His real major contribution was indeed to motion and mechanics but he was no means alone in this others such as Simon Stevin and Isaac Beeckman made substantial contributions to the new developments in these areas. The mathematics thing, to which Livio keeps returning, is baloney and I shall deal with it separately later. Galileo made contributions to the development of experimental science but he was by no means alone in this and to say he revolutionised it is hyperbole.

The only defense remaining to those obstinately refusing to accept the conclusions implied by the accumulating weight of empirical facts and scientific reasoning was to reject the results almost solely on the basis of religious or political ideology

Here Livio betrays his own tactic, put crudely, throughout the book he twists the historical facts in order to try and make out that there no legitimate scientific objections to Galileo’s claims, however there were.

The next chapter is the usual enthusiastic fan boy description of Galileo’s talents as an all round humanist and contains nothing particularly objectionable but does contain a strong indication of the superficiality of Livio’s historical knowledge. He writes, “First, at age twenty-two, Galileo, already had the chutzpah to challenge the great Aristotle on topics related to motion…” People had been consistently challenging the great Aristotle on topics related to motion since the sixth century CE and Galileo was merely joining a long tradition of such work. Livio also casually calls Aristotle’s theory of motion impetus! Impetus was, of course, a theory initially developed by John Philoponus in the sixth century CE when seriously challenging Aristotle’s theory of motion. On a side note Livio says that the tools to treat such variables such as velocity and acceleration, i.e. calculus, were first developed by Newton and Leibniz. Other seventeenth century mathematicians who contributed substantially to the development of the calculus such as Cavalieri, de Saint-Vincent, Fermat, Pascal, Descarte, John Wallis and Isaac Barrow would be very surprised to hear this. On the same page he repeats the myth that Christoph Clavius was “the senior mathematician on the commission that instituted the Gregorian calendar, he wasn’t, Ignazio Danti was.

Clavius turns up as one of the leading mathematicians, who the young Galileo turned to for mentorship when he was trying to establish a reputation as a mathematician and get support to find an appointment as professor of mathematics. Interestingly Galileo’s other mentor Guidobaldo del Monte (1545–1607) appears nowhere in Livio’s book. This is strange as it was del Monte, who acquired the professorship in Pisa for Galileo through his brother Cardinal Francesco Maria del Monte (1549–1627), who was the de ‘Medici cardinal and recommended Galileo to the Grand Duke. It was also del Monte, who devised the experiment that led Galileo to the parabola law, which Livio calls one of Galileo’s crowning achievements.

In the next chapter on Galileo’s work on the theory of fall Livio can’t help taking a sideswipe at alchemy and astrology:

It is certainly true that, at their inception, the sciences were not immune to false beliefs, since they are sometimes connected to fictitious fields such as alchemy and astrology. This was partly the reason why Galileo decided later to rely on mathematics, which appeared to provide a more secure foundation.

This off hand rejection ignores completely that astrology was the main driving force behind astronomy since its beginnings in antiquity down to the seventeenth century and that all the leading Renaissance astronomers, including Galileo, were practicing astrologers. The practice of astrology/astronomy, of course, requires a high level of mathematical ability. Alchemy developed virtually all of the experimental methods and the necessary equipment to carry out those experiments on which chemistry was built.

Now in Padua, where Galileo was also professor of mathematics, a position that he once again acquired with the assistance of del Monte, we get the story of Galileo’s three lectures on the nova of 1604. Livio informs us that “Christoph Clavius confirmed the null parallax determination–that is, no shift had been observed–but refused to accept its implications as compelling.”

This is once again Livio’s tactic of trying to discredit the Jesuits. The implications that he is talking about are that the heavens are not unchanging as claimed by Aristotle. Clavius observed the nova of 1572 and already in 1581 published a digression on the subject fully accepting that the nova was supralunar and that the heavens were not unchanging. He included this in his Sphaera in 1585, the most widely read astronomy textbook in the late sixteenth and early seventeenth centuries and he probably thus had the most influence in persuading others that change had occurred in the heavens. He also included the same results for the novae of 1600 and 1604, so what is Livio talking about? Clavius was unable to explain what these novae were but then again nobody else in the seventeenth century could either.

We now move on to Galileo, telescopic astronomy and the Sidereus Nuncius. Although he actually talks about other telescopic astronomers–Scheiner, Marius, Harriot, Fabricius–they are only offered bit parts in Livio’s screenplay, which follows the usual path of giving Galileo credit for everything. He attributes the discovery of Earthshine, the Moon illuminated by sunlight reflected by the Earth, to Galileo, whereas it was previously discovered by Leonardo, who didn’t publish, and Michael Mästlin, who did. He attributes the discovery of stars that can’t be seen without a telescope to Galileo, whereas this was already noted in the printed account of the first telescope demonstration in Den Hague, the source of Sarpi’s and thus Galileo’s first knowledge of the telescope. We then get one of the most bizarre claims made by Livio in the book:

Even more consequential for the future of astrophysics was Galileo’s discovery that stars varied enormously in brightness, with some being a few hundred times brighter than others.

Coming from a professional astrophysicist I find this statement mind boggling. The difference in brightness between celestial objects is obvious to anybody with reasonable eyesight, who simply looks up at the night sky in an area without light pollution. Astronomers even use a six-point scale to designate the different levels of brightness, which is termed magnitude; this was first introduced by Ptolemaeus around 150 CE!

We then get a very brief account of the star size argument as originated by Tycho, which Livio falsely claims Galileo dismissed by saying that the observed star discs are merely artefacts. They are in fact merely artefacts but Galileo didn’t say this. He accepts their existence and uses a completely different argument to try and dismiss the star size argument.

We now arrive at the Moons of Jupiter and Simon Marius. Livio mentions Marius several times in his book but insists on calling him Simon Mayr, his birth name, why? Marius issued all of his publications under the Latinised version of his name and so historian refer to him as Simon Marius. Livio doesn’t call Copernicus, Kopernik or Tycho, Tyge their birth names, so why does he call Marius, Mayr? What he writes about Marius and the Moons of Jupiter left me, as a Marius expert, totally flabbergasted:

What would have undoubtedly annoyed Galileo no end is that the Galilean satellites are known today by the names assigned to them by the German astronomer Simon Mayr rather than as the “Medici stars.” Mayr may have independently discovered the satellites before Galileo, but he failed to understand that the moons were orbiting the planet. [my emphasis]

First off, the names were suggested by Kepler not Marius, who however first published them specifically mentioning the fact that they were suggested by Kepler. Secondly Marius discovered the moons, famously, one day later than Galileo, any confusion about who discovered what when being produced by use of different calendars, Gregorian and Julian. Thirdly, the clause that I have emphasised above is pure and utter bullshit. Marius knew very well that the moons orbited Jupiter and he calculated the orbits, calculations that he published before Galileo. Marius’ calculations are also more accurate than those of Galileo. Should Livio doubt any of this I can send him scans of the relevant pages of Mundus Jovialis in the original Latin or in German and/or English translation. Livio now brings the story of Galileo hating Marius because he accused him of being behind Baldessar Capra’s plagiarism of Galileo’s proportional compass pamphlet in 1606. Marius had been Capra’s mathematics teacher earlier in Padua. Livio fails to mention that the accusations are provably false. Galileo in 1607 had himself cleared Marius of any involvement in the case and the whole episode took place a year after Marius had left Padua.

We now move on to the peculiar shape of Saturn and the discovery of the phases of Venus. In the later case we get absolutely no mention that the phases of Venus were discovered independently by Harriot, Marius, and the astronomers of the Collegio Romano, the latter almost certainly before Galileo. Livio notes correctly that the discovery of the phases definitively refutes the possibility of a pure geocentric system. However, it does not refute a geo-heliocentric Tychonic system. Livio admits this very grudgingly:

…but could not definitely dispose of Brahe’s geocentric-heliocentric compromise […]. This left a potential escape route for those Jesuit astronomers who were still determined to avoid Copernicanism.

Throughout his book Livio tries to imply that there is no real justification for supporting the Tychonic system, whereas it was not only the Jesuits, who did so but many other astronomers as well because the empirical evidence supported it more that a heliocentric one, of which more later. However, Livio consistently ignores this fact because it doesn’t fit his fairy-tale narrative.

Livio deals fairly conventionally with the telescopic discovery of sunspots and the discussion on their nature between Galileo and Christoph Scheiner and although he ends his account by noting the publication of Scheiner’s Rosa Ursina sive Sol (1626–1630) he makes no mention of the fact that the book is a masterpiece of astronomy, far better than anything Galileo published in the discipline. As should always be noted, due to the haste in which he wrote and published it, Sidereus Nuncius was closer to a press report than a scientific publication. He does however mention, what he calls “some further comments he made later in the book The Assayer, which the Jesuit astronomer took to be directed at him personally, did turn him into an unappeasable enemy.” Galileo actual vehemently and totally falsely accused Scheiner of plagiarism in The Assayer, which he later compounded by plagiarising Scheiner’s work in his own Dialogo. Scheiner’s antagonism is understandable. We now get the real reason why Livio keeps badmouthing the Jesuits; he sees them as behind Galileo’s trial in 1633. He writes, “This marked just the beginning of a conflict with the Jesuits, which would culminate in the punitive actions against Galileo in 1633.” This is an old myth and quite simply not true, the Jesuits did not come to Galileo defence but they were also not responsible for his trial.

We now come to objections to the telescopic discoveries:

How could anyone be sure that what Galileo was seeing was a genuine phenomenon and not a spurious artifact produced by the telescope itself?

Not only wasn’t there a convincing theory of optics a that could demonstrate that the telescope doesn’t deceive, they contended but also the validity of such a theory in itself based on mathematics, was questionable. [my emphasis]

 

Livio tries to imply that both objections are just anti-science nit picking but they are in fact very solid, very necessary scientific question that had to be asked and to be answered if people were going to accept the validity of the telescopic discovery. To the first general objection, although Galileo, an excellent observer, made none himself, there were numerous cases of published discoveries that turned out to be merely optical artefacts in the early years of telescopic astronomy. Not really surprising given the really poor quality of the instruments being used, Galileo’s included.

That an optical theory of the telescope didn’t exist was a very serious problem, as it would be with any new scientific instrument. If you can’t explain how the instrument works how do you expect people to accept the results? Kepler solved the problem with his Dioptrice published in 1611, which explained fully and scientifically how lenses and lens combinations function, describing various different types of telescope. Galileo dismissed and mocked, what is now regarded as a milestone in the history of geometrical optics. The last clause is, once again, Livio spouting total crap. Theories of optics had been geometrical, i.e. mathematical, since at least, in the fourth century BCE and even Aristotle classified optics as one of the mixed sciences, i.e. those such as astronomy that are dependent on mathematics for their proofs. Kepler’s book was accepted by all those qualified to pass judgement on the matter, with the notable exception of Galileo, who didn’t want to share the limelight with anybody, and together with Kepler’s earlier Pars Optica (1604) formed the foundations of modern scientific optics.

The reference to mathematics here is Livio’s attempt to create or propagate a myth that before Galileo, nobody conceived of a mathematics-based science. It is time to tackle that myth. Livio argues that Aristotle rejected mathematics in science and that Aristotelians regarded anything proof based on mathematics as not valid. He, of course, finds an obscure Aristotelian contemporary of Galileo’s to quote to prove this but does not quote any evidence to the contrary or even appear to think that some might exist. He is very wrong in this. Because, in Aristotle’s opinion, mathematics does no deal with the real world the results of mathematic are not episteme or scientia or as we would say knowledge. He however makes allowances for the so-called mixed sciences, astronomy, optics and statics. Livio acknowledges this status for astronomy but argues with the medieval Aristotelians that astronomical mathematical models are mere calculating devices and not models of reality; describing cosmological reality was the domain of the philosophers and not the mathematical astronomers. He also claims that this was still the situation in the second decade of the seventeenth century, it wasn’t. Beginning with Copernicus astronomers began to claim that their mathematical models were models of reality and by the time of Galileo’s first dispute with the Catholic Church this had become the generally accepted state of the discipline. The debate was which mathematical model describes the real cosmos?

It is a standard cliché in the history of science that one of the major factors that drove the so-called scientific revolution was the mathematization of science. Like many clichés there is more that a modicum of truth in this claim. Livio believes it is absolutely central and one of the major themes of his book is that Galileo was the first to mathematize science in his experiments on motion and the laws of fall. This is quite simply not true and Livio can only maintain his claim by steadfastly ignoring the history of mathematics in science prior to Galileo or did he even bother to look if there was any?

Starting with Galileo’s researches into motion and fall there is a three hundred year history of experimental and mathematical investigation into exactly this area starting with the Oxford Calculatores, who derived the mean speed theorem, which lies at the heart of the laws of fall and going down to Giambattista Benedetti (1530–1590), who produced all of the arguments and thought experiments on the subject for which Galileo is famous. There is much more, which I have already dealt with in an earlier post and won’t repeat here.Galileo knew of all of this work. The Archimedean renaissance in mathematics and the sciences, replacing the authority of Aristotle with that of Archimedes, in which Galileo is a major figure, does not start with Galileo but goes back at least to Regiomontanus (1436–1476).  The works of Archimedes were edited by Thomas Venatorius (1488–1551) and printed and published in a bilingual Greek and Latin edition in Basel in 1544. In general the sixteenth century saw a massive increase in the application of mathematics to a wide range of subjects, a development that was already well underway in the fifteenth century, including linear perspective in art, cartography, surveying, navigation, physics and astronomy. Galileo in no way started the mathematization but represents, together with several of his contemporaries such as Johannes Kepler, Simon Stevin, Christoph Clavius and Isaac Beeckman, a temporary high point in these developments. All four of those contemporaries were actually better mathematicians than Galileo.

On the question of the epistemological status of mathematical proofs, which Livio clearly states was still doubted in Galileo’s time, Christoph Clavius, who many people don’t realise was an excellent epistemologist, had already changed perceptions on this when Galileo was still a child. Clavius a Jesuit and thus by definition a Thomist Aristotelian used Aristotle’s own arguments to demonstrate that mathematical proofs have the same epistemological status as philosophical proofs. He even went to the extent of translating parts of the Elements of Euclid into Aristotelian syllogisms to show that mathematical proofs transport truth in the same way as philosophical, logical ones. Clavius’ influence was massive, he fought to get mathematics accepted as part of the educational reform programme of the Jesuits and then got the mathematical sciences established as a central part of the curriculum in Catholic schools, colleges and university also training the necessary teachers to carry out his programme. There is a reason why the young Galileo turned to Clavius, when seeking a mentor for his mathematical ambitions.

Taking all of this together the roll of mathematics and status of mathematical proofs in the sciences was very different in the early seventeenth century than the picture that Livio serves up. Far from being ground breaking Galileo’s (in)famous quote from The Assayer  “the book of nature is written in the language of mathematics” (which Livio offers up several times in his book) was actually stating a truth that had been generally accepted by many natural philosophers and mathematicians for many decades before Galileo put pen to paper.

Returning to Galileo’s telescope discoveries, Livio tells us that Kepler published his letter praising Galileo’s telescopic discoveries under the title Dissertio cum Nuncio Sidero (1610) then goes on to write: “Galileo was clearly pleased with its content, the letter was reprinted in Florence later in the year.” What Livio neglects to mention is that Galileo was responsible for that edition in Florence, which was a pirate edition published without Kepler’s knowledge and without his permission or consent. Livio makes it appear that the Jesuit astronomers of the Collegio Romano only reluctantly started to try and confirm Galileo’s discoveries and then only when ordered to do so. This is a complete distortion of what actually happened.

The astronomers in the Collegio Romano had their own telescopes and had been making astronomical telescopic observations well before Galileo published the Sidereus Nuncius. They immediately leapt on the pamphlet and set out to try and confirm or refute his observations. They had some difficulties constructing telescopes good enough to make the necessary observations and Christoph Grienberger (1561–1636), who was acting head of the school of mathematics due to Clavius’ advanced age, corresponded with Galileo, who provided copious advice and tips on observing and telescope construction. This was a work of friendly cooperation under fellow mathematicians. After some difficulties they succeeded in providing the necessary confirmation, which they made public and celebrated by throwing a banquet for Galileo when he visited Rome in 1611. As already stated above the Jesuit astronomers probably observed the phases of Venus before Galileo.

Livio then goes on to draw parallels with the fact that, “The current debate on global warming had to go […] through a similar painful [my emphasis] type of confirmation process.” I find this statement, quite frankly, bizarre coming from a scientist. All scientific discoveries have to be independently confirmed by other scientists, it is a central and highly important part of the whole scientific process. What the astronomers of the Collegio Romano did for Galileo was in no way “painful” but a necessary part of that scientific process for which Galileo was very thankful. I find it particularly bizarre given the very lively current debate on the significant number of scientific papers that have to be retracted because of failing confirmation. Reading Livio in the worst possible light, and not just here but at numerous other points in his narrative, he seems to be saying, if Galileo says it is so, then it must be true and anybody, who dares to criticise him, is in the wrong.

Of course, Livio cannot avoid the myth that, “First Copernicus and Galileo removed the Earth from its central position in the solar system.” Having previously quoted the “Copernicus principle”: the realisation that the Earth, and we human beings, are nothing special…” Also: “ What’s more the Copernican system was bound to be at odds with a worldview that had placed humans at the very center of creation, not only physically but also as a purpose and focus of for the universe’s existence.” Although geometrically central, the philosophers and astronomers in the Renaissance did not regard the Earth’s position as central in any special way. It was far more the bottom, the dregs of the universe. Trying to move the Earth into the heavens was moving it into an exalted place. At least Livio is honest enough to admit that Galileo remained blind to Kepler’s work, although Livio reduces it to just the discovery of elliptical orbits, whereas Kepler actually contributed more to modern astronomy than Copernicus and Galileo together.

Livio now moves on to Galileo’s entry into theology and his Letter to Castelli. As with all Galileo apologists, whist admitting that Galileo was trespassing in the territory of the theologians, he thinks that Galileo was right to do so and what he wrote was eminently sensible and should have been acknowledged and accepted. What Galileo did struck at the vey heart of the Reformation/Counter Reformation dispute that had been raging in Europe for one hundred years and just three years later would trigger the Thirty Years War, which devastated central Europe and resulted in the death of somewhere between one and two thirds of the entire population. The Catholic Church had always claimed that they and only they were permitted to interpret Holy Scripture. Luther claimed in opposition to this that every man should be allowed to interpret it for themselves. This led to schism and the Reformation. The Catholic Church confirmed, with emphasis, at the Council of Trent that only the Church’s own theologians were permitted to interpret the Bible. Now along comes a mere mathematicus, the lowest rang in the academic hierarchy, and cheerfully tells the theologians how to interpret the Holy Writ. The amazing thing is that they didn’t simply throw him into a foul dungeon and throw away the key.  I mentioned earlier that the Church was a judicial organ and the decisions of the Council of Trent were binding laws on all Catholics. Galileo knowingly and very provocatively broke that law and got mildly and unofficially admonished for doing so. Whatever a modern observer may think about the quality of Galileo’s theological arguments is completely irrelevant, it’s the fact that he made them at all that was the offence. However, in doing so he together with Foscarini provoked the Church into taking the heliocentric hypothesis under the microscope. He had been warned, as early as 1613, by various friends including Cardinal Maffeo Barberini, the future Pope Urban VIII not to do so.

Livio thinks that because he finds Galileo’s arguments in the Letter to Castelli reasonable and ‘because of science’ that the Catholic Church should have cut Galileo some slack and let him reinterpret the Bible. The Catholic Church should abandon their exclusive right to interpret Holy Writ, one of the fundaments of their entire religion, so that a nobody, and despite his celebrity status, in the grand scheme of things Galileo was a nobody, could promote an unproven astronomical hypothesis! This is the same exclusive right for which the same Church was prepared to engage in one of the most devastating wars in European history, just three years later. In his pseudo-historical narrative Livio has here completely lost touch with the historical context.  In fact Livio is not writing history at all but making presentist moral judgements with hindsight.

There is another bizarre statement by Livio where he writes:

All this notwithstanding, however, the Church might have still accommodated (albeit with difficulty) a hypotheticalsystem that would have made it easier for mathematicians to calculate orbits, positions, and appearances of planets and stars as long as such a system could be dismissed as not representing a true physical reality. The Copernican system could be accepted as a mere mathematical framework: a model invented so as to “save the appearances” of astronomical observations–that is, to fit the observed motion of the planets.

I am frankly baffled by this paragraph because that is exactly what the Church did in fact do. They fully accepted heliocentricity as a hypothesis, whilst rejecting it as a real physical description of the cosmos. This is shown very clearly by their treatment of Copernicus’ De revolutionibus, which unlike Kepler’s books, for example, was not placed on the Index of forbidden books but was only placed on it until corrected. This correction was carried out by 1620 and consisted only of changing or removing the comparatively few statement in the book claiming that heliocentricity was a real physical description of the cosmos. From 1621 Catholics were free to read the now purely hypothetical De revolutionibus. Livio relates all of this fairly accurately and then drops another clangour. He writes:

In reality, the modifications introduced by Cardinal Luigi Caetani and later by Cardinal Francesco Ingoli were indeed relatively minor and the publication of the revised version was approved in 1620. However, the new edition never reached the press, and so Copernicus’s book remained on the Index of Prohibited Books until 1835!

This is once again complete rubbish. The Catholic Church never intended to publish a new or revised edition of De revolutionibus. What they did was to issue the list of corrections deemed necessary and every Catholic owner of the book was expected to carry out the corrections in the own copies themselves. Quite a few obviously did and we have a number of surviving copies, including Galileo’s own private copy, with the corrections carried out according to the issued instructions. Interestingly almost all of the thus censored copies are in Italy or of Italian provenance, it seems that Catholics outside of Italy didn’t take much notice of the Vatican’s censorship order. De revolutionibuswas of course removed from the Index in 1620 having been corrected. Also, I know of no case of anyone being prosecuted for reading or owning an uncensored copy of the book.

Livio tries to counter the argument that I have presented above that Galileo was admonished because he meddled in theology by claiming that the motivation was one of anti-science. Livio. “[They] were trying only to convince Galileo not to meddle in theology, as a few modern scholars have concluded.” To counter this he brings statements from Grienberger and Bellarmino saying that elements of Copernicus theory contradict passages of Holy Writ. He writes:”[they] were quite intent on crushing the Copernican challenge as a representation of reality because, from their perspective, they were vindicating the authority of Scripture in determining truth.” Dear Dr Livio that is theology! As Bellarmino wrote in his letter to Foscarini, if a contradiction exists between Holy Writ and a proven scientific fact, the heliocentric hypothesis was of course at this point in time no where near being a proven scientific fact, then the theologians have to very carefully considered how to reinterpret Holy Writ; that is what theologians do!

This brings us to Roberto Bellarmino famous letter to Paolo Antonio Foscarini. Foscarini, a monk, had written a book defending heliocentricity and reinterpreting the Bible in a similar way to Galileo. Criticised, he sent his book to Roberto Bellarmino for his judgement; he hoped it would be favourable. The title contains the word Pythagorean, so Livio explains that the Pythagoreans thought Earth etc. orbited a central fire, therefore the comparison with Copernicus’ theory. Livio then writes, “Greek philosopher Heraclides of Pontus added, also in the fourth century BCE that the Earth rotated on its axis too…” As far as can be determined Heraclides proposed diurnal rotation in a geocentric system and not in a heliocentric or Pythagorean one.

Livio goes into a lot of detail about Foscarini’s text and Bellarmino’s letter but I will only mention two points. Livio quotes the paragraph that I have already paraphrased above, “…if there were a true demonstration that the sun is at the center of the world and the earth in the third heaven, and that the sun does not circle the earth but the earth circles the sun, then one would have to proceed with great care in explaining the Scriptures that appear contrary, and say rather that we do not understand them, than what is demonstrated is false.” Livio adds, “But I will not believe that there is such a demonstration, until it is shown me. Nor is it the same to demonstrate that by supposing the sun to be at the center and the earth in heaven one can save the appearances, and to demonstrate that in truth the sun is at the center and the earth in the heaven; for I believe the first demonstration may be available, but I have very great doubts about the second, and in case of doubt one must not abandon the Holy Scripture as interpreted by the Holy Fathers.”

This is of course eminently sensible and rational. If you want me to accept you scientific theory then show me the proof! Livio doesn’t accept this and goes of into a long diatribe, which demonstrates his own prejudices rather more than any faults in Bellarmino’s logic. He then comes with a totally spurious argument:

If two theories explain all the observed facts equally well, scientists would prefer to adopt, even if tentatively, the simpler one. Following Galileo’s discoveries, such a process would have definitely favoured the Copernican system over the Ptolemaic one, which was what Galileo had been championing all along. The requirement of simplicity would have also given an advantage to Copernicanism over Tycho Brahe’s hybrid geocentric-heliocentric model.

Ignoring the fact that the Ptolemaic system was dead in the water after the discovery of the phases of Venus and so the comparison is a waste of time, any alert reader will immediately spot the massive error in this argument. The two theories, Copernicus and Brahe, do not explain all the observed facts equally well. The Copernican system requires something very central that the Tychonic system does not, terrestrial motion. Livio adds this in a very off hand way, “Of course the ultimate test would have been to find direct proof for the Earth’s motion…” There was in fact absolutely no empirical proof of the Earth’s motion and wouldn’t be until Bradley discovered stellar aberration in 1725! To give the “advantage to Copernicanism over Tycho Brahe’s hybrid geocentric-heliocentric model” would be under the circumstances actually unscientific.

A little bit further on Livio delivers another highly spurious comment, he writes, “…but Bellarmino’s position was extremely rigid. He did not believe that a proof of Copernicanism could ever be found.” Livio is here putting words into Bellarmino’s mouth, who never said anything of the sort, rather he expressed doubt that that such a proof existed.  Livio finishes off his series of spurious attacks on Bellarmino by claiming to prove him theologically wrong. I find it slightly amusing that a twenty-first century astrophysicists claims that Bellarmino, who was universally regarded as the greatest living Catholic theologian and whose reputation as a theologian was such that at the end of his life he was both head of the Index and head of the Inquisition, was theologically wrong.

Things developed as they must and we now have Galileo rushing off to Rome to try and rescue the situation with his infamous theory of the tides. Livio explains the theory and its possible origins then he drops the following jewel:

Albeit wrong, Galileo’s commitment to mechanical easy-to-understand causation made his theory of tides at least plausible.

There is only one possible answer to this claim, bullshit! A theory that states there is only one high tide and one low tide at the same time every day, when there are in fact two of each of which the times travel around the clock over the lunar month (a strong indication of the correct theory of the tides) is anything but a plausible theory. It is as I said bullshit.

We now turn to the committee of consultors set up to examine the theological implications of heliocentricity. Livio of course has much to say against this. His first objection:

Ironically, the same office that had objected vehemently to scientists intruding into theology was now asking the theologians to judge on two purely scientific questions–two of the central tenets of he Copernican model.

Once again Livio appears to have no idea what theology is. The discipline of theology covers all forms of human activity in their entirety. There is absolutely nothing in human existence that doesn’t fall under the remit of theology. Secondly the function of the consultors in this case were being asked to examine the two central tenets of heliocentricity in relation to Catholic religious belief, not a scientific question at all.

Next up, Livio objects to the consultors themselves: “Not one was a professional astronomer or even an accomplished scientist in any discipline.” All of the consultors were highly educated, learned men, who would have had a solid instruction to Ptolemaic astronomy during there education and were more than capable of asking an expert for his advice if necessary.

Consultor: Is there any empirical evidence that the Earth moves and the Sun stands still?

Astronomer: No

Consultor: Is there any empirical evidence that the Sun and not the Earth is at the centre of the cosmos?

Astronomer: No

Simple wasn’t it.

 

The decisions of the consultors are well know:

On February 24 the Qualifiers delivered their unanimous report: the proposition that the Sun is stationary at the centre of the universe is “foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture”; the proposition that the Earth moves and is not at the centre of the universe “receives the same judgement in philosophy; and … in regard to theological truth it is at least erroneous in faith. (Wikipedia)

Foolish and absurd in philosophy is the scientific judgement and sounds somewhat harsh but can be simply translated as, is not supported by the available empirical evidence. Livio would disagree with both the judgement and my interpretation of it but it is historically fundamentally accurate. The second part of each judgement is of course the theological one. As is also well known the Pope commissioned Cardinal Bellarmino to inform Galileo of the decision and to instruct him not to hold or teach the heliocentric theory. Books, such as those of Kepler, claiming the physical reality of heliocentricity, were placed on the Index and De revolutionibus, as detailed above until corrected, which it was.

Bewilderingly Livio accuses Bellarmino and the Jesuits of failing to support Galileo against the Pope, which displays an incredible ignorance of the Catholic Church, the Pope and the Jesuit Order in the seventeenth century. As stated at the beginning the Catholic Church was a religious, political and judicial power in an age of absolutism and the Pope was an absolutist ruler. The Society of Jesus (Jesuits), and Bellarmino was also a Jesuit, is a religious order dedicated to and directly under the authority of the Pope. Livio’s accusations are totally insane.  He, of course, can’t resist making ahistorical and inaccurate comments about the decision, he writes:

The ruling made by officers of the Church for whom retaining authoritative power over areas totally outside their expertise took priority over open-minded critical thinking informed by scientific evidence.

Livio here continues to ignore/deny the simple fact that the scientific evidence in the early seventeenth century simply did not support an interpretation of heliocentricity as a physical reality and whilst it appears somewhat draconian the Church decision doesn’t actually say anything else.

Livio also launches the presentist moral outrage attack, “[some] argue that some of the responsibility for the prohibition of Copernicanism lies with Galileo himself, because he wouldn’t keep his mouth shut. Such claims are outrages.” Firstly the heliocentric hypothesis was never prohibited only the heliocentric theory, which given its scientific status at the time was in fact, although unnecessarily harsh, justifiable and secondly if Galileo had displayed somewhat more tact, instead of behaving like the proverbial bull in a china shop, things would never have taken the turn that they did.

We move on to the dispute over the nature of comets between the Jesuit astronomer Orazio Grassi and Galileo. Here Livio again displays his ignorance of the history of astronomy. He writes:

Grassi’s theory of comets deviated courageously from the Aristotelian view, which placed comets at about the distance of the Moon. Instead following Tycho Brahe, Grassi proposed that the comets were further out between the Moon and the Sun.

[…]

As to the actual nature of comets, many astronomers at the time were sill adopting Aristotle’s theory, which stated that these represented exhalations of the Earth that became visible above a certain height due to combustion, disappearing from view as soon as that inflammable material was exhausted. Grassi, however, again followed Brahe in suggesting that comets were some sort of “imitation planets.”

 

The modern debate on the nature of comets and whether they were sub- or supralunar began in the fifteenth century with Toscanelli (1397–1482), who tried to track the path of Comet Halley in 1456, as if it were a supralunar object. The debate continued in the work of Georg von Peuerbach (1423–1461), Toscanelli’s one time student, and Peuerbach’s student, Regiomontanus (1436–1476), who wrote a work on how to detect parallax in a moving comet. The debate continued in the 1530’s with many leading European astronomers taking part, including, Johannes Schöner (1477–1547), who published Regiomontanus’ work on comets, Peter Apian (1495–1552), after whom the law concerning comets’ tails in named, Copernicus (1473–1543), Gerolamo Cardano (1501–1576) and Jean Pena (1528–1558). The latter two both proposed a theory that comets were translucent, supralunar, bodies that focused the Sun’s rays like a lens creating the comets tail. Tycho’s comet, the great comet of 1577 was observed by astronomers all over Europe and Tycho, Michael Mästlin (1550-1631) and Thaddaeus Hagecius ab Hayek (1525–1600), three leading astronomers, all determined that comets were supralunar. Clavius accepted these results and included the fact that comets were supralunar in his Sphaera. This meant that the official view of the Catholic Church in general and the Jesuits in particular was that comets were supralunar. This view was confirmed again by astronomers throughout Europe observing Comet Halley in 1607. The was nothing courageous about Grassi’s theory of comets and in fact you would be hard put to it to find a serious European astronomer, apart from Galileo, who still adhered to Aristotelian cometary theory in 1618. In the same year Grassi’s Jesuit colleague Johann Baptist Cysat (c. 1587–1657), a student of Christoph Scheiner, became the first astronomer to observe a comet with a telescope giving the first ever description of a comet’s nucleus in his Mathemata astronomica de loco, motu, magnitudine et causis cometae qui sub finem anni 1618 et initium anni 1619 in coelo fulsit. Ingolstadt Ex Typographeo Ederiano 1619 (Ingolstadt, 1619). He followed Tycho Brahe in believing that comets orbited the sun. He also demonstrated the orbit was parabolic not circular.

Galileo, who due to ill health had not observed the comets of 1618, launched a vicious and insulting, unprovoked attack on Grassi’s publication, presenting a view of comets that was totally out of date, ignoring all of the accumulated scientific evidence from the last two centuries on the nature of comets just to put one over on the Jesuits and the supporters of Tycho’s theories. Livio does his best to defend Galileo’s disgusting behaviour but even he admits that Grassi was principally in the right and Galileo simply wrong. Livio goes as far as to claim that because comets has an elongated elliptical orbit (actually only some do) that Galileo’s claim that they travel in straight lines was more correct than Grassi’s claim that they orbit the Sun. In all other instances Livio goes out of his way to emphasise that hindsight shows that Galileo was right and his critics wrong so why the opposite tack here? Comets do orbit the Sun. Livio scrabbles around in the cesspit that is Galileo’s paper on comets looking for crumbs for which he can give Galileo credit.

Livio now criticises Grassi’s answer to Galileo’s attack because it contained sarcastic attacks on Galileo. Talk about pot calling the kettle black. He even brings up the obtuse suggestion that it was actually written by Christoph Scheiner because of his antagonism towards Galileo. This theory has a small problem; Scheiner only became antagonistic towards Galileo after Galileo had viciously insulted him in The Assayer, a publication that still lay in the future. Livio’s whole account of the affair is biased in Galileo’s favour so that it serves as a lead up to The Assayer, for the time being the last document in the dispute, because, as already mentioned, Livio sees it as the document in which Galileo established the place of mathematics in science. Livio’s account of The Assayer and its significance is more than somewhat outlandish.

With very little evidence to base this opinion upon, Galileo thought in 1623 that he knew the answer: the universe “is written in the language of mathematics.” It was this dedication to mathematics that raised Galileo above Grassi and the other scientist of his day, even when his specific arguments fell short of convincing–and even though he assigned to geometry a more important role than it seemed to deserve at the time. His opponents, he wrote, “failed to notice that to go against geometry is to deny truth in broad daylight.”

This whole paragraph contains so much that is wrong that it is difficult to know where to start.  I have already explained above that by the time Galileo wrote this infamous piece of purple prose it was widely accepted by both mathematician and natural philosophers that the future of science lay in an intensive mathematization. A process that was well under way when Galileo wrote something that was not new and sensational but a common place. A lot of contemporary scientists were dedicated to mathematics, such as Johannes Kepler, Simon Steven and Isaac Beeckman. In fact the last two both contributed at least as much to the development of mathematical physics in the seventeenth century as Galileo if not more. Unfortunately their achievements tend to get blended out on the popular level by the Galileo myth machine of which, Livio is just the latest in a long line of operators.

To raise Galileo above Grassi because of his dedication to mathematics is more than a joke; it’s grotesque. Earlier in his account of the dispute between Grassi and Galileo, Livio acknowledged that Grassi was an excellent optical physicist and an equally excellent architect both disciplines are fundamentally mathematical disciplines. He also points out that Grassi succeeded Grienberger as professor for mathematics at the Collegio Romano, who had succeeded Clavius. The chair for mathematics at the Collegio Romano was unique in European universities. Clavius had set up what we would now call an institute for advanced mathematics, a roll that both Grienberger and Grassi kept alive. This institute was dedicated to exemplifying, establishing and developing the roll of mathematics in the sciences. The Collegio Romano was quite simply the most advanced school for mathematics and its application anywhere in Europe. As far as geometry goes the standard textbook for geometry throughout most of the seventeenth century was Christoph Clavius’ Euclides Elementorum Libri XV, Rom 1574, note the date. This was not simply a new translation of Euclid’s classic but a modernised, simplified, streamlined textbook that was used extensively by both Catholic and Protestant educational establishments; the last edition was printed in 1717.

Shortly after the above passage on Galileo’s supposed revolutionary thoughts on mathematics we get the following throwaway line:

Galileo introduced the revolutionary departure from the medieval, ludicrous notion that everything worth knowing was already known.

When I read this I didn’t know whether to laugh, cry, rip my hair out (if I had any), or simply go out and throw myself off a high cliff in the face of such imbecilic drivel. I strongly suspect that any of my history of medieval science friends and colleagues will react similarly should they happen to read the above sentence. Starting at the very latest with the translation movement in the twelfth century medieval science was an evolving developing field with advances in a wide range of disciplines. The medieval scholars laid the foundations upon which Galileo built his own achievements. I would be quite happy to give Dr Livio a very long reading list of good books on medieval science to help him find a way out of his ignorance.

At the end of his chapter on The Assayer Livio warms up the old discovery of Pierto Redondi that Galileo was denounced to the Inquisition for the bits of primitive atomism contained in The Assayer. This was indeed true but the accusation was dismissed and nothing came of it, as Livio admits. Livio, however, now writes a whole paragraph about how important atomism, he actually means particle physics, is in modern physics, mentioning quarks, leptons, gage bosons etc., etc. I wonder how Livio would react if he knew that the principle source of atomism in the seventeenth century is now considered to be the German alchemist Daniel Sennert (1572–1637) reviving the theories of the thirteenth century alchemist Paul of Taranto. You remember alchemy one of those fictitious fields together with astrology that scientists sometime connected to.

Next up the Dialogo: Livio acknowledges that there were external political and social factors that affected the situation within the Vatican in the years leading up to the publication of the Dialogo. He starts with the astrological scandal. In 1630 an astrological prognostication predicting the Pope’s death was made and circulated by, to quote Livio, the abbot of Saint Praxedes in Rome. Livio then tells us, “some of Galileo’s adversaries tried to pin the blame on Galileo…” What Livio neglects to mention is that although Galileo was in this case innocent there were plausible ground for suspecting him, it was a case of guilt by association. Firstly, Galileo was known to be a practicing astrologer. Secondly, the abbot of Saint Praxedes, Orazio Morandi had been a good friend of Galileo’s since at least 1613. Thirdly, following an audience with the Pope concerning the forthcoming Dialogo in 1630, Galileo took part in a supper with Moriandi in Saint Praxedes together with Rafaello Visconti (Master of the Sacred Palace), another friend of Galileo’s, who read the manuscript of the Dialogo for Niccolò Ricardi the censor, who never actually read it, and an appraiser of the Inquisition. When Morandi was arrested for his horoscope and thrown into the Vatican’s dungeon, Visconti was also implicated and banished from the Vatican. That Galileo came under suspicion by association is hardly surprising. This was not a plot against Galileo as Livio claims.

We then have a wonderfully mangled piece of history from Livio, who write:

Unfortunately, this was not the end of the trials and tribulations Galileo had to endure for the publication of the Dialogo. Most significant of these was the sudden death on August 1, 1630, of Federico Cesi, the founder and sole source of funding for the Accademia dei Lincei. As a result the printing had to be done in Florence, outside of Riccardi’s jurisdiction. After some negotiations, it was agreed that Father Jacinto Stefani, a consultor of the Inquisition in Florence, would be in charge, but only after Riccardi approved the introduction and conclusion.

Although Cesi’s death was a serious blow to Galileo’s plans because he Cesi was supposed to finance the publication of the Dialogo, but this was not the reason why it was published in Florence and not in Rome. What actually happened is that after Galileo had returned to Florence from Rome with his manuscript the plague broke out in Florence. Restrictions on travel imposed by the authorities meant that Galileo could not return to Rome to oversee the printing and publication of his book. He requested permission from Riccardi to get the book published in Florence instead, but as already mentioned Riccardi hadn’t actually read the book intending to review the pages as they came of the printing press instead, having accepted Visconti’s recommendation. Riccardi was now in a pickle and wanted Galileo to send him a copy of the manuscript but due to the immense cost of producing such a copy, Galileo was very reluctant to do so.  Riccardi agreed to Galileo just sending the introduction and conclusion to Rome to be controlled and the rest being controlled in Florence by Stefani. Galileo and his circle of supporters now manipulated and even oppressed the two censors and played them against each other. The result was that the imprimatur was granted by Stefani under the impression that Ricarrdi had already cleared the manuscript for publication in Rome, he hadn’t, without actually controlling the text himself. Galileo had an imprimatur that had been obtained under false pretences, which meant that he didn’t actually have an imprimatur at all. All of this came out during the investigations following publication, which contributed to Galileo’s being prosecuted but did not play a role in the actual trial.

All of this, which Livio doesn’t mention at all, is important because when dealing with the trial Livio several times emphasises that the Church had given Galileo to publish the book as it was because he had not one but two imprimaturs, whereas in fact formally he didn’t have one at all.

Livio now tells us:

There is a certain sleight of hand in the title. [Dialogue Concerning the Two Chief Systems of the World, Ptolemaic and Copernican, Propounding Inconclusively in the Philosophical Reasons as Much for the One Side as for the Other] Even if one were to ignore the fact that the Aristotelian and the Ptolemaic systems were not identical, there was at least one other world system that in terms of agreement with observations was superior to the Ptolemaic: Tycho Brahe’s Hybrid system in which the planets revolved around the Sun, but the Sun itself revolved around the Earth. Galileo always regarded that system as unnecessarily complex and contrived, and he also thought that he’d found proof for the Earth’s motion through the phenomenon of the tides, so in striving to hand Copernicanism a clear victory (although formally the book was inconclusive) he probably didn’t want to confuse the issue with superfluous qualifications.

Once again so much to unpick. Livio obviously doesn’t understand that the system propagated by the Catholic Church before Copernicus was an uneasy mixture of Ptolemaic astronomy and Aristotelian cosmology, not Aristotelian astronomy, which is a whole different kettle of fish that had been revived by some in the sixteenth century and against which Clavius had fought tooth and nail. In fact he devotes much more space to refuting the Aristotelian homocentric astronomy in his Sphaera than he devotes to refuting Copernicus. The developments in astronomy since Copernicus published De revolutionibus had left Aristotelian cosmology in shreds and Clavius had been quite happy to also jettison that, so for Clavius, speak the Catholic Church, the world system was simply the Ptolemaic.

In fact Galileo’s whole title and thus his whole book is a complete sham By 1630 the two chief systems of the world were the Tychonic system and Johannes Kepler’s elliptical heliocentric system, which was regarded as separate from and as a competitor to Copernicus’ system. The Ptolemaic system had been killed off by the discovery of the phases of Venus and the plausible assumption that Mercury would also orbit the Sun as its general behaviour was identical to that of Venus; the phases of Mercury were first observed in 1639. Galileo just used Ptolemy as a fall guy for his sham Copernican victory. Copernicus’ heliocentric system had been rendered totally obsolete by Kepler’s discovery of the three laws of planetary motion, empirically based mathematical laws I would point out, which Galileo just completely ignored clinging to Copernicus’ ‘unnecessarily complex and contrived’ system of deferents and epicycles. Livio’s dismissal of the Tychonic system as ‘superfluous qualifications’ is put quite simply a joke, especially given that the Tychonic system was at the time the leading contender as the world system because of the failing evidence of terrestrial motion.

Livio without realising it now points out the central problem with the Dialogo:

The Dialogo is one of the most engaging science texts ever written. There are conflicts and drama, yes, but also philosophy, humor, cynicism, and poetic usage of language, so that the sum is much more than its parts.

All of the above is true except that as a piece of astronomy the sum is much less than its parts, which I will explain shortly. There is no doubt whatsoever that for all of his undeniably polymathic talents, Galileo’s greatest gift was as a polemicist. A friend of mine, who is a Galileo expert, calls him the first science publicist and this is a function that he carried out brilliantly. Yes, the Dialogo is a brilliant piece of literature, which is probably unequalled by any other scientific publication in the entire history of science. However, its literary brilliance appears to have blinded many of its readers to the fact that as a piece of astronomy it’s total crap.

As already mention, Galileo struts on to the stage to discuss what he calls the two chief world systems but actually delivers up is a sham battle between two obsolete and refuted systems. He clung stubbornly to his completely false theory that comets are mere optical illusions originating on the Earth against a mass of solid, empirical, scientific evidence that comets were in fact supralunar celestial objects that orbited the Sun. Something that Galileo was no prepared to accept because it was first proposed by Tycho, who saw it as supporting evidence for his system. He clung to Copernicus’ deferents and epicycles rather than acknowledge Kepler’s much simpler, empirically proven elliptical orbits. In fact, Galileo completely ignores Kepler’s three laws of planetary motion, by far and away, the best scientific supporting evidence for a heliocentric system because if he did acknowledge them he would have to hand the laurels for proving the superiority of the heliocentric system to Kepler instead of winning them for himself, his one and only aim in the whole story. Last but by no means least he structures his whole book and his argument around his totally ludicrous theory of the tides. One of the greatest mysteries in Galileo’s life is why he, an undeniably brilliant scientist, clung so tenaciously to such an obviously bankrupt theory.

Galileo’s masterwork sailed majestically past the actually astronomy debate in the 1630s and played little or no role in the ensuing astronomical discussion of the seventeenth century in which it was largely ignored being of no real relevance. It only became crowned as a classic in the late eighteenth and early nineteenth centuries when Galileo was declared to be a scientific martyr

Livio, like so many others, blinded by the radiance of Galileo’s rhetoric sees the matter somewhat differently. In a surprisingly short presentation of the book he praises Galileo’s achievements. There are a couple of minor points that I would like to pick up on, Livio delivers up once again the myth of heliocentricity removing the Earth from its central place in the cosmos:

More important, the act of removing humans from their central place in the cosmos was too brutal to be remedied by some philosophical pleasantries at the end of a debate from a very different tone.

The whole central place in the cosmos myth is one created in the late eighteenth century and I know of no seventeenth century use of it to criticise the heliocentric hypothesis. In a bit of waffle towards the end of this chapter Livio says the “He [Galileo] did his best…” If Galileo had truly done his best he would not have ignored the most compelling evidence for the heliocentric hypothesis, Kepler’s laws of planetary motion. He goes on to say that, “History has indeed proved that Galileo was right,” it hasn’t Galileo was wrong and Kepler was right.

Livio gives a fairly short and largely accurate account of Galileo’s trial by the Inquisition and the events leading up to following the publication of the book. The only major error being, as mentioned above, his insistence that the book had two imprimaturs. Livio acknowledges that the judgement of the three clerics, commissioned to read the book and determine whether Galileo taught or defended in anyway the heliocentric theory, that he had in fact done just that and thus broken the order from 1616 was correct. Although he can’t avoid a dig at Melchior Inchofer, the Jesuit under the three. This was the charge that was brought against Galileo and of which he was found guilty. He also can’t avoid turning up the emotional rhetoric, “What happened on the following day remains one of the most shameful events in our intellectual history.” Galileo deliberately and wilfully broke the law and received the standard punishment for having done so, which included abjuring. There is an old saying under criminals, if you can’t do the time don’t do the crime. Galileo was arrogant enough to think that he could put one over on the Catholic Church and get away scot-free, it turned out that he couldn’t.

We get a short, once again, rather gushing account of the Discorsi, Galileo real claim to fame but Livio rather spoils it by once again trying to claim that Galileo created modern science.

Through an ingenious combination of experimentation (for example, with inclined planes), abstraction (discovering mathematical laws), and rational generalisation (understanding that the same laws apply to all accelerated motions), Galileo established what has since become the modern approach to the study of all natural phenomena.

Although in the case of the studies presented by Galileo in the Discorsi he proved himself to be an excellent experimental scientist, all of these things had been done by others before Galileo and independently by others contemporaneously to Galileo. He was only one amongst other who helped to establish this methodology. Galileo was part of the evolution of a new scientific methodology that had started long before he was born and which he did not initiate. Like many others before him Livio also falsely attributes Newton’s first law, the principle of inertia, to Galileo. Whilst Galileo did indeed produce a version of the principle of inertia, Newton took his first law from the works of René Descartes, who in turn had taken it from Isaac Beeckman, who had formulated it independently of Galileo.

The next chapter of Livio’s book is an obtuse story of an account of the Galileo affair commissioned by the Vatican in the 1940s and then not published but then published under the name of a different author in the 1960s. The sole aim of this chapter is simply to take another gratuitous swing at the Catholic Church. The book closes with a fairly long digression on Einstein’s views on science and religion, which brings us to a major problem with the book, apart from the historical inaccuracies, it tries to be too many things at once.

One thing that I have mentioned in passing is Livio’s attempts to draw parallels between what happened to Galileo and the current crop of science deniers. The analogies simply don’t work because no matter how hard Livio tries to claim the opposite, Galileo’s critics in astronomy, especially the Jesuits, were not science deniers but just as much scientists as Galileo, who argued for an equally valid, in fact empirically more valid, system of astronomy, the Tychonic one, as Galileo’s heliocentric system. All the way through the book Livio keeps trying to disqualify the Tychonic system as unscientific but in the first half of the seventeenth century it was just as scientific as the heliocentric hypothesis. The only person practicing science denial here is Livio. He also wants to present the book as a discussion of the general relationship between science and religion but the whole time he argues from a presentist standpoint and refuses to view the relationship in Galileo’s time in its correct historical context. Lastly he actually wants to sell the book as a new biography of Galileo presented with the insights of a working astrophysicist, his own claim at the beginning of the book. Unfortunately it is here that he fails most.

He enters his story with a preconceived image of Galileo as a white knight on his mighty charger fighting for freedom of speech and freedom of thought in the sciences and as the originator and creator of modern experimental and mathematical science. With this image firmly in mind, from the start of his narrative, he fills out the picture with a classic case of confirmation bias. He completely ignores any real facts from the history of science that might force him to rethink his preconceived image of his hero. There is no mistaking the fact that is a strong element of hero worship in Livio’s vision of Galileo. Instead of describing the real state of science in the early seventeenth century, he present the reader with a comic book version of Aristotelian philosophy from the thirteenth century making it easier for him to present Galileo as some sort of superman, who dragged natural philosophy kicking and screaming into the modern world, whilst singlehandedly creating modern science. Edward Grant the eminent historian of medieval science (a discipline that Livio probably thinks doesn’t exist, because he seems to think that there was no medieval science), once very perceptively wrote that Aristotelian philosophy was not Aristotle’s philosophy and went on to point out that it is very difficult to define Aristotelian philosophy, as it kept on evolving and changing down the centuries. The Thomist philosophy of the Jesuits in the first third of the seventeenth century was a very different beast to the Aristotelian philosophy that Thomas Aquinas propagated in the thirteenth century. The historical distortions that Livio presents would be funny if they weren’t so grotesque.

On the question of Galileo being ‘a symbol of the fight for intellectual freedom, a lifetime of studying and thinking about Early Modern science has brought me to the conclusion that he wasn’t. In my opinion Galileo didn’t really care about such abstractions as freedom of thought, freedom of speech or intellectual freedom, all he cared about was his own vainglory. As Mario Biagioli clearly shows in his Galileo Courtier,[2] Galileo was a social climber. He was a relatively unknown, middle aged, professor of mathematics, who overnight became the most celebrated astronomer in Europe because of his telescopic discoveries. Alone the way he presented those discoveries shows his principle aim was to see what he could gain socially from them. Galileo loved his celebrity status and revelled in it. His engagement for heliocentricity was all motivated by the thought that if he could prove it true, then he would become even more famous and even more feted. To achieve this aim he lied, cheated and plagiarised. He attacked and viciously stomped on all those he regarded as competitors in his strivings for fame and adulations. He also deliberately ignored any evidence for heliocentricity presented by others (see Kepler’s laws of planetary motion) that might mean that they get the laurels and not he. Galileo might have been a great scientist but he was also a vain egoist. I think all of this might go someway to explaining his extraordinary blindness to the enormous inadequacies of his theory of the tides.

Reading this book made me very angry. The only positive thing I can say about it is that Livio is an excellent writer and the book is very well written and easy to read, but in the end even this must be viewed negatively. Mario Livio is a prominent scientist and the very successful author of popular books on mathematics and science. Because of his reputation non-specialist journals will have glowing reviews of his book, mostly written by people, who are neither Galileo experts and nor historians of science. If it follows the normal pattern for such books, specialist journals and professional historians of science will decline to review it, because it’s a pop book. The book will almost certainly become a genre bestseller and another generation of readers will acquire a mythical image of Galileo Galilei and a totally false impression of Renaissance science, something I have battled against in the eleven years that I have been writing this blog.

[1] Mario Livio, Galileo and the Science Deniers, Simon & Schuster paperbacks, New York, London, Toronto, Sydney, New Delhi, 2020

[2] Mario Biagioli, Galileo Courtier: The Practice of Science in the Culture of Absolutism, University of Chicago Press, Chicago & London, ppb. 1994

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May 27, 2020 · 8:35 am

The Electric Showman

The are some figures in #histSTM, who, through some sort of metamorphosis, acquire the status of cult gurus, who were somehow super human and if only they had been properly acknowledged in their own times would have advanced the entire human race by year, decades or even centuries. The most obvious example is Leonardo da Vinci, who apparently invented, discovered, created everything that was worth inventing, discovering, creating, as well as being the greatest artist of all time. Going back a few centuries we have Roger Bacon, who invented everything that Leonardo did but wasn’t in the same class as a painter. Readers of this blog will know that one of my particular bugbears is Ada Lovelace, whose acolytes claim singlehandedly created the computer age. Another nineteenth century figure, who has been granted god like status is the Serbian physicist and inventor, Nikola Tesla (1856–1943).

The apostles of Tesla like to present him in contrast to, indeed in battle with, Thomas Alva Edison (1847–1931). According to their liturgy Tesla was a brilliant, original genius, who invented everything electrical and in so doing created the future, whereas Edison was poseur, who had no original ideas, stole everything he is credited with having invented and exploited the genius of other to create his reputation and his fortune. You don’t have to be very perceptive to realise that these are weak caricatures that almost certainly bear little relation to the truth. That this is indeed the case is shown by a new, levelheaded biography of Tesla by Iwan Rhys Morus, Tesla and the Electric Future.[1]

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If anyone is up to the job of presenting a historically accurate, balanced biography of Tesla, then it is Morus, who is professor of history at Aberystwyth University and who has established himself as an expert for the history of electricity in the nineteenth century with a series of excellent monographs on the topic, and yes he delivers.

Anybody who picks up Morus’ compact biography looking for a blow by blow description of the epic war between Tesla and Edison is going to be very disappointed, because as Morus points out it basically never really took place; it is a myth. What we get instead is a superb piece of contextual history. Morus presents a widespread but deep survey of the status of electricity in the second half of the nineteenth century and the beginnings of the twentieth century into which he embeds the life story of Tesla.

We have the technological and scientific histories of electricity but also the socio-political history of the role that electricity during the century and above all the futurology. Electricity was seen as the key to the future in all areas of life in the approaching twentieth century. Electricity was hyped as the energy source of the future, as the key to local and long distant communication, and as a medical solution to both physical and psychological illness. In fact it appears that electricity was being touted as some sort of universal panacea for all of societies problems and ills. It was truly the hype of the century. Electricity featured big in the widely popular world exhibitions beginning with the Great Exhibition at Crystal Palace in 1851.

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In these world fairs electricity literally outshone all of the other marvels and wonders on display.

The men, who led the promotion of this new technology, became stars, prophets of an electrical future, most notably Thomas Alva Edison, who became known as the Wizard of Menlo Park.

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Far from the popular image of Edison being Tesla’s sworn enemy, he was the man, who brought Tesla to America and in doing so effectively launched Tesla’s career. Edison also served as a role model for Tesla; from Edison, Tesla learnt how to promote and sell himself as a master of the electric future.

Morus takes us skilfully through the battle of the systems, AC vs. DC in which Tesla, as opposed to popular myth, played very little active part having left Westinghouse well before the active phase. His technology, patented and licenced to Westinghouse, did, however, play a leading role in Westinghouse’s eventually victory in this skirmish over Edison, establishing Tesla as one of the giants in the electricity chess game. Tesla proceeded to establish his reputation as a man of the future through a series of public lectures and interviews, with the media boosting his efforts.

From here on in Tesla expounded ever more extraordinary, visionary schemes for the electric future but systematically failed to deliver.

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His decline was long drawn out and gradual rather than spectacular and the myths began to replace the reality. The electric future forecast throughout the second half of the nineteenth century was slowly realised in the first half of the twentieth but Tesla played almost no role in its realisation.

Morus is himself a master of nineteenth century electricity and its history, as well as a first class storyteller, and in this volume he presents a clear and concise history of the socio-political, public and commercial story of electricity as it came to dominate the world, woven around a sympathetic but realistic biography of Nikola Tesla. His book is excellently researched and beautifully written, making it a real pleasure to read.  It has an extensive bibliography of both primary and secondary sources. The endnotes are almost exclusively references to the bibliography and the whole is rounded off with an excellent index. The book is well illustrated with a good selection of, in the meantime ubiquitous for #histSTM books, grey in grey prints.

Morus’ book has a prominent subtext concerning how we view our scientific and technological future and it fact this is probably the main message, as he makes clear in his final paragraph:

It is a measure of just what a good storyteller about future worlds Tesla was that we still find the story so compelling. It is also the way we still tend to tell stories about imagined futures now. We still tend to frame the way we think about scientific and technological innovation – the things on which our futures will depend – in terms of the interventions of heroic individuals battling against the odds. A hundred years after Tesla, it might be time to start thinking about other ways of talking about the shape of things to come and who is responsible who is responsible for shaping them.

If you want to learn about the history of electricity in the nineteenth century, the life of Nikola Tesla or how society projects its technological futures then I really can’t recommend Iwan Rhys Morus excellent little volume enough. Whether hardback or paperback it’s really good value for money and affordable for even the smallest of book budgets.

[1] Iwan Rhys Morus, Tesla and the Electric Future, Icon books, London, 2019

 

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Filed under Book Reviews, History of Physics, History of science, History of Technology

3 into 2 does go!

It would of course be totally unethical for me to review a book of which I am one of the authors. However, as my contribution is only six of two-hundred pages, of which three are illustrations, and the book is one that could/would/should interest some (many) of my readers, I’m going to be unethical and review it anyway.

Thinking 3D is an intellectual idea, it is a website, it is exhibitions and other events, it is a book but above all it is two people, whose idea it is: Daryl Green, who was Fellow Librarian of Magdalen College, Oxford and is now Special Collections Librarian of the University of Edinburg and Laura Moretti, who is Senior Lecturer in Art History at the University of St Andrews. The Thinking 3D idea is the historical investigation of the representation of the three-dimensional world on the two-dimensional page particular, but not exclusively, in print.

The Thinking 3D website explains in great detail what it is all about and contains a full description of the activities that have been carried out. For those quarantined there is a fairly large collection of essays on various topics from the project.

In 2019 Thinking 3D launched a major exhibition with The Bodleian Libraries Oxford as part of the commemorations of the 500th anniversary of Leonardo da Vinci’s death, Thinking 3D From Leonardo to the Present, which ran from March 2019 to February 2020 and which I have been told was quite exceptional.

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As an extension and permanent record of that exhibition Bodleian Libraries published a book, Thinking 3D: Books, Images and Ideas from Leonardo to the Present[1], which appeared in autumn 2019. This is both a coffee table book but also, at the same time, a piece of serious academic literature.

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The book opens with a long essay by Green and Moretti, The history of thinking 3D in forty books, which delivers exactly what the title says. This is an excellent survey of the topic and it is worth reading the book just for this. However, it does contain one historical error that I, in my alter ego of the HIST_SCI HULK, simply cannot ignore, at least not if I want to maintain my hard won reputation. Having introduced the topic of Copernicus’ De revolutionibus the authors write:

As mentioned above, the oft-published heliocentric diagram, and its theoretical propositions, are what launched this book into infamy (the book was immediately put on the Catholic Church’s Index of Prohibited Books [my emphasis]), but the execution of this relational illustration is simple and reductive.

De revolutionibus was published in 1543 but was first placed on the Index sixty-three years later in 1616 and more importantly, as I wrote very recently, not for the first time, it was placed on the Index until corrected. These corrections, which were fairly minimal, were carried out surprisingly quickly and the book became available to be studied by Catholics already in 1621.

Other than this I noticed no other errors in the highly informative introductory essay, which is followed by an essay from Matthew Landrus, Leonardo da Vinci, 500 years on, which examines Leonardo’s three-dimensional perception of the world and everything in it. It was for me an interesting addition to my previous readings on the Tuscan polymath.

The main body of the book is taken up by sixteen fairly short essays in four categories: Geometry, Astronomy, Architecture and Anatomy.

Geometry starts off with Ken Saito’s presentation of a ninth century manuscript of The Elements of Euclid, where he demonstrates very clearly that the author has no real consistent, methodology for presenting a 3D space on a 2D page.   This is followed by Renzo Baldasso’s essay on Luca Pacioli’s De divina proportione (1509). Here the three dimensional solids are presented perfectly by Pacioli’s friend, colleague and one time pupil Leonardo. We return to Euclid for Yelda Nasifoglu’s investigation of the English translation of The Elements by Henry Billingsley in 1570. This volume is totally fascinating as three-dimensional figures are present as pop-up figure like those that we all know from our children’s books. The geometry section closes with a book that I didn’t know, Max Brückner’s Vielecke und Vielflache (1900) presented by George Hart. This is a vast collection of photographs of paper models of three-dimensional figures, which I learnt also influenced M. C. Escher a master of the third dimension.

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Luca Pacioli De divina proportione

 

Karl Galle, Renaissance Mathematicus friend and guest blogger, kicks of the astronomy section with Johannes Kepler’s wonderfully bizarre presentation of the planetary orbits embedded in the five regular Platonic solids from his Mysterium Cosmographicum (1596). Yours truly is up next with an account of Galileo’s Sidereus Nuncius (1610) and it’s famous washes of the Moon displaying three-dimension features. Also covered are the later pirate editions that screwed up those illustrations. Stephanie O’Rourke presents one of the most extraordinary nineteenth century astronomy books James Nasmyth’s and James Carpenter’s The Moon: Considered as a Planet, a World, and a Satellite(1874). This contains stunningly realistic photographic plates of the Moon’s surface but which are not actually real. The two Jameses constructed plaster models that they then lit and photographed to achieve the desired effect. We close the astronomy section with Thinking 3D’s co-chef, Daryl Green, taking on a survey of the surface of Mars with the United Stated Geological Survey, Geological Map of Mars (1978).

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Johannes Kepler Mysterium Cosmographicum

Turning our attention to architecture, we travel back to the twelfth century, with Karl Kinsella as our guide, to Richard of St Victor’s In visionen Ezekielis; a wonderfully modern in its presentation but somewhat unique medieval architectural manuscript. The other half of the Thinking 3D team, Laura Moretti now takes us up to the sixteenth century and Sebastiano Serlio’s catalogue of the buildings of Rome (1544), which has an impossibly long Italian title that I’m not going to repeat here. We remain in the sixteenth century for Jacques Androuet du Cerceau’s Le premier [et second] volume des plus excellent bastiment de France (1576–9), where our guide is Frédérique Lemerle. Moving forward a century we close out the architecture section with Francesco Marcorin introducing us to Hans Vredeman de Vries’s absolutely stunning Perspective (1604–5).

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Hans Vredeman de Vries Perspective

It would not be too difficult to guess that the anatomy section opens with one of the greatest medical books of all time, Andreas Vesalius’ De fabrica but not with the full version but the shorter (cheaper?) De humani corporis fabrica libroum epitome, like the full version published in 1543 in Basel. Our guide to Vesalius’ masterpiece is Mark Samos. Camilla Røstvik introduces us to William Hunter’s The Anatomy of the Human Gravid Uterus (1774), as she makes very clear a milestone in the study of women’s bodies with its revolutionary and controversial study of the pregnant body. For me this essay was a high point in a collection of truly excellent essays. We stay in the eighteenth century for Jacques Fabien Gautier D’Agoty’s Exposition anatomique des organes des sens (1775). Dániel Margócsy present a fascinating guide to the controversial work of this pioneer of colour printing. Anatomy, and the book as a whole, closes with Denis Pellerin’s essay on Arthur Thomson’s Anatomy of the Human Eye (1912). Thomson’s book was accompanied by a collection of stereoscopic images of the anatomy of the eye together with a stereoscope with which to view the 3D images thus created; a nineteenth century technology that was already dying out when Thomson published his work.

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William Hunter The Anatomy of the Human Gravid Uterus

The book closes with a bibliography of five books for further reading for each essay, brief biography of each of the authors, a glossary of technical terms and a good general index. All sixteen of the essays are short, informative, light to read, easily accessible introductions to the volumes that they present and maintain a high academic quality throughout the entire book.

I said at the outset that this is also a coffee table book and that was not meant negatively. It measures 24X26 cm and is printed on environmentally friendly, high gloss paper. The typeface is attractive and light on the eyes and the illustrations are, as is to be expected for a book about the history of book illustration, spectacularly beautiful. The publishing team of the Bodleian Libraries are to be congratulated on an excellent publication. If you leave this on your coffee table then your visitors will soon be leafing though it admiring the pictures, whether they are interested in book history or not. I don’t usually mention the price of books that I review but at £35 this beautifully presented and wonderfully informative volume is very good value for money.

[1] Thinking 3D: Books, Images and Ideas from Leonardo to the Present, edited by Daryl Green and Laura Moretti, Bodleian Library, Oxford, 2019.

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Filed under Book Reviews, Early Scientific Publishing, History of Astronomy, History of Mathematics, History of medicine